William Lane Craig - God, Time, and Eternity

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GOD, TIME, AND ETERNITY The Coherence of Theism 11: Eternity

by

William Lane Craig Talbot School ofTheology, La Mirada, CA, U.S.A.

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-5823-2 ISBN 978-94-017-1715-1 (eBook) DOI 10.1007/978-94-017-1715-1

Printed on acid{ree paper

Cover: Salvador Dali (1904-1989), The Crucifixion. Oil on canvas. Photo graph © 1987 The Metropolitan Museum of Art, Gift of The Chester Dale Collection, 1955. (55.5)

All Rights Reserved © 2001 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint ofthe hardcover 1st edition 2001 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written pennission from the copyright owner.

To ALVIN PLANTINGA who by his work and his life has pointed the way

TABLE OF CONTENTS

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Preface PART I. TIIE NATURE OF DIVINE ETERNITY Section 1: Arguments for Divine Timelessness Chapter 1 The Case for Divine Timelessness Section 2: Arguments for Divine Temporality Chapter 2 Timelessness and Personhood Chapter 3

Timelessness and Divine Action

Chapter 4

Timelessness and Divine Knowledge

3

43 56 112

l34

Conclusion PARTII. GODANDTIME Seetion 1: God, Time, and its Measures Chapter 5 The Classical Concept ofTime

143

Chapter 6

God's Time and Relativistic Time

163

Chapter 7

God, Time, and Relativity

197

Seetion 2: God, Time, and Creation Chapter 8 Creatio ex nihilo Chapter 9

247

God and the Beginning of Time

256 281

Conclusion Bibliography

285

Subject Index

311

Proper Name Index

315

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PREFACE

T

hose who think about time are thinking deeply. Those who think about God are thinking even more deeply still. Those who try to think about God and time are pressing the very limits of human understanding. Undaunted, this is precisely the project which we have set for ourselves in this study: to try to grasp the nature of divine eternity, to understand what is meant by the amnnation that God is etemal, to fonnulate a coherent doctrine ofGod's relationship with time. This study, the second installment of a long-range research program devoted to a philosophical analysis of the principal attributes of God, flows naturally out of my previous exploration of divine omniscience.! For the most contentious issue with respect to God's being omniscient concerns divine foreknowledge of future contingents, such as free acts of human agents. The very concept of foreknowledge presupposes that God is temporal, and a good many thinkers, from Boethius to certain contemporary philosophers, have thought to avoid the alleged incompatibility of divine foreknowledge and human freedom by afflnning the timelessness of God. Thus, in examining the complex of issues surrounding the foreknowledge question, we found ourselves already immersed in the question of divine eternity. In this study, I shall not return to the discussion of the bearing which God's temporal status has on His knowledge of future contingents; rather we wish to press on to consider other arguments aimed at showing that God's eternity is best construed as either temporal or atemporal and to explore how one's answer to this question affects in turn one's understanding of God's relationship to time. Although the biblical data are underdeterminative with respect to the nature of God's eternity, historically the conception of divine eternity as timelessness has, through the influence of Platonie thought-the Church Father Origen and the NeoPlatonist Plotinus were both pupils of Ammonius Saccus in Alexandria-, dominated Christian theology until lohn Duns Scotus, who offered an incisive critique of Thomas Aquinas's own defense of divine timelessness. As I have elsewhere briefly surveyed the thinking of several key Christian theologians from Augustine to Suarez on the nature of divine eternity/ the present study shall forego a historical exposition of the doctrine and focus immediatelyon a critical discussion of the arguments. Unfortunately, the works of contemporary theologians will be of little help here, for the lack of analytical tools or the theological anti-realism which has in recent years blighted systematic theology foil or prevent a significant grappling with the William Lane Craig. The Problem of Dilline Foreknowledge and Future Contingents from Aristotle Suarez, Brill's Studies in Intellectual History 7 (Leiden: E. 1. Brill, 1988); idem, Dilline Foreknowledge and Human Freedom: The Coherence of Theism I: Omniscience, Brill's Studies in Intellectual History 19 (Leiden: E. 1. Brill, 1990). 2 Craig, Problem of Dilline Foreknowledge and Future Contingents. See also Alan G. Padgett, God, Eternity and the Nature ofTime (New Vork: St. Martin's, 1992), chap. 3. (0

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x issues on their part. 3 Fortunately, there has been during the last two decades a burst of interest in the doctrine of divine eternity, no doubt due in large part to the stimulus of the foreknowledge-freedom debate, among analytic philosophers of religion. The construal of divine eternity in terms of infinite omnitemporality has been greatly advanced during the twentieth century through the influence of Whitehead and Hartshome's process theology and its critique of the c1assic conception of God as pure actuality, simple, impassible, immutable, and timeless. For many years, Nelson Pike's God and Timelessness (1970), in which he argued that the doctrine of divine timeless eternity is incoherent, remained the only monograph on the subject. The dearth of material on divine eternity is evidenced by the fact that no entries on this subject were inc1uded in Wainwright's Philosophy 0/ Religion: an Annotated Bibliography 0/ Twentieth Century Writings in English (1978). Then in 1981 Eleonore Stump and Norman KretZInann published in the Journal 0/ Philosophy an artic1e entitled simply "Eternity," in which they defended a conception of divine eternity as atemporal and sought to speil out how a timeless being could be related to temporal entities. Their artic1e sparked a revival of interest in the nature of God's eternity and His relation to time. Since 1987, when I first began this study, a steady stream of monographs (not to speak of journal articles or book chapters) on the problem have issued from the presses: Paul Helm, Eternal God (1988), William Hasker, God, Time, and Knowledge (1989), lohn Yates, The Timelessness o/God (1990), Brian Leftow, Time and Eternity (1991), Alan Padgett, God, Eternity and the Nature 0/ Time (1992), Robert Neville, Eternity and Time 's Flow (1993), Lawrence Fagg, The Becoming o/Time (1995), all conspiring to rob me of anything to say! I hope to show that much original work, especially of an integrative nature, One can only agree, for example, with Jantzen when she concludes that the writing of Karl Barth on the subject of God's etemity (Church Dogmatics [Edinburgh: T. & T. Clark, 1936] vol. 2, pt. I, pp. 608677) amounts to little more than "edifying nonsense" (Grace M. Jantzen, God's Warld, God's Body [London: Darton, Longman, & Todd, 1984], p. 59). Even so level-headed a theologian as Pannenberg is of little help, for he seems to reject the mere timelessness of God in favor of timelessness with a relation to time; but he never explains how this is possible (Wolfhart Pannenberg, Systematic Theology, vol. I, trans. Geoffery Bromiley [Grand Rapids, Mich.: Wm. B. Eerdmans, 1991], pp. 402-409). At least Pannen berg does not repeat his earlier obscure doctrine that God somehow exists in the future, which is unfortunately adopted by Ted Peters, God-the Wor/d's Future (Minneapolis: Fortress Press, 1992). Although Peters says, "God creates from the future, not the past" (lbid., p. 134), what he really describes is God' s bestowing on us a future, i. e., continued existence, hope, etc. EIsewhere he interprets the dictum "God creates from the future" in terms of God's transcending the whole spacetime manifold, such that creation is "a single event incorporating the whole history of the cosmos" (Idem, "Cosmos as Creation," in Cosmos as Creation, ed. T. Peters [Nashville: Abingdon Press, 1989], pp. 88-89), a comprehensible doctrine, but insufficiently supported by argument on Peters' spart. By contrast I do not even understand what Robert Neville is talking about when he says, "Etemity ... is the togethemess of the modes of timepast, present, and future-so that each can be its temporal self' (Robert C. Neville, Eternity and Time 's F/ow, [Albany, N. Y.: SUNY Press, 1993], p. 60). One might think this a garbled affirmation of a tenseless theory of time, except that Neville also says that "Without etemity, time can be conceived only as a static dimension like space ... "; etemity is the "non-temporal togethemess of past, present, and future" (Ibid., pp. 12, 28}-which is just unintelligible. Perhaps the most comprehensible theologian writing on divine etemity today is the process thinker Keith Ward with whose views I shall interact. For arecent survey of theological thought on etemity, focusing on Heim, Barth, and Tillich, see Karl Hinrich Manzke, Ewigkeit und Zeitlichkeit, Forschungen zur systematischen und ökumenischen Theologie 63 (Göttingen: Vandenhoeck & Ruprecht, 1992).

xi bringing together discussions of the philosophy of time and space, philosophy of language, phenomenology, philosophy of science, Special and General Relativity, classical cosmology, quantum mechanics, and so forth, with the concems of philosophy ofreligion and theology, remains to be done. I initially attempted to carry out such an integrative study in a single work. The book grew to two large volumes, which, though having philosophical theology as their central concem, tumed out to be very much like an introduction to the problems of time and space. Being advised that many philosophers of religion and theologians rnight not have the patience to work through the discussion of the issues involved, I decided to distill from that work the central questions of interest to philosophical theology and to publish the remaining two-volume work as a treatise on the so-called A- vs. B-Theories of time, to which I could then refer the interested reader for further discussion. In that work I explore such topics as the reality of tense and temporal becoming, the anisotropy of time, the metric of time, the continuity of time, the conventionality of simultaneity, the relativity of simultaneity, the ontology of spacetime, and so forth. In yet a fourth book to issue from my research I provide an introduction to Relativity Theory and its philosophical underpinnings, with a view toward integrating one's doctrine of divine eternity with scientific conceptions of time. One of the major implications of my study is that a theistic approach to problems of time is surprisingly fruitful. One cannot understand the nature of divine eternity without understanding something of the nature of time; but it is equally true that how one understands the nature of time will be in part determined by one's views on the existence of God. The goal of the Christi an philosophical or systematic theologian is to formulate a doctrine of divine eternity that is at once biblically, philosophically, and scientifically informed and coherent. Because so few of those who have written on divine eternity have undertaken such a synoptic approach to the subject, our examination of this question is sometimes difficult and ground-breaking, but in the end weil worth the effort. I am intellectually indebted in this study to too many persons to recall by name; but I should like to acknowledge specifically my gratitude to Quentin Smith, from whom I have leamed a great deal about language and time, and the late Simon J. Prokhovnik, the eminent Australian physicist, who helped me to see the wisdom of H. A. Lorentz. In this volume I have reproduced a number of figures from textbooks and discussions of relativity theory. For their perrnission to reproduce such figures, I gratefully acknowledge Oxford University Press and Princeton University Press. As always, I am indebted to my wife Jan for her tireless work in the production ofthe typescript. I should also like to thank Edward White and the Day Foundation for their generous grant which helped to fund the production of the camera-ready copy and to Mark Jensen and Jennifer Jensen for meticulously bringing this book into its fmal form. Atlanta, Georgia

William Lane Craig

PART I THE NATURE OF DIVINE ETERNITY

SECTlüN 1: ARGUMENTS FüR DIVINE TlMELESSNESS CHAPTER 1 THE CA SE FüR DIVINE TlMELESSNESS THE BIBLICAL DATA ON DIVINE ETERNITY

G

od, proclaims the prophet Isaiah, is ''the high and lofty One who inhabits eternity" (Is. 57.15). In contrast to the pagan deities of Israel's neighbors, Yahweh never came into existence nor will He ever cease to exist. As the Creator of the universe, He was there in the beginning, and He will be there at the end. "I the LORD, the ftrst, and the last; I am He" (Is. 41.4). The New Testament writer to the Hebrews magniftcently summarized the Old Testament teaching on God's eternity: Thou, LORD, didst found the earth in the beginning, and the heavens are the work of thy hands; they will perish, but thou remainest; they will aB grow old like a garment, like a mantle thou wilt roll them up, and they will be changed. But thou art the same, and thy years will never end (Heb. 1.10-12).

Minimally, then, it may be said that God's being etemal means that God exists without beginning or end. He never comes into or goes out of existence; rather His existence is permanent. J But there consensus ends. For the question now to be addressed concems the nature of divine eternity, and this question is controversial. Speciftcally, is God temporal or timeless? God is temporal if and only if He exists in time, that is to say, if and only if His duration has phases which are related to each other as earlier and later. In that case, God, as a personal being, has experientially a past, a present, and a future. Given His permanent, beginningless and endless existence, God must be omnitemporal, that is to say, He exists at every moment of time there ever iso No matter what moment in time we pick, the assertion, "God exists now," were we to make it, would be literally true. For an analysis of what it means to be permanent, see Brian Leftow, Time and Elernity, Cornell Studies in the Philosophy of Religion (Ithaca, N. Y.: Cornell University Press, 1991), p. 133; cf. Quentin Smith, "A New Typology of Temporal and Atemporal Permanence," Nozis 23 (1989): 307-330. According to Leftow an entity is permanent if and only if it exists and has no first or last finite period of existence, and there are no moments before or after it exists.

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CHAPTERI

4

By contrast, God is timeless if and only if He is not temporal. This definition makes it evident that temporality and timelessness are contradictories: an entity must exist one way or the other and cannot exist both ways at once. If, then, God exists timelessly, He does not exist at any moment oftime. He transcends time; that is to say, He exists but does not exist in time. He has no past, present, and future. At any moment in time it would be true to assert "God exists" in the tenseless sense of existence, but not that "God exists now." If we take Scripture as our guide in matters of theology, the initial question we must ask is: does the biblical teaching on divine eternity favor either one of these views? The question turns out to be surprisingly difficult to answer. On the one band, it is indisputable that the biblical writers typically portray God as engaged in temporal activities, including foreknowing the future and remembering the past, and when they speak directly of God's etemal existence they do so in terms of beginningless and endIess temporal duration: "Before the mountains were brought forth, or ever thou hadst formed the earth and the world, from everlasting to everlasting thou art God" (Ps. 90.2); "Holy, holy, holy is the LORD God Almighty, who was and is and is to come!" (Rev. 4.8b). After surveying the biblical data on divine eternity, Alan Padgett concludes, ''the Bible knows nothing of a timeless divine eternity in the traditional sense.,,2 Defenders of divine timelessness might suggest that the biblical authors lacked the conceptual categories for enunciating a doctrine of divine timelessness, so that their temporal descriptions of God need not be taken literally. But Padgett cites the first century extra-biblical work 11 Enoch 65.6-7 as evidence that the conception of timeless existence was not beyond the reach ofbiblical writers: And then the whole creation, visible and invisible, which the Lord has created, shall come to an end, then each person will go to the Lord's great judgment. And then all time will perish, and afterward there will be neither years nor months nor days nor hours. They will be dissipated, and after that they will not be reckoned.

Such a passage gives us reason to think that the biblical authors, had they wished to, could have formulated a doctrine of divine timelessness. Paul Helm raises a more subtle objection to the inference that the authors of Scripture, in describing God in temporal terms, intended to teach that God is temporal. 3 He claims that the biblical writers lacked the "reflective context" for formulating a doctrine of divine eternity. That is to say, the issue (like the issue of geo-centrism, for instance) had either never come up for explicit consideration or else simply fell outside their interests. Consider the parallel case of God's relationship to space: just as the biblical writers describe God in temporal terms, so they describe Him in spatial terms as weIl: Am I a God at hand, says the LoRD, and not a God afar off? Can a man hide hirnself in secret places so that I cannot see hirn? says the LORD. 00 I not fill heaven and earth? says the LORD (Jer. 23.23-24).

Whither shall I go from thy Spirit? Alan G. Padgett, God, Eternity and the Nature ofTime (New York: St. Martin's, 1992), p. 33. Paul Helm, Etemal God (Oxford: Clarendon Press, 1988), pp. 5-11.

THE CASE FOR DIVINE TIMELESSNESS

5

Or whither shall I flee frorn thy presence? If I ascend to heaven, thou art there! IfI rnake rny bed in Sheol, thou art there! If I take the wings of the rnoming and dweil in the uttermost parts of the sea, even there thy hand shaillead rne, and thy right hand shall hold rne (ps. 139.7-10).

Yet most theologians would not take Scripture to teach that God is literally a spatial being. The authors of Scripture were not concemed to craft a metaphysiCal doctrine of God's relation to space; and parity would require us to say the same of time as weIl. Padgett considers Helm's point to be weIl-taken: "The Biblical authors were not interested in philosophical speculation about eternity, and thus the intellectual context for discussing this matter may simply not have existed at that time. ,,4 Thus, the biblical descriptions of God as temporal may not be determinative for a doctrine of divine eternity. Moreover, it must be said that the biblical data are not so one-sidedly in favor of divine temporality as Padgett would have us believe. Johannes Schmidt, whose Ewigkeitsbegriff im Alten Testament Padgett calls ''the longest and most thorough book on the concept of eternity in the OT,"s argues for a biblical doctrine of divine timelessness on the basis of creation texts like Gen. 1.1 and Provo 8.22-23. 6 Padgett brushes aside Schmidt's contention with the comment, ''Neither of these texts teaches or implies that time began with creation, or indeed say [sie] anything about time or eternity.,,7 This summary dismissal is all too quick. Gen. 1.1, which is neither a subordinate clause nor a summary title, 8 states, "In the beginning God created the heavens and the earth." According to James Barr, this absolute beginning, taken in conjunction with the expression "And there was evening and there was moming, one day" (v. 5), indicating the first day, may very weIl be intended to teach that the beginning was not simply the beginning of the physical universe, but the beginning of time itself and that, consequently, God may be thought of as timeless. 9 This conclusion is rendered all the more plausible when the Genesis account of creation is read against the backdrop of ancient Egyptian cosmogony.IO Egyptian cosmogony includes the idea that creation took place at ''the first time" (sp tpy). Analyzing the relevant texts, John Currid takes both the Egyptian and the Hebrew cosmogonies to involve the notion that the moment of creation is the beginning of time. II Certain New Testament authors may be taken to Padgett, God, Etemity and the Nature ofTime, p. 36. Ibid., p. 24. Johannes Schmidt, Der Ewigkeitsbegriff im Alten Testament, Alttestamentliche Abhandlungen 13/5 (Münster in Westfalen: Verlag des Aschendorffschen Verlagsbuchhandlung, 1940), pp. 31-32. 7 Padgett, God, Etemity and the Nature ofTime, p. 25. See exegesis by Claus Westermann, Genesis 1-11, trans. John Scullion (Minneapolis: Augsburg, 1984), p. 97; John Sailhammer, Genesis, Expositor's Bible Commentary 2 (Grand Rapids, Mich.: Zondervan, 1990), pp. 21-22. 9 James Barr, Biblical Wordsfor Time (London: SCM Press, 1962), pp. 145-147. 10 See John D. Currid, "An Examination of the Egyptian Background of the Genesis Cosrnogony," Biblische Zeitschrift 35 (1991): 18-40. 11 Ibid., p. 30.

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construe Gen. 1.1 as referring to the beginning of time. The most striking New Testament reflection on Gen. 1.1 is, of course, In. 1.1: "In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God; all things were made through him, and without him was not anything made that was made." Here the uncreated Word, the source of all created things, was already with God and was God at the moment of creation. It is not hard to interpret this passage in terms ofthe Word's timeless unity with God-nor would it be anachronistic to do so, given the first century lewish pllllosopher Philo's doctrine of the divine Logos (Word) and Philo's holding that time begins with creation. 12 As for Provo 8.22-23, this passage is certainly capable of being read in terms of a beginning of time. The doctrine of creation was a centerpiece of Jewish Wisdom literature and aimed at showing God's sovereignty over all creation. Here Wisdom, personified as a woman, speaks: The LORD possessed me at the beginning ofHis way, Before His works of old. From everlasting I was established, From the beginning, from the earliest times ofthe earth.

The passage, which doubtless looks back to Gen. 1.1, is brimming with temporal expressions for a beginning. R. N. Whybray comments, It should be noted how the writer ... was so insistent on pressing horne the faet of Wisdom's unimaginable antiquity that he piled up every available synonym in adeluge of tautologies: re 'sit, beginning, qedem, tbe first, me 'az, or old, me 'o/am, ages ago, mero 's, at tbe first or 'from the beginning' (compare Isa. 40.21; 41.4, 26), miqqad'me 'ares, beCore tbe beginning or tbe eartb: the emphasis is not so much on the mode ofWisdom's coming into existence ... but on the/act ofher antiquity.1l

The expressions emphasize, not Wisdom's mere antiquity, but that there was a beginning, a departure point, at or before which Wisdom existed. This was a departure point not merely for the earth, but for time and the ages; it was simply the beginning. Commenting on this text, Plöger concludes that through God's creative work "the possibility of speaking of 'time' was first given; thus, before this time, right at the beginning, Wisdom came into existence through Yahweh [the LORD].,,14 The passage was so understood by other ancient writers. The Septuagint renders 12 For a discussion ofthe similarities between John's prologue and Philo's De opijicio 16-19, in which his Logos doctrine of creation is described, see C. H. Dodd, The Interpretation 0/ the Fourth Gospel (Cambridge: Cambridge University Press, 1953), pp. 66-73, 276-277; on the beginning of time at creation, see Philo of Alexandria, On the Creation 0/ the Cosmos according to Moses, trans. with an Introduction and Commentary by David T. Runia, Philo of Alexandria Commentary Series 1 (Leiden: Brill, forthcoming); cf. Richard Sorabji, Time, Creation and the Continuum (Ithaca, N. Y.: Comell University Press, 1983), pp. 203-209. 13 R. N. Whybray, Proverbs, New Century Bible Commentary (Grand Rapids, Mich.: Wm. B. Eerdmans, 1994), pp. 131-132. 14 Otto Plöger, Sprüche Sa/omos, Biblisches Kommentar Altes Testaments 17 (Neukirchen-Vluyn: Neukirchner Verlag, 1984), p. 92. Cf Meinhold's comment: "lts [time's] beginning is set at the first aet of creation" (Amdt Meinhold, Die Sprüche, vol. I, Zürcher Bibelkommentare [Zürich: Theologischer Verlag Zürich, 1991], p. 144).

THE CASE FOR DIVINE TIMELESSNESS

7

me 'olam in Prov. 8.23 aspro tou aionios (before time), and Sirach 24.9 has Wisdom say, "Before the ages, in the beginning, he created me, and for all ages I shall not cease to be" (cf. 16.26; 23.20). Significantly, certain New Testament passages also seem to affrrm a beginning of time. This would imply just the same sort of timelessness "before" the creation of the world which Padgett sees in II Enoch "after" the end of the world. For example, we read in Jude 25, ''to the only God, our Savior through Jesus Christ our Lord, be glory, majesty, dominion, and authority, before all time and now and forever" (pro pantos tou aionos kai nun kai eis pantas lous aionas). The passage contemplates an everlasting future duration but affirms a beginning to past time and implies God's existence, using an aImost inevitable falfon de parler, "before" time began. Similar expressions are found in two intriguing passages in the pastoral epistles. In Tit. 1.2-3, in a passage laden with temporallanguage, we read of those chosen by God "in hope of eternallife (zoes aioniou) which God, who never lies, promised before age-long time (pro chronon aionion) but manifested at the proper time (kairois idiois)." And in II Tim. 1.9 we read of God's ''purpose and grace, which were given to us in Christ Jesus before age-long time (pro chronon aionion), but now (nun) manifested by the appearing of our Savior Christ Jesus." Arndt and Gingrich render pro chronon aionion as ''before time began."IS Similarly, in I Cor. 2.7 Paul speaks of a secret, hidden wisdom of God "which God decreed before the ages (pro ton aionon) for our glorification." Such expressions are in line with the Septuagint, which describes God as ''the one who exists before the ages (ho hyparchon pro ton aionon)" (LXX Ps. 54.20 [Ps 55.19]). Expressions like ek lou aionos or apo Ion aionon might be taken to mean "from ancient times" or "from eternity." But these should not be conflated with pro expressions. That such pro constructions are to be taken seriously and not merely as idioms connoting "for long ages" (cf. Rom. 16.25: chronois aioniois) is confirmed by the many similar expressions concerning God and His decrees "before the foundation of the world" (pro kataboles kosmou)(Jn. 17.24; Eph. 1.4; I Pet. 1.20; cf. Rev. 13.8). Evidently it was a common understanding of the creation described in Gen. 1.1 that the beginning of the world was coincident with the beginning of time or the ages; but since God did not begin to exist at the moment of creation, it therefore followed that He existed "before" the beginning of time. God, at least "before" creation, must therefore be atemporal. Thus, although Scriptural authors speak of God as temporal and everlasting, there is some evidence, at least, that when God is considered in relation to creation He must be thought of as the transcendent Creator of time and the ages and therefore as existing beyond time. It may weIl be the case that in the context of the doctrine of creation the biblical writers were led to reflect on God's relationship to time and chose to affirm His transcendence. Still the evidence is not clear, and we seem forced to conclude with Barr that "if such a thing as a Christian doctrine of time has

IS W. Bauer, A Greek-English Lexicon 0/ the New Testament, trans. and ed. W. F. Arndt and F. W. Gingrich (Chicago, University of Chicago Press, 1979), s.v. "aionios."

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to be developed, the work of discussing it and developing it must belong not to biblical but to philosophical theology.,,16 ARGUMENTS FOR GOD'S ATEMPORALITY

If the biblical data concerning the nature of divine eternity, while lending prima facie support to the notion of God as omnitemporal, are not completely determinative, are there then good reasons to construe God's etemality in terms of timelessness? Are there countervailing arguments in favor of divine temporality? In this section, I wish to examine the principal arguments in favor of each construal of divine eternity with a view toward adjudicating the fundamental question of the nature of divine eternity. We shall discover, I think, that many of the arguments will hinge on our understanding of certain key notions derived from the philosophy of time or the philosophy of language or Relativity Theory. At the appropriate junctures I shall therefore refer the reader to my treatment of the issues in my companion volumes The Tensed Theory of Time: a Critical Examination and The Tenseless Theory of Time: a Critical Examination for a fuller discussion. Readers lacking background in Relativity Theory are referred to my Time and the Metaphysics ofRelativity. A quick and easy demonstration of divine timelessness rnight appeal to the doctrine of God's simplicity as a basis for affirming His atemporality.17 For a simple God could change neither intrinsically nor extrinsically, since He has no properties as such nor stands in any real relation to things, whereas a temporal God would have to change at least relationally with respect to the different moments of time at which He exists. The problem with such an argument, however, is that the doctrine of divine simplicity is even more difficult and controversial than the doctrine of divine timelessness, so that to try to prove the latter doctrine on the basis of the former is to try to prove what is not obvious on the basis of the even less obvious. \8 Thus we must look elsewhere for persuasive arguments for divine timelessness. In his major study Time and Eternity, Brian Leftow provides without appealing to the doctrine of simplicity a catalogue of weIl over a dozen arguments in defense of divine timelessness, which may serve us weIl in assessing the case for the construal ofGod's etemality as atemporal. 19

Barr, Biblical Words/or Time, p. 149. Hugh J. McCann, "The God beyond Time," in Philosophy 0/ Religion, ed. Louis Pojman (Indianapolis: Hackett Publishing Company, 1993), p. 234. McCann argues that God cannot undergo accidental change, i.e., change in His non-essential properties, because He does not have such properties. But McCann's first reason for this assertion, viz., that the explanation for any divine accidental property can neither be found in the world nor in God, fails to take account of God's freedom, which could explain, e.g., why God is contingently the Creator ofthe worId rather than not. His second reason appeals to the identity ofGod's essence and existence, whichjust is the disputed doctrine of divine simplicity. \8 See Christopher Hughes, On a Complex Theory 0/ a Simple God, Comell Studies in Philosophy of Religion (Ithaca, N. Y.: Comell University Press, 1989). 19 Brian Leftow, Time and Eternity, chap. 12. 16 17

THE CASE FOR DIVINE TIMELESSNESS

9

1. Timelessness and the Finitude of the Past. Leftow opens bis case with an examination of Paul Helm's argument for divine timelessness based on the impossibility of an infinite past, an argument wbich Leftow finds unconvincing. According to Helm, the idea that God exists in an infmitely backward extending time runs up against the idea of an actual infinite. For such a prospect requires that an infinite number of events must have elapsed before the present moment eould arrive. And since it is impossible for an infmite number of events to have elapsed, and yet the present moment has arrived, the series of events cannot be infmite. Therefore, either there was a time when God began to exist, whieh is impossible, or God exists timelessly. Therefore, God exists timelessly.20

Leftow rightly observes that the claim that it is impossible for an infinite munber of events to have elapsed is "bighly contentious"; nevertheless, since he declines to "delve into its pros and cons,,,21 it is impossible to assess the basis for bis denial of this premiss. I myself find it quite plausible. 22 Leftow also asserts that an infinite past need not imply an infinite series of past events: there could have been an infinite empty time prior to the. commencement of events or an infmitely long event prior to the finite series of past events. But I find these hypotheses dubious. The same arguments against the lapse of an infinite series of past events would apply mutatis mutandis to the lapse of an infinite number of finite intervals of past metric time prior to the beginning of the series of events. Moreover, on a relational or quasi-relational view of time, there plausibly would not even be an empty time in the absence of events. 23 Unfortunately, the debate between relationalism and substantivalism is one of those issues from philosophy of space and time which neither Leftow nor Helm discusses. 24 As for the hypothesis of an infinitely long event, I am doubtful that this is even a coherent notion. An infinitely long event, that is to say, one which is not composed of discrete sub-events or changes, seems to me to be astate rather than an event. If the series of temporal events issued from such a changeless state, then it is not at all obvious that such astate would not in fact be timeless. Leftow's retort that such a situation would be an event, not astate, because "it is something actually going on,,25 begs the question. I see no reason to think that anything, particularly the lapse of time, is "going on" rather than just existing. If, on the other hand, this state or "event" is temporal, then, if we are to avoid the problem of an infinite regress of past intervals of metric time, the time of 20 Paul Helm, Eternal God, pp. 37-38. 21 Leftow, Time and Eternity, p. 269. 22 My reasons for this opinion are laid out and debated in William Lane Craig and Quentin Smith, Theism, Atheism, and Big Bang C osmology (Oxford: Clarendon Press, 1993). 23 In his discussion of this problem, Lodzinski seems to presuppose some sort of verificationism or relationalism, for on a substantival view oftime his three objections against empty time fmd no purchase. If infinite time exists because God exists, as Newton believed, Lodzinski's arguments become doubly irrelevant. Lodzinski argues against an infmite regress of events in God's Iife; but this reasoning goes to show the impossibility of an infinite metrie past, not the impossibility of an empty time (Don Lodzinski, "Empty Time and the Eternality ofGod," Religious Studies 31 [1995]: 187-195). Still even the possibility ofrelational views oftime suffices to invalidate Leftow's argument. 24 We shall reeur to this problem in ehapter 9. 25 Leftow, Time and Eternity, p. 268.

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1

this state or event must be a non-metric, undifferentiated time. But Helm at least provides an argument that God could not have existed in undifferentiated time prior to the creation of the world, namely, that proponents of divine temporality could not view such a static God as a living being. Nevertheless, I must in the end agree with Leftow that Helm's argument does not suffice to prove divine timelessness. At least two temporalist, or quasitemporalist, models of divine eternity are compatible with the finitude of the (metric) past and of the temporal series of events: (1) an Ockhamist model, according to which God exists timelessly without creation and in time subsequent to the commencement of the temporal series of events/6 and (2) a model akin to Alan Padgett's notion of "relative timelessness," according to which God, prior to creation, exists in an undifferentiated, non-metric time. 27 According to the first alternative, God in the eventless, changeless state of existing alone without creation is timeless, since time does not exist in the total absence of events. Time originates with the first event, the creation of the world, and God endures throughout time from the moment of creation on. On such a model, as Leftow points out, God's having a first moment of existence does not entail that God's existence has a limit or that He came into existence: If God existed in time once time existed and time had a first moment, then God would have a first moment of existence: there would be a moment before which He did not exist, because there was no 'before' that moment.... Yet even if He ... had a fust moment of existence, one could still call God's existence unIimited were it understood that He would have existed even if time did not. For as long as this is true, we cannot infer from God's having had a first moment of existence that God came into existence or would not have existed save if time did. 2I

On such a model, the past is finite, God exists atemporally without the world, and yet God exists temporally from the inception of the world and His creation of time. If such a model is coherent, Helm's argument does not entail that God is unqualifiedly timeless. According to the second alternative, God does exist literally prior to creation, so that time does not begin with the first event. Nonetheless, the time prior to creation, See Marilyn McCord Adams, William Ockam, (Notre Dame, Ind.: University ofNotre Dame Press, 1987), 2: 853-899 and brief discussion in William Lane Craig, The Problem of Divine Foreknowledge and Future Contingentsfrom Aristotle to Suarez, Brill's Studies in Intellectual History 7 (Leiden: E. 1. Brill, 1988), p.262. Senor has dubbed such a model "accidental temporalisrn" (Thomas D. Senor, "Divine Temporality and Creation ex Nihilo," Faith and Philosophy 10 [1993]: 88). The accidental temporal ist agrees that God exists at all times but denies that God's existence is always at a time. Senor sees two challenges to accidental temporalism, viz., (i) the coherence of a timeless person and (ii) the artificiality of the asymmetry of maintaining that the act of creation temporalizes but does not spatialize God. I discuss (i) in chap. 2. The question of whether creating temporalizes God is discussed in chap. 3. The reason that creation would not spatialize God is that creating is not itself a spatial act, even if, on tensed theories of time, it is atemporal act. Such a model also undercuts McCann's argument that a temporal deity cannot be the Creator oftime (McCann, "God beyond Time," p. 233). 21 See Padgett, God, Etemity, and the Nature ofTime, pp.122-146. Padgett's position has also been defended by his doctoral mentor Richard Swinbume, "God and Time," in Reasoned Faith, ed. Eleonore Stump (Ithaca, N. Y.: Comell University Press, 1993), pp. 204-222. 2' Leftow, Time and Etemity, p. 269; cf. p. 201. 26

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11

in which nothing occurs, is geometrically and topologically amorphous, so that it cannot be divided into finite intervals which elapse successively. Therefore, the arguments against an infinite regress of intervals of metric time have no foothold in this region. Whether God then endures in metric time subsequent to its creation is an open question. 29 Helm's riposte to such a model is ineffective with respect to those who, like Padgett and Leftow or, for that matter, Helm hirnself, do not consider a succession ofmental events in God's mind essential to His personhood. 30 There are other motivations for construing divine eternity as temporal or quasitemporal, as we shall see in the next section, than the idea that temporality is essential to life or personhood. Thus, the demonstration that (metric) past time is finite does not suffice to prove that God is strictly timeless. 2. Timelessness and Unlimited Duration. Leftow next employs an Anselmianstyle argument to show that timelessness is aperfeetion which a supremely perfect being must have. 31 "Unlimited duration is aperfeetion, so we ought to ascribe to God the least limited duration compatible with the rest of His attributes.,,32 But a being which is timeless has even less limited duration than a being which is everlasting, since even an omnitemporal being which has an inflnite past and an infinite future can have a beginning or end, sinee time can have a beginning or an end, whereas a timeless being can have neither a beginning nor an end to its existence. 33 This argument strikes me as quite uneonvincing. In the first place, the comparison of everlasting duration with timelessness in respect of their duration seems to be just a category mistake. Duration is a category which is prima facie not even applicable to a timeless being in any literal sense, so that to talk ab out the limits of its duration is just wrong-headed. 34 Since timeless being does not literally 29 See Alan Padgett, "God and Time: Toward a New Doctrine of Divine Timeless Eternity," Religious Studies 25 (1989): 209-215; William Lane Craig, "God and Real Time," Religious Studies 26 (1990): 335-347; Alan Padgett, "Can History Measure Eternity? A Reply to William Craig," Religious Studies 27

(1991): 333-335. Padgett's view is very difficult to sort out, and 1 am not sure that even he understands itl Hence, 1 have characterized alternative (2) as "akin to" his model, lest 1 should have misconstrued it. 30 See Leftow, Time and Eternity, chap. 13; Helm, Elernal God, chap. 4. Padgett's agreement is evident from the fact that he argues that given what he calls a stasis theory of time, according to which temporal becoming is not an objective feature of reality, a coherent model of divine timelessness can be constructed (Padgett, God, Eternity, and the Nature o/Time, chap. 4). 31 Cf. the similar approach by Nelson Pike, God and Timelessness, Studies in Ethics and the Philosophy of Religion (New York: Schocken Books, 1970), chap. 8, who, however, concludes, "I have been unable to discover any dear logical connection between the idea that God is a being a greater than which cannot be conceived and the idea that God is timeless" (p. 165). 32 Leftow, Time and Eternity, p. 270. 33 Ibid., pp. 201-202. Iassume that this is the relevant passage referred to by Leftow. He rejects the position which holds that God has less limited duration than an ornnitemporal being because even an ornnitemporal being began to exist at the first moment of time, whereas God did not. This does give a clear sense in which God's duration is less limited, but Leftow accepts Aquinas's position that there is no necessity that time began to exist. In any case, the argument would not demonstrate timelessness, since it is compatible with the two models discussed above. 34 On the well-known claim of Stump and Kretzmann that atemporal duration is a coherent notion and that this notion lay at the heart of the c1assical conception of eternity, see William Lane Craig, Problem 0/

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endure at all, there is just no point of comparison between a temporal being and a timeless being with respect to their duration. Moreover, why should we think that having (un)limited duration is a modal property, as Leftow supposes? Intuitively, a being which contingently endures for all time is just as unlimited in its duration as a being which necessarily endures for all time. After all, they both endure for the same amount of time! Perhaps the latter can be said to have unlimitable duration in contrast to the former and in that sense to be superior; but they seem de facta to be equally unlimited in their duration. In any case, Leftow has not demonstrated any necessary connection between necessary existence and atemporality, nor is such a connection intuitively evident. Why should we think that a temporal being cannot be metaphysically necessary? If God is both temporal and metaphysically necessary, then His duration is as limitless and unlimitable as one could please. 3. Timelessness and Necessary Existence. Continuing in the same vein, Leftow argues that necessary existence does in fact entail timelessness and that since God must have the perfection of necessary existence, He must therefore be timeless. Leftow's argument here is rather obscure, and I am unable to [md any straightforward argument that whatever exists necessarily is timeless. Leftow appears to reason that if God is temporal, He is necessarily temporal; and that since He is a necessary being, time therefore exists necessarily; but that since time is in fact contingent, God is therefore not temporal. In support of the premiss that if God is temporal, He is necessarily temporal, Leftow appears to argue that a timeless God could not possibly be temporal because "temporal and timeless beings will have to have properties so radically different as to make transworld identification of such beings implausible."35 Given God's necessary existence, it therefore follows that time also exists necessarily. Leaving aside for the moment the merits of this argument, why, we may ask, could time not in fact be necessary in virtue of God's necessary existence, as Isaac Newton held?36 Leftow's apparent response is that a temporal God must also be spatial, which is incompatible with orthodox theism. According to contemporary physics, time is one dimension of a four-dimensional space-time manifold. Accordingly, Leftow explains,

Divine Foreknawledge and Future Contingents, pp. 92-95; see also Richard Sorabji, Time, Creation, and the Continuum, pp. 108-124, as weH as Dictionnaire de la theologie catho/ique, ed. A. Vacant and E. Mangenot (paris: Letouzey et Am::, 1913), s.v. "Eternite," by A. Michel, vol. 5, cols. 912-921. Leftow acknowledges the lack of textual support for the Stump-Kretzmann interpretation but thinks to bring new support by appealing to Boethius' s phrases with respect to an eternal being that "nothing future is absent from it, and nothing past has flowed away" and it "embrace[s1 its whole extent simultaneously," as weH as from Boethius's claim that everlasting existence is an imitation of eternity (Leftow, Time and Eternity, pp. 116-119). But the context of the quoted phrases makes it evident that Boethius is talking in the first case about the presence to God of things future or past in time (not in eternity) and in the second case about the extent of atemporal being (not of an eternal being). Everlasting existence mirrors eternity in that it does not pass away (not in that both have duration). See also Katherin A. Rogers, "Eternity Has No Duration," Re/igious Studies 30 (1994): 1-16. 3S Leftow, Time and Eternity, p. 44. Again I think this is the passage to which Leftow vaguely refers. 36 See Chap. 5.

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something is loeated in one dimension of a geometry if and only if it is loeated in alt. So if it is eorreet to represent time as another dimension, it follows that whatever in [sie] time is also in space: only spatial things are temporal .... ifGod is in the time of OUT world, God is also in spaee. Any objeet with a space-time loeation is a physieal object. Hence if the time in whieh God exists is the same physical time in whieh we exist, then God is a physieal objeet with a spatialloeation. 37

Since God is not a physical object, He is timeless and, hence, necessarily timeless. Leftow's appeal to the argument from divine spacelessness is curious because that argument constitutes a quite independent justification for divine timelessness which is brought into play here only to rescue the inconclusive argument from necessary existence. It is also odd that Leftow would reject a position on the grounds of its incompatibility with orthodox theism while propounding a theory of eternity whose conclusion is itself incompatible with orthodox Christian doctrines concerning angelology/demonology and the intermediate state of the soul after death. 38 But never mind; the argument itself is unsound. In the first place, one could dispute the argument on purely physical grounds alone in that it fails to take sufficient cognizance of the difference between co ordinate time and parameter time. 39 It is true that insofar as time plays the role of a coordinate, it is connected with a system of spatial coordinates, so that anything to which a temporal co ordinate can be assigned is such that spatial coordinates are assignable to it as weIl. But insofar as time functions as a parameter, it is independent of space, and something which possesses temporal Iocation and extension need not be held to exist in space as weIl as time. In Newtonian mechanies time plays the role of a parameter, not a co ordinate, and, interestingly, the same is true of Einstein's formulation of the Special Theory of Relativity (SR}--the now farniliar space-time formulation derives later from Minkowski. The Special Theory can be validly formulated in either way. Moreover, since the Special Theory is a local theory only, we must, in order to achieve aglobai perspective, consider time as it functions in cosmological models based on the General Theory of Relativity (GR), on which matter Leftow is silent. Weshall have a good deal more to say about these matters in chapter 7, but for now we may note in passing that while time is defmed in the standard Friedman models by means of spatial hypersurfaces, the time parameter in the Robertson-Walker line element which describes the space-time metric is distinguished precisely by its independence of space. Moreover, spatio-temporal coordinates in the General Theory are purely conventional and have no physical significance. Thus, it is not

Leftow, Time and Eternity, p. 36. Leftow admits that if only spatial things are temporal, then non-spatial entities such as ehangeable angels or disembodied souls do not exist (Brian Leftow, "Etemity and Simultaneity," Faith and Philosophy 8 [1991]: 163). This is by no means insignificant. The doctrine ofthe interrnediate state of the soul after death may prove to be essential to the eoherence of the Christian doetrine of esehatologieal resurrection and final judgement, due to the need to preserve personal identity between earthly and resurreeted human beings. Doetrines pertinent to angelology/demonology may have important praetical ramifications for Christian spirituality (Eph. 6.12). 39 For more on this, see Craig, Time and the Metaphysies 0/ Relativity (Dordreeht: Kluwer Aeademic Publishers, 2001), pp. 207-208. 37 J8

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obvious that a being could not exist at a certain moment of cosmic time without being spatially located as weIl. But Leftow's argument suffers from a far more serious shortcoming than this. The argument appears to rest upon a crucial presupposition which will affect fundamentaIly one's theories of time and etemity and which I believe to be profoundly mistaken,40 namely, the reductionistic equation of time with physical time, that is to say, with time as it plays a role in physics. That this equation is mistaken is obvious from the simple fact that whereas physical time came into existence after the Big Bang singularity, time itself may weIl have existed prior to the initial cosmological singularity. A succession of mental events in God's mind, His counting for example, would alone suffice to generate a temporal series in the absence of any physical objects whatsoever. 41 Thus, it is plainly not the case that something is in time if and only if it is in space-and that metaphysical truth is not negated by the fact that in physical theory an event which is assigned a temporal coordinate in space-time also has spatial coordinates as well. 42 The appeal to God's spacelessness thus proves to be unavailing as a demonstration that God cannot be necessarily temporal and so time itself necessary in virtue of God's necessary existence. But now what about the premiss that a temporal God is necessarily temporal? Why could God not be contingently temporal, but possibly timeless? Let us suppose that God is in fact temporal. Since according to the Christian doctrine of creation, God's decision to create is freely wiIled, there are possible worlds in which God exists alone, with no reality extra se (apart from any timeless abstract objects which Platonists among us might want to posit). If in such a world God is unchanging-as Leftow believes that He (necessarily) is-, then on some sort of relational theory of time God would be timeless in such a world. Indeed, there would be no time at all in such a world, since literally nothing happens; there are no events to generate relations of befare and after. God as He exists in such an atemporal world would differ in respect to See Craig, The Tenseless Theory of Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, 2000), chap. 6. 41 Thus, I agree with Grace Jantzen when she says, "Time is more basic than space. For instance, the theory of relativity does not of itself solve the problem of whether disembodied persons are possible, persons who, if they had conscious processes ... would clearly be temporal even though ex hypothesi not spatial. The theory of relativity applies to the relationship and measurement of space and time in the physical contents of the universe; it does not address itself to the question whether non-spatial entities might exist, nor whether they would be temporal or non-temporal if they did ... it might not be possible for us to measure the duration of a non-spatial entity or event, but this is not the same as saying that whatever is temporal must be spatial" (Grace M. Jantzen, God's World, God's Body, with a Foreword by John MacQuarrie [London: Darton, Longman, and Todd, 1984], p. 44). See also the remarks of W. Norris Clarke, The Philosophical Approach to God (Winston-Salem, N. c.: Wake Forest University, 1979), p. 94, with respect to a time based on "the pure succession of contents of consciousness" in the mind of God, in contrast to the temporal succession based principally on "the continuous physical motion going on in our world." 42 The two contemporary thinkers who have signaled the distinction between time and physical time most clearly are Quentin Smith, Language and Time (New York: Oxford University Press, 1993), chap. 7 and Alan Padgett, God, Eternity, and the Nature ofTime, chap. I.

40

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15

some of His properties which He has in the postulated actual world-sueh as knowing what time it is, experiencing tense and temporal becoming, changing in His awareness, and so forth-, but none of these differences seems so major as to preclude transworld identity. Indeed, when one refleets that only a difference in an essential property would suffiee to preclude the stipulated transworld identity, then Leftow's argument takes on the air of begging the question, assuming that temporality and atemporality are essential attributes of beings which possess them. 43 In short, once one abandons the false conclusion that all temporal beings are spatial, there seems to be no reason left to think that God is not eontingently temporal or atemporal. 4. Timelessness and Spatiality. Like an aeeordion, Leftow's arguments continue to collapse into one another seriatim: he now argues that sinee things located in time are also located in space and God is spaceless, God is also without loeation in time. But now he attempts to come to grips with the objection that his reductionist view of time is unjustified, that time as such is not to be equated with time as it plays a role in physics. This objection, Leftow figures, is most plausibly construed to mean that the Special Theory of Relativity does not tell us "the literal truth about the nature of time.,,44 Fair enough; but the anti-reduetionist would also deny that the various definitions of time in the General Theory of Relativity, Quantum Theory, and Quantum Cosmology represent the literal truth about time either. 4S Leftow's response is two-fold. First, one can say that spaee and time possess objectively just the structure deseribed in the Special Theory. We can generalize Leftow's claim to include Other physical theories as weil. But clearly this response fails to turn back the force of the objection: at best the response only shows that it is epistemically possible that the structure of space and time is literally described by such theories. But that does not show that it actually is literally described by those theories. Indeed, we have seen what I consider to be a knock-down argument that these theories do not give us the literal truth about time: it is impossible to extend physical time through the Big Bang singuIarity, but God could have created time itself prior to the initial cosmological singularity simply by generating a sequence of mental events. It seems clear then that to be in time is not also to be in space. Now perhaps in fact the physical quantities representing time in scientific theories contingently coincide with or provide aecurate measures of time itself. But to claim that whatever is in time is therefore also in space is to confound time and space with their measures. Leftow's seeond response to the anti-reductionist objection is that the very fact that the defender of divine temporality is driven to deny the literal truth of SR

Cf. Robert Oakes, "Temporality and Divinity: An Analytic Hurdle," Sophia 31 (1992): 11-26, who asserts that because it is impossible for God to exist and fail to be eternal, it follows that if God is atemporal He is so essentially and if He is temporal He is so essentially. This does not, of course, follow, since eternity is a generic concept meaning something like "without beginning or end" and so encompasses both timelessness and ornnitemporality. Hence, God can be essentially eternal without being essentially timeless or essentially temporal. 44 Leftow, Time and Eternity, p. 272. 4S On various scientific conceptions oftime, see Craig, Time and the Metaphysics 0/Relativity, fig. 8.2.

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confinns Leftow's argument that if SR is true, then a spaceless God is timeless. This response is just misconceived. Leftow labors under the misimpression, apparently communicated to him personally by William Hasker, that "What forces us, in our Einsteinian universe, to regard time as a fourth dimension is the relativity of simultaneity.'.46 This, as I have mentioned, is inaccurate, since in Einstein's original formulation of SR time is a parameter, not a coordinate. Nothing in the theory itself requires us to say that whatever is temporal is ipso facta spatial. Moreover, we need to keep c1early in view that when Leftow says that he assumes that SR is true, he means much more than the theory's admitted empirical adequacy or even its accuracy in describing physical space and time; he means that physical space and time, as these are defined in that theory, are literally space and time themselves, which is an enormous metaphysical assumption which begs some justification. Is there some other reason to think that divine temporality implies divine spatiality? Paul Helm has argued that if a certain argument for divine temporality goes through, then there is a parallel argument for divine spatiality, based on the paralleis between temporal and spatial indexical terms like "here" and ''nOW.''''7 Just as "The kettle is boiling now" expresses (according to the partisans of tensed facts) factual information which "The kettle boils (tenselessly) on 19 January" fails to convey, information which only a temporal being can know, so also "The kettle is boiling here" conveys factual information which "The kettle is boiling in the Old Kent Road" does not, information which only a spatially located being can know. So if God, in virtue of His omniscience, must be temporal, He must also be spatial. Since God is not spatial, neither is He temporal. Helm's argument only has force against a person who holds to the reality of tensed facts. Partisans of the tenseless theory of time deny the objective reality of both temporal and spatial tenses and so would deny that there are any facts of this sort to be known by GOd. 48 In fact, this is Helm's own position, so that the argum~nt constitutes, in bis view, no grounds for affrrming divine timelessness. Helm's argument is hypothetical in structure: If there are tensed facts, then God is either spatial or not omniscient. Since neither disjunct of the consequent is theologically acceptable, the antecedent must be denied. What Helm has presented is really an argument against the tensed theory of time, not for divine timelessness. The question, then, is whether the partisan of tensed facts can escape Helm's dilemma. If he, like Leftow, Stump, and Kretzmann, also holds to the doctrine of divine timelessness, his burden will be to showeither how a timeless deity can know tensed facts or why His ignorance of such facts does not impugn His omniscience. On the other hand, if he adheres to the doctrine of divine temporality, like Wolterstorff, Swinburne, and Kiernan-Lewis, then he will have to show either why the existence of temporally tensed facts does not imply the existence of "spatially

Leftow, Time and Etemity, p. 272. Leftow's citation from personal correspondence with William Hasker. 47 Helm, Eternal God, pp. 42-44. 4' For example, Murray MacBeath, "God's Spacelessness and Timelessness," Sophia 22 (1983): 23-32. 46

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tensed" facts or how a spaceless deity could know such facts. These questions shall be taken up in chapter 4. 5. Timelessness and Omnipotence. Leftow argues that temporal series exist contingently and that there is a possible world in which alternate temporal series exist. A temporal God, however, cannot create an alternate temporal series. Therefore, if God is temporal, He is not omnipotent, since possibly there is a contingent entity which He cannot create and a contingent state of affairs which He cannot actualize. Since God is omnipotent, He must be timeless. This ingenious argument needs some explaining. When Leftow speaks of the possibility of alternate time series, he is not talking about a hyper-time in which onedimensional time is located. Rather, what he has in mind are two wholly discrete (spatio-) temporal manifolds which we can imagine to be embedded in a fictitious higher dimensional space. 49 Events occurring in one manifold would have no temporal relation to events occurring in the other. Leftow thinks that it is possible that two such non-intersecting spatio-temporal manifolds exist. His reason for so thinking is that there is no contradiction in such a supposition. Such justification is far too quick, however, since there may be synthetic propositions which are metaRhysically necessary, whose negation involves no contradiction but cannot be true. 0 It may be the case that while discrete spatio-temporal manifolds are possible with respect to physical time and space, nevertheless, given the metaphysical time in which God lives and acts, events in the two physical manifolds are temporally related to each other in metaphysical time. SI But let that pass for now; Leftow furnishes the following argument in support of his contention that a temporal God could not create an alternate time series: A God who exists in our time series could not create a second time series. For if God creates at time t, what God creates begins to exist at time t. So if God exists at t in time series A and at that point creates series B, B begins to exist at t: the fIrst moment of B is simultaneous in A with a moment in A, and so A and B are not discrete. .. . On the other hand, if God is timeless and ... His creating time does not locate Him in time, then He can create in etemity both A and B without its following that any moment in A is temporally simultaneous in A or in B with any moment in B.'2

A moment's reflection on this argument reveals that Leftow is using the expression "alternate time series" equivocally, to mean on the one band "discrete time series" and on the other "additional time series." He uses the former sense in asserting the possibility of alternate time series, but the second sense in denying the possibility of 49 Ibid., pp. 21-22,29-31. '0 See remarks by A1vin Plantinga, "Is Theism Really a Mirac1e?" Faith and Philosophy 3 (1986): 117 and a couple of examples in William Lane Craig, Divine Foreknowledge and Human Freedom, Brill's Studies in Intellectual History 19 (Leiden: E. J. Brill, 1990), pp. 111-113. >I Thus, Herbert Nelson, postulating two separate space-time manifolds Alpha and Beta, recognizes, "if God's activity and its products in Alpha and Beta were temporally ordered in such a way that to the set of distinct effects and products of God's activity there corresponds a temporally ordered set of distinct divine activities, ... then that set of divine activities would provide a common frame of temporal reference within which events in Alpha and Beta would be temporally related" (Herbert 1. Nelson, "Time(s), Etemity, and Duration," International Journalfor Philosophy ofReligion 22 [1987]: 9). " Leftow, Time and Eternity, pp. 29, 31.

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a temporal God's creating an alternate time series. The argument at best shows that a temporal deity cannot create an additional time series independent of his own; but, of course, such a task is equally impossible for a timeless God. Since such a God is not in time, He cannot create an additional time series to His own; what He can purportedly do is create two time series A and B which are discrete from each other. But cannot a temporal God do the same? If God exists in temporal series C, can He not create two temporal series A and B which are discrete from each other? If He creates them at different times in C, they will not share even an initial instant. If we confme our discussion to physical space-time manifolds, this seems to be unproblematic: God could create at Ctl a space-time with a wholly different metric than the space-time He creates at Ct2. In fact, on a strictly physical level a temporal God could even create an additional temporal series. Our temporal series terminates in the initial Big Bang singularity at t = O. But t = 0 is not itself an instant of time or a space-time point; rather it constitutes a boundary to space-time. Time has no initial instant but approaches arbitrarily close to the singularity from any point t through the open interval (O,t]. If, then, God exists in our temporal series and created at t = 0 not only our space-time but also other space-time manifolds, it would follow that He has created additional, discrete temporal series besides our own, for these series do not share even so much as an instant of time with ours. If we elevate the discussion to the level of metaphysical time, as seems proper with respect to God, then God in metaphysical time could certainly create two mutually discrete physical space-times A and B, even if their events are related in metaphysical time. Could God create mutually discrete metaphysical times? I see no reason why the theist should think that such distinct times are metaphysically possible. If, as theists like Newton believed, metaphysical time is essentially connected with God's being or activity, it may well be as impossible for there to be another metaphysical time as it is for there to be another God. Could a timeless deity create two discrete metaphysical times? The answer to that question will depend upon whether a timeless deity can be the Creator of a temporal world without sacrificing divine timelessness, a question which we shall take up in chapter 3. For the moment, pending that discussion, Leftow's argument remains inconclusive. 6. Timelessness and the Modal Status ofTime. The sixth argument picks up on Leftow's contention that if God is temporal, He is so necessarily. If God is necessarily temporal, time is a necessary precondition of God's existence. But since time is contingent, God must be contingent. Since God is not contingent, He must be atemporal. We have already seen, however, the implausibility of Leftow's argument from transworld identity for the claim that God cannot be contingently temporal. The falsity of that claim causes this argument also to collapse. Moreover, it is doubtful that Leftow's three arguments for time's contingencl3 would convince atheist of Newtonian stripe who believes that time is a concomitant of God's existence and therefore necessary. To take his arguments in reverse order: (i) Time is a physical 53

Ibid., pp. 32-34.

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reality, and a physically empty world is conceivable. This argument is reductionistic and therefore unconvincing to anyone, not just the Newtonian, who holds that God could exist temporally even in a physically empty world. Cii) The propositions "No time exists" and "No temporal things exist" seem to be possibly true. This assertion would not impress the Newtonian, however, since he connects the existence of time (and space) necessarily to the being of God as emanent effects of God's existence and therefore regards these propositions as impossible. (Hi) Space-time has a beginning and so must be contingent. If it is rejoined that since time exists at every moment oftime and therefore can exist necessarily even though it has a beginning, one may reply that possibly there is a moment prior to the beginning of our time series T. so that possibly there is a time at which T does not exist. Again, however, the beginning of physical space-time would not in the least phase the Newtonian, who holds that God's metaphysical time preceded any creation on His part ofphysical space-time. Moreover, even Leftow's answer to the rejoinder is unsatisfactory. We may agree that anything that begins to exist within time in a world W cannot be necessary because there will be a possible world W* exactly similar to that segment of Ws history during which that thing does not exist. But (paradoxically) no matter how brief its existence, there is in no world a time during which time does not exist and so no means of pointing thereby to a world devoid of time. Leftow's reply to the rejoinder only shows that there are worlds in which T-the actual series of times-does not exist, not that there are worlds in which time does not exist. Even if every time series is contingent, it does not follow that time itself is contingent, just it does not follow from the contingency of every shape of an object that it is contingent that the object have a shape. It does seem bizarre to say that time can be necessarily existent and yet have a beginning, but Leftow needs to say more than he has to refute this position. In sum, Leftow's arguments for time's contingency are ineffectual against the Newtonian position which regards time as a necessary concomitant of God's existence. What is wanted here is some sort of critique of the view that God's existing entails the existence of time (and space). Leftow's appeal to God's spacelessness at this juncture is nugatory with respect to the classical Newtonian, since he holds that God does exist in infinite space as weH as time. A more thorough analysis of time and space will be necessary to refute these heterodox opinions. Of course, even the rejection of these opinions concerning time's necessity still leaves us with an unsound argument employing the false premiss that if God is temporal He is so necessarily. 7. Timelessness and the Creation of Time. The seventh argument is also based on the false premiss that God cannot be contingently temporal. Leftow reasons that if God is essentially temporal, then His creating time wouId involve His making His own existence possible, which is absurd. Therefore, a temporal God cannot create time, which impugns His being the source of all that is other than Himself. Fortunately, Leftow frees this argument from the noted false premiss by arguing that even if God is contingently temporal, He cannot act at any moment of time t to bring it about that the set of times has members. God cannot act at t to create times prior to t, since there is no causal power over the past. He cannot create t at t, for His action presupposes His existence and the existence of t is a precondition of His existence. He can at t only create times later than t; but then the existence of t is

20

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unaccounted for. No matter what point of time one picks, there is no action of God at that time which can account for the fact that the set of times has members. Is none of these alternatives possible? And are they exhaustive? Let us examine them in reverse order. Alternative (iii): God's creating t at t* O? lf not, how is etemity different from a point? If so, how does God have possession of His life "at once"? Similarly, for any three points a, b, and c, if b is between a and c, is the distance (a, b) > distance (a, c)? The same two questions arise with respect to negative and affirmative answers to this question. 69 The best analogy for Stump-Kretzmann etemity which I can think of would be aseries of points having a light-like separation in Minkowski space-time. The metric of such a manifold requires that the 65

66

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Stump and Kretzmann respond to this criticism, first, by asserting that it has not been shown that divisibility is essential to extension?O They note that on discrete theories oftime there exist extended but indivisible atoms (or chronons). Moreover, the specious present, though extended, is as such not divisible, even conceptually. The eternal present may be thought of as God's specious present which covers all of time. Moreover, even if space and time are continuous, one may not licitly generalize that all extensions are divisible. Secondly, Stump and Kretzmann attempt to provide some rationale for regarding eternity as an extension despite its indivisibility.71 Eternity must be thought of as extended because the alternative-that eternity belongs to the evanescent realm of becoming-is metaphysically impossible. Eternal extension or atemporal duration are predicated analogically of God, and although it is impossible to state what features are shared by temporal and atemporal extension, we can say that "eternal duration .. .is a measure of existence, indicating some degree of permanence of some sort on the part of something that persists-although, of course, divine existence, permanence, and persistence will be analogous to, not identical with, temporal existence, permanence, and duration.,,72 This two-fold response seems clearly unavailing. First, it belongs analytically to the concept of extension that a multiplicity of points can be, at least conceptually, specified within it. Indeed, for eternal duration to be "a measure of existence" some metric on this manifold must be specified, which is impossible without a multiplicity of ordered, specifiable points. The proffered counter-examples of chronons and the specious present are based on misunderstandings. For a moment oftime even to be a chronon one must be able to specitY instants which constitute its boundaries, or, at least, if its boundaries are fuzzy, which do not lie outside its span. If chronons endure for 10'23 second, we can conceptually, if not physically, divide it into lengths

intervaI, or space-time separation, between any two points Iying a10ng the path of a light ray in vacuo be zero. This is the case even for events which occur millions of years apart and light years away from each other: their space-time separation is zero. Lucas and Hodgson comment, "Topology is concemed with 'neamess', points and sets of points that are elose together, that is those where the distance between them tends toward zero. In an ordinary space the distance between two points can be zero only if the two points are coincident, but in Minkowski space two points on the path of a light ray are not, according to our criterion, separated, even though they are, according to intuitive reckoning, a great distance apart. Hence whereas in an ordinary space two points are near only if the distance between them is tending toward zero, which can happen only when they are themselves actually coincident, in Minkowski space two points can be counted as being topologically near to each other without approximating in the least to be coincident" (J. R. Lucas and P. E. Hodgson, Spacetime and Electromagnetism [Oxford: Clarendon Press, 1990], pp. 34-35). Perhaps Stump and Kretzmann could model divine etemity on the world-line of a light ray, conceding that it is, after all, made up of a multiplicity of points, but having a metric such that the separation of any two points is zero. Perhaps such a feature could be interpreted as God's possessing His Iife a1l at once. 10 Stump and Kretzmann, "Etemity, Awareness, and Action," pp. 466-468; idem, "Atemporal Duration," pp. 215-216. 11 Stump and Kretzmann, "Etemity, Awareness, and Action," pp. 468-469; idem, "Atemporal Duration," pp. 218-219. 12 Stump and Kretzmann, "Etemity, Awareness, and Action," p. 469.

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of 10-33 second. 73 As for the specious present, Stump and Kretzmann conflate the psychological present with the ontological present. The psychological present has for us a minimal duration, but whatever interval of time is actually present is conceptually divisible into smaller intervals. The etemal present, however, is not supposed to be God's psychological present, but the actual mode of His existence. The indivisibility of His psychological present does not imply the indivisibility of His mode of existence. If the mode of His existence is conceptually indivisible, then His eternity is topologically point-like, even ifHis psychological present necessarily takes in the whole extent oftime. Finally, the essential conceptual divisibility of an extension is not due to over-generalization from the cases of space and time. We can conceive, for example, of other sotts of extensions in logical space, such as a gradient recording temperature and pressure, and all these must be susceptible to specification of non-identical points along the extension, or one simply does not have an extension. An extension without conceptually specifiable points is as much a contradiction as atemporal duration. When we examine Stump and Kretzmann's reasons for thinking of eternity as an extension, I think it is evident that they have been misled by the metaphor of the "etemal present." Since they conceive of eternity on the model ofthe tensed present rather than of a tenseless state, they are exercised to deny of eternity that "radically evanescent existence" which characterizes the temporal present and which "could not be the existence of an absolutely perfect being," which must be "permanent, utterly immutable actuality.,,74 Thus, they explicitly state their aim as attempting "to frame the notion of a mode of existence consisting wholly in a present that is limitless rather than instantaneous.,,75 This attempt to combine presentness with permanence forces them to the conclusion that the etemal present "is indivisible, like the temporal present, but it is atemporal in virtue of being limitless rather than instantaneous, and it is in that way infinitely enduring.,,76 The best sense that I can make of the Stump-Kretzmann notions of the etemal present and atemporal duration is that our time dimension is embedded in a hypertime in which God endures, such that at every moment of hyper-time the entire temporal series is present (Figure 3.1).

See G. 1. Whitrow, The Natural Philosophy ofTime, 2d ed. (Oxford: Clarendon Press, 1980), p. 201: "Acceptance of the ideas of spatial and temporal atomicity in physics does not, of course, preclude us from applying mathematical concepts of space and time involving numerical continuity in our calculations, but the infinite divisibility associated with these concepts will then be purely mathematical and will not correspond to anything physical." Also relevant in this connection is Philip 1. Quinn, "On the Mereology of Boethian Etemity," International Journal for Philosophy ofReligion 32 (1992): 57. 74 Stump and Kretzmann, "Atemporal Duration," p. 218; cf idem, "Prophecy, Past Truth, and Etemity," in Philosophy ofReligion, ed. Jas. Tomberlin, Philosophical Perspectives 5 (Atascadero, Calif.: Ridgeway Publishing, 1991), p. 396: "The existence of an absolutely perfect being must be an indivisibly persistent present actuality." 7S Stump and Kretzmann, "Atemporal Duration," p. 218. 76 Ibid. 73

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universe t4 t3 t2

God

tl to

To

TI

T2

T3

T4

The horizontal T-axis represents hyper-time, in which God endures infinitely. The vertical t-axis represents time, in which our universe endures. When T2 is present for God, the entire temporal series of events is present to Hirn. Figure 3.1.

On this view even though our temporal present is radically evanescent, for God in hyper-time, or eternity, a11 our presents are equally real in His hyper-present. By the same token, the hyper-present is permanent from the standpoint of any temporal observer and is in that sense etemal. The present instant of hyper-time encompasses the whole of time and, as an instant, is indivisible. In God's etemal present the whole temporal series of events is laid out before Him. He can survey the whole series of events in that single hyper-instant and act at any point in our temporal series without changing or waiting for events to elapse. God can be said to have atemporal duration in the sense that He does not endure throughout time, but does endure in hyper-time, or eternity. Thus, on this model the notions of the etemal present and atemporal duration turn out to be coherent. 77 Remarkably, several statements by Stump and Kretzmann suggest that they are struggling to express just such a view. For example, in response to Brian Leftow's allegation that since, on Stump and Kretzmann's view, eternity cannot contain distinct positions, "eternity is pointlike, not extension like,,,78 they assert, "this inference holds only if it exhausts the possibilities for any mode of existence to describe it either as linelike or as pointlike, and there is no good reason to think that modes of existence higher up the ladder of being or of more dimensions than our 77 Curiously, however, ET-Simultaneity may not survive in this re-interpretation, since in twodimensional time simultaneity becomes relativized to a dimension, as explained by Murray MacBeath, "Time's Square," in The Philosophy ofTime, ed. R. Le Poidevin and M. MacBeath, Oxford Readings in Philosophy (Oxford: Oxford University Press, 1993), p. 196. 78 Leftow, Time and Eternity, p. 128.

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own are limited in that way.,,79 Here they explicitly appeal to higher dimensional reality in order to explain how what appears to us as a point is extended in a higher dimension. Again, they state, "On the doctrine of eternity, the eternal present persists, encompasses time, and is unbounded."so Here eternity is conceived as an infinite, embedding dimension in which time exists. Finally, Stump and Kretzmann attempt to illustrate their model by describing the attempts of a three-dimensional person to communicate his spatial location to one-dimensional creatures via spatial indexical expressions like "here."Sl This analogy suggests construing eternity as a hyper-time in which God attempts to communicate to creatures in time that all of them regardless of their temporallocation exist ''now.'' Thus, construing eternity as an embedding hyper-time not only renders coherent much of what Stump and Kretzmann say, but is even suggested by not a few of their own statements. Nevertheless, it is obvious that they would not accept such a construal of their view. The chief difficulty lies in the fact that in hyper-time God would not have complete possession all at once of His interminable life. We could eliminate this problem by limiting hyper-time to a single hyper-instant in which the whole series of temporal events in the universe exists; but such a solution is hardly acceptable, since God would then have evanescent existence in hyper-time. If His life is extended in hyper-time, then the hyper-present is constantly shifting for God, and our whole universe passes Him by in a fleeting hyper-instant. We could solve this difficulty in part by having God sustain our time dimension across hyper-time, so that it does not instantly pass away (Figure 3.2).

Stump and Kretzmann, "Etemity, Awareness, and Action," p. 471. Ibid., p. 466. "' Ibid., pp. 470-473. Unfortunately, the analogy is misconstructed due to a misuse of indexical expressions. In the one-dimensional world, the creatures are supposed to recognize an absolute here, which is the location of the creature which occupies the mid-point of the line segment which is their world. The aim of this analogy is c1early to construct a spatial tense on the analogy of "now." But the attempt misfires; for creatures elsewhere on the line segment the specified point cannot be truly regarded as here, but as there. It can only be truly regarded as here for the creature who occupies it. The customary view of spatial indexicals is that none of the points on the line is objectively here or there, these being person-dependent expressions of spatially tenseless facts. Objective spatial tenses would require us to say that in the postulated one-dimensional world there really are objective, personindependent facts like The end-point is here or The mid-point is up ahead. But it does not require the absurdity that only one point in space qualifies as being here. That would be like saying that only one point in time ever qualifies as now, when in fact objective tense requires merely that any time the expression "now" is correct1y used the time of usage be objectively present. In general, Stump and Kretzmann seem to have been misled by the world "absolute" with which they preface "here" and "present." Tbe upshot is that when the 3-0 person says to the 1-0 creature "We're all here together," the 1-0 creature will recognize that the expression "here" has a different referent than when he uses it, just as he recognizes that each of his fellow creatures would refer to his own place on the line segment as "here. " It is also significant to note that the 3-0 person does in fact share the same single dimension with the 1-0 creatures; he fails to be on the line only in virtue of being off it in the second and third dimensions, and co-ordinates can be assigned to him in that one shared dimension. Similarly, a hyper-temporal being causally connected to our temporal world have to share our temporal dimension at minimally one point where the dimensions intersect. 79 &0

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-

universe

-

t4 t3

t2 t1

God

(0

To

TI

T2

Tl

T4

Figure 3.2. By sustaining time across moments of hyper-time, time acquires width as weil as length.

If God chose to create time from the infinite hyper-past and sustain it into the infinite hyper-future, nothing in time would ever pass away for God. Still, if hypertime is tensed, it remains the case that God would not possess His life all at once. Perhaps we could avoid this problem by denying that hyper-time is tensed, so that God's life exists tenselessly as a B-series of events. But then God still has, at least, the experience of hyper-temporal becoming and so does not possess His life all at once in that sense. I have suggested in the previous chapter that this drawback is considerably reduced for an omniscient being, but Stump and Kretzmann would no doubt be unimpressed by such a rescue attempt ofGod's perfect life. Perhaps we could adopt their suggestion that God's specious present in tenseless hyper-time embraces the whole of hyper-time, so that nothing is lost or gained by Hirn experientially or metaphysically. But we have already seen the fatal flaws in such a view with respect to God's timely action in a tenseless time, and the same goes for hyper-time. God could not act to create or destroy time at a certain moment of hyper-time, since all moments ofhyper-time would appear to Him as equally "now." But perhaps a final gambit could be played: we could conceive of God's hyper-time as tenseless and composed of a single hyper-instant which is speciously present to God and in which our time dimension is embedded. On this view, etemity consists of a single, tenseless instant of hyper-time at which God creates our whole temporal series of events. This hyper-instant is not a duration, but neither is it evanescent, since it is tenseless. It appears as present to God, but there is no problem with timely action, since hyper-time, or etemity, consists of a single instant. Such a model comes startlingly elose to the elassical conception of etemity. The central difference consists in the fact that etemity was taken by its elassical defenders to be astate of timelessness, not an embedding hyper-temporal dimension. If we construe etemity as hyper-time, it follows that God must exist at minimally one instant of

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time where His hyper-temporal world-line (even if only a point) and the world-line ofthe universe intersect. 82 Thus, curiously, at some arbitrary point in time it would be true to say, "God now exists." Before that time it would be true to assert "God will exist" and thereafter "God did exist." Ironically, we were forced to such a model by attempting to provide a coherent interpretation of Stump and Kretzmann's notions of atemporal duration, etemal extension, and the eternal present; but all of these have now been sacrificed by the model suggested. Moreover, the model of hyper-temporal etemity depends for its metaphysical possibility on the tenseless theory of time, since God's hyper-time, if not our time, is conceived to be a tenseless time. But Stump and Kretzmann are eager to expound a model of etemity which is compatible with theories of time that are essentially tensed. Thus, the construal of eternity as a tenseless hyper-time would be doubly objectionable to them. Ultimately, then, I have been unable to find an acceptable, coherent model of Stump-Kretzmann eternity. This negative conclusion requires us to regard such expressions as "eternal present" and "atemporal duration" as metaphors appropriate to God's mode of existence. Stump and Kretzmann practically admit as much in characterizing such expressions as wholly analogical. For analogical predication without some univocal, conceptual content cannot be regarded as anything more than metaphor. 83 Such metaphors are apt for divine eternity because they convey to us that God's timeless state does not pass away like a temporal instant, that it is permanent. The opposite of evanescence is not duration or extension, but permanence. Permanence is really what Stump and Kretzmann are anxious to safeguard, and this property of eternity is guaranteed by God's tenseless existence and action on theories of divine timelessness, not by incoherent notions like atemporal duration or conceptually indivisible extension. 84 Defenders of divine timelessness who conceive of etemity a& topologically point-like have not in the least thereby compromised God's permanence.

This would seem to be the hyper-time at which God acts causally to create time and the universe. Since this point of intersection is shared by time and hyper-time and could be at any time, it follows that God may have created the world in, say, 1898--or maybe He has not yet created the world! From God's perspective such mid-time creation would not involve backward causation, since God in hyper-time aets to create the whole time-Iine at one hyper-instant, but for us temporal creatures His action would seem to involve backward causation, since it also occurs at amoment of ordinary time. These sorts of difficulty might weil cause one to doubt the metaphysical possibility of higher temporal dimensions, in contrast to higher spatial dimensions. BJ See Williarn P. Alston, "Aquinas on Theological Predication: A Look Backward and a Look Forward," in Reasoned Faith, ed. Eleonore Stump (lthaca, N. Y.: Comell University Press, 1993), pp. 145-178. 14 For an analysis of pennanence, see Quentin Smith, "A New Typology of Temporal and Atemporal Permanence," Noüs 23 (1989): 307-330, and Leftow, Time and Eternity, pp. 132-133. I should add merely that Leftow conflates instants (which are durationless) with moments (which have arbitrarily short non-zero duration). Etemity is not like a single moment which is both a frrst and last moment; rather it is Iike an instant and so has no first or last finite period of existence. 82

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ET-Simultaneity This long excursus on the nature of the etemal present has been necessary, not only in order to clarify the new species of simultaneity introduced by Sturnp and Kretzmann, namely, eternal simultaneity, but also because the notion of the present-both the temporal present and the eternal present -features prominently in their definition of ET-simultaneity. If we take eternity to be a tenselessly existing state topologically like a point, then two eternal entities can both be located tenselessly at the same point which represents eternity. But what about the case in which one entity is etemal and the other temporal? The problem seen by Sturnp and Kretzmann in relating an etemal entity to a temporal entity is that there is no single mode of existence shared by the two entities. Hence, one cannot draft a formulation of ET-simultaneity on the usual pattern "existence or occurrence at one and the same__ ." "What is temporal and what is etemal can co-exist, ... but not within the same mode of existence and there is no single mode of existence that can be referred to in filling in the blank in such a definition of ET-simultaneity. ,,85 At this point Sturnp and Kretzmann turn to the Special Theory of Relativity in order to provide an analogy to the type of simultaneity relation they will propose. In SR simultaneity is redefmed as existence or occurrence at the same time within the re/erence frame 0/ a given observer. This conception of simultaneity relative to a reference frame suggests a way to defme ET-simultaneity. Sturnp and Kretzmann propose that we construe a mode of existence as analogous to a reference frame and construct a definition in terms of two reference frames and two observers. First attempt Accordingly, Sturnp and Kretzmann formulate the following definition of ETsimultaneity: For every x and for every y, x and y are ET-simultaneous iff (i) either x is etemal and y is temporal, or vice versa; and (ii) for some observer, A, in the unique etemal reference frame, x and y are both present-i.e., either x is eternally present and y is observed as temporally present, or vice versa; and (iii) for some observer, B, in one ofthe infinitely many temporal reference frames, x and y are both present-i.e., either x is observed as eternally present and y is temporally present, or vice versa.·6

The first thing to notice about this definition is that it is not really analogous to simultaneity in SR at all. In SR two simultaneous events both occur at one and the same time relative to a given reference frame. The analogy to this would be that two events (or entities), one eternal and one temporal, are simultaneous itIrelative to the etemal ''reference frame" both occur at one and the same etemal point and relative to the temporal ''reference frame" both occur at one and the same time. ET85 86

Stump and Kretzmann, "Etemity," p. 436. Ibid., p. 439.

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simultaneity as defmed by Stump and Kretzmann only remotely resembles relativistie simultaneity in that two ''referenee frames" are employed. But beyond that it is quite non-analogous to simultaneity as defmed in SR. A further clarifieation of clause (iii) is in order. When the defmition refers to "the infinitely many temporal referenee frames," it might naturally be thought that physieal referenee frames in SR are being referred to. But tbis would eontradict Stump and Kretzmann's repeated statements that their aeeount presupposes no more than a Newtonian, absolute time, and that SR serves as merely an introduetory analogue to their defmition of ET-simultaneity. 87 Their defmition utilizes ''referenee frame" metaphorieally to refer on the one hand to God's atemporal mode of existenee and on the other hand to our temporal mode of existenee. Thus, the "infinitely many temporal referenee frames" refers to the different moments of time. A referenee frame is thus not strietly analogous to a mode of existenee, but rather to loeations on a geometrieal representation of a mode of existenee. lt is noteworthy that in the proposed defmition simultaneity is not defmed in terms of a shared loeation, but in terms of a shared property. Relative to a loeation either in time or in eternity, both x and y are said to be present. Tbis is not a shared loeation (eontrast: "in the present"), sinee x and y are not both located in the "etemal present" nor in any temporal present. Such a procedure seems peculiar, sinee two entities' sharing a property relative to some loeation hardly suffices for simultaneity. Relative to the etemal reference frame, for example, God and Jones are both intelligent, but they are not therefore in any way simultaneous. But when it comes to the property of presentness, I think, we ean make sense of such a procedure. For example, we eould defme temporal simultaneity by stating that x and y are simultaneous iff relative to time t x and y are both present. The problem with the Stump-Kretzmann definition is that the word "present" in the definition refers to entirely different properties, namely, temporal presentness and etemal presentness, so that there is no shared property involved. The fact that the "etemal present" must be taken as metaphorical only underseores tbis eonclusion. We cannot circumvent tbis problem by giving tenseless, token-reflexive truth conditions relative to eternity or to moments of time for statements like ''y is present," since in eternity as well as at most moments of time there are no sueh tokens. 88 Rather we must fmd some common property shared by God and temporal entities relative to either's "reference frame" wbich intuitively suffices to found a simultaneity relation. I think that the essence of the Stump-Kretzmann definition would be preserved if we state that relative to either frame "x and y are both real," one etemally real and the other observed as temporally real relative to the etemal "reference frame" or one temporally real and the other observed as etemally real relative to a moment of time. 89 If Stump and Kretzmann insist on a shared property of literal presentness, Ibid., pp. 437. 438. For discussion of token-reflexive truth conditions of tensed sentences, see my The Tensed Theory of Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, 2000), chap 3. 89 Not only does real seem to be the univocal element common to the etemal present and the temporal present, but, as we shall see, Stump and Kretzmann revise their definition of Er-simultaneity in such a 87

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then I fear that the incoherence found in their notion of the etemal present will also bring down their deflnition ofET -simultaneity. On the basis of their deflnition of ET-simultaneity, Stump and Kretzmann believe to have solved the problem of a timeless deity's being active in the world. In virtue oftheir ET-simultaneity God and events in time are co-existent: ... if anything exists etemally, its existence, although infinitely extended, is fully realized, a11 present at once. Thus the entire life of any etemal entity is co-existent with any temporal entity at any time at which that temporal entity exists. From a temporal standpoint, the present is ET-simultaneous with the whole infinite extent of an etemal entity's Iife. From the standpoint of etemity, every time is present, co-occurrent with the whole of infinite atemporal duration. 90

As an illustration of this co-existence, Stump and Kretzmann invite us to imagine two infinite, parallel, horizontal strips, the upper one (representing etemity) being a strip of light (light representing the present) and the lower one (representing time) being dark except for a dot of light moving steadily along it. "For any instant of time as that instant is present, the whole of etemity is present at once; the infmitely enduring, indivisible etemal present is simultaneous with each temporal instant as it is the present instant. ,,91 Whatever one may think of their doctrine, tbis illustration is plainly confused, mixing as it does spatial and temporal imagery.92 From the standpoint of etemity, the etemal "present" is wholly simultaneous with each instant as it becomes present (illuminated). Thus, etemity is simultaneous with each moment of time in succession; otherwise, from the standpoint of etemity the lower strip would have to be wholly illuminated, like the upper strip. Given that the etemal "present" is successively simultaneous with one temporal present at a time, etemity is not atemporal at all but has been temporalized in virtue of its real relation to time. In other words, Stump and Kretzmann's illustration portrays vividly precisely the objection currently under consideration, which their account is supposed to resolve. A more apt illustration of their view would have drawn upon the relativity of simultaneity: from the standpoint of any temporal present, the lower strip is a single dot of light at that point and the upper strip is observed as wholly illuminated, and from the standpoint of etemity, etemity is a single, indivisible point of light and the entire temporal strip is observed as illuminated. 93

way as to make it tenseless. Their use of the word "present" is confusing and, I fear, inconsistent. They even speak of spatiallocations as being present to a non-spatial God. 90 Stump and Kretzmann, "Etemity," p. 441. 91 Stump and Kretzmann, "Atemporal Duration," p. 219. 92 As noted by Herbert 1. Nelson, "Time(s), Etemity, and Duration," International Journal for Philosophy ofReligion 22 (1987): 12. 93 See their revised version of the illustration in Stump and Kretzmann, "Etemity, Awareness, and Action," p. 475. They still fai! to appreciate, however, the radical disanalogy between tensed time and space. For in response to Lewis's objection that in order to be ontologically (as opposed to merely epistemically) present or real to an atemporal God, a thing would have to be atemporal itself (Delmas Lewis, "Etemity, Time, and Timelessness," Faith and Philosophy 5 [1988): 72-86), Stump and Kretzmann retort that if spatial locations can be present to God without God's being spatial, then temporal moments can be present to God without God's being temporal (Stump and Kretzmann,

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The upshot of the doctrine of ET-simultaneity is that all temporal events are observed as present (or, as I have suggested, real) by God. Stwnp and Kretzmann make it quite clear that by the expression "observed as present" they do not mean merely "epistemically present" to God, that is, "gathered into one specious present" by God. Rather all temporal events are ontologically real for God. Stwnp and Kretzmann emphasize that this doctrine does not imply that temporal events exist in eternity or that tense and temporal becoming are illusory; rather it implies a sort of ''metaphysical relativism.,,94 Reality is composed of two incommensurable modes of real existence, time and eternity, which cannot be brought together into a single frame of reference. God veridically experiences every temporal event as having presentness in relation to eternity. Perhaps we can get a better understanding of Stwnp and Kretzmann's view by drawing once more upon Relativity Theory: just as at a single spacetime location different observers will observe different simultaneity classes of events depending upon each observer's velocity at that point and none of these can claim to be preferred as the uniquely correct simultaneity class, so at the point of eternity there is no unique, preferred class of temporally simultaneous events which are observed as real and so temporally present by God, but God observes different classes of temporally simultaneous events to be real in accordance with the ET-simultaneity relation. The disanalogy in the eternity/temporality case is, of course, that instead of a plurality of observers we have only one observer, God, and there is no ground, such as a physical observer's velocity and the constancy of light's speed, of this metaphysical relativity. The unicity of the etemal observer, however, need not be taken as a serious drawback of the analogy. For in Relativity Theory the postuiated observers are merely hypothetical anyway, and a single ob server at aspacetime point can change his reference frame simply by changing his mind. Since there is no state, on the Einsteinian interpretation of SR, of absolute rest, any observer at aspacetime point can consider himself to be either at rest or in motion relative to some hypothetical rest frame. Thus, there is no dass of events absolutely simultaneous for him nor a reference frame in which he uniquely exists. Similarly, we could understand God in eternity to observe one or another dass of temporally simultaneous events to be simultaneous with Him depending on His chosen perspective. If temporal events are considered one way, Nixon's resignation is temporally present or real to Him; but if they are considered another way, Nixon's death is real to God. God considers events in all ways, and no class of temporal events is uniquely real for Him. The second disanalogy mentioned above-the lack of any basis for such a metaphysical relativity-is a more serious drawback. It might be tempting to say that such relativity is rooted in the simple fact of the timelessness of God and the temporality of creatures. But such a ground is inadequate, since timelessness and temporality need not be related in any way. Indeed, the objection under "Eternity, Awareness, and Action," p. 476). This response is based upon a clear conflation of time (which is tensed) with space (which is tenseless). 94 Stump and Kretzmann, "Etemity," pp. 442-443. They should have said "relativity," I think.

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consideration is that they cannot be really related in the way the doctrine of creation demands. Metaphysical relativity must be taken simply as a brute fact about reality. But is this really so different from SR? In Einstein's understanding, the relativity of simultaneity is ultimately rooted in the non-existence of Newton's absolute space and time, that is to say, of an absolute rest frame such as the aether frame of nineteenth century physics and of unique, world-wide, successive dasses of events as present. The constancy of light's velocity and the relative motion of hypothetical observers are relevant only to providing a new definition or determination of simultaneity at a distance. The ultimate basis of the relativity of simultaneity lies in the absence of absolute time and space, and this is just a surd metaphysical fact postulated by the Einsteinian interpretation of SR. Similarly, the ET-simultaneity advocated by Stump and Kretzmann postulates a reality which lacks any absolute frame ofreference yielding a unique description ofwhat is real. The radical metaphysical relativity postulated by ET-simultaneity implies that all events in time are present or real to God in eternity and therefore open to His timeless causal influence. "Even though His actions cannot be located in time, he can bring about ejJects in time .... ,,95 Every action ofGod is ET-simultaneous with any temporal effect ascribed to it, and "ET-simultaneity is a sufficient condition for the possibility of a causal connection in the case of God's bringing about the existence of a temporal entity .... ,,96 Thus, God's causal relation to the world is grounded in His being ET-simultaneous with every event in time. Now in order to be ET -simultaneous with some temporal event y, x must be atemporally real and y be observed to be temporally real. But as many critics have pointed out, the language of observation in the defInition of ET-simultaneity is wholly obscure. 97 In SR physical operations involving dock synchronization via light signals are stipulated in order to give physical meaning to simultaneity at a distance. When y is "observed" to be simultaneous with x according to SR, the word "observed" might more perspicuously be replaced with "calculated;" the determination of y's simultaneity with x is based not on physical observation of y, but on the solution to a mathematical equation. But in the defInition of ETsimultaneity no hint is given as to what is meant, for example, by x's being observed as eternally present relative to a time t. In the absence of any procedure for determining ET -simultaneity, the language of observation becomes vacuous. All that is meant is that relative to the ''reference frame" of eternity x is etemally present (or real) and y is temporally present (or real) and that relative to some temporal Ibid., p. 448 (myemphasis). Ibid., p. 451. 97 Davis, Logic and the Nature o/God, p. 20; Delmas Lewis, "Etemity Again: A Reply to Stump and Kretzmann," International Journal/or Philosophy 0/ Religion 15 (1984): 74-76; Helm, Eternal God, pp. 32-33; William Hasker, God, Time, and Knowledge, pp. 164-166; Yates, Timelessness o/God, pp. 128130; Leftow, Time and Eternity, pp. 170-172. Unfortunately, many ofthese critics, misunderstanding the role of hypothetical observers in Relativity Theory, think that Stump and Kretzmann require that a temporal person somehow actua11y observe God as etemally present, which is impossible. But Stump and Kretzmann are clear that for them an observer is anything with respect to which a reference frame is deterrnined (Ibid., p. 438; idem, "Eternity, Awareness, and Action," p. 474). Actually Stump and Kretzmann concede too much, for a11 thai is required in Relativity Theory are hypothetical observers. 9l

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"reference frame" x is etemally present (or real) and y is temporall~ present (or real). It hardly needs to be said that such a definition clarifies nothing. 8 It only restates the fact that x is atemporal and y is temporal without explaining in what sense they are simultaneous. Nor will an appeal to metaphysical relativity help to make sense of the definition. In the absence of operational definitions which serve to re-defme distant simultaneity in SR, there really are no simultaneous events at all at a distance. Absent these operational definitions, there just is no fact of the matter conceming the simultaneity of spatially separated events. Only events at the same spacetime point are simultaneous. Thus, if reality is bifurcated into two irreducible modes of existence, and there is no way of observing or determining what is ET-simultaneous with x or y, there just is no ET-simultaneity between them. Only events cooccurring at the same time or at the same etemal point are simultaneous, that is to say, only temporal and eternal simultaneity obtain. It follows that an atemporal God could not be causally related to the world. Moreover, even if we grant metaphysical relativity on the analogy of temporal relativity, it will not yield ET-simultaneity. To say that y is observed by God as temporally present or real just means that relative to God y is temporally present or real. But if w < y < Z, then insofar as y is temporally present to God w is past and z is future. Of course, since, as McTaggart insisted, all events are eventually present, it follows that due to metaphysical relativity w is also temporally present relative to God in another metaphysical frame of reference, as is z in yet another metaphysical frame of reference. But insofar as we consider reality from the perspective in which God is etemal and y is temporally present relative to God, there are events earlier and later than y which are past and future respectively relative to God. But if y is temporally present relative to God, while w is past and z is future relative to God, then God and y are temporally simultaneous, not ET-simultaneous. Thus, the sort of simultaneity suggested by metaphysical relativity is not ET-simultaneity, but an extension of physical relativity of simultaneity into metaphysics, that is to say, God is temporally simultaneous with every temporal present. From our perspective, these temporal presents are evanescent, but from God's multitude of perspectives each present is simultaneous with Him in some perspective on reality. Such a view obviously fails to preserve God's timelessness. No doubt stump and Kretzmann would cry foul at such a critique, in that I have pushed the analogy to Relativity Theory far beyond their intent. I concede the point; but then I simply cannot make sense out of the language of observation found in their definition nor of the metaphysical relativity appealed to in its explication. Stump and Kretzmann are not really metaphysical relativists but hold that God has a

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So also Leftow, Time and Etemity, p. 174. Helm's harsh verdict seemsjustified: "The 'solution' to the problem is found simply by rewording the problem with the help of the device of ET-sirnultaneity. ET-simultaneity has no independent merit or use, nothing is illuminated or explained by it.... For the problem is, how can something which is an event in time be wholly present 'to an eternal entity'? Tbe answer given is that it is ET-wholly present. But this answer is wholly obscure" (Helm, Etemal God, p. 33).

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unique perspective on the world according to which all events are in some unexplained way equally real to Him. Given, then, that Stump and Kretzmann's definition of ET-simultaneity is merely a non-explanatory restatement of the doctrine that while God is timeless all things in time are temporally present or real to Hirn, it cannot do the explanatory work necessary to show why 8. If God is really related to the temporal world, God is temporal. is not necessarily true. Second Attempt Fortunately, Stump and Kretzmann have for theological reasons tried to free their definition from observation language, and perhaps this will give some explanatory content to the definition ofET -simultaneity. They now propose: For every x and every y, x and y are ET-simultaneous if and only if (i) either x is etemal and y is temporal, or vice versa (for convenience, let x be etemal and y temporal); and (ii) with respect to some A in the unique etemal reference frame, x and y are both present-i.e., (a) x is in the etemal present with respect to A, (b) Y is in the temporal present, and (c) both x and y are situated with respect to A in such a way that A can enter into direct and immediate causal relations with each of them and (if capable of awareness) can be directly aware of each ofthem; and (iii) with respect to some B in one of the infinitely many temporal reference frames, x and y are both present-i.e., (a) x is in the eternal present, (b) y is at the same time as B, and (c) both x and y are situated with respect to B in such a way that B can enter into direct and immediate causal relations with each of them and (if capable of awareness) can be directly aware of each ofthem. 99

This new definition is quite strange. Although the observation-words are absent, the two ob servers A and B remain. Since the role in the original definition of A and B was simply to specify ''reference frames," one might surmise that we could simply eliminate them altogether and just label the etemal "frame" "A" and the temporal "frame" "B", so that relative to the etemal "reference frame" A, x is in the etemal "present" and y is in the temporal present-but then we fmd that clause (ii. c) requires that A itself enter into causal relations, which a mere reference frame cannot do. A and B have in this re-definition become real, causally efficacious beings. Moreover, since God alone is etemal, A=x=God. It follows that according to (ii. c) God is so situated in respect to Hirnself that He can enter into causal relations with Himself. God must be in some sense self-caused. Furthermore unless Stump and Kretzmann are willing to countenance creatures in some way causally influencing God, (iii. c) must imply that the creature B can be merely a direct and immediate effect of God. Another curious feature and serious drawback of tbis definition is that the only temporal events wbich are ET-simultaneous with God turn out to be present events. 99 Stump and Kretzmann, "Eternity, Awareness, and Action," pp. 477-478; idem, "Prophecy, Past Truth, and Eternity," p. 407.

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For relative to etemity, (ii. b) stipulates that y must be in the temporal present, not just at some moment of time. Thus, from God's perspective only the temporal moment which now exists is ET-simultaneous with Him. 100 Since (iii. b) is not parallel to (ii. b) in that, unlike the latter, it refers not to the temporal present, but to any moment in time, it rnight be thought that relative to any moment of time a temporal event at that time is ET-simultaneous with God. But if the verbs "can enter" and "can be" in (iii. c) are tensed, then again only present events are ETsimultaneous with God, since B can (presently) enter into causal relations only if B exists now. God's being ET-simultaneous with only present events rnight appear at first blush to be acceptable to the partisan of a tensed theory of time, who holds to metaphysical presentism and regards past and future thingsIevents as non-existent. One cannot, after all, be simultaneous with non-existent entities, so perhaps God's being ET-simultaneous with present events alone is not so bad. Sturnp and Kretzrnann would probably not welcome the consequence that their theory is incompatible with the tenseless theory oftime, however. And a moment's reflection reveals that God's being ET-simultaneous with only present events leads to incoherence. For relative to God, the only events He is ET-simultaneous with are present events. But since which events are present is constantly changing, God acquires continually new relations of ET-simultaneity. Hence, He is changing and therefore temporal. Thus, if God is simultaneous only with present events, His relation to them is ordinary temporal simultaneity, not ET-simultaneity. Hence, Sturnp and Kretzrnann's new definition needs to be read tenselessly throughout, including clause (iii. c), and (iL b) must be arnended to state 'y is at some point in time." So arnended, the definition successfully stipulates that God is ET-simultaneous with every temporal event, whether it be past, present, or future. But now we come to what appears to be an irremediable problem with the new definition. Notice that although ET-simultaneity is still defined in terms of a shared property of presentness, presentness is now explicated in terrns of different locations and a shared property of being situated in a certain way. Thus, unlike the first definition, this re-definition does provide a univocal sense in which God and creatures are said to be present, narnely, that although they are differently located, in time and etemity, they can enter into direct and immediate causal relations and be directly aware of each other. The problem with this new definition of ET-simultaneity, however, is that it makes Sturnp and Kretzrnann's account of divine etemity viciously circular. For ET-simultaneity was originally invoked in order to explain how a timeless deity could be causally active in time, but now ET-simultaneity is defined in terms of a timeless being's ability to be causally active in time. As Leftow states, '00 Stump and Kretzmann want to say that God sustains relations of ET-simultaneity with a11 events only insofar as each has the property of temporal presentness (as opposed to pastness or futurity). But that is not what (ii. b) stipulates. The grarmnaticaI mies goveming indexicals require that ''the temporal present" in (ii. b) refer to now. Oddly, (iii. b) lacks any reference to y or B's having the property ofpresentness or being in the present. They could be past events, ifthe definition is read tenselessly. Thus, an event could be ET-simultaneous with God, not as present, but as past, which is incoherent.

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... any definition of ET-simultaneity which invokes any form of ET-causality (or ... other causally implicated ET-knowledge) is implicitly circular. For to fully explain how ETcausation can occur, we must bring in the concept of ET-simultaneity. If we do, we cannot then defme ET-simultaneity by invoking ET-causation, for then the concept to be defined in effect recurs in the definition. 101

The new definition proffered by Stump and KretzInann (once [ii. b] is amended) simply takes it for granted that God and temporal events are so situated (whether with respect to God or to events) that God can be directlyand immediately causally related to them while remaining atemporal. But the objection which drives our present concern is precisely that a timeless God and temporal events cannot be so situated. How can God be really related to a present event without Himself being present? The answer is supposed to be that they are ET-simultaneous. But now ETsimultaneity is explicated in terms of God's ability to be causally related to temporal events while remaining atemporal. Such an account will remain viciously circular unless Stump and KretzInann provide an independent explanation of how the timeless God can be directly and immediately causally related to events in time. In summary, it seems to me that Stump and KretzInann have failed to provide any coherent model which explains how God can be both atemporal and yet causally active in the world. The best sense I could make out of the prima facie selfcontradictory notion of atemporal duration is that God is hyper-temporal, not atemporal. Their first definition of so-called ET-simultaneity was explanatorily vacuous, a mere restatement of the fact that God is atemporal and temporal events are present. Their re-definition explicated ET-simultaneity in terms of causal and epistemic relations, which they had previously tried to explain in terms of ETsimultaneity, thus closing a vicious circle. In short, they have said nothing which would undercut the argument that in virtue of His real relation to the temporal world God is temporal. LEFTOW'S DOCTRINE OF THE EXISTENCE OF ALL THINGS IN ETERNITY The central difficulty and in the end fatal flaw of Stump and Kretzmann's attempt to enunciate an informative doctrine of ET-simultaneity is their inability to bring together temporal things and God into a common frame of reference. They never could explain how God and temporal creatures could be in any sense simultaneous so as to allow a causal relation to obtain between them. As we have seen, they eschew a consistent application of the analogy of the Special Theory of Relativity to time and eternity, which would have required that relative to God the entities/events at any time t exist at the eternal point, whereas relative to the entities/events at t God exists at t. Since they resist the idea that temporal entitieslevents somehow exist in or at eternity, Stump and KretzInann failed to bring together such entitieslevents and God into a coherent relationship, existing as they do in two utterly disparate modes ofbeing.

101

Leftow, Time and Eternity, p. 173.

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Brian Leftow' s proposal is, in effect, to eliminate this defect by maintaining that temporal things really do exist in eternity, that is to say, from God's perspective all events do occur timelessly at the timeless point of eternity. Thus, God and temporal things do share a mode of existence and can be brought together within a single frame of reference, so that God and temporal entities are E-simultaneous and causally connected in that timeless state. Leftow will not allow the analogy with Relativity Theory to be applied symmetrically, however. 102 We have seen in Chapter 1 that he gives a whole array of arguments to prove that God is (absolutely) atemporal, and as a partisan of divine simplicity Leftow cannot countenance the notion that God's mode of existence should be relative to anything, much less temporal in relation to sometbing else. God 's Asymmetrical Relativistic Reference Frame

Leftow is therefore obliged to support the asymmetrical relativity between God and temporal creatures by means of argument. Why think that relative to God temporal entities co-exist with God in eternity in such a way that relative to creatures God does not co-exist with them in time? Leftow bases bis defense of tbis asymmetry on what he calls the Zero Thesis: that the distance between God and every spatial being is zero. The argument for tbis thesis is simple: if God is not located in space, there can be no spatial distance between God and spatial beings; therefore, there is none. Leftow acknowledges that tbis argument seems to involve a category mistake: ... God is not the kind of thing of which we can affirm or deny distance: ... 'there can be no spatial distance between God and spatial creatures' is a category-negation rather than an ordinary negation, and so its semantics are such that it does not entail the Zero Thesis. . ... the Zero Thesis is actually ill-formed. For it arguably is equivalent to 'there is a distance between God and spatial creatures, and this distance is zero,' a conjunctive proposition whose first conjunct the doctrine of categories declares nonsensical. 103

One may not therefore validly infer from God's spacelessness that the distance between God and any spatial being is zero. Leftow's misgivings are, I think, well-founded. The dispute between Lorentzian and Einsteinian Relativity provides arelevant example from the bistory of science of the crucial difference between a category-negation and the negation of a property. Nineteenth century aether theories originally posited as the medium of transmission 102 This occasions difficulty for Leftow's theory, for he affirms that while God is eternally Lord in the eternal "reference frame", nevertheless in time He is not Lord except at the appropriate time (Brian Leftow, "Aquinas on Time and Eternity," American Catholic Philosophical Quarterly 64 [1990]: 396). That is to say that God's extrinsic properties do change in the temporal "reference frame" and, hence, God is temporal with respect to the temporal frame-and that even if relative to the eternal frame God is changeless. Thus, Leftow seems obliged to affirm with Aquinas that relative to the temporal frame, at least, God sustains no real relation to the world. The only way to prevent his solution from collapsing into the no real relations doctrine would therefore seem to be to deny the symmetry of the analogy to the simultaneity relation in Relativity Theory. 103 Brian Leftow, "Eternity and Simultaneity," Faith and Philosophy 8 (1991): 162; cf. idem, Time and Eternity, pp. 222-223.

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of electromagnetic radiation an invisible, rigid liquid, like glass, which was nonetheless completely intangible and utterly at rest with respect to absolute space. With the publication of his SR paper in 1905, Einstein rejected the existence of the classical aether and along with it the privileged rest frame. But in 1916, at the prompting of Lorentz that the General Theory of Relativity (GR) admits the possibility of a stationary aether, Einstein introduced a new relativistic conception of the ether: the space-time itself as described by the metrical tensor gl'v. 104 When Einstein lectured at Lorentz's UniversityofLeiden in 1920, he drewa fundamental distinction between the classical aether and his new relativistic ether on the basis of the applicability ofthe category ofmotion to the aether frame: As regards the mechanicaI nature of Lorentz's aether, one might say of it, with a touch of humor, that immobility was the only mechanical property which H. A. Lorentz left it. It may be added that the whole difference which the special theory of relativity made in our conception of the aether lay in this, that it divested the aether of its last mechanicaI quality, namely immobility .... The most obvious viewpoint which could be taken ofthis matter appeared to be the following. Tbe aether does not exist at a11. ... However, c10ser reflection shows that this denial ofthe aether is not demanded by the special principle of relativity. We can assume the existence of an aether; but we must abstain from ascribing a definitive state of motion to it, i.e., we must by abstraction divest it of the last mechanical characteristic which Lorentz had left it. ... Generalizing, we must say that we can conceive of extended physical objects to which the concept of motion cannot be applied.... Tbe special principle of relativity forbids us to regard the aether as composed of particles, the movements of which can be followed out through time, but the aether hypothesis as such is not incompatible with the special theory of relativity. Only we must take care not to ascribe astate of motion to the aether. lOS

Privately Einstein confessed to Lorentz, "It would have been more right if I had limited myself, in my previously published papers, to lay emphasis only on the nonexistence of any velocity of the ether instead of the defense of the total nonexistence ofthe ether."I06 When Einstein denied a velocity or state of motion of the ether, he was emphatically not ascribing to it the property of immobility. For that would be to admit that the ether constitutes a reference frame, as Lorentz claimed, and therefore serves in virtue of its immobility as a privileged frame relative to which absolute motion, simultaneity, and length exist. Rather the relativistic ether is, as Kostro puts it,107 an ultra-referential reality to which the category of motion does not even apply. When Leftow infers from God's spacelessness that the distance between God and spatial things is zero, he seetns to commit the same error as would someone who inferred from the ultra-referential status of the relativistic ether that its motion is 104 A. Einstein to H. A. Lorentz, June 17, 1916, item 16-453 in the Mudd Library, Princeton University, cited in Ludwik Kostro, "Einstein's New Conception of the Ether," proceedings of "Physical Interpretations of Relativity Tbeory," conference of the British Society for the Philosophy of Science, Sept. 16-19, 1988, Imperial College of Science and Technology, London. lOS A. Einstein, ither und Relativitätstheorie (Berlin: Julius Springer Verlag, 1920), pp. 7-9. 106 A. Einstein to H. A. Lorentz, Nov. 15, 1919; item 16-494 in Mudd Library, Princeton University, cited in Kostro "Einstein's New Conception." 107 Kostro, "Einstein's New Conception."

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zero. Leftow defends bis inference by asking how, if the Zero Thesis and its equivalent "There is a distance between God and spatial creatures, and this distance is zero" are ill-fonned nonsense, we can understand them weIl enough to tell that they are equivalent. The answer is that we sufficiently understand analogous, wellfonned statements about spatially distant objects (and rest frames) to see what has gone wrong in these ill-fonned statements about a spaceless being or an ultrareferential reality. Leftow further defends bis inference by asserting that the equivalent mentioned is problematic only if a zero distance is a positive distance. By ''positive'' he does not mean positive in the numerical sense, for that would be not merely problematic but contradictory. Rather he means positive in the sense of ontological status. But if Leftow means to assert more than a category-negation, he must be ascribing positive, existential status to the zero distance between creatures and God. That is just as problematic as ascribing zero motion to the relativistic ether. Finally, Leftow defends his Thesis by claiming that it is an entailment of the true and intelligible statement that "Necessarily, there is no distance between God and any spatial thing." But this statement is true and intelligible only insofar as it is a category-negation, and as such it does not entail the Zero Thesis. The reductio ad absurdum of Leftow's Zero Thesis is that it entails a definition of spatial contiguity which forces one to accept that ''yellow, the number 3, and any other entity without a spatial loeation are s~atially contiguous with all spatial things," since the distance between them is zero. 1 8 This untoward result makes painfully evident that the Zero Thesis is just a category mistake. 109 What is disquieting about this evident failure ofthe Zero Thesis is that Leftow's entire theory of divine eternity appears to balance like an inverted pyramid on this thesis, so that with the untenability of that thesis the whole theory threatens to toppie. Without the Zero Thesis, I do not know how to save Leftow's theory, for without it there is no "frame of reference" in which all things exist changelessly relative to GodllO-which fact should become clearer as we proceed. Leftow, Time and Eternity, p. 225. In Time and Eternity, p. 224, Leftow ascribes to the critic of the Zero Thesis the general claim "if x has spatial relations x has a spatial loeation," whieh Leftow regards as false, based on the counterexample of the spatial relation ia not located in. This general claim does not, pace Leftow, underlie the eritie's misgivings. Rather the critic maintains that in order for a distanee metric to be defmed with respeet to two entities (such that the distance between them ean be, say, zero), those entities must have locations in a shared space on which the metrie is defmed. This contention is unremarkable. Moreover, Leftow's counter-example, with respect to a spaceless being, is not a spatial relation, but onee again a category negation. In a sort of last-ditch defense of the Zero Thesis, Leftow asserts, "The Zero Thesis lets one give literal meaning to the claim that a spaceless God is omnipresent. If one denies the Zero Thesis, is Iiteral omnipresenee at all possible for a spaceless God7" (lbid., p. 228). This piece de resistance fails because the Zero Thesis itself fails to provide any Iiteral eontent to divine omnipreSence over and above the traditional understanding of God's being eausally active and aware of everything happening at any point in space. What the Zero Thesis implies is really divine omni-absenee (if the traditional understanding inadequately eaptures omnipresence), for it implies that God does not exist at any point in space but is at best continuous with it. 110 As admitted by Graham Oddie and Roy W. Perrett, "Simultaneity and God's Timelessness," Sophia 31 (1992): 127, who, unlike Leftow, do not offer any theoretical justification for taking all events as simultaneous in relation God. 101

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According to Leftow, the Zero Thesis has a startling consequence: since the distance between God and any creature is always the same (zero), there is no motion relative to God. Now, of course, in the sense of a category-negation there is no motion relative to God, since God is not a reference frame any more than is the relativistic ether. But Leftow takes this consequence to mean that God is or has a reference frame and that the motion of things in space relative to that frame is zero. He writes, "That there is no motion relative to God does not entail that there is no motion relative to other things. There is nothing problematic in the thought that an object at rest in one frame ofreference (e.g. God's) is in motion in other referenceframes.,,111 What is problematic, however, is the slide from speaking colloquially of God's "frame of reference" to treating this as a sort of reference frame related relativistically to other physical reference frames. Such a conception obviously cannot be applied to God in any literal sense; when Stump and Kretzmann spoke of God's reference frame they were using the terms metaphorically for God's mode of existence. It is simply inept to speak, as Leftow does, of objects at rest (zero motion) relative to God. Leftow proceeds to broach the following thesis, which he characterizes as "eminently defensible,,:112 M. There is no change of any sort involving spatial, material entities unless there is also a change of place, i.e., a motion involving some material entity. Tbis is a sweeping claim which would require for its defense some account of what constitutes a change (cf. Cambridge changes). But let that pass. I simply want to observe at this point that (M) is incompatible with a tensed theory of time. For according to that theory, the physical world undergoes objective changes in tense; indeed, this is the essence of temporal becoming. There are tensed facts, such as that I1 is presenlly I, that are constantly changing whether anything changes spatially or not. 1I3 Temporal change does not, plausibly, entail spatial change. 1I4 Insofar as he endorses (M), therefore, Leftow is implicitly endorsing a tenseless theory of time. Tbis conclusion is important because Leftow avers that bis theory is compatible with a tensed theory of time and becoming. Since there can be no spatial motion relative to God, (M) is said to imply that no spatial thing can change in any way in relation to God. Leftow then goes on to make the surprising assertion that "if there is any truth in contemporary physics," then even non-spatial entities such as changeable angels or disembodied souls do not exist. IIS He justifies this assertion by pointing out that time is one of the dimensions Leftow, "Eternity and Simultaneity," p. 163; idem, Time and Eternity, p. 226. Leftow, "Etemity and Simultaneity," p. 163; cf. idem, Time and Eternity, pp. 226-227. lJ3 See A. N. Prior, "Changes in Events and Changes in Things," in Papers on Time and Tense (Oxford: Clarendon Press, 1968), pp. 1-14. 114 See Sydney Shoemaker, "Time without Change," Journal ofPhilosophy 66 (1969): 363-381; cf. W.H. Newton-Smith, The Structure of Time, International Library of Philosophy (London: Routledge, Kegan & Paul, 1980), chaps. 4, 10. m Leftow, "Eternity and Simultaneity," p. 163; cf. idem, Time and Eternity, p. 227. 111

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in the four-dimensional space-time manifold and that whatever is located in one dimension is ipsa facta located in the others as weIl. Therefore, if it is correct to represent time as a dimension of the manifold, nothing can be in time unless it is also in space; only spatial things are temporal. Since only temporal things can change, it follows only spatial things can change. We have already encountered Leftow's claim that if God is temporal, He is also spatial,116 and the deficiencies pointed out with that claim attend the argument here as weIl. The most important of these is that Leftow's understanding of time as constricted to the time of physics seems to be positivistic and reductionist, leading him in turn to deny the existence of non-spatial, temporal beings and thus evincing a scientistic attitude which even some positivists would consider too narrow. I am reminded in this connection of Alvin Plantinga's advice to Christian philosophers that they have their own agenda to pursue and should display more boldness and autonomy over against the concems which secular philosophy deerns legitimate. ll7 It would be ironic if a Christian philosopher like Leftow were, out of some misplaced deference to the "truth of contemporary physics," led to adopt a positivistic view of time and to deny, as a consequence, important Christi an doctrines pertinent to angelology/demonology and to the intermediate state of the soul after death. Of course, Leftow's motivation for denying the existence of changeable angels/demons and disembodied souls is clear: if there are non-spatial, changing beings, then there will exist a metaphysical time and, hence, a "frame of reference" in which things are changing relative to God. But then it will be false that all things are timelessly present to God in eternity. Therefore Leftow is obliged to deny the existence of temporal, non-spatial beings. This he accomplishes by the positivistic constriction of time to physical time. There is not only a theological price to be paid for this reduction, however; since physical time seems to be a tenseless time only, Leftow's theory of the relationship of eternity to time may again be incompatible with the tensed theory, which fact he is anxious to deny. On the basis of the Zero Thesis, (M), and the constriction of time to physical time, Leftow concludes that there is no change relative to God. Unfortunately, none of the supporting theses for this inference is plausibly true. All of the errors described thus far seem to come horne to roost in the following conclusion: "So if a frame of reference is a system of objects at rest relative to one another, then it appears that God and all spatial objects share a frame of reference, one in which nothing changes.,,118 This conclusion is analogous to the statement that spatial objects and space-time (the relativistic ether) are at rest relative to one another and therefore exist in a common reference frame-as though God or space-time could be said to constitute a reference frame and so be at rest with respect to spatial objects or to exist in the same reference frame as spatial objects! See pp. 12-14. A1vin Plantinga, "Advice to Christi an Philosophers," Faith and Philosophy 1 (1984): 253-271. Plantinga specifically blasts verificationism as a philosophical fashion which Christian thinkers ought to have rejected tout court. 118 Leftow, "Etemity and Simultaneity," p. 164; idem, Time and Eternity, p. 227. 116 117

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Since an event occurring in one reference frame occurs in all (albeit simultaneous with different groups of events), explains Leftow, all events which occur in other reference frames also occur in the frame at rest relative to God. All temporal events are therefore timelessly present to God. So in answer to the question of how a timeless entity can act on events in time, Leftow asserts that "an etemal entity acts on those temporal entities which are present with it in eternity, and these actions have consequences for temporal entities as they exist in time.,,119 The objection under consideration fails because ''the coming to be actual in time of the events which occur at t in no way entails a change in God or in his presence to creatures. For this coming to be actual exists as well in eternity; it is just that to which God is etemally present.,,120 By invoking Relativity Theory at this point in his argument, Leftow is able to stave off the Eleatic conclusion that because God is changeless and there is no change relative to God, therefore motion and change are mere illusions masking a static reality. By holding that change is real in physical reference frames and making all change relative change, Leftow is able to hold that while change is real relative to some frames it is non-existent relative to God's "frame." But the difficulty with this account of how all temporal events can be timelessly existent relative to God's "frame of reference" is that there just does not seem to be any such "frame of reference" in which all events are simultaneous. Certainly there is no such physical reference frame, and the addition to these of God's "frame of reference" does not seem to change the picture, since the timelessness of events in the eternal frame depends upon the defective Zero Thesis, (M), and the reduction of time to physical time. Unless some more secure foundation can be found for the existence of such a frame, it will remain problematic how all temporal events can exist timelessly relative to God. Timeless Existence

0/All Things in Eternity

On the basis of his argument for the existence of temporal things in eternity Leftow claims that ''relative to God, the whole span of temporal events is always actually there, all at once. Thus in God's frame of reference, the correct judgment oflocal simultaneity is that all events are simultaneous.,,121 This is a dark saying. If we are to make sense of it, we must construe "always" to mean something like ''tenselessly,'' since God's frame of reference is timeless, not sempitemal. For the same reason, Leftow cannot mean by "simultaneous" "occurring at the same time," but something like "co-existent" or "coincident." The statement that God judges all events to be locally simultaneous is very obscure. Leftow cannot mean that all events exist in God's timeless frame of reference, but are tenselessly ordered by a "later than" relation such that no event occurs (tenselessly) later than any other, for that would be to affirm that there is only one time and all events occur at that

119 120 121

Leftow, "Aquinas on Time and Eternity," p. 399. Ibid., p. 395. Leftow, "Etemity and Simultaneity," p. 164; idem, Time and Eternity, p. 228.

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moment of time. If we take literally Leftow's appeal to SR's doctrine of the relativity of simultaneity to reference frames, then we must say that just as a given set of causally unconnectable events will be calculated to sustain among themselves different relations of earlier than. simultaneous with, and later than in various reference frames, so in God's "frame of reference" no events are judged to be earlier or later than any other or even as occurring simultaneously. Rather in God's "frame" all events are judged to be timelessly coincident. In other words, in God's "frame of reference" the very topology of time is voided. It would be as though one took the series of real numbers and removed from it any ordering relation such as "greater than." The one-dimensional temporal continuum has been divested in God's "frame of reference" of those topological properties which make it isomorphous to a geometricalline, so that all that is left is an amorphous collection of points. Notice that in God's "frame" even causally connected events, such as one's birth, development, decline, and death, are judged to sustain no temporal relations among themselves; they are all just timelessly coincident. It might be objected that if God judges one's birth to be coincident with one's death rather than earlier than it, then He is surely deceived. But if we take relativity seriously, as Leftow wishes to do, that is not the case. There is no privileged frame. Hence, no observer can impugn the temporal ordering of events determined by any other observer in another reference frame. Of course, in all physical frames the temporal order of causally connectable events is invariant. But in the special case of God, if Leftow's argument for the existence of all things in eternity is correct, this invariance does not hold with respect to His "frame of reference." In fact, if anyone's frame is privileged, it will surely be God's, for the relativity of simultaneity arises only for events spatially distant from the observer; judgements of local simultaneity are neither conventional nor relative. But given Leftow's Zero Thesis, all events are in a sense local for God. Therefore, His judgement that all events are timelessly coincident should be absolute, and it is we who are deceived when we judge that they are temporally ordered. In fact, it is not dear to me that Leftow can avert also voiding space as well as time of any topological properties in God's "frame of reference." For in Relativity Theory, a difference in the value of the temporal coordinate of some event relative to two distinct reference frames requires a mathematically determinate difference in the spatial coordinates of the event as weIl. Doubtless, Leftow would not say that the Lorentz transformation equations hold relative to God's "frame of reference" as for physical frames. Nonetheless, since an event's spatial coordinates are partially dependent upon its temporal coordinates, events in God's "frame of reference," lacking any temporal coordinates, cannot be located in space either. To paraphrase Leftow: something is located in one dimension of a geometry if and only if it is located in all; so if it is correct to represent time as another dimension, it follows that whatever is not in time is not in space either: only temporal things are spatial. It therefore seems to follow that in God's "frame of reference" events not only occur timelessly but spacelessly as weIl. The topological structure of the four-dimensional space-time manifold has come completely unglued in the divine "frame of reference" so that all God is confronted with is a chaotic collection of points which are ordered neither spatially nor temporally.

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Leftow, however, clearly does not interpret the "local simultaneity" of all events in God's "frame ofreference" in the above way. He states, "In eternity events are in effect frozen in an array of positions corresponding to their ordering in various Bseries.,,122 In defending his theory against the charge that temporal beings' existing in etemity makes them etemal beings, Leftow lists the following characteristics of a temporal being in the ''reference frame" of eternity, which serve to distinguish it from an etemal being: a. b. c. d. e.

its fourth-dimensional extension or duration would have parts. not a11 parts of its duration would occur at the same temporal present its duration's parts would be ordered as earlier and later. in most cases, its duration would have a beginning and an end if it had no duration, still it would stand in a sequence representing the earlier-later relations obtaining between it and other events. 123

These characteristics make it evident that Leftow conceives of the existence of a temporal being in etemity as the tenseless existence of its four-dimensional world line. In Leftow's view the entire B-series of events occurs (tenselessly) in God's etemal now. In a footnote he explains that God does not see all events spread out in one B-series, since each reference frame generates its own unique B-series. There are thus a plurality of B-series and God must be aware of all of them. 124 Now this seems an eminently more reasonable account of the existence of temporal events in God's "frame of reference," but I do not see how this account concords with Leftow's proposed theory of timeless etemity. It needs to be understood that that account does not merely eliminate the tensed determinations of events (monadic predicates like past, present, and future) relative to the divine "frame of reference," for SR itself takes no cognizance of such predicates in handling temporal relations among events in physical reference frames. Rather Leftow's account must also eliminate the tenseless determinations of events as weil (dyadic predicates like earlier than, simultaneous with, and later than) relative to God's "frame of reference." For the relativity of simultaneity, which Leftow employs in order to stave off the Parmenidean conclusion that change is illusory and reality is a static whole, entails that events are classed relative to a reference frame as being either earlier than, simultaneous with, or later than any arbitrarily chosen point on the inertial trajectory of a hypothetical observer and that observers in 122 Leftow, "Etemity and Simultaneity," p. 170. Cf his defmition: " ... R is an etemal reference-frame iff within R, the relations earlier, and later, can hold only between locations in the atemporal analogues of a B-series ... " (Ibid., pp. 171-172). Cf idem, Time and Eternity, pp. 239-240. An A-series is, in McTaggart's terminology, the temporal series of events as ordered by post, present, andfoture. The Bseries, according to McTaggart, is the temporal series of events as ordered by earlier than, simultaneous with, and tater than. The former series is therefore a tensed time (an A-Theory oftime) and the latter a tenseless time (a B-Theory ofTime). For discussion see my Tensed Theory ofTime, chap. 6. l2l Leftow, Time and Eternity, p. 237. 124 Leftow, "Etemity and Simultaneity," p. 179; cf idem, Time and Eternity, p. 239; idem, "Aquinas on Time and Etemity," p. 393. Leftow also tries to defend his view by construing temporality as a modal notion: a being is temporal if it can be located in aseries of earlier and later events. Here I must side with Stump and Kretzmann against Leftow. As we have seen, God could exist timelessly alone and yet be capable of entering into temporal relations if He wished to do so. That mere capability does not remove His atemporality.

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different frames will draw at any arbitrary point on their world-lines different lines of simultaneity connecting events detennined to be simultaneous with that point and dividing later from earlier events. Hence, relative to God's timeless "frame of reference," God must judge of any two events that one is neither earlier than the other, nor later, nor even strictly simultaneous; they are just timelessly coexistent relative to His frame. Therefore, Leftow's theory must void even tenseless relations relative to the divine "frame of reference." Of course, an omniscient God must also know the lines of simultaneity which would be drawn by hypothetical observers relative to any physical reference frame; but in His "frame" events are chaotically co-existent. If the proponent of divine timelessness wants to preserve the tenseless relations among events, then it seems to me that his most plausible move will be to identify God's "frame of reference" with the four-dimensional space-time manifold itself, which God transcends, and hold that that manifold exists tenselessly. In short: the tenseless theory of time is correct. Leftow, however, denies that his theory of divine eternity entails the tenseless theory. He claims that "a defender of God's eternity can assert that (in a strictly limited sense) one and the same event is present and actual in eternity though it is not yet or no longer present or actual in time."12S He explicates this by saying, "That is, it can be true at a time t that an event dated at t+l has not yet occurred in time, and yet also correct at t to say that that very event exists in eternity. That all events occur at once in eternity does not entail that they all occur at once in time.,,126 Unfortunately, it is not apparent to me that this explication is anything but a statement ofthe tenseless theory. A theorist oftenseless time would be adamant that at t an event at t+l has not yet occurred in time (otherwise it would be earlier than t) and nonetheless this event exists tenselessly with as much actuality as the event at t; moreover, the tenseless theory does not assert the absurdity that all events occur at once in time, for then there would be only one moment of time! What Leftow needs to show is that his theory of the timeless existence of all things relative to God is compatible with the reality of tense, the objectivity of temporal becoming, the denial that all events exist tenselessly, and so forth. It is at this point that the Einsteinian interpretation of SR takes center stage in Leftow's defense. He argues, If simultaneity and presentness are relative to reference-frames, then if present events are actual in some way in which future events are not, this sort of actuaIity is itself relative to reference frames. Thus there is a (strictly limited) sense in which the relativity of simultaneity entails a relativity of actuaIity, if one restricts fuH actuaIity to present events. 127

Leftow, "Etemity and Simu1taneity," p. 165; cr. idem, Time and Etemity, p. 232. Ibid. 127 Ibid. Unfortunately, the way Leftow supports this conclusion is by means of a defective illustration from SR of the relativity of simultaneity. (Idem, Time and Etemity, pp. 232-233). All Leftow's illustration shows is that his event C is simultaneous with H in R, but simultaneous with G in R*, not that C is actual in R before C is actuaI in R *. One could with equal justification say that C becomes actuaI at the same time in R and R* and that G and H occur earlier in R* than in R! In fact none of these comparisons is licit without designating a third reference frame. 12S

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This represents one way of integrating objective temporal becoming with SR, though it strikes me as enormously implausible. 128 However that may be, Leftow explains the result ofrelativizing actuality to reference frames: If we take eternity as one more frame of reference, then, we can thus say that a temporal event's being present and actual in eternity does not entail that it is present and actual at any particular time in any temporal reference frame (though it does follow that this event is, was or will be actual in all temporal reference frames). 129

Again, one must protest that God's "frame of reference" is not literally a reference frame; there is no reference frame in which all events are present and actual, since there are in every frame space-time regions designated absolute future or absolute past as determined by the light-cone structure at any event. The only thing corresponding to God's "frame of reference" as described by Leftow, so far as I can see, is Einstein's relativistic ether, the space-time manifold itself. But since it is not a reference frame, the relativity of simultaneity relation does not obtain between it and Iocal frames. Thus, on Leftow's theory temporal becoming cannot be objective, for all events simply exist tenselessly in the four-dimensional manifoId. 130 When pressed, Leftow shows himselfprepared to fall back, ifnecessary, to a sort of Stump-Kretzmann model which does not appeal to the Zero Thesis but reHes exclusively on the reiativity of simultaneity in order to justify the claim that actuaHty is reference frame dependent and therefore events which are not actual with respect to various temporal reference frames may all be actual with respect to God's "frame.,,131 The problem with the naked appeal to analogy, however, is that

128 See Lawrence Sklar, "Time, Reality and Relativity," in Reduction, Time and Reality, ed. R. Healey (Cambridge: Cambridge University Press, 1981), p. 138; see also my discussion in rny Time and the Metaphysics 0/ Relativity, chap. 5. 129 Leftow, "Eternity and Simultaneity," p. 167; idem, Time and Eternity, p. 234. 110 Suspicions that Leftow's theory really presupposes a tenseless theory of time are accentuated by his remarks on God's knowledge ofwhat is happening now: "That in God' s frame of reference all events occur simultaneously does not entail that God does not know all the facts about simultaneity which obtain in temporal reference frames. God's being located in just the eternal frame of reference does not put a limit on what he knows. From any reference frame one can extrapolate what judgments of simultaneity would be correct in other reference frames. Presumably, then, an eternal God can have this knowledge in His own way. So ... for every temporal now, God knows what is happening now (i.e., simultaneous with that now) ... " (Leftow, "Eternity and Simultaneity." p. 168; cf. idem, Time and Eternity, p. 235.) Notice the conflation ofthe indexical tensed determination "now" and the non-indexical tenseless relation "simultaneous with." God could know the appropriate simultaneity c1asses relative to every reference frame and still not have any idea which c1ass of events is occurring now with respect to any frame. This can be c1early seen by reflecting on the fact that appropriate lines of simultaneity can be drawn on a Minkowski diagram through any point on the inertial trajectory of a hypothetical observer connected to that frame. Leftow's theory of divine eternity will not result in an attenuation of divine omniscience only if he holds, with the tenseless time theorist, that there are no objective tensed facts and therefore divine knowledge of simultaneity relations is sufficient to grasp a11 that there is to be known with respect to the facts about what is happening now. III Brian Leftow, "Time, Actuality and Omniscience," Religious Studies 26 (1990): 303-321. "The claim that actuality is a function of a relation may seem bizarre, but if time is tensed and the special theory of relativity is true, this claim folIows .... one can hold ... that events really occur sequentially in

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one then lacks any justification for denying the symmetry demanded by the relativity of simultaneity, namely, that relative to temporal beings God exists in time, just as temporal beings, relative to God, exist in eternity. Moreover, one lacks any grounds for eonstruing eternity and temporality on the analogy of reference frames, since, pace Leftow, such terminology is only metaphorical with reference to God. Finally, a deeper issue, unaddressed by either Stump and Kretzlnann or Leftow, is whether there is any reason to think that the relativity of simultaneity obtains at all. Leftow's appeal to SR to ground this relation, it seems to me, evinces a certain naivete concerning the philosophieal foundations of the received physical interpretation of Relativity Theory and an uncritieal acceptance of that interpretation, whieh is then (mis)applied to metaphysics. There are, after all, other physieal interpretations of the Lorentz transformation equations that constitute the mathematieal core of SR which are empirically equivalent to the received interpretation and which, if correet, would lead to completely different conc1usions when applied metaphysically. On the Einsteinian view, there exists no preferred spatio-temporal order; rather space and time are relative to inertial frames, and no frame is privileged. According to the neoLorentzian view, absolute spaee and time exist, not necessarily in the substantival, as opposed to relational, sense of "absolute," but rather in the sense that there exists a spatio-temporal order which is privileged. We thus have two different interpretations of Relativity Theory which are radically different in their metaphysical foundations and yet which are, to date, experimentally An indistinguishable and therefore insuseeptible to scientific adjudication. examination of the philosophical foundations of Relativity Theory is therefore indispensable if we are to decide between these competing interpretations. If a neoLorentzian interpretation is philosophically preferable, then the rug is pulled from beneath the feet of theories of divine eternity appealing to SR in order to justify notions like ET-simultaneity or the presenee of all things to God in timeless eternity. It therefore seems to me that it is of the utmost moment that proponents of divine timeless eternity address themselves more c10sely to the scrutiny and justification of the interpretation of Relativity Theory whieh they prefer and on which their theories are predicated. \32 In conc1usion, it seems to me that Leftow has failed to save the doetrine of divine timelessness by means of his proposal that temporal entities exist not only in time, but also in eternity. His argument for this asymmetrleal relation between time and eternity commits a fatal eategory mistake, presupposes a reductionist view of time, and is incompatible with a tensed theory of time. His attempt to demonstrate the compatibility of objective tense and temporal becoming with the existence of all things in eternity rests on these same errors, never in fact advances beyond a tenseless theory of time, and depends upon an uneritical acceptance of the

time and also all at once for God, without it thereby being the case that they really do all occur at once" (Ibid., pp. 318, 320). \32 For a discussion of Relativity Theory and its interpretation, see my Time and the Metaphysics of Relativity.

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Einsteinian interpretation of SR. Leftow's theory therefore fails to show why God's real, causal relation to the temporal world would not involve Hirn in time itself.

A WAY OUT FOR ADVOCATES OF DIVINE TIMELESSNESS? The foregoing discussion does suggest a possible way of escape for defenders of divine timelessness: deny the objectivity of tense and temporal becoming and therefore also the (necessary) truth of 4. If God is really related to the temporal world, God is temporal. The argument I have given on behalf of (4) presupposes a tensed theory of time and, hence, the reality of temporal becoming and tensed facts. But if one embraces a tenseless theory of time, according to which there are no tensed facts and temporal becoming is merely a subjective feature of consciousness, then the argument is undercut. For in that case all events comprising the four-dimensional space-time manifold simply exist tenselessly, and God can be conceived to exist "outside" this manifold, spacelessly and timelessly. \33 Both God and what Einstein characterized as the relativistic ether l34 would be extrinsically timeless, in Leftow's terminology, while the four-dimensional ether is of the two alone intrinsically temporal. But this intrinsic temporality would not involve temporal becoming or tensed facts; all events are on an ontological par and no events are ever objectively present. The temporality of events consists solely in their standing in mutual relations of earlier than, simultaneous with, and later than, relations which are construed as being as tenseless as the relations less than, equal to, and greater than. Thus, there is no objective matter of fact concerning any two events B and C that, for example, God was once sustaining B or that God is presently sustaining C. Advocates of a tenseless theory of language will argue that such tensed locutions are either reducible in meaning to tenseless expressions or have tenseless truth conditions, thus rendering the postulation of corresponding tensed facts otiose. Moreover, since B and C never really come into being or pass away, no change is required on God's part to produce B at t4 and C at 15' In the absence of temporal becoming, B and C, as weil as their respective moments, never change in their ontological status but simply exist tenselessly (though standing in the relations earlierllater than). Therefore, they are changelessly real in relation to God, who also exists tenselessly. By the same act of power, God can produce tenselessly B at

\33 As Denbigh puts it, "The B-series is as if the Deity could timelessly witness a11 events, laid out in order a10ng the time coordinate, as we can witness objects laid out in space" (K. G. Denbigh, An Inventive Universe [London: Hutchinson, 1975], pp. 30-31). Cf. Keith Seddon, Time: a Philosophical Treatment (London: Croon Helm, 1987), p. 135. 134 Einstein asserts, "It appears therefore more natural to think of physical reality as a four-dimensional existence, instead of, as hitherto, the evolution of a three-dimensional existence. This rigid four-dimensional space of the special theory of relativity is to some extent a fourdimensional analogue of H. A. Lorentz's rigid three-dimensional aether" (A. Einstein, Relativity: The Special and General Theory (New York: Crown, 1961], pp. 150-151).

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t4 and C at t5• 135 His single creative exercise ofpower is as timeless and unchanging as His intention to create, and the temporal products of His creative power exist as extrinsically timelessly as does He. The adoption of a tenseless theory of time thus gives a coherent sense to the notion that temporal events exist in eternity, and many of the statements of classical advocates of divine atemporality seem to presuppose just such a tenseless theory oftime. 136 Finally, since God and the creation would coexist tenselessly, then-absent any embedding hyper-timt>-there is no state of affairs in the actual world which consists of God's existing alone sans the universe, nor does the universe come into being. It begins to exist only in the sense that a meter stick has a beginning: there is a front edge to the space-time manifold, that is to say, it is finite in the earlier than direction. But God never brought the fourdimensional world into being; it just co-exists tenselessly with Hirn in an asymmetrical relation of ontological dependence. Had He freely determined otherwise, God could have existed alone sans creation; but He has freely chosen to produce a temporal world instead. Whether He chooses to exist alone or to produce tenselessly a co-existing temporal creation, God exists timelessly. Given a tenseless theory of time, God either exists tenselessly without creation or co-exists tenselessly with creation, depending upon the free decree of His will, but no world includes both states of affairs. Thus, God, in creating the world, enters into no new relations whatsoever. He tenselessly stands in the relation of creating the Big Bang at to. The date to indicates, not the time of His acting, but the time of the effect. God does not come into the relation Creator ofwith the Big Bang singularity at to and then cease to stand in this relation to it at t\; rather He timelessly stands in the Creator· 0/ relation to all events at their respective times. By a single, timeless act God tenselessly produces events at to, t(, t2,. ... Thus, on the tenseless theory oftime, one can successfully divorce God's action from its effects in such a way that the action is tirneless and the effects temporal. By denying the reality of temporal becoming and tensed facts, the advocate of divine tirnelessness undercuts the arguments for the necessary truth of(4), therebyallowing one to maintain God's atemporality and His creative activity in the temporal world without denying God's real relation to that world. One of the interesting features of Padgett's book is that he recognizes the viability of the doctrine of divine timelessness, despite his arguments for God's temporality, if one adopts a tenseless theory, or in his words, stasis theory, of time. He writes,

13S Objections to timeless causation are not impressive. For example, Le Poidevin's conclusion that causality entails time over-reaches his argument, which, even if sound, would only show that atemporal cause is chronologically prior to its effect (Robin Le Poidevin, Change, Cause and Contradiction: A Defense of the Tenseless Theory of Time, Macmillan Studies in Contemporary Philosophy (London: Macmillan, 1991], pp. 88-94). 136 See William Lane Craig, "Was Thomas Aquinas a B-Theorist of Time?" New Scholasticism 59 (1985): 475-483; idem, "St. Anselm on Divine Foreknowledge and Future Contingency," Laval theologique et philosophique 42 (1986): 93-104. See also Padgett, God, Etemity and the Nature ofTime, pp.56-81.

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CHAPTER3 ... on the stasis theory of time, no particular episode or event is timeless, because they will have dates. But the totality of the world, considered from a four-dimensional perspective, is both timeless and changeless... God could tbus sustain the fourdimensional space-time universe .... For the fundamental ontological status ofthings is etemally the same. Changes in the sense of things having incompatible properties at different dates will still occur. But things and events will not change in tbeir fundamental ontological status. Things and events will exist at the time they exist, no matter when "now" is according to humans. It is this fundamental ontological change that is at issue when we consider the act of God sustaining the world. And it is this sort of fundamental ontological change that the stasis theory denies. Such a conception of how a timeless God can sustain the world including dates depends upon the stasis theory oftime .... . . . Any model of absolute divine timelessness that wisbes to retain the important notion of God sustaining the world should also affirm the stasis theory of time. 137

Most advocates of divine timelessness, however, have been unwilling to pin their hopes on the tenseless theory of time. \38 Ihe notable exception is Paul Helm, who, more than any other contemporary pbilosopher or theologian, has understood the dependency of the doctrine of divine timelessness on the tenseless theory and has advocated the same. 139 He explicitly advocates construing the distinction between past, present, and future as analogous to "the spatial distinctions between here and there, and before and behind.,,140 Without an objective present, there is no real temporal becoming, and hence, in bis view, no need for any kind of EI-simultaneity such as is advocated by Stump and Kretzmann. "Do the times wbich are at present future to us exist, or not?" Helm asks; "Answer: they exist for God ... and they exist for those creatures contemporaneous with that future moment, for that moment is present for them, but it is not now present to US.,,141 In the same way, ''the past event ... belongs in its own time, and is therefore real, belonging to the ordered seris Padgett, God, Eternity and the Nature ofTime, pp.61-76. See, for example, Zagzebski, Freedom and Foreknowledge, pp. 175-178, who vainly struggles to preserve the A-series while inconsistently affirming four-dimensionalism, the perspectival nature of tensed facts, and God's perceiving things as present in the fourth dimension (while not transcending space-time)! See also L. Nathan Oaklander, "Time and Foreknowledge: A Critique of Zagzebski," Religious Studies 31 (\995): 101-103. 139 Helm was preceded by A. C. Ewing, who held that for God time exists as a B-series apprehended in one specious present. Ewing appealed to the argument from "Time's Tooth" to justify his view: "It seems plain that a perfect being would not experience the world-process as an A series in the way we do. For he would then be incomplete in a way whicb is quite incompatible witb perfection. He would never be more than aminute fraction of his total being, and each such minute fraction would be lost for ever as it was succeeded by thenext." By knowing the B-series, God is capable of responding to prayer at appropriate times and feeling sympathy when misfortune befalls us (A. C. Ewing, Value and Reality, Muirhead Library ofPhilosophy [London: George Allen & Unwin, 1973], pp. 281-283). Other atemporalists advocating a tenseless theory oftime as a basis for understanding divine timelessness include Encyclopaedia ofReligion and Ethics, ed. James Hastings, s.v. "Etemity," by J. S. MacKenzie, p. 404 and 1. L. Tomkinson, "Divine Sempitemity and Atemporality," Religious Studies 18 (\982): 187; Seddon, Time, p. 135. See also the discussion by Yates, Timelessness ofGod, pp. 67-95, who rejects the tenseless theory, but recognizes how considerably easier it makes the reconciliation of etemity and time. 140 Helm, Eternal God, p. 47. 141 Paul Helm, "Etemal Creation: The Doctrine of the Two Standpoints," in The Doctrine ofCreation, ed. Colin Gunton (Edinburgh: T. & T. Clark, 1997), p. 42. 137 138

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of times which comprise the creation and which are ... eternally present to God.,,142 Thus, "in creation God brings into being (timelessly) the whole temporal matrix," and "God knows al a glance the whole of his temporally ordered creation .... ,,143 Helm is thus the one prominent advocate of divine timelessness who has advocated a coherent doctrine of God's atemporality, predicated upon the tenseless theory of time. The bottom line to our discussion of the objection to divine timelessness based on God's action in the world is therefore that this objection is cogent just in case a tensed theory of time is correct. If this conclusion is right, then significant advance of the discussion can only take place by tackling the difficult and multi-faceted problem ofthe tensed versus tenseless theory oftime.

Ibid., p. 43. Helm, Eternal God, pp. 27,26. Cf. Paul Helm, "Gale on God," Religious Studies 29 (\993): 247. So also McCann, "God beyond Time," p. 239, who holds that God "in a single, unchanging, timeless act" creates "the entire universe ... through all of its history. " 142

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n the last chapter we saw that the objective reality of tense and temporal becoming would present an insuperable obstacle to a timeless deity's being active in the world. But even if God were not really related to the temporal world, the reality of tense and becoming would still seem to be problematic for the doctrine of divine atemporality. For if a tensed theory of time is correct, there exist tensed facts, of which God, as an omniscient being, cannot be ignorant. But since tensed facts can only be known by a temporal being, God must therefore be temporal. Moreover, since tensed facts are in constant flux, so must be God's beliefs or cognitive state, which entails that God is temporal. THE OBJECTION TO TIMELESS OMNISCIENCE

IronicaIly, it was Norman Kretzmann who first brought this problem to the attention of analytic philosophers some 15 years before the publication of his coauthored defense of divine timeless eternity.l Kretzmann's attack was not directed at divine timelessness, but immutability, which he considered essential to perfect being. Observing that a perfect being knows everything, Kretzmann contended that God always knows what time it is and is therefore subject to change. The state of His knowledge changes incessantly with respect to propositions of the form It is now In. Kretzmann consciously presupposed that tense was part of the propositional content expressed by tensed sentences. He overtly rejected a tenseless theory of language and particularly of temporal indexicals. In response to the objection that an omniscient being can know the state of the universe at every instant aB at once rather than successively, Kretzmann agreed that an omniscient being knows when Kretzmann was writing his article and how much time separated his birth from his writing and his writing from his death, but, he insisted, "I am writing these words just now, and on this view of omniscience an omniscient being is incapable of knowing that that is what I am now doing, and for all this omniscient being knows I might just as weIl be dead or as yet unbom.,,2 In other words, while God could know the tenseless dates of events and the temporal distances between them, He could not know the tense-determinations of events or moments. His knowledge, said Kretzmann, would be like a person's knowledge of a movie which he knows from beginning to end. He would be so familiar with the movie that he would know what happens in every frame of the film, but he still would not know what is now Nonnan Kretzmann, "Omniscience and Imrnutability," Journal ofPhilosophy 63 (1966): 409-421. Ibid., p. 414.

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being projected on the screen in the distant theater downtown. An omniscient being must know not only the entire scheme of contingent events from beginning to end at once, but also at what stage 0/ realization that scheme now is. Kretzmann explicitly rejected the notion that God transcends space and time in the sense that from God's point of view the passage of time is a universal human illusion. The subjectivity of temporal passage would imply that either no moment or only one moment is ever now and that a being could always know what time it is and yet not be subject to change, which imposes immutability on everything else-conclusions which Kretzmann found incredible. Kretzmann's argument thus rested on an explicit rejection of the tenseless theory of time and on the presupposition of tensed facts and temporal becoming. In their later "Eternity," Stump and Kretzmann attempt to undo the damage caused by Kretzmann's argument. Their fIrst attempt to undercut the argument consists in adopting the de-tenser's analysis of the temporal indexical "now." They construe the claim that God always knows what time it is now to mean that for any time experienced as present by a temporal entity, God knows all the events actually occurring at that time (as weH as the dating of that time and its being experienced as present by a temporal entity).3 This is clearly a tenseless understanding of presentness as purely subjective, the only objective fact known by God being the simultaneity class of events at the time picked out as the time of the sentient subject's experience. Indeed, this proffered solution is not dissimilar to Hector-Neri Castafieda's tenseless account of indexical reference, which he utilized in response to Kretzmann's original argument. 4 According to Castafieda, the claim that God knows at each time ta proposition ofthe form It is now tn may be analyzed as saying that at t l God knows both that it is then t b but not 12 , and that somebody would know at t 2 that it would then be 12 , but not t l • Castafieda assumed that God existed at t l with changeless knowledge of what someone at every value of t n would characterize as occurring "now". This is a tenseless analysis of the indexical "now," since such knowledge would not allow God to know when any t n actually became present. 5 He merely knows that for someone at t2, say, t2 would be described by that person as "now." Stump and Kretzmann modify this account merely by placing God outside

Eleonore Stump and Norman Kretzmann, "Eternity," Journal o/Philosophy 78 (1981): 456-457. Hector-Neri Castafieda, "Omniscience and Indexical Reference," Journal 0/ Philosophy 64 (1967): 203-210. 5 See the critique of Quentin Smith, Language and Time (New York: Oxford University Press, 1993), pp. 58-60. Castafieda's argument also depends upon the principle that if a sentence ofthe form "X knows that a person Y knows that. .. " formulates atme statement, then the person X knows the statement formulated by the clause filling the " ... ", a principle which he later recognized with some embarrassment to be false (Robert Adams and Hector-Neri Castafieda, "Knowledge and Self: A Correspondence between Robert Adams and Hector-Neri Castafieda," in Agent, Language, and the Structure 0/ the World, ed. James E. Tomberlin [Indianapolis: Hackett Publishing, 1983], pp. 293-308). Stump and Kretzmann do not endorse this principle, which makes it even more obvious that on their account God does not know what time it is in knowing what events are simultaneous with a temporal entity's experience of presentness.

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of time with the same knowledge of what any temporal entity would describe as "now.,,6 Stump and KretZIDann recognize that this solution will not satisfy the partisans of tensed facts: they want to know ''whether God knows what is actually happening as it is happening.,,7 Yes, they claim, and here they fall back on ET-simultaneity: The whole of etemity is ET-simultaneous with each temporal event as it is actually happening; the only way in which an etemal entity can be aware of any temporal event is to be aware of it as it is actually happening. And from the etemal viewpoint every temporal event is actually happening.'

Unfortunately, we have already seen how opaque the notion of ET-simultaneity iso It merely states that every temporal present is real to and, hence, known by God in timeless eternity. How this is possible is not explained. Even if we posit some sort of metaphysical relativity such that God experiences in different frames of reference different events as temporally present, it is inexplicable why He WOuld not share that temporal "now" in each respective frame, since He knows of each time what He WOuld express by saying "tn is now." In the end, as we have seen, Stump and KretZIDann are reduced to simply defining ET-simultaneity to be (in part) a timeless being's ability to be directly aware of present temporal beings, which makes the whole enterprise viciously circular. Thus, the pseudo-explanatory idea of ETsimultaneity solves nothing, and we are left with the tenseless analysis of the present. The centrality of the question of the objectivity of tense with regard to God's knowledge of all facts was underlined by Nelson Pike in a particularly prescient discussion of the problem. Pike compares temporal indexicals to spatial indexicals, imagining a game in which Jones and Smith locate each other in different circles as "here" or ''there,'' while Brown, who is not in the game, keeps score. Brown could not say, with Smith, "Jones is here," but would say, "Jones and Smith are in the same circle." Smith and Brown would each justify his locution by appealing to the same facts. When it comes to temporal indexicals, Pike asks, is there a fact (for example, that the first scene in the movie is on the screen) which a timeless being could not know? As in the case of spatial indexical expressions, locutions involving temporal indexicals seem to be justified on the basis of facts which can be reported Interestingly, Castaileda reported to Gale in personal correspondence that his intention was to refute the timeless version of the onmiscience-immutability argument (Richard M. Gale, "OmniscienceImmutability Arguments," American Philosophical Quarterly 23 [1986]: 335). 7 Stump and Kretzmann, "Etemity," p. 457. See, e.g., Arthur N. Prior, "The Forrnalities of Onmiscience," in Papers on Time and Tense (Oxford: Clarendon, 1968), p. 29, who argues against restricting God's knowledge to timeless truths because on such an account God could not know, for example, that the 1960 fmal examinations are now over. All that could be known timelessly is that the finishing date of the 1960 fmal examinations is earlier than a certain date or event-and this is not what we know when we know that the exams are over: " ... what we know when we know that the 1960 final examinations are over can 't be just a relation between dates because this isn 't the thing we're pleased about when we're pleased that the examinations are over." See also Delmas Lewis, "Etemity Again: A Reply to Stump and Kretzmann," International Journalfor Philosophy ofReligion 15 (1984): 78-79, who charges that on a tensed theory of time God suffers from a sort of "actuality-blindness" if He is atemporal and that Stump and Kretzmann's analysis oftemporal presentness is deficient. • Stump and Kretzmann, "Etemity," p. 457.

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by non-indexical expressions. "If called upon to justify my original comment ['The first scene is now on the screen'], I would point to the fact that at 3:47 p.m. on the sixth of September-the moment at which I said: 'the first scene is now on the screen'-the first scene was on the screen.,,9 Unlike proponents of the Old Tenseless Theory of Language contemporaneous with Pike, Pike did not claim that the relevant tensed and tenseless sentence tokens have the same meaning. "Even if we grant that the utterances under consideration do not have the same meaning ... , we would not have enough to conclude that they are not reports of the same fact. ,,10 This is a remarkable anticipation of the New Tenseless Theory of language, which does not claim synonymy of tensed and tenseless sentence tokens, but asserts that they are either made true by or report the same tenseless facts. 11 Pike concludes that the opponent of divine timeless omniscience has yet to show two things: (1) that true statements in which temporal indexical expressions are used cannot be formulated in statements having equivalent meanings, but free of temporal indexical expressions, and (2) that if there are no such meaning-equivalent formulations of statements utilizing temporal expressions, the facts reported in these statements cannot be reported in statements free of indexical expressions. Pike's conclusion amounts to saying that the detractor of divine timelessness has yet to show that there are tensed facts, or that the tensed theory of time is true. The issue concems not just temporal indexical expressions, but the whole range of tensed expressions, including verbs. The position rejected in (1) above is that of the Old Tenseless Theory of language and the position rejected in (2) in an anticipation of the New Tenseless Theory, as I have elsewhere explained. 12 The question of whether a timeless being can be omniscient, then, hinges upon whether the tensed or the tenseless theory of time is correct. Only on a tenseless theory of time, it seems, can God's omniscience be sustained. The objection, then, is that 1. God is timeless. 2. God is omniscient. and 3. A temporal world exists. are broadly logically inconsistent, as is evident from the necessary truth of 4. If a temporal world exists, then if God is omniscient, God knows tensed facts. 5. If God is timeless, He does not know tensed facts. Nelson Pike, God and Timelessness, Studies in Ethics and the Philosophy of Religion (New York: Schocken Books, 1970), pp. 92-93. 10 Ibid., p. 93. 11 See D. H. Mellor, REal Time (Cambridge: Cambridge University Press, 1981), pp. 40-46; Michelle Beer, "Temporallndexicals and the Passage of Time," Philosophical Quarterly 38 (1988): 158-164. 12 See my The Tensed Theory of Time: a Critical Examination, Synthese Library (Dordrecht: K1uwer Academic Publishers, 2000).

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Since (2) is essential to theism and (3) is evidently true, (1) must be false. The tenseless time theorist escapes this argument by denying that there are any tensed facts, so that (4) is false. The tenseless time theorist holds that God knows all the facts there are about the temporal world in knowing tenseless facts. Thus, if one embraces a tenseless theory oftime, he eludes the objector's snare. Most defenders of divine timelessness, however, are eager to free their doctrine from dependency on the tenseless theory. The question, then, is how one may affirm the reality of tensed facts and yet maintain either that God knows them or that His ignorance of them does not impugn His omniscience. TIMELESS KNOWLEDGE OF TENSED FACTS Some atemporalists have attempted to argue that God does know tensed facts, thus denying the truth of (5). For example, Hugh McCann affirms that there are tensed propositions, such as that expressed by "John is mowing bis lawn," and that these are known by God, though He is timeless. God need not be in time to know tensed propositions because, according to McCann, ''tensed propositions do not change in truth value.,,13 He attempts to support this remarkable thesis by arguing that the propositional content of tensed sentences contains reference to the time of their assertion. For example, the tensed proposition expressed by "John is mowing bis lawn" might be more accurately expressed by "John iS(thi. moment) mowing bis lawn." Thus, two non-simultaneous tokens of "John is mowing bis lawn" in fact express two different propositions. McCann is not claiming that tensed sentences tacitly refer to the times at which the described events occur. For then "Yesterday John was mowing bis lawn," asserted today, would express the same proposition as "John is mowing bis lawn today," asserted yesterday, and the proposition's tense would have been lost. Rather the propositional content of "John was mowing bis lawn" is more accurately expressed as "John was(thi. moment) mowing bis lawn." The subscript ''this moment" refers, not to the moment at which John was mowing, but to the temporal vantage point of the speaker. According to McCann, "Each time I use a tensed sentence to make an assertion then, I am asserting a different proposition, even if the sentences are indistinguishable.,,14 Thus, each successive token of "John was mowing bis lawn" expresses a different proposition because the time of assertion changes. On McCann's view, then, the propositional content expressed by "John was mowing bis lawn" is that Relative to tn John was mowing his lawn. He says, Each proposition is tied to the perspective of a particular temporal moment, and different conditions determine its truth .... tensed propositions depend for their truth only on what obtains from the perspective in time to which they are indexed. It follows that they cannot change in truth value .... the truth or falsity of propositions, even tensed

lJ Hugh J. McCann, "The God beyond Time," in Philosophy 01 Religion, ed. Louis Pojman (Indianapolis: Hackett Publishing Company, 1993), p. 242. 14 lbid.

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Now McCann is certainly correct that propositions of the same form as Relative tn John was mowing his lawn are timelessly true; but it is equally evident that these are not tensed propositions. They inform us of mere tenseless relations. Dur sampie teUs us merely that John's mowing is earlier than In. A God who knew only such propositions wou1d not know whether John has yet to mow his lawn or not. Thus, He wou1d not knowany tensed facts. McCann attempts to meet the objection that in order for God to know tensed facts via such propositions, He wou1d also have to know what time it is: "The answer is that there is no such fact to be known, for there is never anything to 'what time it is' beyond the events whose simu1taneous occurrence constitutes any given stage of the world's history.,,16 McCann thereby reveals himself to be a cryptotenseless time theorist who denies that there is anything more to presentness than mere simu1taneity. Even on a relational theory oftime, the reality oftense demands that some stage ofthe world's history be uniquely present. In denying this, McCann rejects the reality oftensed facts and hence God's knowledge ofsuch facts. McCann's coUeague Jonathan Kvanvig holds both to the objective reality of tensed facts and to God's timeless knowledge of aU facts, which together imply that God has timeless knowledge of tensed facts. Kvanvig's defense of this position reHes upon his analysis of propositions expressed by sentences containing personal indexicals. 17 In Heu ofpositing privately accessible propositions, he analyzes belief in terms of a triadic relation between an intentional attitude, a proposition, and a particu1ar manner of accessing, or grasping, the proposition. Personal indexicals express individual essences, which are part of the propositional content of the sentence containing such indexical words. But this propositional content is differently accessed by different persons. When Kvanvig says, "I'm Kvanvig," he expresses the same proposition as I do when I say to him, "You're Kvanvig," but this propositional content is directly grasped by Kvanvig and indirectly grasped by me. Kvanvig suggests that the proposition is grasped through the meanings of the sentences involved; since these are different, the propositional content is differently accessed by Kvanvig and me. Thus, an omniscient God has the same knowledge of the facts as we do with respect to the propositions we express through sentences containing personal indexicals, but we directly access those propositions involving our respective individual essences, while God accesses this same propositional content indirectly. Kvanvig proposes an analogous solution for dealing with tensed facts expressed by sentences like "It is now 1 June 1984." He asserts that the demonstrative ''now'' expresses the individual essence of the time to which it refers. He maintains that ''temporal demonstratives are just particu1ar ways of referring to the essences of (0

Ibid., pp. 242-243. Ibid., p. 243. 17 Jonathan L. Kvanvig, The Possibility 66-70. IS

16

0/ an All-Knowing God (New York: St.

Martin's, 1986), pp.

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moments.,,18 Such an interpretation of temporal indexicals permits us to hold that God grasps the same propositional content that we do when we use sentences like "It is now 1 June 1984." Kvanvig writes, ... because a certain proposition is expressed at present with a use of demonstratives such as 'now', it does not follow that the essence of the moment picked out by the use of that demonstrative is inaccessible to a timeless being. All that the use of demonstratives shows is how we, as temporal beings, access the essence in question .... God, from the standpoint of etemity, is acquainted with the essence of every moment of time; and thus, even though we are subject to temporal becoming, ... there might seem to be no good reason to think that this particular way of accessing the essences in question is necessary. Hence, ... the apparent incompatibility between timelessness and omniscience disappears. 19

On Kvanvig's view the same proposition is expressed by the sentence "Today is 1 June 1984" uttered on that date as is expressed by the sentence "Yesterday was 1 June 1984" uttered on June 2. The difference in behavior resulting from these two beliefs is due to the meanings of the sentences through which the identical propositional content is accessed. A person grasps a proposition containing the essence of a time directly only if that person grasps the proposition at that time, which issues in a present-tense belief; otherwise the proposition is grasped indirectly, which in the case of temporal persons will yield beliefs involving other tenses. Hence, "one can affinn the doctrines of timelessness, immutability and omniscience by affinning that God indirectly grasps every temporal moment, and directly grasps none of them. ,,20 At face value, Kvanvig's analysis would not seem to be a defense of God's timeless knowledge of tensed facts, but the claim that tense in some way derives from the manner of accessing propositional content, which itself is tenseless. For the essences of the times picked out by temporal indexicals do not include their tensed properties (for example, presentness), or it becomes inexplicable how indexical expressions like ''today'' and ''yesterday'' could refer to the same individual essence and how God could timelessly grasp propositional content involving such essences. But Kvanvig denies that there is any temporal element expressed by tensed sentences which is not part of their propositional content. Referring to what he calls the "proposition" 1.

It is now 1 June 1984.

and lA. The essence of the moment picked out by the use of the demonstrative 'now' in (1) is mutually exemplified with the property of being 1 June 1984, Kvanvig asserts,

lB 19

zo

Ibid., p. 155. Ibid. Ibid., p. 159.

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... the apparent infection of propositions such as (1) by temporality is eliminated by noting that (l A) lacks this temporality and further contains all the same temporal elements as (I). If (lA) is not identical to (I), it is not because of some temporal dimension; it must be for some other reason. 21

It is odd that Kvanvig refers to bis (1) as a proposition, for on bis own view propositions lack indexicality. Rather (1) is a sentence, and the question is whether the proposition expressed by (1) is infected by temporality, that is to say, whether that proposition is such that it cannot be expressed ''without implying temporal indexicals.,,22 Kvanvig's claim is that the pröpositional content of (1) can be expressed by sentences not implying temporal indexicals. His reason for this claim is that (lA) is not so infected (either it expresses the same proposition as (1) without the use of temporal indexicals or else it represents the propositional content of (1) and can be expressed other than by (1) through a sentence not implying temporal indexicals) and, moreover, contains all the same temporal elements as (1). But (lA) is true only ifthe "is" in (lA) is tenseless. Otherwise (1A) is false, having been true only on 1 June 1984. If (lA) is tensed, the time of its truth is just the same as that of (1). Thus Kvanvig errs when he says that if (lA) is not identical to (1) it is not because of some temporal element-on the contrary, it is precisely because of the absence oftense from (lA) that it is not identical to (1). If all the temporal elements of (1) are contained in (1A) and God's knowledge is of propositions expressible by sentences like (lA), then God knows no tensed facts nor, indeed, is tense any objective temporal element at all, either of the propositional content of (1) or of the way of accessing that propositional content. Tense is merely a feature of language and nothing more. Kvanvig's analysis thus miscarries: it implies that the propositional content of tensed sentences is tenseless and that such sentences imply no temporal element not described by their propositional content, which in turn implies the non-objectivity oftense?3 A somewhat similar, but crucially adjusted, account of divine omniscience is offered by Edward Wierenga, who considers tense to belong to the propositional content expressed by tensed sentences, so that God must, in virtue of His omniscience, know tensed facts. 24 In order to explain why such knowledge does not involve God in temporality, Wierenga appeals, like Kvanvig, to the analogy of

Ibid., p. 156. Ibid., p. 154. Kvanvig erroneously assimilates all tensed expressions to temporal indexical expressions. A proposition which can be expressed without employing temporal indexicals but not without employing tensed verbs should still count as an essentially temporal proposition. It is also not clear what Kvanvig intends by "implying." Verbally tensed expressions need not imply temporal indexical expressions; e.g., the proposition that No sentient creatures exist can be expressed by the relevant present-tense sentence without implying the sentence "No sentient creatures now exist." Kvanvig should substitute "employing" for "implying" and "tensed expressions" for "temporal indexicals. " 23 Kvanvig also erred (as he now acknowledges) in claiming that the linguistic meaning of indexical expressions serves to distinguish direct from indirect grasping of the propositional content. For discussion see my Tensed Theory o/Time, chap. 4. 24 Edward R. Wierenga, The Nature 0/ God: An Inquiry into Divine Attributes, Comell Studies in the Philosophy of Religion (lthaca, N. Y.: ComeJl University Press, 1989), pp. 179-185. 21

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propositions expressed by sentences containing first-person pronouns. 25 Adopting, like Kvanvig, Plantinga's notion of an individual essence-a property wbich something can possess essentially and no other thing can possess at all-, Wierenga asserts that we should hold one of a person's essences to be special, namely, the one expressed by that person's use of the word "I." In my case this essence is the property of being me. Wierenga calls this special essence one's haecceity, and he claims that propositions expressed by sentences involving the first person pronoun entail the haecceity of the person using such expressions; such propositions he calls "first person propositions." Now Wierenga does not think that I am the only person who can grasp a proposition entailing my haecceity. Rather what is crucial is that I cannot believe such a proposition without having a de se belief, that is, a belief about me myself. A person S believes de se that he himself is F just in case there is a haecceity E such that S has E and S believes a proposition having E as a constituent and which attributes being F to whomever has E. ·Being omniscient, God also believes those propositions which have my haecceity as a constituent, but since the haecceity is mine, not God's, His believing them does not issue in de se beliefs for Him, as my believing them does for me. On the analogy of personal haecceities, Wierenga asserts that moments of time also have special essences or haecceities. A proposition containing the haecceity of a time he calls a ''present-time proposition." We temporal beings can only grasp present-time propositions at the time whose haecceity is contained in the proposition, not before or after. When a person believes a present-time proposition at its time, that person has a de praesenti belief. A person S believes de praesenti at a time t that it is then the case that p just in case there is a haecceity T such that t has T and at t S believes a proposition having T as a constituent and which attributes being such that p to whatever time has T. Wierenga analyzes the proposition expressed by A. N. Prior's ''The 1960 exams are over" as a proposition entailing the conjunction of the haecceity of the time of Prior's belief and the property of being such that the 1960 exams have finished be/ore then. Now Wierenga contends that there is no reason why God cannot believe all true present-time propositions, just as He believes all true first-person propositions. Just as His belief in a first-person proposition does not give Him a belief de se unless it is a belief in His own first-person proposition, so a belief in a present-time proposition does not give Him belief de praesenti unless He believes that proposition at its time. Being timeless, God did not have to wait, as did Prior, until August 29, 1960, in order to grasp the proposition Prior expressed by saying, ''The 1960 exams are over." He grasps and believes the relevant proposition timelessly and so forms no de praesenti belief in so doing. Thus, a timeless God knows all present-time propositions, and so there are no tensed facts unknown to Him. It seems to me that Wierenga's account of God's knowledge of propositions expressed by tensed discourse is multiply defective. To begin with, bis account of what it is to have a de praesenti belief isimplausible. Suppose I glance out the windowand form the judgement, "It's raining." On Wierenga's account, what I 25

Ibid., pp. 47-54.

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actually believe is a proposition about a certain time wbich attributes to that time a peculiar property, being such that it is raining then. But surely I do not believe anything of the sort. I may be utterly unconscious of the present time and certainly am not forming beliefs about its properties or its haecceity. Whatever plausibility attends Wierenga's analysis of de se beliefs derives from the fact that such beliefs involve the use of first-person indexicals, so that S can be conceived to believe a proposition involving S's haecceity and a property F. But the temporal analogue to such beliefs de se are beliefs involving present-tense indexicals like "now." When we have beliefs about what is going on now, then we do plausibly believe a proposition involving in some way the relevant time. Wierenga's analysis would most plausibly account for beliefs having similar form to a belief like "Now is when the meeting starts." In such a case we do seem to be ascribing a property to a tensed time. But not all beliefs de praesenti involve temporal indexicals, and the range of those doing so which also ascribe properties to the present is narrow, indeed. Wierenga might attempt to adjust bis analysis, such that in having a belief de praesenti I grasp (even ifI do not believe) a proposition such as he describes. 26 But if through my tensed beliefs I grasp information wbich essentially involves a certain time and its properties, why is there no necessary reference to that time in my conscious belief in the form of temporal indexicals like ''now''? Just as first-person propositions must be expressed via first-person indexicals, so present-time propositions, as Wierenga conceives them, must seemingly be expressed via present-tense indexicals. The absence of temporal indexicals from most of our Wierenga's notion of grasping a proposition is very obscure. On the one hand, he claims that present-time propositions do not change their tmth values over time. This seems to imply that the propositional content of a sentence like "The 1960 exams are over" is the tenseless information that the 1960 exams are over by tn. But Wierenga seems to preclude such an interpretation in his insistence that we cannot grasp a present-time proposition before or after its time. The above tenseless information can be grasped at any time. The propositional content expressed by "The 1960 exams are over" includes not only the noted tenseless information, but also the haecceity of tn. This seems to be the factor precluding our premature or tardy grasping ofthe present-time proposition. But why can we not grasp a proposition involving a temporal haecceity too soon or too late? Granted, if we do so, the proposition will be false; but we will have grasped the same propositional content as we do when it is true. The only answer I can think of is that the haecceity includes the property of presentness. Thus, the propositional content of "The 1960 exams are over" involves the moment having presentness and the property being such that the 1960 exams are over by then. I cannot grasp this proposition too soon or too late because the moment having presentness will be different if lutter "The 1960 exams are over" too soon or too late. On this analysis, non-simultaneous utterances of "The 1960 exams are over" express different propositions. Thus, one can grasp the proposition only at the time the utterance is made, since at different times other propositions are expressed. But would this not contradict Wierenga's claim that propositions do not change their truth values? Not necessarily; for on an ontology of presentism, just as moments come to and cease to exist, so, Wierenga might maintain, propositions involving such moments also come to and cease to exist. Thus, they do not change their truth value, but only have tmth value while the respective moments which they include are present; if the moments do not exist, neither do the propositions involving them. This makes it even more perspicuous why present-time propositions cannot be grasped before their time: they do not then yet exist. But such a strategy would backfire for Wierenga, since then God could only know such propositions while they existed, which entails God's temporality. Wierenga needs timeless or at least omnitemporal tmth bearers in order for God to know their changeless truth timelessly; but then I cannot make sense of his strictures conceming our grasping of present-time propositions. 26

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tensed beliefs renders implausible the idea that by means of them we grasp propositions which involve essentially the ascription of properties to a time. Moreover, Wierenga's analysis of tensed beliefs is drastically incomplete, since it overlooks all but present-tense beliefs. Howare beliefs like "John left at 8:00" or "John will come horne at 3:00" to be analyzed? It seems that Wierenga's analysis would require him to say that such beliefs express a proposition involving the haecceity of the time at which the belief is held and which attributes to that time properties specifying certain tenseless relations to events, for example, the time in question is such that John's leaving at 8:00 is earlier than then and his coming horne at 3:00 is later than them. This analysis serves to bring out that the property attributed to the time must be tenseless, not only in past- and future-tense beliefs, but also in beliefs de praesenti, lest the propositional content of God's beliefs be constitutive of a past, present, and future for God. If God is to know tensed facts, then, such knowledge comes, not through the property being such that p which is attributed to the time, but through the haecceity which the relevant time has. Does the haecceity of any time t, then, include its tense? If not, then the propositional content of God's beliefs is wholly tenseless, and all He grasps are the tenseless relations between times and events. Indeed, it might be argued that a time's haecceity cannot include its tense, since specific tense determinations are accidental to times. A haecceity is an individual essence; but since times are not essentially present, but acquire and lose presentness, their particular tense determinations cannot be part of their respective haecceities. Thus, the haecceity of a time must be a wholly tenseless property. Since the attribution to a tenseless time of a property involving tenseless relations of earlier than, simultaneous with, or later than does not serve to introduce tense, it turns out that what God knows are wholly tenseless propositions, not present-time propositions. Wierenga could escape this conclusion by advocating an ontology of presentism, according to which past and future times do not exist. Since the only time that exists is the present time, presentness could be conceived to be essential to any time. Just as existence is essential to any thing, since a thing has existence in every possible world in which it exists,27 so presentness is essential to any time, since a time has presentness at every time at which it exists. Since a time cannot exist without being present, presentness therefore belongs to its haecceity. The analogy with first-person propositions clearly suggests that for Wierenga a time's haecceity involves its tense, indeed, its presentness. Just as first-person propositions are exactly those which entail one's haecceity, so present-time propositions are just those containing a time's haecceity. But then it becomes extraordinarily difficult to understand how God can grasp the haecceity of a time without that time's being present for Him, which entails God's temporality. Consider the analogy of first-person indexicals. If the individual essence which is my haecceity is not the property of being Wil/iam Craig, but the special property of being me, then how can God possibly grasp a proposition which includes this 27 See A1vin Plantinga, The Nature Clarendon Press, 1974), p. 61.

0/ Necessity, C1arendon Library of Logic and Philosophy (Oxford:

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haecceity?28 Such a proposition is a private proposition which God cannot grasp because He is not I. If He can grasp such a proposition, then I faH to see why someone who addresses me as ''you'' does not also grasp such a proposition--in which case we are not talking about first-person propositions at all. Analogously, if a haecceity involves more than a tenseless determination, if it involves being present, then a timeless God cannot grasp a proposition containing such a haecceity. To grasp a proposition attributing a tenseless relation to some time which is objectively present entails one's being present. For example, in order to know the tensed fact expressed by Prior's utterance, "The 1960 exams are over," God must know more than the tenseless fact that the close of the exams is earlier than August 29, 1960; he must know of August 29, 1960 that it is present, or past in relation to the present. God's having such knowledge entails His temporality. Wierenga's analysis fails to explain how God can grasp propositions involving haecceities which include the property of presentness without His being temporal. It therefore also fails as a defense of a timeless God's knowledge oftensed facts. Finally, consider Leftow's defense of God's timeless knowledge of tensed facts. The key to Leftow's solution is bis SR-inspired distinction between events' occurrence relative to various temporal reference frames and their occurrence relative to God's ''reference frame" of eternity. Relative to eternity, all events are eternally preseIit, even though relative to various temporal reference frames they may be past, present, or future respectively. Thus, relative to eternity there simply are no temporally tensed facts to be known. Leftow explains, " . all events are actual at once, in etemity. But it does not follow that time is not tensed. Events also occur in temporal referenee frames, and the time of these reference frames may be tensed. ... The reason a timeless God does not know the essentially tensed fact that (T) is that in His framework of reference, etemity, this is not a fact at all. (T), again, is the claim that a proper subset S of the set of temporal events, consisting of a, b, c, etc., now has present-actuality. In etemity this claim is false. In etemity all temporal events ... have present-actuality at onee. 29

By (T) Leftow surely means that the members of S, rather than S itself, now have present-actuality. But how is this claim false in eternity? Since oll events have present-actuality in eternity, would not also the members of S? Perhaps the problem is that all events have present-actuality ot once in eternity, whereas (T) states that the members of S have present-actuality now. But in eternity, the indexical ''now'' in (T) refers either to the etemal present or to the time of a, b, c. If it refers to the etemal present, then the members of S do have present-actuality along with allother events. If it refers to the time of a, b, c, then it remains in Leftow's view a fact in Plantinga, who holds that one can grasp the individual essenee or haecceity of another person, does not take a haecceity to be or include the property of being me, but takes it to be just an individual essenee (Alvin Plantinga, "De Essen/ia," in Essays on /he Philosophy 0/ Roderick M Chisholm, ed. Emest Sosa, Grazer philosophische Studien 7/8 [Amsterdam: Rodopi, 1979), pp. 101-106). By siding with Chisholm (Roderick M. Chisholm, "Objects and Persons: Revision and Replies," in Philosophy 0/ Chisholm, p. 320) in taking a haecceity to be a special individual essence which involves the property of being me, Wierenga has forfeited the right to pubIic graspability of a haeceeity. 29 Brian Leftow, Time and Eternity, Comell Studies in Philosophy ofReIigion (lthaca, N. Y.: Comell University Press, 1991), p. 333. 28

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etemity that a, b, c have present-actuality then. So the problem does not reside in the contrast between now/at once. Perhaps the problem is that the present-actuality which a, b, c now have is temporal present-actuality, whereas in eternity they have etemal present-actuality. While this might seem to make sense, it sits ill with Leftow's insistence that The same events that A-occur in our temporal present A-occur in God's etemal present. They are there 'in their presentness': the very A-occurrence that is B-simultaneous with certain events within temporal reference frames is A-simultaneous with a timeless being's existence and with a11 temporal events within an etemal reference frame. Thus God can timelessly perceive, a11 at once, the very A-occurring that we perceive sequentially, under the form of change. 'D

Since, on Leftow's definitions, to A-occur is to occur now/ 1 we face the same indexical difficulty as above. If an event A-occurs in eternity, the ''now'' refers either to the etemal present or to the temporal present. If it refers to the etemal present, then it is not "the very A-occurring that we perceive," since that occurring refers to the temporal now. But if we say that it refers to the temporal present, then since the very same A-occurring takes place in time and etemity, (T) is a fact in eternity after all. In order to bring consistency into bis account, it seems to me that Leftow ought to say that for an event to A-occur is for that event to be present and that wbile the same events exist in time and eternity, they are not present in the same way with respect to these two "frames": events are temporally present only in time and etemally present only in eternity. Therefore, in etemity there are no temporally tensed facts; there are only etemally tensed facts, and these are all in the eternal present-tense. Accordingly, (T), referring as it does to the temporal present, is false in eternity, but it is also false that the very same A-occurring that transpires in time takes place in eternity. Now thus far Leftow's account seems to deny, not grant, God knowledge of (temporally) tensed facts. All He knows are the etemal present-tense facts. But Leftow maintains that God also knows the essentially tensed facts relative to temporal frames of reference. He writes, A factually omniscient being can only be required to grasp direct1y such facts as are genuinely facts within that being's framework of reference. Thus the fact that a timeless being grasps directly only the essentially tensed facts of etemity does not count against His strict factual omniscience, provided that He has some other access to the essentially tensed facts of other reference frames. But. .. a timeless God can know a11 the facts of simultaneity that obtain in other reference frames. Thus He can know what the essentially tensed facts of these other frames are, though He cannot be directly presented with these facts: it is just not true that the only way God can know facts is by some sort of direct presentation. '2

Leftow's appeal to the distinction between direct and indirect grasping will not serve to provide God with a knowledge of tensed facts, however. At best God can know what are the simultaneity classes of events relative to any arbitrarily specified lD

11 J2

Ibid. Ibid., p. 239. Ibid., p. 334.

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reference frame or hypothetical observer, but He cannot know what point on the world line of that observer or which simultaneity class of events is present in that frame. 33 When we recall that the "etemal present" is just a metaphorical description of a tenseless state of existence, then it is evident that on Leftow's account God knows no tensed facts. At the very least He knows no temporally tensed facts, which is what was to be proved. Indeed, Leftow's account of what he caUs "factual omniscience" implies that there really are no tensed facts. 34 According to Leftow a fact is either the existing of a subject or a subject's exemplifying of an attribute. The same fact can render a number of distinct propositions true. In Leftow's view the same fact that renders It is then (i.e., at 3 P.M) 3 P.M true also renders true what is expressed by the sentence token "It is now 3 P.M." These are distinct truths, different propositions, rendered true by the same fact. That fact is accessible at all times in varying ways and the various modes of access one can have to this fact generate distinctive truths that can only be known at various times. So even if God cannot be propositionally omniscient conceming events in time, He can still be factually omniscient in regard to them. The above account makes it evident that Leftow is really a partisan of tenseless time in spite of himself, holding that there are no tensed facts. On his account a tensed fact would be a subject's exemplifying a tensed property like presentness or the subject's presently existing. But such a fact is not accessible at all times, but only at the time it obtains or exists. The proposition that It is then 3 P.M does not access such a present-tense fact, for we do not know by it whether 3 P.M. is past, present, or future. The fact that renders such a proposition true must therefore be tenseless, even if that tenseless fact generates a tensed proposition at 3 P.M. Since there are no facts that escape God's omniscience and the only temporal facts God knows are tenseless facts, it follows that tensed facts do not exist. Moreover, Leftow's account ofGod's factual omniscience seems untenable. For Leftow does not think that the propositional context expressed by tensed sentences is tenseless and that tense results from the mode of presentation to or access by language users. Rather he holds that there are tensed propositions which can be known only at certain times. But unless Leftow is prepared to reject a view of truth as correspondence, there must be facts corresponding to true tensed propositions, for JJ Cf. Leftow's explanation: "From any reference frame, one can extrapolate what judgments of simultaneity would be correct in other reference frames.... So ... for every temporal now, God knows what is happening now (i.e., simultaneous with that now) ... " (lbid., p. 235). God cannot know with respect to any reference frame which simultaneity class of events has presentness. It occurs to me that Leftow may, like Stump and Kretzmann, being speaking metaphorically of times as reference frames and thus saying that for every present moment in time, God knows the events occurring at that time. In this case, the rejoinder remains basically the same: God cannot know which one of all the times in the world is present. For an effective illustration of the impossibility of extrinsic knowledge of internal temporal determinations, see Herbert 1. Nelson, ''Time(s), Etemity, and Duration," International Journal for Philosophy of Religion 22 (1987): 4-8. In Ian (sie) Leftow, "Timelessness and Divine Experience," Sophia 30 (1991): 43-53, Leftow fails to see that the problem is not the immediacy ofGod's knowledge, but the temporalizing character of knowledge of tensed facts. 34 Leftow, Time and Eternity, pp. 335-336. Leftow's view was anticipated by Murray MacBeath, "Ornniscience and Eternity I," Aristotelian Society Supplementary Volume 63 (1989): 65-66.

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example, that 3 P.M is present. Ifthis proposition is true, then it states a fact about the world. Even if we agree with Leftow that there are facts which are stated by no proposition, he has not given us any reason to doubt that every true proposition states a fact. Indeed, a view of truth as correspondence seems to require it. It follows, therefore, that a timeless God is not only not propositionally omniscient, but not even factually omniscient. At any rate, Leftow's explanation of God's knowledge of tensed facts is system dependent upon his theory of divine eternity, which we have seen to be misconceived in a number of ways. Even if Leftow's account did secure for God a knowledge oftensed (temporal) facts, it would still collapse under the weight ofthe objections to his theory of divine timelessness, given its unsound philosophical underpinnings. OMNISCIENCE DESPITE IGNORANCE OF TENSED FACTS It seems evident, then, that if God knows tensed facts, He is temporal, so that a denial of (5) is untenable. What prospect is there then for escaping the present objection by a denial of (4)? Here it is not enough simply to assert that a timelessly existing being cannot be expected to know tensed facts, on the basis that this is to demand the logically impossible. 35 Of course, such a feat is logically impossible; that is the point ofthe necessary truth of (5). But so long as we retain the customary defInition of omniscience

0: S is omniscient =dfFor all p, if p, then S knows that p and does not believe that -po and agree that tense is part of the propositional content expressed by tensed sentences, then it follows that God, in order to be omniscient, must know tensed facts. If such knowledge is prec1uded by His timelessness, then He is not omniscient. The above suggests that the most promising strategy for the atemporalist will be either to revise the traditional defInition of omniscience or to deny that tense, though objective, belongs to the propositional content oftensed sentences. Generally speaking, the difficulty encountered in the fIrst approach is that any adequate defInition must be in accord with our intuitive understanding of the definiendum, so that we are not at liberty to "cook" the defInition of omniscience in order to resolve the difficulty without the defInition's becoming unacceptably ad hoc. So what plausible alternative to 0 does the atemporalist suggest?

J5 Nelson. for example, brushes aside the problem of God's knowing what time it is now as a "pseudoquestion" because God is timeless (Nelson, "Time(s), Etemity, and Duration," p. 18); cf. William Hasker, God, Time, and Knowledge, Comell Studies in the Philosophy of Religion (Itbaca, N. Y.: Comell University Press, 1989), p, 159, who, despite his adherence to tensed facts, dismisses the question of God's knowing what time it is because tbere '1ust is no fact" about the temporal relation between a timeless being and temporal beings.

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Wierenga, in a sort of second line of defense, is prepared to accept that some propositions are "perspectival," true at some perspectives and false at others. 36 With respect to tense what this amounts to is the admission that propositions have their truth values relative to times and thus sometimes change their truth values. 0 would require God to know all such true propositions and, hence, to be temporal and changing. But Wierenga, observing that believing that a proposition is true at a perspective is different from believing at a perspective that a proposition is true, proposes the following re-definition of omniscience: 37

0': Xis omniscient = df For anY proposition p and perspective , (i) ifp is true at , thenXknows thatp is true at , and (ii)if Xis at and pis true at , then at , Xknows p. According to 0' God must know which tensed propositions are true at which times, but He need not know the tensed propositions themselves. Wierenga concludes, "if some propositions really do change their truth value over time, if propositions are thus 'perspectival,' then ... an omniscient being is required to know a perspectival proposition only if the being is at a perspective at which the proposition is true"; thus, "it follows from the claim that God is omniscient that he is not eternal only on the assumption that he is at some temporal perspective .... ,,38 Wierenga's definition 0' strikes me as unacceptably contrived. In Wierenga's view, God has knowledge of propositions stating exclusively tenseless facts, such as that p is true at t, whereas temporal persons know a multitude of objectively true propositions which remain unknown to God. Persons located at t know not merely that p is true at t; they know p simpliciter, an objectively true proposition of which God is ignorant. Wierenga does not solve the problem of God's knowledge of tensed facts; he merely re-defines omniscience in such a way that a being which is ignorant of tensed facts Can nonetheless be declared to be omniscient. In the absence of independent grounds for accepting 0', such a procedure is unacceptably ad hoc. If we wish to include temporal perspectives in our definition of omniscience, then why not adopt Davis's following definition?39 0": S is omniscient =

df F or

all p, if P at t, then it is true at t that S knows that p and does not believe -po

]6 Cf. Emest Sosa, "Propositions and Indexical Attitudes," in On Believing: Epistemological and Semiotic Approaches, ed. Herman Parret, Foundations of Communication (Berlin: Walter de Gruyter, 1983), pp. 316-332; Richard Feldman, "Saying Different Things," Philosophical Studies 38 (1980): 7984. The doctrine that propositions are true at personal perspectives has bizarre consequences, e.g.,· we should be forced to say that when two people each say "I was insulted" they are asserting the same proposition. 37 Wierenga, Nature ofOod, p. 189. 38 Ibid., pp. 198, 189. ]9 Stephen T. Davis, Logic and the Nature ofOod (Grand Rapids, Mich.: Wm. B. Eerdmans, 1983), p. 37.

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On 0", unlike 0', God would know every true proposition instead of just some; this intuitively commends 0" as a more adequate definition of omniscience. 40 Hut 0" would require that God know tensed propositions, as (4) states. Leftow also entertains the idea that omniscience be re-defmed in such a way that God not be required to know all truths, inc1uding tensed truthS. 41 He argues, in effect, that there are plausib1y many sorts of truths that God cannot know, so what harm is there in admitting one more c1ass of truths of which God is ignorant? But Leftow' s strategy is misconceived. This reasoning does not constitute grounds for revising the concept of omniscience as such (which does not even involve reference to God), but rather for denying that God need be omniscient. That is a moot question to which we shall return. A more plausible and independently motivated re-definition of omniscience would be to deny that God's knowledge is propositional in nature and therefore not adequately described by 0, which gives a propositional account of omniscience. 42 God's knowledge may be construed as a simple intuition of reality which we fmite knowers represent to ourselves in terms of discrete propositions. If facts are propositional in nature (a fact being a true proposition, for example), then God could be said not to know facts as such, tensed or otherwise, though He is omniscient. 43 But I think that such a re-construal, while plausible and attractive, does not serve to avert the force of the present objection. The critic of divine timelessness will simply re-formulate (4) in such a way that the problem re-appears, for example: 4'. If a temporal world exists, then if God is omniscient, God knows what we cognize as tensed facts. If God were ignorant of what we represent to ourselves propositionally as tensed facts, He would not deserve to be called omniscient. No good reason has been given, then, for revising the definition of omniscience in such a way that omniscience does not encompass knowledge of (what we cognize as) tensed propositions. Suppose, then, that the atemporalist tries the other route to a denial of (4), maintaining that tense does not belong to the propositional content expressed by tensed sentences. Like personal and spatial indexicals, temporal indexicals and tensed expressions could reflect features of the mode of presentation or the context of believing or the way of grasping the propositional content expressed by sentences containing such locutions. 44 Or they could be analyzed in terms of our self-Assuming that there are no timelessly true propositions. lf there are, then codicils have to be added to 0' and 0" a1ike to ensure that God knows these, too. 4\ Leftow, Time and Etemity, pp. 321-323. 42 For abrief discussion, see William Lane Craig, Divine Foreknawledge and Human Freedom, Studies in Intellectual History 19 (Leiden: EJ. Brill, 1990), pp. 10-11 and the references there; see additionally William Hasker, "Yes, God Has Beliefs!" Religious Studies 24 (I 988): 385-394. 43 This would be a controversial assumption, as Leftow, Time and Etemity, p. 318, notes, since there seem to be facts which are non-propositional in nature, e.g., that I am William Craig. If tensed facts are non-propositional in nature, then God's knowledge's being non-propositional does not undercut the necessary truth of (4). For an omniscient, non-propositional knower must know tensed facts. 44 See discussion in my Tensed Theory ofTime, chap. 4. 40

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ascription of properties rather than, or in addition to, our believing propositions. 45 Such analyses need not deny the objective reality of tense but could simply exclude tense from the propositional content of tensed expressions, having it lodge somewhere else. Given the customary definition 0, a timeless God would count as omniscient, even given the necessary truth of (5), because there are no tensed facts, where facts and true propositions are extensionally equivalent. Again, it seems to me that such analyses are both attractive and plausible, but I doubt that they ultimately serve to avert the problem raised by the present objection. Iftense is an objective feature ofreality, then one might plausibly insist with Leftow that there are non-propositional facts (say, first-person facts) and that tensed facts are also among these. Since, according to Christian theism, God is not merely propositionally omniscient, but maximally excellent cognitively, He must know such tensed facts, just as He must possess non-propositional knowledge de se. His cognitive excellence would not require Hirn to possess everyone's knowledge de se, so that He would not be, pace Leftow, factually omniscient, since it would be a cognitive defect for God to believe that He is Napoleon (not to mention His believing Himself also to be Washington and Reagan and ... ). Similarly, it would be a cognitive defect for God to believe that it is now 44 BC (not to mention His believing it also to be 1895 and 2020 and ... ). But it is a cognitive perfection to have a knowledge of what time it really is, of what episode in the history of the actual world is present. A being who is ignorant of all tensed facts is less excellent cognitively than one who knows all such facts. 46 The latter being knows infinitely more than the former and suffers no cognitive defect in so doing. On the contrary, if the argument of the last chapter is correct, it is only by the grace of such knowledge that God can act providentially in the temporal world at all. Hence, (4) can be reformulated as 4*.If a temporal world exists, then if God is maximally excellent cognitively, God knows tensed facts. With a similarly recast (2) the argument goes through as before. In case one still sticks at non-propositional facts, one may substitute in (4*) for ''tensed facts" an expression like ''what time it is" and revise (5) accordingly. In short, the prospects for turning back the force of (4) seem no better than those for denying (5). Given the existence of the temporal world, an omniscient or cognitively perfect being must know tensed facts. Since omniscience is essential to 4S See brief discussion in Craig, Divine Foreknowledge and Human Freedom, pp. 7-8, 71-72, 230-232 and therein cited literature. 46 So also the judgement of Richard M. Gale, "Omniscience-Irnrnutability Arguments," p. 332; cf. idem, On the Nature and Existence ofGod (Cambridge: Cambridge University Press, 1991), pp. 90-91. In response to Gale, Yates argues that a temporal God could not conceivably be omniscient in view of future contingents and that Relativity Theory would require Hirn to know a multiplicity of temporal now's, which is impossible (John C. Yates, Timelessness of God, [Lanham, Md.: University Press of Arnerica, 1990), pp. 231-232). I have refuted the first ofthese allegations in my Divine Foreknowledge and Human Freedom. As for the second, a temporal God would plausibly possess a privileged reference frame in which a privileged present exists (see my The Tenseless Theory ofTime: a Critical Examination, Synthese Library [Dordrecht: K1uwer Academic Publishers, 2000), sec. 1).

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theism and such knowledge is incompatible with divine timelessness, God must not be tirneless. MUST GOD BE OMNISCIENT? Our discussion has assumed the truth of 1. God is omniscient, but some defenders of divine timelessness, determined to preserve God's atemporality, are prepared to deny (2). Kvanvig, in response to the objection that "Just as we cannot hold the view that God is never intirnately enough acquainted with himself to know himself as himself, so it would be a mark of irnperfection were God never to be intirnately acquainted with any temporal. . .location," observes that there are two options open. 47 First, one could reject divine tirnelessness. In order to exhibit maximal perfection, God must direcdy grasp whatever moment is present and so be constantly changing. According to Kvanvig, the traditional motivations for the doctrine of timelessness are not compelling, so that it can be sacrificed if found incompatible with omniscience or cognitive perfection. 48 Such a verdict goes down hard with Leftow, who advocates rejecting (2) rather than (1) if these are incompatible. 49 He argues that God is ignorant of several classes of truth and that it is not a serious attenuation of divine omniscience to hold that He is also ignorant of tensed truths. It might be thought that we should construe God's knowledge as robustly as possible, so that even if there turn out to be some truths He cannot know, so that He is not omniscient, nevertheless that constitutes no justification for further eroding the extent of His knowledge by holding Hirn to be ignorant of tensed truths. But Leftow is so deeply committed to the doctrine of divine tirnelessness that he is prepared to jettison God's omniscience in order to preserve His tirnelessness. But does Leftow succeed in showing that God cannot know aIl true propositions? His example of something God cannot know is how it feels to be, oneself, a walker, a breather, or a sinner. 50 But such knowledge is not propositional knowledge at aIl and so fails to furnish examples of truths which God does not know; hence, on 0 God is omniscient even though He does not know how it feels to be oneself a sinner. Leftow recognizes the non-propositional character of such knowledge but insists that God's lacking such knowledge entails His ignorance of certain truths as weIl. If I arrange for a person to fail a test, I can say to him afterwards, "Being a failure oneselffeels like (his." According to Leftow, This is a proposition we both grasp .... You and I can know that being a failure oneself feels like this, but if God cannot fail, God cannot (though He can know how failure feels to you). For if God cannot fail, God cannot have the kind of experience 'this'

41 48

49

so

Kvanvig, Possibility 0/ an All-Knowing God, p. 159. Ibid., p. 151. Leftow, Time and Eternity, pp. 323-326. Leftow, Time and Eternity, p. 322.

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picks out and so in a sense cannot even understand the proposition that 'being a failure oneself feels like rhis. ,SI

It seems to me that the defender of God's omniscience will very plausibly reply that "Being a failure oneself feels like this" is a sentence, not a proposition, as is evident

from the presence of the demonstrative ''this'' (the italicizing of which does nothing to change its semantic content). Demonstratives serve to focus the hearer's attention on the referent and, like indexicals, are typically not construed to be part of the propositional content of the utterance involving them. 52 The propositional content expressed by "this" in the example will be the feelings of humiliation, depression, and so forth that attend being oneself a failure. Leftow seems to think that because God cannot have such feelings, He cannot know the propositional content expressed by the utterance. But this is to confuse God's ability to have the non-propositional knowledge of how it feels to be a failure oneself with His ability to know that being a failure oneself feels like being humiliated, and so forth. Even in Leftow's own example, the referent of ''this'' is not the speaker's own feelings, since he did not fail, but rather the other person's feelings who did fail. Yet Leftow asserts that they both know the same proposition. Similarly God can know the same propositional content that we do when we make such utterances, even though He does not share our experiences and so does not know how it feels to be oneself a failure. It might well be questioned whether preserving God's atemporality is worth the price of rendering Hirn ignorant of what state of the universe presently exists, as weIl as of aIl other tensed truths. But Leftow surmises that a God who is timeless but not omniscient with respect to tensed truths would be more perfect over all than a God who is temporal and possesses such knowledge. Leftow's many arguments for divine timelessness aim to extol the perfeetion accruing to God due to this attribute; but we have found all but one to be unsound or inconclusive. The argument of the last chapter in effect extols the greatness of divine temporality, since God could not be creatively active in the world were He timeless. Leftow also attempts to cheapen the value of omniscience, arguing that it is not a necessary property of a perfect knower. He rightly points out that cognitive perfection involves many other qualities than the range of one's knowledge; but that does nothing to show that cognitive perfection should not also encompass knowledge of tensed facts. Leftow proceeds to attack the possibility of propositional omniscience, appealing to private propositions expressed by sentences containing first-person indexicals. But we have already seen how such knowledge de se can be handled non-propositionally, not to mention the objections to private propositions. 53 In any case, positing one restriction on the range of God's knowledge hardly makes it a matter of indifference whether further restrictions are proposed. The fact that propositional omniscience and maximal cognitive excellence have not been shown to be impossible undercuts Leftow's response to what he calls the semantic argument against divine timelessness. In summary, it

SI

S2 S3

Ibid., p. 323. See discussion in my Tensed Theory o/Time, chap. 1. On those objections see Kvanvig, Possibility 0/ an All-Knowing God, pp. 48-56.

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seems to me that it is far more important, given a tensed theory of time, to safeguard God's omniscience or cognitive perfection rather than His timelessness and that a rejection of (2) rather than (1) is therefore theologically misguided. But what about Kvanvig's other alternative? He proposes that God be conceived to grasp all temporal moments directly.54 Such an understanding, he claims, would be analogous to a plausible construal of omnipresence as the direct grasping of the essence of every spatiallocation. What this analogy would imply, however, is that all times are literally present for God, not in the metaphorical sense of the eternal present, but in the literal temporal sense of the term. That is simply incompatible with there being a temporal series of events ordered by relations of earlier thanl/ater than. 55 In order to rebut this objection, Kvanvig is forced to resort either to the explanatorily vacuous ET-simultaneity of Stump and Kretzmann or to the suggestion that omniscient beings can grasp essences of moments directly without being in time, which is both ad hoc and self-contradictory.56 In short, the prospects for tuming back the force of (4) seem no better than those for denying (5). Given the existence of the temporal world, an omniscient or cognitively perfect God must know tensed facts. Since such knowledge is incompatible with divine timelessness and omniscience is essential to theism, God must not be timeless. A WAY OUT FOR DEFENDERS OF DIVINE TIMELESSNESS? Of course, this whole argument is predicated on the assumption that a tensed theory of time is correct. Atemporalists who advocate a view of time as tenseless easily refute the argument by denying that there are any tensed facts, so that (4) is false. Thus, Murray MacBeath, maintaining that the temporal indexical ''now'' merely serves to indicate a date just as the spatial indexical "here" specifies a location, asserts, "if I were now to say 'It is now 1989,' what would make my utterance true iso .. that my utterance is made in 1989.,,57 Thus God can know what time it is now in that He can always answer that question for anyone who asks it: When God is faced with the question whether the kettle is boiling now, all he needs to do is look at temporal cross-sections of the world until he finds the one in which the question is being asked of hirn, and then look to see whether, in that same cross-section,

Ibid., p. 160. As Geach wrote, "To say that God sees future events as they are in themselves, in their presentness, and not as future, is to ascribe to God either misperception or a patently self-contradictory feat. Misperception is involved if God is supposed to perceive what really is future not as future but as present; f1at self-contradiction, if what God sees is both future and simultaneous1y (since in itself it is just as God sees it) also present" (peter Geach, Providence and Evil [Cambridge: Cambridge University Press, 1977], p. 57). 56 Kvanvig more or less admits that this solution is ad hoc, making a bland appeal to divine omnipotence as its rationale. Ultimately, however, the solution is incoherent, since on his view tense arises precisely from direct grasping, not being part of a time's essence. If God directly grasps events as present and yet they are not really present, He does not in fact directly grasp them. 51 MacBeath, "Omniscience and Etemity," p. 61. 54 55

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the appropriate kettle BOILS. If it does, 'Yes,' he says, 'the kettle is, as you would put it, boiling now'. 58

Similarly, Helm, agreeing that God cannot Himself use "now" to express what He knows, sees little philosophical importance in this, since He knows the "essential facts" concerning what time it is now, namely, tenseless facts. 59 Thus, Helm brushes aside objections to divine timelessness based on God's knowledge of what is expressed by temporal indexical expressions like ''now,'' ''yesterday,'' or ''tomorrow,'' by citing D. H. Mellor and commenting "it has been plausibly argued that the use of such indexicals depends on there being a non-indexical concept of time for their proper employment.,,6o Helm has in mind Mellor's denial of tensed facts based on his provision of tenseless truth conditions for tensed sentence tokens. On Helm's view the logic of temporal indexicals is no different than that of their spatial analogues, which are, of course, tenseless. 61 God knows the tenseless truth conditions of sentences containing temporal indexicals, since He knows when things are in time, just as He knows where things are in space. 62 On a tenseless theory of time there no more are temporally tensed facts than there are spatially or personally tensed facts. Tense is merely a feature of linguistic or mental judgements from certain subjective perspectives which can either be translated into tenseless versions (Old Tenseless Theory of Language) or be given truth conditions which are wholly tenseless (New Tenseless Theory ofLanguage). There just are no tenseless facts to be known, and therefore (4) is false. So as with the argument based on God's action in the world, the argument for divine temporality based on God's omniscience only goes through if a tensed theory oftime is correct. Ifthe tenseless theory is preferable, no objection based on God's complete knowledge ofthe facts remains.

58 Murray MacBeath, "God's Spacelessness and Timelessness," Sophia 22 (1983): 31. Though a partisan of tenseless time, MacBeath seems to reject divine timelessness on the grounds that God could not use temporal indexicals and so could not know which is my present asking of the question nor share our feelings of relief when a dreadful episode is over (idem, "Onmiscience and Eternity," pp. 67-70). The first difficulty is unproblematic for a tenseless time theorist, since there is no objective present and so God, knowing the unique configuration of particles in the universe at the time of the asking, can answer whatever question is simultaneous with any given configuration. The second difficulty concerns, not so much onmiscience, but God's religious availability. As Leftow points out, there will be innumerable cases of how something feels which God carmot have, even if He is temporal. The question here is whether God is greater if He shares our feelings of anticipation and relief or not. 59 Paul Helm, "Onmiscience and Eternity II," Aristotelian Supplementary Volume 63 (1989): 77. 60 Paul Helm, Eternal God (Oxford: Clarendon Press, 1988), p. 25; cf. pp. 78-80. 61 Ibid., p. 44. 62 Ibid., pp. 79, 52.

CONCLUSION TO PART I

T

he implication of our discussion in Part I concerning the nature of divine etemity is that the question of whether a tensed or a tenseless theory of time is correct is truly a watershed issue for the doctrine of divine etemity. Specifically whether tense and temporal becoming are objective features of reality will be determinative for whether it is possible for God to be unqualifiedly timeless. For example, some ofthe arguments for divine timelessness which we examined hinged upon one's presupposition of a tensed or tenseless theory oftime. The fourth argument-that if God is temporal in virtue of His knowledge of tensed facts, He is also spatial-amounted to an argument against a tensed theory of time. I indicated that partisans of tensed time who hold to divine atemporality must in response show either how God can know tensed facts without being drawn into time (and space) or why His ignorance of tensed facts does not impugn His omniscience. But in the last chapter we saw that this seems to be an impossible task. On the other hand, if the advocate of tensed time holds to divine temporality, he must explain why the existence of temporally tensed facts does not imply the existence of spatially ''tensed'' facts as weIl or how a spaceless deity could know such facts. l Or again, the fifth argument-that only a timeless God could create two discrete time seriesended inconclusively, pending a discussion of creation on tensed and tenseless theories of time respectively. If our subsequent argument in chapter 3 was sound, we have now seen that a timeless deity could not in fact create two discrete time series if a tensed theory of time is correct, since such a deity could not even create one time series and remain timeless. The fifth argument therefore depends for its cogency upon the presupposition of a tenseless theory of time, on which the timeless creation of multiple time series becomes unproblematic. Or again, the thirteenth argument-that only a timeless God could be a perfect knower-seemed to backfrre on the atemporalist, for it left him with the task of explaining how a timeless God could know tensed facts about events in addition to the tenseless dates and temporal relations of events. We saw in the last chapter that this task seems hopeless, given a tensed theory of time. In our discussion of arguments for divine temporality, we found that the two most powerful arguments-the one based on God's creative action in the world and the other on God's omniscience-are sound only on the presupposition of a tensed theory of time. The proponent of tenseless time, who denies tensed facts and temporal becoming, eludes these arguments because God and the universe co-exist tenselessly and there just are no tensed facts to be known.

-an issue I take up in my The Tensed Theory 0/ Time: a Critical Examination, Synthese Library (Dordrecht: Kluwer Academic Publishers, 2000), chap. 4.

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The doctrine of divine timelessness is thus, so far as we have seen, unobjectionable given a tenseless theory of time. In the absence of such objections, the argument from the imperfection arising from the transiency of temporal experience might well justify a doctrine of divine timelessness. How might such a theory look? Certainly not like the unintelligible Stump-Kretzmann model or the pseudo-scientific Leftow model; rather it would postulate the tenseless, or Though extrinsically timeless, existence of the four-dimensional world. extrinsically timeless, this tenselessly existing block universe is ordered along one of its dimensions by tenseless relations of earlier than, simultaneous with, and later than, akin to the tenseless relations less than, equal to, and greater than, so that it is intrinsically temporal. Temporal becoming is a subjective illusion of consciousness; all things/events simply exist tenselessly at their temporal locations. There is no objective distinction between past, present, and future, these predicates being subjective ways of relating things/events/moments to oneself. Similarly, tensed discourse and temporal indexicals are subjective forms of referring and relating to things/events/moments. Einstein's relativistic ether, while no reference frame, may nonetheless be conceived as God's "frame of reference" for the physical world. He and it may be imagined to co-exist in a fictitious higher dimensional space in which the four-dimensional block universe is embedded. All points in space, time, and space-time are equally real and accessible to Hirn; indeed, creation just is the tenseless, ontological dependence of this four-dimensional block and all its constituents on God. Though it never comes into nor passes out of being, it is nevertheless radically contingent in its existence. God knows all the temporal facts about the universe, what is happening (tenselessly) at every moment and every place. Since there really is no past, present, or future, God's knowledge oftenseless facts is exhaustive of all the facts there are, and His knowledge of the world may be conceived in terms oftenseless propositions describing the world. Given a tenseless theory of time we have no need of devices like ET-simultaneity or the Zero Thesis; God's timelessness in relation to the world becomes perspicuous. On the other hand, given a tensed theory of time, divine timelessness seems to be metaphysically impossible. A pure tensed theory enjoins an ontology of presentism, according to which only the present "slice" of space-time exists. Things come into and pass out of existence; events happen as they do; time elapses. The distinction between past, present, and future is real; the past no longer exists and the future does not yet exist, even tenselessly. Therefore, God cannot co-exist with any time but the present, for that is the only time there iso The universe does not merely depend upon God for its (present) existence; it was literally brought into being by God and subsequently sustained by Hirn. Tense is an objective feature of reality which is mirrored in our language. Therefore, there are tensed facts ab out what has happened, is happening, and will happen in the universe, which any omniscient being must know. Given a tensed theory of time, therefore, God's timeless existence is, as we have argued, metaphysically impossible. On a tensed theory oftime God's temporal existence is, however, unproblematic. God exists simultaneously with every time; that is to say, He existed in the past, exists in the present, and will exist in the future, so long as time shall last. He

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sustains every thing in existence at the moment of its being present and knows every present-tense truth at that same time. His activity and knowledge are thus constantly changing, but there is no reason to think that He is not therefore immutable in His perfection. Being omniscient, He will have complete knowledge of the past and of the future, in virtue of His knowledge of all tensed facts. Many interesting philosophical questions will remain to be answered concerning God's creation of time, the relation of God's time to physical time, and so forth, but the notion that God is temporal seems perspicuous on a tensed theory oftime. That leads us to wonder whether the tenseless theory is compatible with divine temporality. The tenseless theory accords so naturally with a doctrine of divine timelessness that it seems at first blush bizarre to suggest that God exists as a sort of one-dimensional string or world line. Though few have espoused such a view, a notable exception is D. H. Mellor, the most important contemporary defender of a tenseless view of time. In a remarkable article in the Neue Zeitschrift für systematische Theologie und Religionsphilosophie, Mellor tries to persuade theologians to adopt a tenseless theory of time. He declares, "Clearing our vision of time in this way is a good example of the service that true, i.e. analytic, philosophy can render to theology.,,2 According to Mellor the right way to think of a tenseless creation is not to think that God created a temporally extended world "all at once," for this would mean "at one time"; rather it is to think that God successively creates every thing at the time of its existence. "So God does create the world's contents successively, but not because anything is ever future and therefore does not then exist. Everything always exists, but because it is always spread out in time, so is its Creator.,,3 On this view God exists co-temporally with the products of creation in a B-series of moments. Such a view might seem to make God a part of the world, so that the question arises: what sustains the four-dimensional block consisting of God and the universe in existence? But Mellor insists that such a question is illicit. So long as God is other than and independent of His creation, God may be said to be "outside" the world and even "outside" time. Not that God exists in some sort of eternity, which Mellor characterizes as "problematic." Oddly, however, the problems Mellor mentions with respect to timeless eternity are the difflculties the doctrine faces if a tensed theory of time is true. He specifically notes the incoherence that arises from trying to reconcile God's timelessness with the traditional notion oftime's flow. He thinks that the doctrine of divine timelessness is motivated by adesire to exempt God from changes in His knowledge wrought by the flux of tensed facts and champions bis alternative because "on the tenseless view, there are no such changing facts: God can be in time without His knowledge ever needing to change.,,4 Mellor's view is that God knows only the tenseless facts which serve to D. H. Mellor, "History without the Flow ofTime," Neue Zeitschriftfür systematische Theologie und

Religionsphilosophie 28 (1986): 75. J

Ibid., p. 73. Ibid., p. 74.

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make our tensed beliefs true, so that there is no change in God's knowledge, although He is temporal. Thus, Mellor denies to God those very tensed beliefs which MacBeath, the only other theorist of tenseless time I know of who inclines toward divine temporality, found so important to God's experience of our world that he for that very reason seemed disposed to place God in time. s Mellor's view faces the severe difficulty of explaining how God, lacking tensed beliefs, can act in a timely fashion, since He never knows at what moment He exists: He lacks all beliefs de praesenti. Since He is not timeless, but exists moment by moment successively, He must act at each moment to bring about the effects at that moment. But MeHor's God never knows at what moment He is located. If Mellor holds that by a single, continuing action at every time God brings about at each time all the effects in the entire B-series (which also seems necessary to preserve God's immutability), then he must posit action at a distance on God's part, which Mellor specifically rejects in arguing that God creates successively, moment by moment. It seems to me, therefore, that if God is temporal on a tenseless theory of time, we have to adopt MacBeath's, rather than Mellor's, viewpoint and accede to God tensed beliefs as weH as a succession of actions. But then God's possessing such a non-veridical experience of the way the world really is becomes difficult to reconcile with His cognitive perfection. Moreover, if God exists in time on a tenseless theory of time, the question of whether He is composed of temporal parts or stages cannot be avoided. If the tenseless theory implies that entities are temporally extended objects and the doctrine of temporal parts proves to be unacceptable, then God cannot be rightly conceived to exist in tenseless time. 6 In any case, what is clear is that the doctrine of divine timelessness stands or falls with the tenseless theory of time. The tenseless theory of time is the metaphysical presupposition of divine timelessness. Not that the defender of divine atemporality must prove this theory to be correct; he may simply presuppose it in the absence of good reasons to prefer the tensed theory of time. Thus, the doctrine of divine timelessness is tenable so long as the tensed theory has not been shown to be a superior account of temporal reality. As the tenseless theory of time fares, so also fares the doctrine of divine timelessness. An adjudication of the doctrine of divine timelessness is therefore made feasible by-and probably necessitates-an adjudication of the tensed vs. tenseless theory of time. Few philosophers of religion have been wiUing to undertake seriously this task. But apart from such an assessment, as we have seen, the most importarit arguments for and against divine timelessness remain inconclusive. The adjudication of this debate within the philosophy of space and time is therefore of critical importance and cannot be avoided.

See Murray MacBeath, "Omniscience and Etemity I," Aristotelian Society Supplementary Volume 63 (1989): 55-73. 6 See discussion in my The Tenseless Theory 0/ Time: a Critical Examination Synthese Library (Dordrecht: Kluwer Academic Publishers, 2000), chap. 9.

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I have undertaken this task in extenso in two companion volwnes 7 and shall in the practical interests of space rest content with swnmarizing my findings there. The superiority of the tensed theory of time over the tenseless theory of time may be shown by means of the following considerations. I. Argwnents for the Tensed Theory ofTime A. Tensed sentences, which can neither be translated into synonymous tenseless sentences nor be given tenseless, tokenreflexive truth conditions, correspond, if true, to tensed facts. B. The experience of temporal becoming, like our experience of the external world, is properly regarded as veridical.

11. Refutation of Argwnents against the Tensed Theory ofTime A. McTaggart's celebrated paradox is based upon the misguided marriage of a tenseless ontology of events or things with objective temporal becoming, as weIl as the unjustified asswnption that there should exist a unique, complete description of reality. B. The passage oftime is not a myth, but a metaphor for objective temporal becoming, a notion which can be consistently explicated on apresentist metaphysic. III. Refutation of Argwnents for the Tenseless Theory ofTime A. Temporal becoming is compatible with Relativity Theory ifwe reject space-time realism in favor of a neo-Lorentzian interpretation ofthe formalism ofthe theory. B. Time as it plays a role in physics is a pale abstraction of a rieher metaphysical reality, omitting indexical elements such as the "here" and the ''now'' in the interest of universalizing the formulations of naturallaws. IV. Argwnents against the Tenseless Theory of Time A. In the absence of objective distinctions between past, present, and future, the relations ordering events on the tenseless theory are only gratuitously regarded as genuinely temporal relations of earlierllater than. B. The claim that temporal becoming is mind-dependent is selfdefeating, since the subjective illusion of becoming involves itself an objective becoming in the contents of consciousness.

See my Tensed Theory ofTime and Tenseless Theory ofTime.

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C. The tenseless theory entails perdurantism, the doctrine that objects have spatio-temporal parts, a view which is metaphysically counter-intuitive, incompatible with moral accountability, and entails the bizarre counterpart doctrine of transworld identity.

D. The tenseless theory is theologically objectionable, since its claim that God and the universe co-exist tenselessly is incompatible with a robust doctrine of creatio ex nihilo. For aB these reasons I am convinced that time is tensed and that therefore God exists in time. What remains, then, is to explicate a coherent doctrine of divine eternity in light ofwhat contemporary philosophy and physics tell us about the nature oftime.

PART II GODANDTlME

SECTION 1: GOD, TIME, AND ITS MEASURES CHAPTER5 THE CLASSICAL CONCEPT OF TIME

I

n Part I I argued on the basis of the tensed theory of time that God is temporal rather than timeless. But many questions remain unanswered. How does God's time relate to ours? How shall we understand divine temporality in light of what contemporary physics, particularly Relativity Theory, has to say about the nature of time? How shall we conceive ofGod's relationship to time if, as modem cosmology teaches, time had a beginning? P. C. W. Davies has recently written, "No attempt to explain the world, either scientifically or theologically, can be considered successful until it accounts for the paradoxical conjunction of the temporal and the atemporal, of being and becoming."1 Charles Hartshome has identified this as "the problem for me": "how God as prehending, caring for, sensitive to, the creatures is to be conceived, given the current non-Newtonian idea of physical relativity, according to which there is apparently no unique cosmic present or unambiguous simultaneity.,,2 If there is no absolute present, no privileged temporal ordering of events, but only an infinity of distinct times (and spaces) associated with various reference frames, then which time is God's time? How can divine temporality be related to the fragmented world of temporal creatures occupying different streams of time? In order to address these questions adequately, it will be helpful to gain some background knowledge of the pre-relativistic, or c1assical, concept of time. Therefore, as an Ansatz to these questions, let us recur to the fount of the c1assical concept of time, the Philosophiae naturalis principia mathematica of Sir Isaac Newton, with a view toward acquiring some insight into the concept of time in contemporary physics and its implications for one's doctrine of divine eternity. Paul Davies, The Mind ofGod (fJew York: Simon and Schuster, 1992), p. 38. Charles Hartshorne, "A Reply to My Critics," in The Philosophy ofCharles Hartshorne, ed. Lewis Edwin Hahn, Library of Living Philosophers 20 (LaS alle, Ill.: Open Court, 1991), p. 616. Musing that "relating the divine becoming to the problem ofsimultaneity in physics exceeds my capacity," Hartshorne confessed, "I feel incapable of solving the problem ... " (Ibid., p. 642). EIsewhere he reports that "For decades 1 suffered philosophically from this [problem]," before the tests on Bell's Theorem showed an exuberant Hartshome the solution (Charies Hartshorne, "Bell's Theorem and Stapp's Revised View of Space-Time," Process Studies 7 [1977]: 185). Unfortunately, Hartshorne misguidedly thinks that temporal order should and can be decoupled from the absolute order of things' coming into existence (cf. Henry Pierce Stapp, "Quantum Mechanics, Local Causality, and Process Philosophy," Process Sludies 7 [1977]: 177). We shall see in the sequel why this move is misconceived. Cf. William B. Jones, "Bell's Theorem, H. P. Stapp, and Process Theism," Process Studies 7 (1977): 251.

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CHAPTER5

ABSOLUTE AND RELATIVE TIME

The Scholium to bis Deftnitions in the Prineipia is the [oeus classieus of Newton's exposition ofbis concepts oftime and space. 3 Newton observes that such quantities as time, space, pi ace, and motion are ''popularly conceived solely with reference to the objects of sense perception" in terms of "the relation they bear to sensible objects," and thence arise certain prejudices. 4 In order to overcome these, Newton draws a dichotomy with respect to these quantities between "absolute and relative, true and apparent, mathematical and common." With regard to time and space he asserts: I.

11.

Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything externaI, f10ws uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and extemal measure (precise or imprecise) of duration by means of motion; such a measurefor example, an hour, a day, a month, a year-is commonly used instead of true time. Absolute space, of its own nature without reference to anything extemal, always remains homogeneous and immovable. Relative space is any movable measure or dimension ofthis absolute space; such a measure of dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space, as in the case of space under the earth or in the air or in the heaven, where the dimension is determined from the situation of the space with respect to the earth. Absolute and relative space are the same in species and in magnitude, but they do not always remain the same numerically. For example, if the earth moves, the space of our air, which in a relative sense and with respect to the earth a1ways remains the same, will now be one part of the absolute space into which the air passes, now another part of it, and thus will be chan ging continually in an absolute sense.'

Isaac Newton, The Principia, trans. I. Bemard Cohen and Anne Whitrnan, with a Guide by I. Bemard Cohen (Berkeley: University ofCalifomia Press, 1999), pp. 408-415. 4 Ibid., p. 408. "vulgus quantitates hasce nonaliter quam ex relatione ad sensibilia concipiat." (The critical edition of the Principia is Isaac Newton, Philosophiae Naturalis Principia Mathematica, 3d ed. [1726], ed. Alexandre Koyre and I. Bemard Cohen, 2 vols. [Cambridge, Mass.: Harvard University Press, 1972]; for the Scholium on time and space see vol. I, p. 46.) , Ibid. "I. Tempus absolutum, verum, & mathematicum, in se & natura sua, sine relatione ad extemum quodvis, aequabiliter f1uit, a1ioque nomine dicitur Duratio: Relativum, apparens, & vulgare est sensibilis & extema quaevis durationis per motum mensura (seu accurata seu inaequabilis) qua vulgus vice veri temporis utitur, ut hora, dies, mensis, annus. 11. Spatium Absolutum, natura sua sine relatione ad extemum quodvis, semper manet similare & immobile: Relativum est Spatii hujus mensura, seu dimensio quaelibet mobilis, quae a sensibus nostris per situm suum ad corpora definitur, & a vulgo pro spatio immobili usurpatur: uti dimensio spatii subterranei, aerii vel coelestis definita per situm suum ad terram. Idem sunt spatium absolutum & relativum, specie & magnitudine; sed non permanent idem semper numero. Nam si terra, verbi gratia, moveatur, spatium aeris nostri, quod relative & respectu terrae semper manet idem, nunc erit una pars spatii absoluti in quam aer transit, nunc aha pars ejus; & sic absolute mutabitur perpetuo."

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Though much misunderstood and greatly vilified, Newton's distinction deserves our thoughtful consideration.6 The most evident feature of this distinetion is the independence of absolute time and space from the relative measures thereof. Absolute time or simple duration exists regardless of the sensible and external measurements which we try, more or less successfully, to make of it. In other words, clock time may or may not register the true time. J. R. Lucas calls this the ''rational theory of clocks.,,7 We cannot measure time directly because we cannot take an interval of, say, an hour and lay it out against another interval, and compare the two in the way that we compare lengths. Rather we must measure time indirectly by having rules which enable us to pick out pairs of instants and to say that the interval between one pair is equal to, or greater than, or twice as great as, the interval between another pair. If two intervals are isochronous, or equal in duration, it is not because of our fiat, but because they really are. The witness to this fact is that our clocks are corrigible. Thus, " ... time is not what the clocks say, but what they are trying to tell, are there to tell.,,8 In stating that absolute time "flows uniformly" without relation to anything external, Newton implies that time itself is not metrically amorphous. As Kroes explains, Newtonian absolute time possesses its own intrinsic metric with which our clocks seek to stay in harmony: To Newton it was self-evident that there exists just one fundamental metric for time: the intrinsic metric of absolute time. Physical processes of whatever kind couid provide a more or less accurate 'sensible measure' thereof. A 'true' sensible measure of absolute time could only be reached in the case of a perfectly isolated, completely undisturbed With respect to the opprobrium heaped upon Newton at this point, John Earman remarks, "What I fmd especially disturbing about such condenmations of Newton is not the injustice they do to Newton but rather the fact that they are possible only after an abdication of philosophical responsibility. In all the philosophicalliterature with which I am acquainted, there is precious little attempt to give reasonably clear and precise answers to the questions which are central to the cluster of philosophical issues which revolve around Newton's conception ofspace and time .... . . . it seems to me that Newton demonstrated a much deeper understanding of the nature of space and time than Berkeley, Leibniz, and Mach. And so far as I can see, neither modern philosophers of science ... nor the people identified by modern philosophers as major philosophical figures of the 17th, 18th, and 19th centuries, have succeeded in raising any compelling philosophical objections to absolute space, absolute time, or absolute spacetime... " (lohn Earman, "WhO'8 Afraid of Absolute Space?" Australasian Journal 01 Philosophy 48 [1970): 288, 317). J. R. Lucas, A Trealise on Time and Space (London: Methuen, 1973), p. 62-64, 69. Ibid., p. 64. He concludes, "Tbe fact that we have a rational theory of clocks vindicates Newton's doctrine of absolute time. If we really regarded time simply as the measure of process, we should have no warrant for regarding some processes as regular and others as irregular .... Even our best clocks are subject to correction. So long as we are prepared to assess the time-keeping qualities of a clock, and are prepared in principle to replace it by a more regular one, if it could be obtained, we are committed to an idea of absolute time which is not simply what the clocks actually say" (lbid., p. 91). Cf. thejudgement ofRichard Swinburne, Space and Time, 2d ed (London: Macmillan, 1981), p. 202, who agrees that Newton was correct: "there is a true time which might or might not be recorded by actual measuring instruments."

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CHAPTER5 periodical system which would constitute an ideal clock. In a certain sense, all physical processes had to obey, according to Newton, the rhythm of absolute time; an ideal dock, of whatever nature (mechanical, gravitational, etc.) could provide an exact measure of the unique, fundamental metric of absolute time. 9

The clock retardation that occurs in the context of SR and GR would not have disturbed Newton, since, as we shall see, he freely concedes that we may not have any accurate measure of time. Newton, of course, did not anticipate the relativistic phenomenon of clock retardation, but it would have troubled him little to learn that docks in motion or in gravitational fields run slowly. Kroes concurs that if we reject Newton's distinction between time and its measures, then the statement that two time intervals are isochronous can only be conventionally true. 1O Without absolute time, our temporal metrics as determined by, say, mechanical, gravitational, or electromagnetic docks, may not stay in synchronism, and the unity of time becomes a mere assumption. 11 Similarly, Newtonian space is absolute in the sense that it is distinct from the Max Jammer has relatively moving spaces associated with inertial frames. emphasized that the absolute statement ofNewton's first law ofmotion, I. Every body perseveres in its state of being at rest or of moving

uniformly straight forward, except insofar as it is compelled to change its state by forces impressei 2 requires the assumption of absolute space as aprerequisite of its validity.\3 The dassical principle of inertia becomes meaningless apart from astate of absolute rest Peter Kroes, Time: Its Structure and Role in Physical Theories, Synthese Library 179 (Dordrecht: D. Reidel, 1985), p. 49. Cf. John Earman, World Enough and Spacetime (Cambridge, Mass.: MIT Press, 1989), p. 8. 10 Thus Sklar observes that Newton is on to something "of vital importance" in drawing his distinction (Lawrence Sklar, "Real Quantities and their Sensible Measures," in Philosophical Perspectives on Newtonian Science, ed. Phillip Bricker and R. l. G. Hughes [Cambridge, Mass.: MIT Press, 1990], p. 61). Sklar notes that there are natural measures of time which yield simple, elegant laws of nature and that a wide variety of clocks will not only agree with each other in their metric oftime but will measure time in a way that approximates the natural measure. If, on the other hand, time itself is not distinguished from its measures, then any process has equal right to the status of the standard measure, regardless of how sporadic it might be relative to the concordant "natural" measures. See further J. R. Lucas and P. E. Hodgson, Spactime and Electromagnetism (Oxford: Clarendon Press, 1990), p. 239. 11 David Park seems oblivious to the vicious circularity ofhis reasoning when he says, "Time is what is measured by a dock. What is a dock? A dock is a device whose law o/motion is known .... How is it that we can define time in terms of docks and docks in terms of time without running into trouble? There is an assumption of regularity in the world that underlies the definition. We assume, in fact, that there is a universal time that govems all motion.... And the basis for the assumption is our knowledge of the world. It might have been otherwise--at least one can easi1y imagine it otherwise--but it is not" (David Park, The Image 0/ Eternity [Amberst, Mass.: University of Massachusetts Press, 1980], p. 40). 12 Newton, Principia, p. 416. "Corpus ornne perseverare in statu suo quiesciendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare. " lJ Max Jammer, Concepts 0/ Space (Cambridge, Mass.: Harvard University Press, 1954), pp. 99-103. Cf. Einstein's verdict that this realization was "one ofNewton's greatest achievements" (Albert Einstein,

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relative to which bodies may be said to be in astate of motion. The first law of motion, while necessitating the existence of absolute space, provides no means by which that space can be experimentally distinguished from relative spaces. Since the laws of motion hold in all inertial frames, "it tums out that the condition that absolute space be that space in which Newton's laws hold fails to specify a unique space as absolute space. The condition picks out an infinite set of spaces, the inertial spaces, which are the relative spaces of a set of observers moving uniformly with respect to one another in inertial motion.,,14 Jammer muses that "If Newton bad been a confinned positivist he would have acknowledged all uniformly moving inertial systems as equivalent to each other. As it was, only one absolute space existed for him.,,15 Newton proposed to pick out experimentally the privileged frame of absolute space, not by his laws of motion, but by means of rotation, which is experientially distinguished from merely relative motion with respect to its effects. 16 Modern commentators have observed that Newton's Gedankenexperimente of the rotating bucket and the revolving globes only succeed in demonstrating the existence of absolute motion, not absolute space. A spinning bicycle tire, for example, will be rotating in every inertial frame, whether, for example, the bicycle is taken to be moving and the earth at rest, or the earth moving and the bicycle at rest; but such absolute motion does not serve to pick out any reference frame as preferred. Absolute space, in contrast to the plurality of relative spaces, is one and immovable. In stating that absolute and relative space are the same in species and magnitude, differing only in that a volume of relative space moves through different (equal) volumes ofabsolute space, Newton shows that he has no suspicion ofwbat came to be known as the Lorentz-FitzGerald contraction. Sklar observes the oddity that Newton does not mention measuring rods as a more or 1ess accurate measure of the absolute metric of space. 17 But it is implied that absolute space, like absolute time, is endowed with an intrinsic metric which determines whether the distances we measure are equal. Because ''these parts of space cannot be seen," Newton explains, we use in their stead "sensible measures," so that ''we define all places on the basis of the positions and distances of things from some body that we regard as immovable.,,18 On the other hand, "in philosophy abstraction from the senses is required.,,19 Again, ifwe reject Newton's distinction, then it becomes impossible to "Foreword" to Concepts oj Space, by Max Jammer, p. xiv). See also Fritz Rohrlieh, From Paradox to Reality (Cambridge: Cambridge University Press, 1987), chap. 5. 14 lohn D. Norton, "Philosophy of Space and Time," in lntroduction to the Philosophy ojScience, ed. Merrilee Salmon (Englewood Cliffs, N. 1.: Prentice-Hall, 1992), p. 181. IS Jammer, Concepts ojSpac:e, pp. 100-101. 16 Newton, Principia, pp. 412-414. 17 Sklar, "Real Quantities," p. 61. 11 Newton, Principia, p. 410. "Verum quoniam hae Spatii partes videri nequeunt, & ab invicem per sensus nostros distingui; earum vice adhibemus mensuras sensibilis. Ex positionibus enim & distantiis rerum a corpore aliquo, quod spectamus ut inunobile, definimus loca universa." 19 Ibid. "in Philosophicis autem abstrahendum est a sensibus."

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hold that two spatial distances are objectively congruent, and we must swallow metric conventionalism with respect to space, the view that there are no objective facts conceming the comparative lengths ofnon-nested spatial intervals. 20 Newton's distinction thus far discussed contrasts absolute time and space with measured time and space. But, of course, Newton also conceived of time and space as absolute in a more profound sense, which is expressed in the "absolute-relational" distinction; namely, he held that time and space are absolute in the sense that they exist independently of any physical objects whatsoever. He claims, as we have seen, that absolute time "in and of itself and of its own nature, without reference to anything external, flows uniformly" and that absolute space "of its own nature without reference to anything extemal, always remains homogeneous and immovable." Usually, this is interpreted to mean that time and space would exist even if nothing else existed, that there exists a possible world which is completely empty except for the container of absolute space and the flow of absolute time. But here we must be very careful. Modem secular scholars have tended frequently to forget how ardent a theist Newton was and how central a role this theism played in his metaphysical outlook. Noting that Newton considered God to be temporal and therefore time to be everlasting, David Griffin observes that "Most commentators have ignored Newton's heterodox theology, and his talk of 'absolute time' has been generally misunderstood to mean that time is not in any sense a relation and hence can exist apart from actual events.,,21 In fact, Newton made quite clear in the General Scholium to the Principia, which he added in 1713, that absolute time and space are constituted by the divine attributes of eternity and omnipresence: He is eternal and infinite ... ; that is, he endures from eternity to eternity and he is presently from infinity to infinity .... he is not eternity and infinity, but eternal and infinite; he is not duration and space, but he endures and is present. He endures a1ways and is present everywhere, and by existing a1ways and everywhere he constitutes duration and space. Since each and every particle of space is always, and each and every indivisible moment of duration is everywhere, certainly the maker and lord of all things will not be never or nawhere. 22

20 For a compelling demonstration of just how indigestible metric conventionalism is see Graham Nerlich, The Shape 0/Space, 2d ed. (Cambridge: Cambridge University Press, 1994). 21 David Ray Griffin, "Introduction: Time and the Fallacy ofMisplaced Concreteness," in Physics and the Ultimate Significance o/Time, ed. David R. Griffin (Albany, N. y.: State University ofNew York Press, 1986), pp. 6-7. See also w'-H. Newton-Smith, "Space, Time, and Spacetime: A Philosopher's View," in The Nature 0/ Time, ed. Raymond Flood and Michael Lockwood (Oxford: Basil Blackwell, 1986), p. 27, who errs, however, in saying that space and time are aspects of God, rather than concomitants of God. 22 Newton, Principia, p. 941. "Aeternus est & Infinitus, ... id est, durat ab aeterno in aeternum, & adest ab infinito in infinitum.... Non est aeternitas & infinitas, sed aeternus & infinitus; non est duratio & spatium, sed durat & adest. Durat semper, & adest ubique; & existendo semper & ubique, durationem & spatium constituit. Cum unaquaeque spatii particula sit semper, & unumquodque durationis indivisibile momentum ubique, certe rerum omnium Fabricator ac Dominus non erit nunquam, nusquam."

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Because God is eternal, there exists an everlasting duration, and because He is omnipresent, there exists an infInite space. Since God exists in all possible worlds and is essentially eternal and omnipresent, absolute time and space also exist in all possible worlds, whether in those worlds there exists any creation at all. Thus, time and space are absolute in the sense that they exist independently of any physical objects, but that is not to say that they exist wholly non-relationally.23 In Newton's thinking, metaphysical time, God's time, is tensed time and the foundation of becoming. We have seen that metaphysical time "of its own nature, without reference to anything external, flows uniformly." To Newton therefore it makes perfectly good sense to imagine that all ideal docks and physical processes in the universe should start to run twice as fast as they previously had?4 God could simply speed up everything so that events occur as in a fIlm being run on fastforward. His time, metaphysical time, would remain unaffected by this alteration in physical time. In the absence of metaphysical time, such a speed-up becomes literally meaningless. Since docks would defIne what a temporal interval is, it would be nonsense to say that docks could all run twice as fast as they had, for the minute hand's circling the face of a dock one time is the temporal interval we call an hour. The hand would not cirde the dock's face twice in an hour; rather two hours would elapse. That is not to say that two hours would elapse in an interval previously designated as one hour, for that is to presuppose the standard of metaphysical time to which physical time is relative. Rather in the absence of metaphysical time, it is just two hours elapsing in two hours' time, and any talk of a speed-up is meaningless. For Newton, however, it would seem obvious that it lies within God's power to make all physical processes occur more quickly, which implies the existence of metaphysical time.

23 According to Earrnan, by "without relation to anything external," Newton meant without relation to material bodies (Earrnan, "Absolute Space," p. 289). It is worth drawing attention to the fact that while the absolute-relational distinction implies the absolute-measured distinction, the converse is not the case. That is to say, if time is absolute in the non-relational sense, then it is also absolute in the sense that its metric is the standard for isochronous intervals; but it is not obviously the case that if time transcends our attempts to measure it then time exists non-relationally, wholly independently of all events. One could quite consistently maintain, as Leibniz did, that time would not exist in the utter absence of events but is in some sense constituted by the fact of change (perhaps in God's actions or thoughts), and also maintain that there is a true time (God's time) which our physical docks approximate. Similarly, one could maintain that space is absolute in the sense that it is approximated but not constituted by our measurements of it without holding that it is absolute in the sense of either "non-relational" or "nondynamica\." Newton never provides anyargument, so far as I can determine, as to why God's existence must be spatia\. Contra Newton, one could consistently hold that in the absence of physical objects space would not exist and also that the metaphysical space which does exist is non-Eudidean globally and locally and yet maintain that it is absolute in the sense that it constitutes a privileged fundamental frame which provides the background for local reference frames (relative spaces), against which absolute motion or rest is determined. 24 For interesting discussion see George N. Schlesinger, "What Does the Denial of Absolute Space Mean?" Australasian Journal ofPhilosophy 45 (1967): 44-60; AdolfGrünbaum, "The Denial of Absolute Space and the Hypothesis of a Universal Nocturnal Expansion: A Rejoinder to George Schlesinger," Australasian Journal ofPhi! osophy 45 (1967): 61-91.

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NEWTON'S THEISM AND THE CLASSICAL CONCEPT OF TIME Scholars writing during the positivist era tended to treat Newton's theological disquisitions dismissively as incidental intrusions into otherwise sober scientific thinking. E. W. Strong, for example, writing in 1952, contended that the absence of any references to God in the original editions of the Principia and OptickY showed that God was irrelevant to works written by a scientist for a scientific purpose: Newton nowhere asserts that space and time are postulated as absolute because they are the sensorium of God and hence cannot be other than absolute in natural philosophy without impropriety .... When it is said that he constitutes duration and space, it may, with equallogic be said that he constitutes bodies also in their composition and in their motions relative to one another. 25

Similarly Jammer seems to see Newton's references to God as indications of the onset of senility: "So a comparison of the first and later editions of the Principia shows that the identification of absolute space with God, or with one of his attributes, came into the foreground ofNewton's thought only toward the end ofhis life, that is, at the beginning of the eighteenth century.,,26 Even a contemporary philosopher like Howard Stein insists that Newton's ideas are not based in theology; rather a certain theol0lB' was acceptable because its conceptions agreed with those required by mechanics. With the demise of positivism and the awakening of interest in the history of science, contemporary historians and philosophers of science have come to realize that Newton's statements concerning God need to be taken seriously, and this has led to a new appreciation ofthe role ofNewton's theology in his scientific thinking. Observing that "Metaphysics is both a starting point and the final aim of Newton's physics" and that his declared commitments on the subject of God's place in his system must therefore be taken at face value, Zev Bechler reflects the consensus of contemporary Newtonian historiography when he writes, The effort to present Newton as a sober positivistic, no-nonsense scientist fit for incorporation into the venerable origins of the twentieth century tradition leads scholars to attribute to him ideas about the autonomy of science which are strangely out of tune with his declared commitments. 2'

E. W. Strong, "Newton and God," Journal of/he His/ory ofIdeas 13 (1952): 154. Jammer, Concepts ofSpace, p. 108. 27 Howard Stein, "Newtonian Spacetime," Texas Quarterly 10 (1967): 198. Cf the emotional reactions in L. A. Whitt, "Absolute Space: Did Newton Take Leave of His (Classieal) Empirical SensesT Canadian Journal ofPhilosophy 12 (1982): 709-710, to Newton's giving theologieal reasons for absolute space (which the author mislocates as being in the Scholium to the Definitions!). Whitt huffs: "Newton has given way (or perhaps vent) to his theological scruples and has, for the brief space of this scholium, gone off the (empirieal) rails" (lbid., p. 711). 21 Zev Bechler, "Introduction: Some Issues of Newtonian Historiography," in Contemporary Newtonian Research, ed. Zev Bechler, Studies in the History ofModem Science 9 (Dordrecht: D. Reidel, 1982), p. 13. Cf A1an Gabbey, ''Newton and Natural Philosophy," in Companion to the History of Modern Science, ed. R. C. Olby, G. N. Cantor, 1. R. R. Christie, and M. 1. S. Lodge (London: Routledge, 1990). 25

26

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In editing the Principia, Bemard Cohen discovered that in Book III, Proposition 8, Corollary 5 of the first edition, Newton explicitly states that God placed the planets in their orbits at appropriate distances, but that this reference to the deity was dropped in subsequent editions. 29 ''The result ofthis alteration has been that almost all commentators ofNewton have erroneously assumed that Newton mentioned God in the Principia only in the later editions," specifically in the General Scholium, Cohen notes; "We may now reject wholly the view that Newton's introduction of God into the Principia was a result of senility, intellectual decline, or even a later development" after the first edition.30 In fact, on 10 December 1692, Newton confided to Richard Bentley, "When I wrote my Treatise about our System, I had an Eye upon such Principles as might work with considering Men, for the Belief of a Deity, and nothing can rejoice me more than to find it useful for that purpose.,,31 Similarly, in the Latin edition of the Opticks (1706), Newton declares space to be ''the Sensorium of a Being incorporeal, living and intelligent, who sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself.. .. "32 But the most important factor in the reassessment ofthe role ofNewton's theology in his science was undoubtedly the scholarly excavation of Newton's unpublished manuscripts, roughly a third of which are theological in character, which disclose that the themes of the General Scholium were lifelong concerns of Newton. The Yahuda manuscripts 15.3, f. 59 and 15.5, f. 98, housed at the Jewish National and University Library in Israel, are in part virtually identical to the text of the General Scholium. 33 Newton's "On the Gravity and Equilibrium ofFluids" (1666-70) is an especially rich resource for his ideas on space, time, and divinity, which are echoed in the General Scholium. 34 McGuire has also identified an untitled manuscript on time, place, and God in the Cambridge University Portsmouth Collection which constitutes an intermediate stage between these two. 3S In De gravitatione Newton argues that space (and by implication time) is neither substance, nor accident, nor nothing at all. It cannot be nothing because it has

Newton, Prineipia, Ed405.35}, p. 383. I. Bernard Cohen, Introduetion to Newton 's 'Prineipia' (Carnbridge: Carnbridge University Press, 1971), p. 156. 31 Isaac Newton to Richard Bentley, December 10, 1692, in Isaae Newton's Papers and Letters on Natural Philosophy, 2d ed., ed. with a General Introduction by I. Bemard Cohen (Carnbridge, Mass.: Harvard University Press, 1978), p. 280. 12 See Richard S. WestfalI, Never at Rest: A Biography 0/ Isaae Newton (Carnbridge: Carnbridge University Press, 1980), p. 647. 33 See WestfalI, Never at Rest, p. 749. 14 Isaac Newton, "On the Gravity and Equilibrium of Fluids," [De gravitatione et aequipondio jluidorumJ in Unpublished Seientifie Papers o/Isaae Newton, ed. A. Rupert Hall and Marie Boas Hall (Carnbridge: Carnbridge University Press, 1962), pp. 89-156. 35 Manuscript Add. 3965, section 13, folios 54I r-542r ; 545 r-546r. See 1. E. McGuire, ''Newton on Place, Time, and God: An Unpublished Source," British Journal/ar the History 0/ Seienee 11 (1978): 114-129. 29

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properties, such as infinity and isotropy. It cannot be an accident because it can exist without bodies. Neither is it a substance: It is not substance; on the one hand, because it is not absolute in itself, but is as it were

an emanent effect of God, or a disposition of all being; on the other hand, because it is not among the proper dispositions that denote substance, namely actions, such as thoughts in the mind or motions in the body.36

Contrary to the conventional understanding, Newton here declares explicitly that space is not in itself absolute (non absoluta per se) and therefore not a substance. Rather it is an emanent-or emanative-effect of God (Dei ejJectus emanativus). The notion of emanative causality had played a key role in the metaphysic of the Cambridge Platonist Henry More. In bis Axiom XVI More explained, "By an Emanative Cause is understood such a Cause as merely by Being, no other activity or causality interposed, produces an Effect.,,37 Correlatively, More explained in bis Axiom XVII: An Emanalive Effecl is coexiSlenl wilh Ihe very Subslance oflhal which is said 10 be Ihe Cause thereof

This must needs be true, because that very substance which is said to be the Cause, is the adequate and immediate Cause, and wants nothing to be adjoined to its bare essence for the production of the Effect; and therefore by the same reason the Effect is at any time, it must be at all times, or so long as that substance does exist. 38

Three times in De gravitatione Newton calls space an emanative effect of God. It is uncreated and co-existent with God and yet ontologically dependent upon Hirn for its being. Newton calls space a disposition or affection ofbeing (entis ajJectio). To be is to be spatially and, as Newton goes on to explain, temporally. Space is a disposition of being qua being. No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies: and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being [enlis primario existentis effectus emanativus), because when any being is postulated, space is postulated. And the same may be asserted of duration: for certainly both are dispositions of being or attributes according to which we denominate quantitatively the presence and duration of any existing individual thing. So the quantity of the existence of God was etemal, in relation to duration, and infinite in relation to the space in which he is present; and the quantity of the existence of a created being was as great, in relation to duration, as the duration since the beginning of

36

Newton, De gravilatione, p. 132. "Non est substantia turn quia non absolute per se, sed tanquam Dei effectus emanativus, et omnis entis affectio quaedam subsistit; turn quia non substat ejusmodi proprijs affectionibus quae substantiam denominant, hoc est actionibus, quales sunt cogitationes in mente et motus in corpore." 37 Henry More, "The Irnmorta1ity of the Soul," in Philosophical Writings of Henry More, ed. with an Introduction and Notes by Flora Isabei MacKinnon, Wellesley Semi-Centennial Series (New York: Oxford University Press, 1925), p. 74. 38 Ibid.

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its existenee, and in relation to the size of its presence as great as the spaee belonging to it. 39

Both space and time are thus inherent to being. God's infinite being therefore has as its consequence infinite time and space, wbich represent the quantity of His duration and presence. In the Neo-Platonic tradition represented by More the doctrine of emanation is associated with pantheism or panentheism. But, as Newton makes clear in the General Scholium, he does not conceive of space or time as in any way aspects of God Himself. Similarly, in the manuscript on time and place, Newton cautions, By reason of its eternity and infmity spaee will neither be God nor wise nor powerful nor alive, but will merely be inereased in duration and magnitude; whereas God by reason of the eternity and infinity of his spaee (that is, by reason of his eternal ornnipresenee) will be rendered the most perfect being' 4O

In thls same manuscript Newton foreshadows the famous passage in bis Opticks concerning space and God's sensorium. He writes, Tbe most perfeet idea of God is that he be one substanee, simple, indivisible, live and making live, necessarily existing everywhere and always, understanding everything to the utmost, freely willing good things, by his will effecting all possible things, and containing all other substances in Him as their underlying principle and plaee; a substanee whieh by his own presenee diseerns and rules all things, just as the cognitive part of man pereeives the forms of things brought into the brain, and thereby governs his own body; whieh always and everywhere ean bring to aet all possible things, which most freely brings about all things that are best and most aecord with reason, and cannot be indueed to act otherwise by error or blind fate. 41

39

40

41

Newton, De gravitatione, pp. 136-137. "Spatium est entis quaetenus ens affectio. Nullum ens existit vel potest existere quod non aliquo modo ad spatium refertur. Deus est ubique, mentes ereatae sunt alieubi, et corpus in spatio quod implet, et quiequid nee ubique nee ullibi est id non est. Et hinc sequitur quod spatium sit entis primario existentis effeetus emanatiws, quia positcf quolibet ente ponitur spatium. Deque Duratione similia possunt affirmari: scilieet ambae sunt entis affectiones sive attributa secundum quae quantitas existentiae eujuslibet individui quoad amplitudinem praesentiae et perseverationem in suo esse denominatur. Sie quantitas existentiae Dei secundum durationem aeterna fuit, et secundum spatium eui adest, infinita; et quantitas existentiae rei creatae secundum durationem tanta fuit quanta duratio ab inita existentia, et secundum amplitudinem praesentiae tanta ae spatium eui adest." See McGuire, "Newton on Plaee, Time, and God," p. 119. "Spatium ex aeternitate et infinitate nee Deus erit nee sapiens nee potens nec viwrn sed duratione et magnitudine tantum augebitur, Deus autem ex aeternitate et infinitate spatii sui (id est ex aeterna sua ornnipraesentia) reddetur ens perfectissimum." Ibid., p. 123. "Perfectissima Dei Idea est ut sit substantia una, simplex, indivisibilis, viva et vivifica, ubique semper necessario existens, summe inteIligens ornnia, Iibere volens bona, voluntate efficiens possibilia, et substantias ornnes alias in se continens tanquam eorum principium substans & loeus; substantia quae per praesentiam suam cernit et regit ornnia sieut hominis pars eogitans sentil speeies rerum in cerebrum delatas et iIIine regit corpus proprium; quaeque possibilia ornnia semper et ubique in actum dedueere potest,

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God is here declared to contain all other substances, not merely as their first principle, but also as the place where they exist. Since God fills all of space, physical objects literally exist in God. As Newton was to write in the General Scholium, all things are contained in God, yet He neither affects nor is affected by the motion of bodies in Hirn. Since all things are immediately present to Hirn in this way, everything is immediately discemed and ruled by Hirn. It is like, Newton says, the immediate presence of perceptible forms to a man's mind, whereby he may rule bis physical body. In a manuscript dating from the early 1690's Newton similarly speaks of God as "decreeing and ruling all things by means of bis substantial presence (as the thinking part of man perceives the appearances of things brought into the brain and thence its own body).',42 When he wrote the Latin edition of the Opticks, Newton incautiously queried, Is not infinite Space the Sensorium of a Being [Annon Spatium Universum, Sensorium est Entis] incorporeal, living and intelligent, who sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself. .. 743

As if having a premonition of the controversy to follow, Newton tried to recall the entire edition and subsequently changed the passage to read as folIows: Is not the Sensory of Animals that place to which the sensitive Substance is present, and into which the sensible Species ofThings are carried through the Nerves and Brain, that there they may be perceived by their immediate presence to that Substance? And these things being rightly dispatch'd, does it not appear from Phaenomena that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite Space, as it were in his Sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself: Ofwhich things the Images only carried through the Organs of Sense into our little Sensoriums, are there seen and beheld by that which in us perceives and thinks. 44

The addition ofthe phrase tanquam Sensorio sua did not deter Leibniz in bis famous correspondence with Clarke (1715-16) from attacking Newton's views on this score. Leibniz apparently thought that for Newton space was a sort of sense organ for God: "Sir Isaac Newton says, that space is an organ, which God makes use of to perceive things by. But if God stands in need of any organ to perceive things by, it will follow, that they do not depend upon him, nor were produced by him. ,,45 Tbis is

liberime agit quae optima & rationi maxime consentanea sunt, et errore vel fato caeco adduci non potest ut aliter agat." 42 David Gregory MS. 245, fol. 14a, Library of the Royal Society, London, cited in J. E. McGuire, "Force, Active Principles, and Newton's Invisible Realm," Ambix 15 (1968): 190. 43 Cited in Westfali, Never at Rest, p. 647; cf. Alexandre Koyre and I. Bemard Cohen, "The Case ofthe Missing Tanquam," Isis 52 (1961): 555-556. 44 Sir Isaac Newton, Opticks, or a Treatise o/the Reflections, Refractions, Inflections and Colours 0/ Light, based on 4th ed., 1730, with a Foreword by Albert Einstein, an Introduction by Sir Edmund Whittaker, and aPreface by I. Bemard Cohen (New York: Dover, 1952), Bk. m, Pt. 1, Q. 28, p. 370. 45 G. W. Leibniz, "Mr. Leibniz's First Paper," [1715] in The Leibniz-Clarke Correspondence, ed. with an Introduction and Notes by H. G. Alexander (Manchester: Manchester University Press, 1956), p. 11.

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obviously amisinterpretation on Leibniz's part. The sensory is not a physical organ, but a place where sense images appear to the mind. Hence, Clarke rightly replies, Sir Isaac Newton doth not say, that space is the organ which God makes use of to perceive things by; nor that he has need of any medium at all, whereby to perceive things: but on the contrary, that he, being omnipresent, perceives all things by his immediate presence to them, in all space wherever they are, without the intervention or assistance of any organ or medium whatsoever. In order to make this more intelligible, he illustrates it by a similitude: that as the mind of man, by its immediate presence to the pietures or images of things, form'd in the brain by the means of the organs of sensation, sees those pietures as if they were the things themselves; so God sees all things, by his immediate presence to them; he being actually present to the things themselves, to all things in the universe; as the mind of man is present to all the pictures of things formed in his brain. Sir Isaac Newton considers the brain and organs of sensation, as the means by which those pictures are formed: but not as the means by which the mind sees or perceives those pietures, when they are so formed. And in the universe, he doth not consider things as if they were pictures, formed by certain means, or organs; but as real things, form' d by God himself and seen by him in all places wherever they are, without the intervention of any medium at alt. And this similitude is all that he means, when he supposes infinite space to be (as it were) the sensorium of the Omnipresent Being. 46

This strikes me as a careful and accurate exegesis of Newton's statements on this head. 47 But as the illustrious correspondence proceeded, Clarke began to stray from Newton's position. For example, in his third reply Clarke asserts, "Space is not a being, an etemal and infInite being, but a property, or a consequence ofthe existence of a being infInite and eternal. Intinite space, is immensity; but immensity is not God: and therefore infInite space, is not God. ,,48 Here the words "a property" intrude inaccurately into this otherwise faithful Newtonian exposition. By his fourth reply Clarke's error has clearly broken out: Space void of body, is the property of an incorporeal substance. .. . Space is not a substance, but a property, and if it be the property of that which is necessary, it will consequently (as allother properties of that which is necessary most do) exist more necessarily (though it be not itself a substance,) than those substances themselves which are not necessary.49

Similarly, in his fIfth reply Clarke infers that since space and duration are not substances, "It remains, therefore, by necessary consequence that space is a property, in like manner as duration is."sO Clarke has here departed from Newton and is expounding his own position, enunciated in his Boyle Lectures, that eternity and immensity "must needs be Modes or Attributes of a necessary Being actually Samuel Clarke, "Or. Clarke's First Reply," in Correspondence, pp. 12-13. See M. Buckley, "God in the Project ofNewtonian Mechanics," in Newton and the New Direction in Science, ed. G. V. Coyne, M. Heller, and J. Zyncinski (Vatican City State: Specola Vaticana, 1988), pp. 85-105, esp. p. 100 for a similar account. See also the account ofClarke's views in Ezio Vailati, Leibniz and Clarke: a Study oftheir Correspondence (New York: Oxford University Press, 1997), pp. 20-27, 3637. 4& Samuel Clarke, "Or. Clarke's Third Reply," in Correspondence, p. 31. 49 Samuel Clarke, "Or. Clarke's Fourth Reply," in Correspondence, p. 47. so Samuel Clarke, "Or. Clarke's Fifth Reply," in Correspondence, p. 121. 46

47

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existing.,,51 Newton was scandalized, and when the Des Maiseaux edition of the Leibniz-Clarke correspondence appeared in 1720, it carried the following avertissement au lecteur: Since the tenns quality or property have nonnally a sense different from that in which they must be taken here, M. Clarke has asked me to warn his readers that when he speaks of infinite space or immensity and infinite duration or eternity, and gives them, through an inevitable imperfection of language, the name of qualities or properties of a substance which is immense or eternal, he does not claim to take the tenn quality or property in the same sense as they are taken by those who discuss logic or metaphysics when they apply them to matter; but that by this name he means only that space and duration are modes of existence of the Substance which is really necessary, and substantially ornnipresent and eternal. 52

On the basis of multiple drafts of this passage preserved in the Portsmouth Collection 82-84, 96-97, Koyre and Cohen have shown that it was Newton himself who had written this correction. 53 In the drafts Newton bad spoken of space and time once more as "consequents of the existence of a Being which is really, necessari1y & substantially Omnipresent & Eternal.,,54 Newton thus emphatically repudiated the view that space and time are attributes of God. Rather absolute space and time are concomitant consequences ofGod's existence. Although on Newton's view space (and by implication time) is not a substance in the sense that it is an independently existing entity, nevertheless it is very much like a substance. McGuire explains, Newton refers to the nature of space as an existing thing, and has in mind a decided list of properties which he considers belong properly to its nature: it has inherent parts that constitute its structure; in all directions it possesses unlimited extension; it is actually infinite; independently of things external to it, its inherent parts maintain the same eternal and immutable order; a11 true 'positions, distances, and local motions' have reference to these parts alone; and lastly, space is passively receptive to being occupied, and can offer no resistance to motion. It is c1ear that Newton considers space to be an individual in the sense of being the proper subject of certain sorts of predications .... Newton believes space to be a positive individual embodying real properties which derive from its actual extension in three dimensions. Ai> such, it is ... an individual fully actual at all time, and endowed with a rich inherent structure. 55

" Samuel Clarke, A Discourse Concerning the Being and Attributes o/God, the Obligations 0/Natural Religion and the Truth and Certainty 0/ the Christian Revelation [I704-05], in The Works 0/ Samuel Clarke, vol. 2: Sermons on Several Subjects (London: John & Paul Knapton, 1738), 530. 52 Cited in H. G. Alexander, "lntroduction," in Correspondence, p. xxix. For discussion, see John Carriero, "Newton on Space and Time: Comments on J. E. McGuire," in Perspectives on Newtonian Science, pp. 122-124. 53 Alexandre Koyre and I. Bernard Cohen, "Newton and the Leibniz-Clarke Correspondence," Archives internationales d'histoires des sciences 15 (1962): 63-126. 54 Draft A, cited in Koyre and Cohen, "Newton," Cf. the French text: "I'Espace & 1a Duree sont des Modes d'existence dans tous les Etres; & des Modes i'lfinis, & des Consequences, de I'existence de 1a Substance qui est reellement, necessairement, & substantiellement toute-presente, & eternelle" (Ibid., p. 83). 55 J. E. McGuire, "Space, Infinity and Indivisibility: Newton on the Creation of Matter," in Contemporary Newton Research, p. 163.

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Space and time thus have a sort of quasi-substantival status for Newton. What becomes clear from this historical excursus is that the classical, Newtonian concept of time is rooted in a theistic metaphysic. Far from being after-the-fact theological reflections on concepts arising solely from physical considerations, the views of the General Scholium on time and space are the fruit of a long study which from start to finish was metaphysical and theological in character. S6 James Force rightly concludes, Newton would have been astonished to learn that some of his interpreters, following Hume's lead, have claimed that theology, metaphysics, and epistemology have no necessary, integrated, synthetic relationship in themselves, much less that he hirnself has been placed into this school. Newton's own thought is in fact a seamIess unity composed of theology, metaphysics, and epistemology all mixed together because, at their base, is the Lord God of supreme dominion. 57

Our exposition ofNewton's views on God, space, and time makes it evident that when Newton speaks of divine eternity, he does not, like scholastic theologians in the Augustinian tradition, mean astate of timelessness, but rather infinite and everlasting temporal duration. In a preliminary draft of the General Scholium, Newton had explicitly rejected the conception of God's eternity as an eternal now:

Westfall states, "Composed virtually at the end of his active life, the General Scholium contained a vigorous reassertion of those principles which Newton had adopted in his rebellion against the perceived dangers ofCartesian mechanical philosophy. The same principles had continued to govern his scientific career as he followed the consequences of his rebellion into a new natural philosophy and a new conception of science" (Westfali, Never at Rest, p. 749). 57 James E. Force, ''Newton's God of Dominion: The Unity of Newton's Theological, Scientific, and Political Thought," in Essays on the Context, Nature, and Injluence of Isaac Newton 's Theology, ed James E. Force and Richard H. Popkin, International Archives of the History of Ideas 128 (Dordrecht: Kluwer Academic Publishers, 1990), p. 90. Cf. Bechler's comment, ''The view of physics and metaphysics as one indivisible block was inevitable to hirn, for physics was the inquiry into the nature of bodies in space and time, but since space and time were the abode of God, there was no possible way to demonstrate separate compartments of inquiry within all this" (Bechler, "Introduction," p. 14); similarly McGuire: " ... his ontology of space and time cannot be understood without fully appreciating how it relates to the nature of divine existence" (1. E. McGuire, "Existence, Actuality, and Necessity: Newton on Space and Time," Annals ofScience 35 [1978]: 463); and Brooke, "Newton himselfprovides one ofthe most spectacular examples of the integration of scientific and religious interests in one and the same mind" (John Hedley Brooke, "Science and Religion," in Companion to the History ofModem Science, p. 775). Elsewhere Brooke observes, "Iftheistic discourse constitutes part ofnatural philosophy, it becomes anachronistic to ask how Newton reconciled his science with his religion. The right question is more likely to be: how did his distinctive view of God's dominion, in both nature and history, affect his interpretation of nature?" (John Brooke, "The God of !saac Newton," in Let Newton Be!, ed. John Fauvel, Raymond Flood, Michael Shortiand, and Robin Wilson [Oxford: Oxford University Press, 1988], pp. 171-172). So also Ivor Leclerc, "The Relation between Natural Science and Metaphysics," in The World View ofContemporary Physics, ed. with an Introduction by Richard F. Kitchener (Albany: State University ofNew York Press, 1988), pp. 26-27. 56

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"His duration is not a nunc stans without duration, nor is bis presence nowhere."S8 Writing to Des Maiseaux in 1717, he elaborated, The schoolmen made a Nune stans to be eternity & by consequence an attribute of God & etemal duration hath a better title to that name, though it be but a mode of his existence. For a nune stans is a moment Wh always is & yet never was nor will be, which is a contradiction in terms. 59

Far from being atemporal, God's now or present is thus the present of absolute time. Since God is not "a dwarf-god" located at a place in space,60 but is omnipresent, every indivisible moment of duration is everywhere, as we saw in the General Scholium. There is thus a worldwide moment which is absolutely present. Dieks effectively captures the implications of Newton's theism for our understanding of time when he writes, In classical mechanics absolute simultaneity can easily be interpreted in terms of the 'j/awing now' we know from introspection. Just like [sie] our personal 'naw' is connected with our progressing history, the universal 'now' determined by the absolute simultaneity relation may be regarded as related to one history, e.g. the history of the Universe as a whole. For Newton God endures, and thereby constitutes time. This naturally fits in with the conception that there must be a universal succession of moments, determining the existence of one entity .... there is one history, with one 'naw,' dividing past and future. 61

Newton's temporal theism thus provides the foundation for both absolute simultaneity and absolute becoming. These are features ftrst and foremost of metaphysical time, God's time, and derivatively ofmeasured or physical time. NEWTONIAN TIME AND RELATlVISTlC TIME Returning to Newton's Scholium to bis Defmitions, we fmd that Newton, after making further distinctions with regard to absolute and relative place and absolute and relative motion, proceeds to grant freely that we cannot for the most part know whether something is at absolute rest or in absolute motion. But since these parts of space carmot be seen and carmot be distinguished from one another by our senses, we use sensible measures in their stead. For we define all places on the basis of the positions and distances of things from some body that we regard as immovable, and then we reckon all motions with respect to these places, insofar as we conceive of bodies as being changed in position with respect to them. Thus, instead of

" Cited in 1. E. McGuire, "Predicates of Pure Existence: Newton on God's Space and Time," in Philosophieal Perspeetives on Newtonian Scienee, ed. Phillip Bricker and R. I. G. Hughes (Cambridge, Mass.: MIT Press, 1990), p. 93. 59 Newton to Des Maiseaux, in Unpublished Papers, p. 357. See also his rejection of God's existing totum simul in "Place, Time, and God" (ms. add. 3965, sect. 13, f. 545 r·546r , in McGuire, "Newton on Place, Time, and God," p. 121). 60 Newton, "Place, Time, and God," in McGuire, "Newton on Place, Time, and God," p. 123. 61 Dennis Dieks, "Newton's Conception of Time in Modem Physics and Philosophy," in Newton 's Seientifie and Philosophical Legaey, ed. P. B. Scheurer and G. Debrock (Dordrecht: Kluwer Academic Publishers, 1988), pp. 156-157.

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absolute plaees and motions we use relative ones, whieh is not inappropriate in ordinary human affairs, a1though in philosophy abstraetion from the senses is required. 62

But these commonly used relative quantities should not be confused with their absolute counterparts: Relative quantities, therefore, are not the aetual quantities whose narnes they bear but are those sensible measures of them (whether true or erroneous) that are commonly used instead of the quantities being measured. But if the meanings of words are to be defined by usage, then it is these sensible measures whieh should properly be understood by the terms 'time,' 'space,' 'plaee,' and 'motion,' and the manner of expression will be out of the ordinary and purely mathematieal if the quantities being measured are understood here. Aecordingly those who there interpret these words as referring to the quantities being measured do violenee to the Scriptures. And they no less corrupt mathematics and philosophy who eonfuse true quantities with their relations and eommon measures. 63

Newton believed that there were certain properties, causes, and effects which served to distinguish absolute motion and rest from relative motion and rest. 64 It is noteworthy, however, that some of these do not manifest themselves empirically. Others do, such as rotation, and Newton concluded his Scholium with the promise, "But in what follows, a fuller explanation will be given of how to determine true motions from their causes, effects, and apparent differences, and, conversely, ofhow to determine from motions, whether true or apparent, their causes and effects. F or this was the purpose for which I composed the following treatise.,,65 The revolution wrought by Einstein in 1905 is widely believed to have destroyed Newtonian absolute time. But such a claim needs to be carefully qualified. Einstein actually presupposed that absolute space and, hence, absolute simultaneity do not exist, and he then offered in their stead operational definitions of time and simultaneity, which, in the absence of a privileged reference frame, entail that

62

63

64 M

Newton, Principia, pp. 410-411. "Verum quoniarn hae Spatii partes videri nequeunt, & ab invieem per sensus nostros distingui; earum viee abhibemus mensuras sensibilis.... Sie vice locorum & motuum absolutorum relativis utimur; nee incommode in rebus humanis: in philosophicis autem abstrahendum est a sensibus." Ibid., pp. 413-414. "Quantitates relativa:: non sunt igitur ea:: ipsa:: quantitates, quarum nomina pra:: se serunt, sed sunt earum mensura:: illa:: sensibiles (vera:: an errantes) quibus vulgus loco quantitatum mensuratarum utitur. At si ex usu definienda:: sunt verborum significationes; per nomina iIIa Temporis, Spatii, Loci & Moros proprie intelligenda:: erunt ha:: mensura:: sensibilis; & sermo erit insoiens & pure mathematicus, si quantitates mensurata:: hic intelligantur. Proinde vim inferunt sacris literis, qui voees hasee de quantitatibus mensuratis ibi interpretantur. Neque minus contarninant Mathesin & Philosophiarn, qui quantitates veras cum ipsarum relationibus & vulgaribus mensuris eonfudunt." Ibid., p. 411 Ibid., p. 415. "Motus autem veros ex eorum causis, effectibus, & apparentibus differentiis colligere, & contra ex motibus seu veris seu apparentibus eorum causas & effectus, doeebitur fusius in sequentibus. Hunc enim in finem traetatum sequentem composui."

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duration and length are relational, rather than intnnslc, properties. 66 The only justification for that presupposition was the verificationist principle that quantities wbich are physically undetectable are non-existent or even meaningless. The most important pbilosopbical event of the last half century has been the collapse of positivism and the consequent re-opening of traditional metaphysical questions. With SR's epistemological underpinnings now removed, one cannot justifiably simply presuppose that metaphysical space and time do not exist. It may well be the case that Newton was right that there exists a temporal deity whose duration constitutes metaphysical time. How, then, we may ask, did Newton fall short in comparison with Einstein's analysis of time? A little reflection reveals that the shortcoming of Newton's analysis lay not in bis belief in a metaphysical time distinct from physical time, as is so often alleged, but in bis not realizing that the accuracy of physical time in its approximation to metaphysical time depends on the relative motion of one's docks. Though Newton labeled bis distinction between time and the sensible measures thereof "absolute" versus "relative," bis physical time was in fact as absolute as metaphysical time in the sense that it, too, was well-defined independent of any reference frame apart from that of absolute space. The sense in which it was relative is that it was a more or less accurate approximation to metaphysical time. Because docks may not be truly periodic, physical time may not register the true time: In astronomy, absolute time is distinguished from relative time by the equation of common time. For natural days, which are commonly considered equal for the purpose of measuring time, are actually unequal. Astronomers correct this inequality in order to measure celestial motions on the basis of a truer time. lt is possible that there is no uniform motion by which time may have an exact measure. All motions can be accelerated and retarded, but the flow of absolute time cannot be changed. The duration or perseverance of the existence of things is the same, whether their motions are rapid or slow or null; accordingly, duration is rightly distinguished from its sensible measures and is gathered from them by means of an astronomical equation. 67

What Newton did not realize, nor could he have suspected, is that physical time is not only relative, but also relativistic, that the approximation of physical time to metaphysical time depends not merely upon the regularity of one's dock, but also upon its motion. Unless a dock were at absolute rest, it would not accurately register the passage of metaphysical time. Moving docks run slow. Tbis truth,

For an exposition of Einstein's theory and its implication for the time concept see my Time and the Metaphysics 0/Relativity (Dordrecht: Kluwer Academic Publishers, 2001). 67 Ibid., p. 410. "Tempus Absolutum a Relativo distinguitur in Astronomia per requationem temporis vulgi. Inrequales enim sunt dies naturales, qui vulgo tanquam requales pro mensura temporis habentur. Hane inrequalitatem eorrigunt Astronomi, ut ex veriore tempore mensurent motus coelestes. Possibile est, ut nullus sit motus requabilis, quo tempus aceurate mensuretur. Accelerari & retardari possunt motus omnes, sed fluxus temporis absoluti mutari nequit. Eadem est duratio seu perseverantia existentire rerum, sive motus sint celeres, sive tardi, sive nulli: proinde hree a mensuris suis sensibilibus merito distinguitur, & ex iisdem colligitur per requationem astronomieam. " 66

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unknown to Newton, only intimated by Larmor and Lorentz in the concept of "local time," was fmally grasped by Einstein. Where Newton fell short, then, was not in his conception of absolute or metaphysical time-he had theological grounds for positing such a time-, but in his incomplete understanding of physical time. He assumed too readily that an ideal clock would give an accurate measure of metaphysical time independently of its motion. But the above quotation suggests that Newton, if confronted with relativistic evidence, would have we1comed this correction and seen therein no threat at all to his doctrine of metaphysical time. Lucas emphasizes, "It is often said that relativity refuted Newton. But it is a misleading oversimplification. There is no straight opposition between relativity theories and Newtonian, absolute, theories.... Theologically (and not only theologically) speaking we may assign a preferred frame of reference, ... which is at rest. There is no reason why we should not-God may have looked, and seen that it was so, and told Newton. Only there is no physieal reason why we should."68

In short, relativity corrects Newton's concept of physical time, not his concept of

metaphysical time. CONCLUSION Of course, it hardly needs to be said that there is a great deal of antipathy in modem physics and philosophy of space and time toward such metaphysical entities as Newtonian space and time, primarily because they are physically undetectable and serve no physical purpose. In their standard text Gravitation, Misner, Thome, and Wheeler, for example, challenge Newton's metaphysic by asking, "But how does one give meaning to Newton's absolute space, find its cornerstones, mark out its straight lines?" Complaining that "his ideal geometry is beyond observation," they conc1ude, ''Newton's absolute space is unobservable, non-existent.,,69 Newton would have been singularly unimpressed with this verificationist challenge and the positivistic equation between unobservability and non-existence. From his predecessor Isaac Barrow, he had been taught, '" We do not perceive it, therefore it does not exist,' is a fallacious inference .... ,,70 The grounds for metaphysical space and time were not physical, but philosophical, or more precisely, theological, as Lucas explains:

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69

Lucas, Treatise, pp. 197-98. Later he adds, "The relativity that Newton rejected is not the relativity that Einstein propounded; and although the Special Theory of Relativity has shown Newton to be wrong in some respects, ... it has not shown that time is relative in Newton's sense, and merely some numerical measure of process"(Ibid., p. 90). C. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: W. H. Freeman, 1973), p.

19.

Isaac Barrow, The Geometrieal Leetures o/lsaae Barrow, trans. with Notes by J. M. Child (Chicago: Open Court, 1916), p. 36. 70

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CHAPTER5 The critics of Newtonian space, Leibniz (on occasion), Mach, and Einstein, urge an epistemological approach: 'How do we tell whether something is moving or at rest?' ... Newton did not feel the force of the epistemological criticism. He takes a 'God'seye' view of the universe. God is present 'from infmity to infinity' and 'governs all things, and knows all things that are or can be done.' There are no epistemological problems for God. He is 'onmipresent, who ... sees the things themselves intimately and thoroughly perceives them, and comprehends them wholly, by their immediate presence to Himself.' He knows, just knows, where everything is-more, Newton would say, He knows because He puts it there; God places each atom in its place by fiat of His willand so knows where it is because He knows what He is doing, immediately and without any room for any epistemological problem to arise. 7I

Epistemological problems fai! to worry Newton because, as Lucas nicely puts it, "He is thinking of an omniscient, omnipresent Deity whose characteristic relation with things and with space is expressed in the imperative mood."n Modern physical theories say nothing against the existence of such a God or the metaphysical space and time constituted, in Newton's thinking, by His eternity and omnipresence. What Relativity Theory did, in effect, was simply to cut God out of the picture and to substitute in His place a finite observer. "Thus," according to Holton, ''the RT [Relativity Theory] merely shifted the focus of spacetime from the sensorium of Newton's God to the sensorium ofEinstein's abstract Gedankenexperimenter-as it were, the final secularization ofphysics.,,73 But to a man like Newton, who wrote in his General Scholium, ''to treat of God from phenomena is certainly a part of 'natural' philosophy,,,74 such a secular outlook impedes rather than advances our understanding ofthe nature ofreality. And even ifwe do not go so far as Newton in including discourse about God in scientific theorizing, still it is clear that if we are prepared to draw metaphysical inferences about the nature of space, time, and spacetime on the basis of physical science, then we must also be ready to entertain theistic metaphysical hypotheses such as Newton deemed relevant.

Lucas, Treatise, p. 143. Ibid. 7J Gerald Holton, "On the Origin ofthe Special Theory ofRelativity," in Thematic Origins ofScientific Thought: Kepler to Einstein by Gerald Holton (Cambridge, Mass.: Harvard University Press, 1973), p. 171. Cf. Capek's remark that it was the "alliance of theology and cosmology" from tlie Middle Ages through the nineteenth century that provided the basis for the concept of an absolute frame of reference-an alliance broken in the twentieth century (Milic Capek, "Introduction," in The Concepts ofSpace and Time, ed. M. Capek, Boston Studies in the Philosophy of Science 22 [Dordrecht: D. Reidel, 1976], p. xxii). 74 Newton, Principia, p. 943. "Et haec de Deo; de quo utique ex Phaenomenis disserere, ad Philosophiam Naturalem pertinet." 7\

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ehave seen that for Newton God's eternity and omnipresence were ontologically foundational for his views of time and space. Unfortunately in our secular age physicists and philosophers of space and time rarely, if ever, give careful consideration to the difference God's existence makes for our conceptions of time and space. To borrow Sir Arthur Eddington's words, ''physics has in the main contented itself with studying the abridged edition of the book of nature."\ Such indifference was characteristic of Einstein himself. Only after 1930 did he begin to refer more frequently in his non-scientific writings to religious questions. But he was, in Holton's words, "quite unconcerned with religious matters during the period ofhis early scientific publications.,,2 Einstein remarked that by the age oftwelve he had lost his faith because of science and became a free-thinker. 3 Thus, he did not consider what difference theism might make to one's views oftime and space. But in a fascinating passage in his essay "La mesure de temps," Einstein's French precursor Henri Poincare does briefly entertain the hypothesis of "une intelligence infinie" and considers the implications of such a hypothesis. Poincare is reflecting on the problem of temporal succession. In consciousness, the temporal order of mental events is clear. But going outside consciousness, we confront various difficulties. One of these concerns how we can apply one and the same measure of time to events which transpire in "different worlds," that is, spatially distant events. What does it mean to say that two psychological phenomena in two consciousnesses happen simultaneously? Or what does it mean to say a supernova occurred before Columbus saw the isle of Espanola? "All these affmnations," says Poincare, "have by themselves no meaning.,,4 Then he remarks,

Arthur S. Eddington, "A Generalization of Weyl's Theory of the Electromagnetic and Gravitational Fields," Proceedings ofthe Royal Society of London A99 (1921): 108. 2 Gerald Holton, "Mach, Einstein, and the Search for Reality," in Ernst Mach: Physicist and Philosopher, ed. Rohert S. Cohen and Raymond 1. Seeger, Boston Studies in the Philosophy of Science 6 (Dordrecht: D. Reidel, 1970), p. 198; cf p. 188. 3 See also A. Einstein, "Wie ich die Welt sehe," in Mein Weltbild, ed. Carl Selig (Frankfurt: Ullstein Bücher, 1934), pp. 7-18 for Einstein's denial ofpersonalistic theism. 4 Henri Poincare, "The Measure ofTime," in The Value ofScience, 1905, trans. G. B. Halstead, in The Foundations of Science (Science Press, 19\3; rep. ed.: Washington, D. C.: University Press of America, 1982), p. 228.

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CHAPTER6 We should first ask ourselves how one could have had the idea of putting into the same frame so many worlds impenetrable to one another. We should Iike to represent to ourselves the extemal universe, and only by so doing could we feet that we understood it. We know we can never attain this representation: our weakness is too great. But at least we desire the ability to conceive an infmite intelligence for which this representation could be possible, a sort of great consciousness which should see a1I, and which should classify a11 in its time, as we classify, in our time, the IittIe we see. This hypothesis is indeed crude and incomplete, because this supreme intelligence would be only a demigod; infinite in one sense, it would be Iimited in another, since it would have only an imperfect recollection of the past; it could have no other, since otherwise a11 recollections would be equally present to it and for it there would be no time. And yet when we speak of time, for a11 which happens outside of us, do we not unconsciously adopt this hypothesis; do we not put ourselves in the place of this imperfect god; and do not even the atheists put themselves in the place where God would be if he existed? What I have just said shows us, perhaps, why we have tried to put a11 physical phenomena into the same frame. But that cannot pass for a defmition of simultaneity, since this hypothetical intelligence, even if it existed, would be for us impenetrable. It is therefore necessary to seek something else. S

Poincare here suggests that,- in considering the notion of simultaneity, we instinctively put ourselves in the place of God and classify events as past, present, or future according to His time. Poincare does not deny that such a perspective would disclose to us true relations of simultaneity. But he rejects the hypothesis as yielding a definition of simultaneity because we could not know such relations; such knowledge would remain the exclusive possession of God Himself. But clearly, Poincare's misgivings are relevant to a definition of simultaneity only if one is presupposing some sort of verificationist theory of meaning, as he undoubtedly was. The fact remains that God knows the absolute simultaneity of events even if we grope in total darkness. Nor need we be concemed with Poincare's argument that such an infinite intelligence would be a mere demigod, since it is a non sequitur that a being with perfect recollection of the past cannot be temporal. There is no conceptual difficulty in the idea of a being which knows all true past-tense propositions. That such a being would be temporal is evident from the fact that as events transpire, more and more past-tense propositions become true, so that the content of his knowledge is constantly changing. 6 Hence, it does not follow that if God is temporal, He cannot have perfect recollection of the past. Poincare's hypothesis suggests, therefore, that God's present is constitutive of relations of absolute simultaneity. J. N. Findlay was wrong when he said, " ... the influence which harmonizes and connects all the world-lines is not God, not any featureless, inert, mediwn, but that living, active interchange called ... Light, offspring ofHeaven firstbom.,,7 On the contrary, the use oflight signals to establish clock synchrony is a convention which finite and ignorant creatures have been Ibid., p. pp. 228-229. If one takes propositions to be tenselessly true or God's knowledge to be non-propositional, it still follows that God's de se knowledge is constantly changing. For discussion, see my Divine Foreknowledge and Human Freedom (Leiden: E. J. Brill, 1990), Introduction. 7 J. N. Findlay, "Time and Etemity," Review ojMetaphysics 32 (1978-79): 6-7.

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obliged to adopt, but the living and active God, who knows all, is not so dependent. In God's temporal experience, there is a moment which is present in metaphysical time, wholly independently of physical clock times. He would know, without any dependence on clock synchronization procedures or any physical operations at all, which events were simultaneously present in metaphysical time. He would know this simply in virtue of His knowing at every such moment the unique set of presenttense propositions true at that moment, without any need of a sensorium or physical observation ofthe universe. The question now presses: how, then, does God's metaphysical time relate to our physical time? From what has been said thus far, it seems that God's existence in tensed, metaphysical time and His real relation to the world imply that a LorentzPoincare theory of relativity is correct after all. For God in the "now" of metaphysical time would know which events in the universe are now being created by Him and are therefore absolutely simultaneous with each other and with His ''now.'' The argument may be formulated as folIows: 1. God exists. 2. A tensed theory of time is correct. 3. If God exists and a tensed theory of time is correct, then God is in time. 4. If God is in time, then a privileged reference frame exists. 5. If a privileged reference frame exists, then a Lorentz-Poincare theory of relativity is correct. In this study we are taking (1) for granted, though I have tried to justify it elsewhere. 8 Similarly I have argued extensively for the truth of (2) in my companion volumes on the tensed vs. tenseless conceptions of time. In Part I, Section 11 of the present work, I attempted to justify (3) on the basis of divine omniscience and God's real relation to the world. The truth of(4) is based on God's privileged status; the events which He knows to be occurring now can be associated with some hypothetical reference frame which is preferred precisely because it is God's frame. In speaking of God's frame, I mean merely that it is the reference frame on whose associated hyper-plane of simultaneity at the time of any event on the world line of a hypothetical observer at rest in that frame lie those events which God in the ''now'' ofmetaphysical time knows He is then creating. 9 Now it needs to be understood that we are speaking here in the context of SR, which posits a flat spacetime. When we come to GR, which allows a variable curvature due to the presence of mass-energy, it is possible that the events which God knows to be See William Lane Craig, The Kalam Cosmological Argument, Library of Philosophy and Religion (London: Macmillan, 1979); William Lane Craig and Quentin Smith, Theism, Atheism and Big Bang Cosmology (Oxford: Clarendon Press, 1993). 9 I do not mean to endorse Newton's view that God exists spatially. See the sequel.

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simultaneous cannot be gathered into a single inertial frame. In that case, as Lucas and Hodgson explain, the set of events known by God to be simultaneous would constitute a three-dimensional hyper-surface in spacetime, but not a hyper-plane: Only if it were a hyper-plane would it constitute the canon of simultaneity of some inertial frame of reference. Otherwise there would be no world-wide inertial frame of reference, but only different ones for different pairs of events. Instead of the flat spacetime of the Special Theory, we should be having to do with a curved one in which the significant hyper-surfaces were not hyper-planes. But that ... is something we have been forced to countenance in the General Theory anyhow. 10

A discussion of God's relation to time within the context of GR may be reserved for the sequel; our present concern is with the flat spacetime of SR. Within that context, the events which God knows He is now causing alllie on a three-dimensional hyperplane which is associated with some inertial frame. In virtue of that frame's simultaneity relation's being God's, that frame is plausibly privileged. But if there is a privileged frame, then Lorentz and Poincare were right, as (5) states. Einstein's SR presupposes that no such frame exists and therefore cannot be correct. The postulation of a privileged frame is sufficient for some sort of "aether compensatory" theory, even if the so-called aether just is the three-dimensional privileged space. This privileged frame would be associated with a physical time which would constitute, as Newton put it, a sensible measure of God's metaphysical time. Lorentz's understanding of Relativity Theory is well-suited to play the role ascribed to it by the above argument. It is one ofthe marks ofLorentz's genius that he stood out virtually alone among the major figures of early twentieth century physics in resisting the pervasive positivistic epistemology which lay at the root of Einstein's SR. Gracious almost to a fault, Lorentz always spoke appreciatively of Einstein's alternate approach and lectured sympathetically on both SR and GR, while remaining fmally unconvinced that Einstein had abolished the classical conceptions of time and space. A major reason that Lorentz remained unconvinced was that he was not a positivist. In 1913 he wrote, According to Einstein it has no meaning to speak of motion relative to the aether. He Iikewise denies the existence of absolute simultaneity. It is certainly remarkable that these relativity concepts, also those conceming time, have found such a rapid acceptance. The acceptance of these concepts belongs mainly to epistemology.... It is certain, however, that it depends to a large extent on the way one is accustomed to think whether one is attracted to one or another interpretation. As far as this lecturer is concemed, he finds a certain satisfaction in the older interpretations, according to which the aether possesses at least some substantiality, space and time can be sharply separated, and simultaneity without further specification can be spoken of. In regard to this last point, one may perhaps appeal to our ability of imagining arbitrarily large velocities. In that way, one comes very elose to the concept of absolute simultaneity.

10

120.

1. R. Lucas and P. E. Hodgson, Space/ime and Elec/romagne/ism (Oxford: Clarendon Press, 1990), p.

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Finally, it should be noted that the daring assertion that one can never observe velocities larger than the velocity of light contains a hypothetical restriction of what is accessible to us, [a restriction1which cannot be accepted without some reservation. 11

Here Lorentz clearly discems the crucial role played by Einstein's verificationist theory of meaning and rejects it. In defense of absolute simultaneity, he appeals to the use of arbitrarily fast signals, even though they are not presently observable. He quite rightly disregards the assumption that it is meaningless to speak of such unobservables. EIsewhere Lorentz affirms that it makes sense, if there is an aether, to speak of motion relative to it even if observers could not detect such motion. 12 Hewrites, But it needs to be clearly recognized that A could never assure hirnself of the immobility in the ether which we have attributed to hirn by supposition and that physicist B could with the same right, or rather with the same absence of right, claim that it is he who finds hirnself in these privileged circumstances. This incertitude, this impossibility of even disclosing a movement in relation to the ether, led Einstein and numerous other modern physicists to abandon completely the notion of an ether. There, it seems to me, is a question toward which each physicist must take a position which best accords with the manner of thinking to which he is accustomed. JJ

Lorentz clearly feIt no obligation to abandon what seemed to him meaningful notions out of deference to a verificationist epistemology. The subsequent collapse of positivism has vindicated him with respect to this conviction and left his approach to problems of space and time, in contrast to Einstein's, unshaken by this epistemological revolution. Second, Lorentz's conception of the aether was virtually equivalent to space itself. His aether was so dematerialized that Einstein, lecturing at the University of Leiden in 1920, as we have seen, could tease the Dutch physicist by declaring, "As regards the mechanical nature of Lorentz's aether one might say of it, with a touch of humor, that immobility was the only mechanical property which H. A. Lorentz left it.,,14 Later Einstein would speak of Lorentz's "great discovery," namely, that all the phenomena of electromagnetism then known could be explained on the basis oftwo assumptions: that the aether is firmly fixed in space-that is to say, unable to move at all-and that electricity is ftrmly lodged in the mobile elementary

JJ H. A. Lorentz, A. Einstein, H. Minkowski Das Relativitätsprinzip, Fortschritte der mathematischen Wissenschaften 2, mit Anmerkungen von A. Sommerfeld und Vorwort von O. BlumenthaI (Leipzig: 8. G. Teubner, 1913), p. 23 (pais translation). 12 H. A. Lorentz, "Het relativiteitsbeginsel. Voordrachten in Teyler's Stichtung," Archives Musee Teyler 2 (1914): 26. See the outstanding historical study by Jozsef I1\y, "Einstein Teaches Lorentz, Lorentz Teaches Einstein. Their Collaboration in General Relativity, 1913-1920," Archive lor History 01 Exact Sciences 39 (1989): 272, who comments, "Lorentz distinguishes the existence of astate of motion from its observability-a distinction void of meaning according to Einstein. " 13 H. A. Lorentz, "Considerations elementaires sur le principe de relativite," Revue generale des Sciences 25 (1914): 179ff, in H. A. Lorentz, Collected Papers, ed. P. Zeeman and A. D. Fokker (The Hague: Martinus Nijhoff, 1934),7: 165. 14 A. Einstein, ither und Relativitätstheorie (Berlin: Julius Springer Verlag, 1920), p. 7.

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particles. 1S "Today bis discovery may be expressed as folIows: physical space and the ether are only different tenns for the same thing: fields are physical states of space.,,16 For Lorentz the aether just is the privileged spatial frame. He thus accepts a 3+ 1 ontology of spatial objects enduring through time, a metaphysic which is wellsuited to a tensed theory of time. Third, Lorentz distinguished true time, wbich was measured by a clock at rest in the aether frame, from merely local time and ascribed to events absolute simultaneity in true time. Writing in 1910, he contrasted bis view with Einstein 's: Assume there were an aether; then there would be among a11 systems x, y, z, tone singled out in that the coordinate axes as weil as the clock is at rest in the aether. If one conjoins with this the idea ... that space and time are something wholly different and that there is a 'true time' (simultaneity would then exist independently of location, in accord with the circumstance that it is possible for us to conceive of infinitely great velocities), then one easily sees that this true time would have to be indicated just by c10cks which are at rest in the aether. If, then, the principle of relativity were generally valid in nature, then one would not be in a position to determine whether the coordinate system employed is that distinguished one. One thus comes to the same results as when one in agreement with Einstein and Minkowski denies the existence of the aether and the true time and treats a11 coordinate systems as equivalent. Which of the two modes of thought one may agree with is best left to the individual. 17

IS A. Einstein, "The Problem of Space, Ether, and the Field in Physics" [Mein Weltbild, 1934], in Ideas and Opinions, trans. Sonja Bargmann (New York: Crown Publishers, 1954), p. 281. So also Tetu Hirosige, "Origins of Lorentz' Theory of Electrons and the Concept of the Electromagnetic Field," Historical Studies in the Physical Sciences I (1969): 197; idem, "The Ether Problem, the Mechanistic Worldview, and the Origins of the Theory of Relativity," Historical Studies in the Physical Sciences 7 (1976): 69. 16 Einstein, "Space, Ether, and the Field," p. 281. I am skeptical that Lorentz would have agreed that fields are physical states of space rather than that physical fields exist in space. Lorentz held to the classical conceptions of time and space. 17 H. A. Lorentz, "Alte und neue Fragen der Physik," Physikalische Zeitschrift 11 (1910): 1234ff, in Collected Papers, 7: 211. Notice that Lorentz eschews operational definitions of time and does not equate time with c10ck readings. This is particularly evident in his failure to ascribe at first physical reality to his local times. He recalled, "I had the idea that there was an essential difference between the systems x, y z, t and x', y', z', t'. In one one uses-such was my thought-coordinate axes which have a fixed position in the aether and which one can call the 'ttue' time; in the other system, on the other hand, it would be a matter of mere auxiliary quantities whose introduction is nothing but a mathematical artifice. In particular, the variable t' could not be called 'time' in the same sense as the variable t" (H. A. Lorentz, "Deux memoires de Henri Poincare sur la physique mathematique," Acta mathematica 38 (1914): 293ff, in Collected Papers, 7: 262. Eventually Lorentz came to see the reality of c10ck retardation. But even the readings of a clock at rest in the aether are but a sensible measure of true time, not definitive of true time. IIIy comments, "When he says that 'we make the readings of... clocks match our fundamental conception oftime' he implies that time is not to be identified with the mere reading of clocks, in the way that Einstein defmed time in his relativistic paper of 1905; consequently measurements cannot be interpreted without some previous agreement upon fundamental concepts; measurements may not be used for defining time (and space)" (IlIy, "Einstein Teaches Lorentz," p. 275).

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Lorentz, realizing that bis aether compensatory theory is empirically equivalent to the Einstein-Minkowski theory, leaves it up to the individual to choose wbich he shall adopt. But Lorentz preferred the c1assical conceptions of time and space on metaphysically intuitive grounds, as he made c1ear in bis 1922 lectures at Cal Tech: All our theories help us form pictures, or images, of the world around us, and we try to do this in such a way that the phenomena may be coordinated as weil as possible, and that we may see clearly the way in which they are connected. Now in forming these images we can use the notions of space and time that have always been familiar to us, and which I, for my part, consider as perfectly clear and, moreover, as distinct hom one another. My notion oftime is so definite that I clearly distinguish in my picture what is simultaneous and what is not. 11

Here Lorentz quite rightly refuses to jettison the intuitively obvious reality of absolute simultaneity among events in the world just because one cannot determine which spatially separated events are simultaneous or because Einstein's operationally re-defined notion of simultaneity is relative to reference frames. Moreover, he sees no good reason to scrap the intuitive distinctness of space and time in favor of Minkowski's unified reality, spacetime. It seems to me that Lorentz was quite justified in sticking with bis intuitions and, moreover, that bis intuitions were right on target. In any case, the ease with wbich bis approach can be assimilated with our direction of thought is obvious. Finally, Lorentz himself hinted at a theological application of bis ideas. In January of 1915 Lorentz, convinced that Einstein's work on GR was quite compatible with the notion of a privileged aether frame, wrote to Einstein in response to the latter's paper "The Formal Foundations of the General Theory of Relativity.,,19 In a passage redolent of the General Scholium and Opticks of Newton, Lorentz broached considerations whereby "I cross the borderland of physics": A 'World Spirit' who, not being bound to a specific place, permeated the entire system under consideration or 'in whom' this system existed and who could 'feel' irnmediately all events would naturally distinguish at once one of the systems U, U', etc. above the others. 20

18 H. A. Lorentz, Problems 0/ Modern Physics, ed. H. Bateman (Boston: Ginn, 1927), p. 221. Here Lorentz identifies himself as a physicist of the old school who says, 'I prefer the time that is measured by a clock that is stationary in the ether, and I consider this as the true time, though I admit that I cannot make out which ofthe two times is the right one, that of A or that ofB' (Ibid.). I' A. Einstein, "Die formale Grundlage der allgemeinen Relativitätstheorie," Physikalische Zeitschrift 14 (1913): 1249-1262. 20 H. A. Lorentz to A. Einstein, January, 1915, Boerhaave Museum, cited in llIy, "Einstein Teaches Lorentz," p. 274. The text reads, "Ein 'Weltgeist,' der ohne an einem bestimmten Ort gebunden zu sein, das ganze betrachte System durchdränge, oder 'in dem' dieses System bestände, und der unmittelbar alle Ereignisse 'fühlen' könnte, würde natürlich sofort eins der Systeme U. U', u.s.w. vor den anderen auszeichnen." See comment by A. J. Knox, "Hendrik Antoon Lorentz, the Ether, and the General Theory ofRelativity," Archive/or History o/Exact Sciences 38 (1988): 75.

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Such a being could "directly verify simultaneity.,,21 Here we see from Lorentz's own hand the integratability of bis approach to Relativity Theory with a theological perspective such as we have enunciated. I do not mean to suggest, of course, that we should return to Lorentz's own, defunct electron theory. As Zahar has pointed out,22 that theory was doomed by the advent of quantum physics. But Lorentz's own attempted explanation of the phenomenon of length contraction is incidental to bis basic approach. By 1908 Lorentz had already realized the incompatibility ofbis electron theory with Planck's quantum hypothesis, and by the 1911 Solvay Congress there was a general sense that the electron theory would have to be radically reformed in light ofthe advent of quantum physics. 23 Nonetheless, Lorentz continued to adhere to an approach to Relativity Theory wbich preserved the c1assical notions of space and time. A theory may be c1assified as Lorentzian just in case it affirms (i) physical objects are ndimensional spatial objects which endure through time, (H) the round trip vacuum propagation of light is isotropic in a preferred (absolute) reference frame Ro (with speed c= 1) and independent of the velocity of the source, and (Hi) lengths contract and time rates dilate in the customary special relativistic way only for systems in motion with respect to Ro.24 In light of our foregoing argument, any metaphysically adequate theory of space and time must be Lorentzian in this sense. In order to avoid confusion with Lorentz's original electron theory, we may call such theories neo-Lorentzian. ALTERNATIVES TO A NEO-LORENTZIAN APPROACH It seems to me, therefore, that the theist should fmd a neo-Lorentzian approach to Relativity Theory quite attractive. Nonetheless, I must confess that I fmd the conc1usion to our argument somewhat disquieting, not because I do not believe it to be true, but rather because Einstein's SR is so deeply ingrained today-indeed, it seems, as deeply ingrained as were the c1assical views of time and space in the nineteenth century-that many persons fmd it difficult to look at the world another way and might therefore reject theism rather than embrace a neo-Lorentzian theory of relativity.25 It therefore behooves us to see if we can fmd a way out for such thinkers.

Lorentz to Einstein. Elie Zahar, "Why Did Einstein's Progranune Supersede Lorentz's CI & II)?," Brilish Journal/or the Philosophy 0/ Science 24 (1973): 95-123, 223-262. 23 See Russell McConnmach, "H. A. Lorentz and the Electromagnetic View ofNature," Isis 61 (1970): 486-488. 24 See A. K. A. Maciel and 1. Tiornno, "Analysis of Absolute Spacetime Lorentz Theories," Foundations o/Physics 19 (1989): 507-508. 25 Fitzgerald, for exarnple, advises that process philosophers should "reject the God of the Privileged Simultaneity-System," not because we lack clear-cut empirical consequences from such a hypothesis, but "because it is an unnecessary departure from the spirit of relativity theory" (I'aul Fitzgerald, "Relativity Physics and the God of Process Philosophy," Process Studies 2 [1972]: 258). But I see no reason why 21

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Alan Padgett has proffered a novel analysis of divine eternity which he calls ''relative timelessness," according to which God exists in tensed time, but not in any measured time. 26 He adopts Carnap's three rules for the metrication of time: (i) Addivity: when two measured durations are added together, the sum of their given units will equal the length of time which the two durations would take up if they were juxtaposed. (ii) Equality or Congruence: Only if the durations measured by one's standard clock are isochronous, that is, equal to each other, will it yield a metrication properly applicable to all of spacetime. (iii) Unit Rule: Some natural periodic process is chosen as a standard of temporal measure, and the temporal unit is defined in terms of it. Where these three rules cannot be applied, says Padgett, it will not be possible to develop any measured time. 27 The above conditions make it evident that Carnap was laying down conditions for physical, metric time, not simply metric time, as Padgett assumes. For Newton, metaphysical time, God's time, possesses an intrinsic metrication and therefore is not dependent for its metric upon a standard clock or a natural periodic process. Kroes explains, To Newton it was self-evident that there exists just one fundamental metric for time: the intrinsic metric of absolute time. Physical processes of whatever kind could provide a more or less accurate 'sensible measure' thereof. A 'true' sensible measure of absolute time could only be reached in the case of a perfectly isolated, completely undisturbed periodical system which would constitute an ideal clock. In a certain sense, all physical processes had to obey, according to Newton, the rhythm of absolute time: an ideal clock, of whatever nature (mechanical, gravitational, etc.) could provide an exact measure of the unique, fundamental metric of absolute time. 28

Hence, what Padgett is actually arguing is that God is not in any physical, metric time, even though He does exist in metaphysical time. Whether God's metaphysical time is also a metric time remains an open question, since Padgett completely overlooks Newton's alternative. 29 theists should be unduly concemed about departing from the spirit of a positivistic theory which takes no cognizance ofGod's existence. 26 Alan G. Padgett, "God and Time: Toward a New Ooctrine of Divine Timeless Etemity," Religious Studies 25 (1989): 209-215; cf idem, God, Eternity and the Nature ofTime (New York:St. Martin's, 1992), pp. 122-146. He has been followed by Richard Swinbume, "God and Time," in Reasoned Faith, ed. Eleonore Stump (Ithaca, N. Y.: Comell University Press, 1993), pp. 204-222, though Swinbume holds that God exists in cosmic time. 27 Padgett, God, Eternityand Time, pp. 7-10. 28 Peter Kroes, Time: fts Structure and Role in Physical Theories, Synthese Library 179 (Dordrecht: O. Reidel, 1985), p. 49. 29 In reply to an earlier critique, Padgett recurs to Grünbaum's argument for conventionalism based on time's being a continuum in order to show that time itself, God's time, has no intrinsic metric (Alan G. Padgett, "Can History Measure Etemity? A Reply to William Craig," Religious Studies 27 [1991]: 334). But Grünbaum's argument has received devastating criticism (paul Gordon Horwich, "On the Metric and Topology ofTime" [Ph. D. Dissertation, Comell University, 1975], chap. 3; Philip L. Quinn, "Intrinsic Metrics on Continuous Spatial Manifolds," Philosophy of Science 43 [1976]: 396-414; Richard Swinbume, critical notice of Geometry and Chronometry in Philosophical Perspective, by Adolf Grünbaum, British Journal for the Philosophy of Science 21 [1970]: 308-311; Graham Nerlich, The Shape ofSpace [Cambridge: Cambridge University Press, 1976], chap. 8) and so provides no grounds for

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On the basis of the above conditions, Padgett presents two considerations in favor of bis contention that God is not in any measured time: (i) God is not subject to the laws of nature, as anything in measured time must be. Since God is the Creator of the natural order itself, He is not subject to any of nature's laws. Indeed, God could alter the laws that do obtain. Moreover, as a free agent, God does not conform to anY order of nature that would cause Him to repeat the same process over and over again in a uniform manner, as an isochronic clock is supposed to do. Padgett entertains the objection that while God Himself may not be subject to nature's laws and may act in what would be, in effect, a random way, still He can be in measured time because the cosmic time of our universe may act as a clock to measure God's time. Suppose, for example, that between events el and e2 one hour of cosmic time elapses; would it not be true to say that one hour of God's time has elapsed? The response to this objection comes in Padgett's second point: (ii) Any measured time is relative to a particular reference frame, which need not apply to God. Thus, from the fact that the duration between el and e2 is one hour relative to one reference frame it does not follow that the duration between them is one hour in God's time. If for observers associated with different inertial frames in our own spacetime, el and e2 are not invariably separated by one hour's time, how can we insist that the duration between them must be one hour in God's time? Moreover, God could create a thousand universes, all with different times. Cosmic time is contingent and applies to our universe alone. We cannot assume that it applies to anything beyond or outside our universe unless some method of synchronization is set up. But no synchronization can be established with God's time, since He is not subject to the laws of nature. Thus, God is not in any measured time. Still, Padgett admits, God's time cannot be unrelated to our measured time, for God causally sustains the universe. If both cause and effect are temporal, then the cause must be either before or simultaneous with the effect. But then they must be in the same time. Since God is causally related to the world, God and the world must exist in the same time. Since God is not in any measured time, the world must therefore be in God's time. We are, Padgett concludes, in God's time. This is an interesting view of divine eternity which relativistically-inclined thinkers might find quite congenial. It purports to allow one to maintain an Einsteinian interpretation of Relativity Theory and to hold that God exists in a metaphysical time in which all relativistic, physical times exist. Unfortunately, it seems to me that Padgett's view ofthe relation of God's time to physical time is incoherent. Consider Padgett's first objection to God's being in physical, metric time. As Padgett's hypothetical interlocutor discems, God's not being subject to nature's laws is irrelevant to whether God is in physical, metric time. It is not the process to be measured, but one's clock that must be denying an intrinsic metric to time. Earman speaks for the majority when he concludes, "Therefore, I do not see how the contrast between the discrete and the continuous provides any support for or helps to explain the meaning of Grünbaum's metrical amorphous thesis" (John Earman, "Who's Afraid of Absolute Space?" Australasian Journal 0/ Philosophy 48 [1970): 316).

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isochronically periodic. Any conventionally adopted metrication based on a periodic process in the physical world can be applied to God as to any random series of events. God's time need not have any intrinsic metric associated with it in order to be physically measured according to some conventionally adopted metric. That brings us to Padgett's second point, that measured times are relative to reference frames. This statement is misleading. It is true that in SR physical time is relative to reference frames insofar as distant simultaneity relations are concemed; but the metric of time is not relative to a frame of reference. Padgett denies that the metric of physical time applies to God's time: for us 1997 and 1998 are (approximately) isochronous, but for God they are not. Padgett has apparently confused time dilation with variability of the metric, which is simply erroneous. A moving, standard cIock runs slow, but the intervals it measures are still isochronous. There is no reason to think that the cIock at rest in the privileged frame would somehow record isochronous intervals for us but not for God. Moreover, insofar as the relativity of simultaneity is concemed, the inference that no one of the times associated with physical reference frames measures God's time is based on the tacit assumption that no one of these frames is privileged. Padgett agrees that there is in God's time a unique set of physical objects that now exist for Him and are simultaneous with, because caused by, His creatorial activity. All these things exist at the same moment of metaphysical time. Since a signal of infinite, invariant velocity would connect events occurring at the same moment, we can represent the unique set of events in spacetime which are present for God as all events lying on a hyper-plane of simultaneity determined by absolute synchronization based on signals of inftnite, invariant velocity (Figure 6.1).

x

Figure 6.1. All events which are present in God's metaphysical time He on a hyper-plane in spacetime.

But the simultaneity plane so determined is identical in SR spacetime with the simultaneity plane of an ob server associated with an inertial frame in which an exchange oflight signals determines el and e2 to be simultaneous (Figure 6.2).

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x

Figure 6.2.

A hyper-plane of simultaneity determined by standard synchronization procedures coincides with the hyper-plane comprised of events present for God.

The reference frame displayed in Figure 6.2 is, in effect, Poincare's aether rest frame, and the corresponding simultaneity relation the relation known by Poincare's "inftnite intelligence," who classiftes everything in his time. The measured time associated with this frame thus constitutes a sensible measure of God's time. An ideal clock at rest in this frame therefore records God's time as well as the time of its frame. It is irrelevant whether such a frame exists physically in the universe (that is to say, whether some actual object really is at rest in such a frame); the point is that such a frame can be specifted and hypothetical ob servers and ideal docks associated with it. Nor is the notion of costnic time (a technical concept to be discussed in the sequel) here relevant; the specifted frame may or may not ftt into a costnic time. The relevant point is that although physical, metric time is relative to reference frames in SR, the time associated with some reference frame will be privileged because its simultaneity relations coincide with the simultaneity relations in God's time, and, therefore, it gives the correct measure of God's time. The conjecture of other universes is not relevant, for in those worlds, too, privileged reference frames would exist, and all the privileged frames would each give their own, correct metrication to God's time. It is not to be expected that a reference frame in this universe has application to a different universe. God knows what all the privileged frames are, even if this is impenetrable to uso Thus, it seems that we are forced back to a neo-Lorentzian theory whereby a privileged frame exists. 30 But perhaps we have overlooked Einstein's most fundamental metaphysical revision: his denial of metaphysical space. We have seen that, given the reality of tensed time, God must exist in time; but contra Newton there seems to be no comparable necessity of His existence in metaphysical space. In Newton's view, God's etemality and omnipresence entail the existence of an inftnite, metaphysical 30 In his "Can History Measure Etemity?", p. 333, Padgett agrees that there is a privileged "now" which is coincident with God's "now." But that is all that is needed to establish my point that a neo-Lorentzian theory of relativity is correcl.

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time devoid of physical events and an infinite, metaphysical space devoid of physical objects prior to His creation ofthe universe. We may let pass for now the inference concerning inftnite time; but I should like to challenge at this point Newton's inference from God's omnipresence to the etemal existence of inftnite space. Newton's conclusion in this regard seems to be a multiple non sequitur. First, just as "omnitemporal" implies, not "existing throughout infinite time," but "existing at every moment in time that there is" (which is not incompatible with time's having begun and being fInite),3l so "omnipresent" implies, not "existing throughout inftnite space," but "existing at every point in space that there is" (which is not incompatible with space's being curved and fInite). Second, even if omnipresence implied existing throughout infinite space, it would not follow that that inftnite space exists for infInite time. Space could have a fInite temporal duration and have been created by God, who existed in metaphysical time prior to His creation of space. Similarly, God could annihilate space after a ftnite time and continue to exist in metaphysical time in its absence. In either or both cases, He would in such worlds be omnipresent so long as He existed at every point in space that ever exists. Third, it is by no means evident that God must exist in space at alL Since He is incorporeal, He cannot exist in space as an extended object analogous to the aether. There is no parallel argument that in virtue of His being really causally related to objects in space God must be spatial, as His being really causally related to events in time implies His temporality. Thomas Aquinas held God to be omnipresent in the sense that He is cognizant of and causally active at every point in space. 32 That seems to be a coherent view which does not imply God's spatiality or, as a concomitant, the existence of metaphysical space. Thus, there is no good reason, so far as we have seen, to think that God's existence entails the existence of space. So perhaps Einstein, despite his defective epistemology, just happened serendipitously to get it right: there is no metaphysical space. In that case, there is just a multiplicity of different reference frames with no background frame in which they all exist. Is it possible to hold that God exists in metaphysical time but that no reference frame of metaphysical space exists, so that events which are simultaneous in God's "now" cannot be integrated into a single frame? Since physical time is relative to reference frames, if there were no reference frame embracing all and only events which are metaphysically present, then Padgett's view that God is not in any physical, measured time would be defensible. But even this escape route will not seem to work. For while metaphysical space is a sufficient condition of metaphysical time, it is not a necessary condition. As Friedman explains, absolute space is not in fact an essential ingredient of a See Quentin Smith, "A New Typology of Temporal and Atemporal Permanence," NoZls 23 (1989): 310-312. 32 Thomas Aquinas Summa contra gentiles 3.1.68. The furthest one could go toward an immanentist view of omnipresence and still remain orthodox would be to hold that God's consciousness is diffused throughout space even as mine is localized in space, without in either case asserting that consciousness is a spatial object. 31

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Newtonian spacetime theory.33 One may obtain a so-called Galilean spacetime by keeping absolute simultaneity but dropping the hypothesis of absolute space. On such a theory there exist hyper-planes of absolute simultaneity in the universe, but observers associated with different inertial frames will calculate events to be occurring at different points in space and at different spatial distances from each other, unless they occur on the same plane of simultaneity. Events on different hyper-planes of absolute simultaneity will be regarded as occurring at different places because the various observers will be unable to agree whose world-lines represent an observer at rest and whose an observer in motion (Figure 6.3).

Y2

Yl

Y3

51 52

(a)

53

X3

X2

Xl

Y3 51 52

(b)

53

Xl

X2

X3

Figure 6.3. Galilean spacetime. In the absence of absolute space either the xobservers (a) or the y-observers (b) can be considered to be at rest. Onlyon planes of simultaneity Si will events occur at the same location in both inertial frames.

Friedman points out that this alternative theory accomplishes everything that Newton's original theory wanted to, but that Newton could not have known this, since it is only by means of mathematical operations unknown in Newton's day that we can see the theoretical dispensability of absolute space. Michael Friedman, Foundation ojSpacetime Theories (Princeton: Princeton University Press, 1983), pp. 87, 108-11 S. Tbe theory without absolute space, but with absolute time, is still inadequate because it predicts a false result for the Michelson-Morley experiment; physical time must be relativized as weil. 33

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Such a Galilean theory reveals that even in the absence of metaphysical space, there would exist spatial hyper-planes of absolute simultaneity determined by the ''now'' of God's metaphysical time. Therefore, if any such theory is to be empirically adequate, a Lorentz-FitzGerald contraction and retardation of moving clocks will have to be posited. In that crucial sense such a Galilean theory would still be neo-Lorentzian. Perhaps, then, an even more radical solution is required: a sort of Metaphysical Theory ofRelativity.34 Perhaps a theorist oftensed time could maintain that God's time is analogous to the frame-dependent time of observers in the universe in that it is valid only for His metaphysical "frame of reference. " In terms of reality as a whole, there is no "frame of reference" which embraces both God's time and all physical times and so serves to correlate them in a preferential manner. Reality is thus radically disjointed; it falls apart temporally just as completely as do the clock times associated with relatively moving inertial frames. God's ''frame ofreference" is no more privileged than any physical reference frame in the universe and, hence, His classification of wbich events are occurring ''now'' no more privileged than any finite observer's classification ofwhich events are simultaneous with bis "now." On such a Metaphysical Theory ofRelativity, the Einsteinian interpretation ofRelativity Theory can be preserved because none of the clock times associated with physical inertial frames is privileged. Physical relativity is preserved even though a metaphysical time exists because a thorough-going Metaphysical Relativity is posited which makes it impossible to unite God's time with physical time in any preferential way. Closely related to such a Metaphysical Theory of Relativity is the proposed reconciliation of absolute becoming with Relativity Theory supported by many defenders of tensed time, namely, the relativization of becoming to reference frames. According to such thinkers, SR and the tensed theory of time are not incompatible because, just as we relativize simultaneity to reference frames, so should we relativize reality and becoming to reference frames. (This solution can be formulated in the terminology, if not the ontology, of either aspace and time interpretation of SR or aspacetime interpretation of SR.) Thus, Howard Stein,3S in response to Putnam's claim that SR has eliminated the notion of becoming, asserts that this notiori may be epitomized as follows: 34 Such a view of God's relationship to time has actually been advocated by one philosophical theologian, Keith Ward, RIltional Theology and the Creativity 0/ God (OKford: Basil Blackwell, 1982), pp. 165-167. Ward conceives of God as existing not only in His own time, but in a11 frame-relative times as weil, which are a11 mutually incommensurable. Ward, however, seems to have abandoned this view in his Religion and Creation (OKford: Clarendon Press, 1996), pp. 301-303, where he plumps for absolute simultaneity and a privileged cosmic time as God's time. 3S Howard Stein, "On Einstein-Minkowski Spacetime," Journal 0/ Philosophy 65 (1968): 14. See also Milic Capek, "The Inclusion ofBecoming in the Physical World," in Concepts o/Space and Time, ed. M. Capek, Boston Studies in the Philosophy of Science 22 (Dordrecht: D. Reidel, 1976), pp. 501-524; K. G. Denbigh, "Past, Present, and Future," in The Study o/Time II/, ed. J. T. Fraser, N. Lawrence, and D. Park (Berlin: Springer Verlag, 1978), p. 309. For a theological application, see Lewis S. Ford, "Is Process Theism Compatible with Relativity Theory?" Journal 0/ Religion 48 (1968): 124-135.

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For an event at spacetime point a, those events, and only those, have already become (real or determinate), which occur at points in the top010gical c10sure of the past of a. According to this explication, reality is relative to spacetime points and consists in all those events lying inside or on the past-directed light cone of a, inc1uding a itself. According to Stein, in the context of SR we can only think of the temporal evolution of the world from the chronological perspective of each spacetime point. There exists no knife-edge of becoming on this view, even for individual reference frames, but mere pinpoints of becoming constituted by the vertex of any hypothetical observer's past light cone, none of which is privileged. 36 In the same way that temporal simultaneity is relative, so also is temporal becoming. I have elsewhere discussed a number of problems with such a reconciliation of SR and objective temporal becoming. 37 But nowa further difficulty arises. Which events does God experience as present? Since He does not exist at a unique spacetime point, but at all if any, Stein's definition does not apply to Hirn. Intuitively, the events which God experiences as present are those events which He is causally preserving in being, or actualizing, in the "now" of metaphysical time. But if we conceive of God as causally producing in being a set of events lying on a unique hyper-plane of spacetime, then we seem to be back to Poincare's view of an infinite intelligence whose classification of events as present is privileged. For surely His role as the continuing Creator of the universe in every successive moment would entitle Him to regard His "frame of reference" as privileged and therefore as yielding the absolute ontology. Moreover, SR requires that the time order among causally related events is absolute, so that God's creatorial act would be absolutely simultaneous with the events He is creating, thus yielding a preferred foliation of spacetime corresponding to successive divine acts of conservation. 38 If, therefore, we are to preserve Metaphysica1 Relativity, it seems that we must hold that God does not in metaphysical time actualize successively slices of spacetime, but that in His metaphysical time He knows the relative "now's" of every reference frame and what is real for each one and so actualizes reality relative to each reference frame. This is not a tenseless theory of time. For God is conceived of as enduring through metaphysical time even though He is not creating the states of the universe successively in metaphysical time, and becoming is real, albeit relative to reference frames. This is, in fact, a sort of Stump-Kretzmann view of divine eternity (except that here God's duration is temporal, not atemporal). On this view, God does not successively bring into being slices of spacetime, but actua1izes reality relative to

36 See Rob Clifton and Mark Hogarth, "Tbe Defmability of Objective Becoming in Minkowski Spacetime," Synthese 103 (1995): 355-387. 31 See my The Tenseless Theory ofTime: a Critical Examination, Synthese Library (Dordrecht: K1uwer Academic Publishers, 2000), chap.l. J8 A point emphasized by Alan Padgett, "Etemity and the Special Theory of Relativity," International Philosophical Quarterly 33 (1993): 219-223.

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reference frames. Not being in a physical reference frame, He transcends all measured times, and all events are real to Him in His metaphysical ''now.'' Such a view seems nearly inconceivable, but dyed-in-the-wool relativists may find it congenial, especially since it avoids a Lorentz-Poincare interpretation of SR and preserves the Einstein interpretation. Unfortunately, such a view seems to involve an unwarranted extrapolation of a purely physical theory into the metaphysical realm, where the ontological underpinnings for relativity seem to be lacking. For physical relativity results from such factors as the use of clocks as time-keeping devices and measuring rods as indicators of length, relative motion of inertial frames in respect of each other, and clock synchronization by means of signals having a frame invariant velocity of c in vacuo. But none of these factors is relevant to God or to metaphysical time. Even to speak of God's having a metaphysical "frame of reference" is obviously analogical language, since reference frames are physically grounded. There seems to be no ontological foundation for the sort of radical disintegration of reality as is envisaged in Metaphysical Relativity. Indeed, metaphysical time as construed in the rational theory of clocks is something that clocks can and do register; as Newton said, clock time is a sensible measure of absolute time. The sort of metaphysical time envisioned in Metaphysical Relativity is something above and beyond even this and cannot be integrated with any measured time. But what are the ontological foundations of Metaphysical Relativity? It cannot result from synchronization procedures or relative motion. So how does it exist?39 39 Tbe best run for its money that I can give to Metaphysical Relativity is suggested by an analogy given by Anthony Quinton, "Spaces and Times," Philosophy 37 (1962): 130-147, who, under the inspiration of F. H. Bradley, invites us to imagine the time of a dream world in comparison with our public time. Events in the dream world can be coherently and internally temporally ordered and yet are unrelated to public, historical time. One cannot say that events in one's dream occur at the time oftheir appearance in one's mind-that would be like dating the events in a novel by the date ofits publication! Quinton points out that events in my dream world may occur years apart, though the dream lasted oniy 30 seconds in my mind. Moreover, my dream on Tuesday may be about events that occurred earlier than the events dreamt about on Monday, so that to date these events by public time would be incoherent. Quinton goes on to expand his story such that one is awake in public time for sixteen hours and asleep eight, and similarly in the dream world one is awake sixteen hours and asleep eight. Both worlds seem equally real, and yet they cannot be temporally integrated into one time One can make a theological application of this story by holding that God's time is as incommensurable with our time(s) as public time is with dream time. "With the Lord one day is as a thousand years, and a thousand years as one day" (11 Pet. 3.8). Our time(s) may be coherently and internally temporally ordered but cannot be dated by the moments of God's metaphysical time. Hence, His "now" does not pick out some privileged "now" in the universe; all the relative "now's" are equally real to Hirn in His "now." My misgiving about this provocative analogy is that I do not think that the time which characterizes novels and dreams is really time at all. The "time" involved is a mere construction ofthe imagination; in the world of the novel or the drearn 30 years do not actually elapse. One might as weil talk about how a dream rose "smelled" and how this relates to the scent of a real rose. But the time we experience is real, not fictitious or imaginary. So it remains difficult to understand how Metaphysical Relativity makes sense. For discussion ofQuinton's piece, see R. G. Swinburne, "Times," Analysis 25 (1965): 185-191; A. SkilIen, "Tbe Myth ofTemporal Division," Analysis 26 (1965): 44-47; R. G. Swinburne, "Conditions for

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A major difficulty with Metaphysical Relativity, moreover, is its attempt to isolate God in the metaphysical ''now'' from His frame-relative actions, a move analogous to the atemporalist's attempt to preserve God's timelessness while allowing His effects to occur in time. If God is successively actualizing states of reality, not in metaphysical time, but relative to reference frames, then He would exist in the ''now'' of every reference frame, thus destroying the unity of His consciousness. In Fitzgerald's words, "God would have an infinitely split personality, each sub-personality evolving in monadlike isolation from the others"a hypothesis in which he detects the "faint scent of polytheism. ,,40 It seems to me therefore that, as uncomfortable as it may be, a neo-Lorentzian interpretation of some sort is plausibly required for SR in view of the existence of God in tensed time. Among contemporary philosophers of space and time, probably no one has been more emphatic in his defense of a theistically grounded neo-Lorentzian perspective on Relativity Theory than lohn Lucas. 41 We are already familiar with Lucas's defense of Newton's divinely grounded absolute time in the face of SR. 42 Like Newton, Lucas holds that God is essentially temporal, though he gives a personalist twist to this doctrine: "Time is not a thing that God might or might not create, but a category, a necessary concomitant of the existence of a personal being, though not of a mathematical entity.,,43 Since God is omniscient as weH as temporal, Lucas reasons, He must know the time of events as they happen and which events, however distant from one another, occur simultaneously. Divine omniscience must embody some canon of simultaneity contrary to the fundamental equivalence principle of relativity. Such a canon implies the existence of a privileged frame: "The divine canon of simultaneity implicit in the instantaneous acquisition of knowledge by an omniscient being is not incompatible with the Special Theory of Bitemporality," Analysis 26 (1965): 47-50; K. Ward, "The Unity of Spaee and Time," Philosophy 42 (1967): 68-74; Martin Hollis, "Times and Spaces," Mind 76 (1967): 525-536; and especially the hilariously irreverent Martin Hollis, "Box and Cox," Philosophy 42 (1967): 75-78. The solution by J. 1. C. Smart, "The Unity of Spaeetime: Mathematics versus Myth Making," Australasian Journal 0/ Philosophy 45 (1967): 214-217, presupposes a B-Theory of time and so is of little help, though I sympathize with his aversion to the "story-telling" method of doing philosophy. 40 Fitzgerald, "Relativity Physics and the God of Process Philosophy," pp. 259, 260. 41 One might mention as weil Richard Swinbume, who in his Space and Time, 2d ed. (London: Macmillan, 1981), pp. 181-202; his "Verificationism and Theories of Spaeetime," in Space, Time, and Causality, ed. Richard Swinbume, Synthese Library 157 (Dordrecht: D. Reidel, 1983), pp. 63-76; his "Tensed Facts," American Philosophical Quarterly 27 (1990): 117-130; and his "God and Time," pp. 204-222, defends a Newtonian view of tensed, metaphysical time in which God exists, blasts the verificationist presuppositions of Relativity Theory, and champions the privileged status of cosmic time. See also Charles Hartshome, "Bell's Theorem and Stapp's Revised View of Spaee-Time," Process Studies 7 (1977): 183-191; John T. Wilcox, "Is Process Theism Compatible with Relativity Theory?" Journal 0/Religion 40 (1961): 293-300. 42 See citations in chap. 5 from J. R. Lucas, A Treatise on Time and Space (London: Methuen, 1973). 4) John Lucas, The Future: an Essay on God, Temporality and Truth (Oxford: Basil Blackwell, 1989), p. 213. Time, he affirms, "exists because of God: not because of same act of will on His part, but because of His nature: if the ultimate reality is personal, then it follows that time must exist" (Ibid.). For a critique ofLucas's view that personhood entails temporality, see chap. 2.

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Relativity, but does lead to there being a divinely preferred frame of reference in the same way as the aether rnight have constituted an electromagnetically preferred one.,,44 In bis Spacetime and Electromagnetism, co-authored with P. E. Hodgson, Lucas pronounces Einstein's critique of absolute simultaneity ''unconvincing'' due to bis verificationism and characterizes SR's notion of distant simultaneity as "a rather superficial and frame-dependent property" which is necessary to make electromagnetic phenomena coherent but wbich does not determine ''what is currendy going on at distant places.,,45 Lucas and Hodgson emphasize that "although the Special Theory cannot single out any one of a set of frames of reference that are equivalent to one another under the Lorentz transformation as being at absolute rest, there is no reason why the Special Theory plus some other theory or some other consideration should not do SO.'.46 In fact they argue that considerations from both quantum theory and cosmology do imply the existence of a preferred frame. Metaphysical and theological considerations must also be allowed here. For example, "a theist who believes in God, and claims that God is omniscient and can have temporal knowledge of what goes on in the world, is comrnitted to there being a preferred frame of reference toO.,,47 Such a preferred frame supplies the basis for a "world-wide present moment" and a ''universal tide of presentness" wbich serve to distinguish ontologically between past and future. EINSTEINIAN VS. NEO-LORENTZIAN RELATIVITY Although in semi-popular expositions of SR scom is usually poured upon a neoLorentzian interpretation, particularly the Lorentz-FitzGerald contraction, the fact is that a small minority of physicists, including such notable figures as H. E. Ives, Geoffery Builder, and S. 1. Prokhovnik, have continued the Lorentzian research programme down to the present day, so that the correct physical interpretation of Relativity Theory remains a matter of debate. 48 In fact, that debate has intensified in recent years, due to what one participant has called a "sea change" in the Ibid., p. 220. J. R. Lucas and P. E. Hodgson, Spacetime and Electromagnetism, pp. 64-67. 46 lbid., pp. 118-119. Cf. Lucas's earlier statement: "Although we need to say that so far as electromagnetism is concemed, a11 inertial frames are on a par, we should not be flying in the face of empirical facts if we were led by theological or metaphysical considerations or by considerations from some other part of physics to prefer one frame above all others" (Lucas, Future, p. 219). 47 Lucas and Hodgson, Spacetime and Electromagnetism, p. 112; cf. p. 67. 48 See the proceedings of the biennial conferences sponsored by the British Society for the Philosophy of Science, "Physical Interpretations of Relativity Theory," Imperial College of Science and Technology, London. It is noteworthy that in Zahar's analysis, SR did not by itself empirically supersede Lorentz's programme. Zahar can claim that Einstein's research programme superseded Lorentz's only by taking GR to be continuous with SR and by then appealing to the empirical confirmation of GR. (Zahar, "Why Did Einstein's Programme Supersede Lorentz's?," pp. 95-123; 223-262). But as we shall see below, GR is definitely not continuous with SR; it is a theory of gravitation, not a theory of relativity. It therefore follows that Einstein's programme never in fact did supersede Lorentz's, in the sense of demonstrating its superiority over Lorentz' s. 44 45

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fOWldations of physics commWlity conceming the viability of a Bohmian interpretation of quantwn mechanies, which plausibly requires absolute simultaneity and, hence, absolute time. 49 It is acknowledged even by its detractors that the neoLorentzian version is empirically equivalent to the received, Einstein-Minkowskian version of SR, so that the decision between them must be made on the basis of nonempirical considerations. It is often asserted that the received version ofthe theory is simpler and therefore to be preferred. However, as is well-known, one must be very cautious about the connection between the simplicity of a theory and its truth, as opposed to its utility.50 What right do we have to infer that if the received version is simpler, it is therefore true, especially in light of the extraordinary metaphysical commitments it involves (no absolute space, no absolute time, but, plausibly, absolute spacetime)? Moreover, that simplicity is achieved by means of conventional definitions, which makes it difficult to regard the theory as being true rather than merely useful or expedient. One could also argue that cOWlterbalancing the simplicity of the received version is the heuristic superiority ofthe neo-Lorentzian version. 51 Besides all this, the fact remains that we have good reasons for believing that a neo-Lorentzian theory is correct, namely, the existence of God in tensed time implies it, so that concems about which version is simpler become of little moment. In any case, the claim that the received theory is simpler is simply wrong. Although Lorentz's own theory was more complicated than Einstein's, H. E. Ives was able to derive the Lorentz transformation equations from (i) the laws of conservation of energy and momentwn and (ii) the laws of transmission of radiant energy. He showed that there is an apparent discrepancy in the equations for a particle govemed by these laws which demands that the particle's mass vary with velocity. He then derived from these variations of dimensions the Lorentz transformations. "The space and time concepts ofNewton and Maxwell are retained without alteration," he wrote, "It is the dimensions of the material instruments for measuring space and time that change, not space and time that are distorted. ,,52 On Ives's achievement, Martin Ruderfer comments that he succeeded in elevating Lorentz's ad hoc theory to an equal status with SR and did so with the same number of basic assumptions as Einstein, so that his theory has the same "beauty." "The lohn Kennedy, in a paper presented at the Central Division Meeting of the American Philosophical Association, April 23-26, 1997, Pittsburgh, Pennsylvania so Cushing further observes, "Generally agreed upon, objective criteria of sirnplicity do not seem to exist. Hence, simplicity as a guide to truth (as opposed merely to economy of effort) in formulating and developing a theory or hypothesis can be quite subjective" (lames T. Cushing, Philosophical Concepts in Physics [Cambridge: Cambridge University Press, 1998], p. 161). SI See 1. S. Bell, "How to Teach Special Relativity," in Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987), pp. 66-80; see also S. 1. Prokhovnik, "An Introduction to the Neo-Lorentzian Relativity of Builder," Speculations in Science and Technology 2 (1979): 226; G. Builder, "Ether and Relativity," Australian Journal 0/ Physics 11 (1958): 279-297, reprinted in Speculations in Science and Technology 2 (1979): 239-241. S2 Hubert E. Ives, "Derivation of the Lorentz Transformations," Philosophical Magazine 36 (1945): 392-401, reprinted in Speculations in Science and Technology 2 (1979): 247,255.

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Ives and Einstein interpretations represent two different, but equally valid, views of the same set of observations."S3 Hence, assertions that Einstein's version is simpler than a neo-Lorentzian theory are incorrect. Neo-Lorentzian theorists, on the other hand, have complained that the received theory leaves us with physical effects without any causal explanation for them. Thus, for example, Builder asserts, The relative retardation of clocks, predicted by the restricted theory of relativity, demands our recognition of the causal significance of absolute velocities.... The observable effects of absolute accelerations and of absolute velocities must be ascribed to the interaction of bodies and physical systems with some absolute inertial system. We have no alternative but to identify this absolute system with the universe. 54

Builder argues that the universe as a whole constitutes a unique, absolute inertial system, which he calls ''!he ether," that affects the masses and dimensions ofbodies, as weIl as the running of docks, in accordance with their absolute speed. He contrasts this interpretation with the received view: The conceptual difficulties associated with the restricted theory all arise out of the denial that these absolute concepts are permissible, and out of the consequent attempts to avoid them in the presentation of the theory. It is frequently maintained that the theory has forced us to discard entirely the old-fashioned commonsense notions oftime and space, but nothing comprehensible or definable has been offered in their place. Moreover, any questions as to what causes the relativity of simultaneity, the measured constancy of the velocity of light in all inertial reference systems, or the reciprocity of relativistic variations of length, of mass, and of clock rates, are avoided by vague references to the principle of relativity, to the four-dimensional character of spacetime, and so on. On the other hand, the presentation of the restricted theory in terms of the absolute concepts (following generally the lines of its development by Poincare and Lorentz) involves no conceptual difficulties. The relativity of simultaneity, the reciprocity of relativistic variations, and the constancy of the measured velocity of light, then all appear simply as comprehensible effects of the motions, relative to the ether, of the bodies of observers and of the measuring instruments used. 55

Developing Builder's approach, Prokhovnik interprets length contraction and time dilation as retarded potential effects. He explains that Builder's notion of a fundamental inertial frame I(F) implies that energy propagation is strict1y isotropic with respect to this frame. A body moving with respect to this frame will drag its gravitational field with it. The theory of retarded potentials applies to the gravitational or electromagnetic field of a body moving relative to I(F). For such a body energy propagation is not isotropic and its co-moving fields are no longer symmetric, which leads to a whole chain of interacting anisotropy effects. If the field of a moving electron is compressed in the direction of motion, for example, then its surface must be similarly compressed to maintain an equipotential Martin Ruderfer, "Introduction to Ives' 'Derivation of the Lorentz Transformations'," Speculations in Science and Technology 2 CI 979): 243. 54 Builder, "Ether and Relativity," p. 230. S5 Ibid., p. 240.

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equilibriwn state, and the moving electron takes the shape of an ellipsoid. A system of particles would contract in the direction of motion in order to sustain the interpartide equilibriwn of the system. No substantial aether is required for the production of such effects; simply the existence of I(F) itself suffices, as Prokhovnik explains, Fitzgerald and Lorentz considered the contraction as an absolute effect due to movement relative to a unique reference frame associated with an aether. It is clear that the contraction can be even more satisfactorily considered as a secondary effect resulting from movement relative to a unique cosmologically-based fundamental reference frame, I(F), defined in terms of our greatly expanded view of the uni verse since 1930. The retarded potential field effect is a prirnary consequence of movement relative to I(F) and, as seen in the basis and derivation of this effect, it emerges essentially in consequence of the lirniting velocity restrietion on the transmission of energy; no aether or any other property of 'physical space' is required for the emergence of this effect. 56

Length contraction can be considered as the reaction of a moving system to maintain its stationary-in-I(F) equilibriwn state in the circwnstance of an asymmetric gravitational field resulting from its motion in I(F). This phenomenon is thus as universal and general as the gravitational property of matter. Following Builder, Prokhovnik sees time dilation as the consequence of the fact that a moving light dock has a longer unit of time and hence runs more slowly than a similar, stationary dock in I(F) (Figure 6.4).

MI

+ + + 8

---.

(b)

(a)

"

"r

" "1 Po

, (!),// M,

,

I

I

,,

M'

I

I

I

,' ,,, ,,

I

---. ,, ,

,, ,,

09 M'2

~0C3GQQG)Q

Figure 6.4. The light-pulse clock. (a) When at rest a light pulse is reflected back and forth from the mirrors MI and M2; each return ofthe pulse to one end counts as a unit of time. The dial hand moves from A to Bin that time. (b) When the clock is in motion the light travels the distance MzM'IM'z between ticks, so causing it to go slow. The dials underneath the moving clock are those stationary clocks distributed in space and used for comparison with the moving clock times.

This effect can also be generalized, according to Prokhovnik: "The effect will apply to all phenomena involving electromagnetic impulses and energy-exchanges; so it can be considered to apply to all docks and physical phenomena and, by extension, 56

S. 1. Prokhovnik, Light in Einstein 's Universe (Dordrecht, Holland: D. Reidel, 1985), pp. 84-85.

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also to biological phenomena."S7 Thus, dock retardation, the Twin Paradox, and asymmetrical aging become comprehensible phenomena. The adequacy of such causal explanations is not the primary point here. Rather the salient point is that a neo-Lorentzian theory involves appeal to some sort of causal explanation for the physical effects predicted by SR. By contrast, in Einstein's theory, these effects simply follow, as we have seen, from Einstein's denial of the existence of a fundamental frame and his two postulates that the laws of nature have the same form in every reference frame and that light has a constant, frame-independent velocity. Given his postulates, a new kinematics follows according to which reciprocal length contraction and dock retardation occur, but without any dynamical explanation. As a theory of principle rather than a constructive theory, Einstein's SR is based on postulates which are characterized by their very non-empirical character. As Rolton and Goldberg have emphasized, although Einstein insisted early on that his SR was empirically grounded, in fact the two postulates on which the theory is based "were postulates for which there was and can be no direct empirical confmnation"; their status is that of "a non-verifiable and non-falsifiable presupposition."S8 The only version of SR which is experimentally verifiable, according to Builder, "is the theory that the spatial and temporal coordinates of events, measured in any one inertial reference system, are related to the spatial and temporal coordinates of the same events, as measured in any other inertial reference system, by the Lorentz transformations."S9 But this verifiable statement only concems measurements made in inertial reference systems and is neutral with regard to the Lorentzian and Einsteinian interpretations. As a constructive theory, the neoLorentzian approach promises to enrich our understanding of the causal structure of the world in a way that Einstein's cannot. Relativity theorists who are spacetime realists, that is, who believe that physical reality is a tenselessly existing four-dimensional manifold, contend that aspacetime approach to SR is explanatory. For example, in the famous Twin Paradox the reason the traveling twin is younger than his stay-at-home brother upon his return is that in four-dimensional spacetime, the path of the travelling sibling is actually

Ibid., p. 89. See also S. 1. Prokhovnik, "The Logic ofthe Clock Paradox," Physical Interpretations Theory I, Proceedings of the International Conference of the British Society for the Philosophy of Science, September 16-19, 1988, London. 5. Gerald Holton, "Where Is Reality? The Answers of Einstein," in Science and Synthesis, ed. UNESCO (Berlin: Springer Verlag, 1971), pp. 52-64; idem, "Mach, Einstein, and the Search for Rea1ity," p. 178; idem, "Poincare and Relativity," in Thematic Origins 0/ Scientific Thought: Kepler to Einstein (Carnbridge, Mass.: Harvard University Press, 1973), p. 190; so also Stanley Goldberg, Understanding Relativity: Origin and Impact 0/ a Scientific Revolution (Boston: Birkhäuser, 1984), p. 105; idem, "Putting New Wine in 01d Bottles: The Assimilation of Relativity in Arnerica," in The Comparative Reception 0/ Relativity, ed. Thomas F. Glick, Boston Studies in the Philosophy of Science 103 (Dordrecht: D. Reidel, 1987), pp. 15-21. 59 G. Builder, "The Constancy ofthe Velocity ofLight," Australian Journal o/Physics 11 (1958): 457480; reprinted in Speculations in Science and Technology 2 (1971): 422. 51

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shorter than that of the earthbound twin. 60 Therefore, it is not surprising that bis clock records less time. A similar account could be given of length contraction. Therefore, on aspacetime interpretation Einstein's SR does explain why these relativistic phenomena occur. But here it needs to be seriously called into question whether any such metaphysical reality as spacetime actually exists. In the first place, there are no compelling reasons to prefer aspacetime ontology over a classical ontology of space and time as the latter comes to expression in a neo-Lorentzian theory of relativity. Spacetime realists are self-confessed, post-positivistic metaphysicians, and so cannot complain that the classical concepts of space and time are obnoxiously metaphysical. As Earman and Friedman write, "Newton's theory, and especially bis conceptions of space and time, have often been criticized on operational and positivistic grounds; but it is rarely pointed out that Relativity Theory, which is often taken as vindicating Newton's pbilosopbical critics, is not less subject to the same criticisms ... .',6) When spacetime realists champion aspacetime ontology over aspace and time ontology, virtually all their arguments are aimed at demonstrating the superiority of the spacetime interpretation of SR over an interpretation of SR in which time and space are not united and yet no absolute time or space exists. The Lorentz-Poincare approach is simply passed over in benign neglect, under the assumption that any such theory is no longer a viable option. Spacetime realists are all of them Einsteinians and so take no notice of contemporary neo-Lorentzians. The irony of this situation is that the self-restrlction of spacetime realists to Einsteinian interpretations of Relativity Theory is rooted in the very positivism and verificationism which would be inimical to their own approach to questions of space and time. Having freed themselves from the metaphysical straitjacket of positivism, spacetime realists now need to ask why they should continue to pbilosopbize only within the familiar walls of Einsteinian relativity and should not rather begin to explore alternatives in previously proscribed realms. Probably at the root of many physicists' rejection of a neo-Lorentzian approach to Relativity Theory is the deep-seated conviction that comes to expression in Einstein's aphorism: "Subtle is the Lord, but malicious He is not.',62 That is to say, if there exists a fundamental asymmetry in nature, then nature will not conspire to conceal it from us by precisely countervailing effects. D'Abro expresses this sentiment clearly:

See Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics (San Francisco: W. H. Freeman, 1966), p. 34; cf Hermann Bondi, Relativity and Common Sense (New York: Dover, 1964), p. 67; L. Marder, Time and the Space-Traveller (London: George, Allen & Unwin, 1971), p. 78. 61 1. Earman and M. Friedrnan, "The Meaning and Status ofNewlon's Law oflnertia and the Nature of Gravitational Forces," Philosophy ojScience 40 (1973): 341. 62 "Raffiniert ist der Herr Gott, aber boshaft ist er nicht," remark of Albert Einstein during a visit to Princeton, upon being informed that D. C. Miller, a former colleague ofMichelson, had claimed to have detected the ether wind (cited in Abraham Pais, 'Subtle is the Lord... '; The Science and Life oj Albert Einstein [Oxford: Oxford University Press, 1982], pp. 113-114). 60

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IfNature was blind, by what marvelous coincidence had all things been so adjusted as to conceal a velocity through the ether? And if Nature was wise, she had surely other subjects to attend to, more worthy of her consideration, and would scarcely be interested in hampering our feeble attempts to philosophize. In Lorentz's theory, Nature, when we read into her system all theseextraordinaryadjustrnentsadhoc.is made to appear mischievous; it was exceedingly difficult to reconcile one's self to finding such human traits in the universal plan. 63

One difficulty with this objection is that it seems to be guilty of greatly overexaggerating the extent ofthe alleged conspiracy. After all, SR is a restricted theory of relativity: it is only uniform motion relative to the privileged frame that fails to manifest itself. But in all other cases of motion, the absolute character of that motion is disclosed. This is not to say that acceleration or rotation proves the reality of privileged space, but it is to say that, given the classical concepts of time and space, nature does not at all conspire to conceal either absolute motion or the privileged space from uso Moreover, as we shall see in the next chapter, there are modern equivalents of the classical aether which serve to disclose a privileged frame. Indeed, when Einsteinians complain that no evidence of a privileged space and time exist, one wonders what it would take to convince them of the contrary. If no empirical evidence of a ftmdamental frame is incapable ofbeing explained away, then the supposed failure of nature to disclose such a frame to us becomes trivial. The more difficult it is for nature to provide evidence of the existence of a privileged frame, the less compelling the charge that she is conspiring against us to conceal it. But even considered in abstraction from these wider considerations, why accept the assumption that ftmdamental asymmetries in nature must disclose themselves to us? This assumption is by no means obvious, as Martin Carrier explains: Science would be an easy matter if the fundamental states of nature expressed themselves candidly and frankly in experience. In that case we could simply collect the truths Iying ready before OUT eyes. In fact, however, nature is more reserved and shy, and its fundamental states often appear in masquerade. Put less metaphorically, there is no straightforward one-to-one correspondence between a theoretical and an empirical state. One of the reasons for the lack of such a tight connection is that distortions may enter into the relation between theory and evidence, and these distortions may alter the empirical manifestation of a theoretical state. As a result, it is in general a nontrivial task to excavate the underlying state from distorted evidence. 64

A. d' Abro, The Evolution 0/ Scientific Thought, 2d rev. ed. (1927; rep. ed.: n.p.: Dover Publications, 1950), p. 138. 64 Martin Carrier, "Physical Force or Geometrical Curvature?" in Philosophical Problems 0/ the Internal and External Worlds, ed. John Earman, Allen I. Janis, Gerald 1. Massey, and Nicholas Rescher (pittsburgh: University of Pittsburgh Press, 1993), p. 3. Tim Maudlin has emphasized and iIIustrated Carrier's point in his Quantum Non-Locality and Relativity, Aristotelian Society Series 13 (Oxford: Blackwell, 1994). He surveys what he characterizes as the "teratological collection" of theories attempting to explain the Bell Inequalities and integrate the EPR results with Relativity Theory and concludes, "One way or another God has played us a nasty trick" (Ibid., p. 241). One cannot dismiss neoLorentzian relativity on the grounds that it would be deceptive, since partisans of each theory could say the same of rival positions. " ... the real challenge falls to the theologians of physics, who must justify the ways of a Deity who is, if not evil, at least extremely mischievous" (Ibid., p. 242). 63

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On a neo-Lorentzian theory, Carrier's general remarks on distortions of a theoretical state in its empirical manifestation are quite literally true, for the result of uniform motion relative to privileged space is length contraction and dock retardation, phenomena which are every bit as real under the Einsteinian theory.65 If it is in general difficult to excavate the underlying state of nature from distorted evidence, if nature's fundamental states often appear in masquerade, then why are the relativistic phenomena which mask the privileged frame improbable on a dassical ontology? As for d' Abro's concem with finding "human traits in the universal plan," the neo-Lorentzian might plausibly appeal to the Anthropic Principle in response. 66 According to that principle, features of the universe can only be judged in their correct perspective when due allowance has been made for the fact that certain features of the universe are necessary if it is to contain ob servers like ourselves. 67 Since our existence depends on the maintenance of equilibrium states within us, the Lorentz-FitzGerald contraction and dock retardation are necessary pre-requisites of our existence as observers. Thus, nature's alleged conspiracy, when seen in anthropic perspective, seems much less mischievous. Unless it can be shown that length contraction and dock retardation are extremely improbable (and thus evidence ofthe universe's [me-tuning for intelligent life), then we should hardly be surprised at nature's "conspiracy." In any case, given the theistic perspective from which we approach these issues, even [me-tuning should not surprise uso Given that God designed the universe to contain intelligent beings like us, we should expect that He will have chosen laws of nature that serve to maintain the equilibrium essential to our existence. Even if, as d' Abro says, Nature is blind, God is not; and if Nature is not wise, God iso It is not Nature, then, who is concemed with our feeble selves, who deerns us worthy subjects to attend to, but the Creator and Sustainer of the universe who is mindful of man. Raffiniert ist der Herr Gott, barmherzig ist er auch. It has been suggested that a neo-Lorentzian interpretation of SR is disfavored because of the excessive spacetime structure it posits with respect to the laws of motion. 68 Recognizing the failure of verificationist critiques of absolute space on the basis of its unobservability, Earman, for example, suggests that ''this objection of

See A. Einstein, "Zum Ehrenfestsehen Paradoxon," Physilwlische Zeitschrift 12 (1911): 509-510; lohn A. Winnie, "The Twin-Rod Thought Experiment," American Journal 0/ Physics 40 (1972): 10911094; M. F. Podlaha, "Length Contraction and Time Dilation in the Special Theory of Relativity-Real or Apparent Phenomena?" Indian Journal o/Theoretical Physics 25 (1975): 74-75; Dieter Lorenz, "Über die Realitat der Fitzgerald-Lorentz Kontraction," Zeitschrift für allgemeine Wissenschaftstheorie 13/2 (1982): 308-312. lt is perhaps noteworthy that d' Abro holds that "The Fitzgerald contraction is no longer areal physical contraction, as it was assumed to be in Lorentz's theory" (d' Abro, Evolution 0/ Scientific Thought, p. 151). 66 I owe this point to Robin Collins. 67 lohn D. Barrow and Frank 1. Tipier, The Anthropic Cosmological Principle (Oxford: Clarendon Press, 1986), p. 15 . •8 This has been suggested to me by Yuri Balashov. 65

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lUlobservability is more accurately stated as an objection based on Occam's razor.,,69 What Earman has in mind are criteria which would serve to establish what sort of structure spacetime is endowed with. He proposes two "symmetry principles" which he presents as conditions of adequacy on theories of motion: 8Pl: Any dynamical symmetry of a theory T is a space-time symmetry of T 8P2: Any space-time symmetry of a theory T is a dynamical symmetry of T. What justification is there for these criteria? Earman explains, "Behind both principles lies the realization that laws of motion cannot be written on thin air alone, but require the support of various space-time structures. The symmetry principles then provide standards for judging when the laws and the space-time structure are appropriate to one another.,,70 With respect to (8Pl), which will be crucial in the case at hand, Earman writes, The motivation for (SPl) derives from combining a particular conception ofthe main function oflaws ofmotion with an argument that makes use ofOccam's razor. Laws of motion, at least in so far as they relate to particles, serve to pick out a class of a1lowable or dynamically possible trajectories. If (SPl) fails, the same set of trajectories can be picked out by the laws working in the setting of a weaker space-time structure. The theory that fails (SPI) is thus using more space-time structure than is needed to support the laws, and slicing away this superf1uous structure serves to restore (SPl)n

A prime example of (8Pl) at work is the. demonstration that Newtonian mechanics does not, in fact, require Newtonian spacetime, but only Galilean spacetime. While the spacetime symmetries of the theory are Newtonian, the dynamic symmetries are Galilean, a "clear violation" of (SP1).72 By excising absolute space, one produces a theory whose spacetime symmetries and dynamic symmetries are both Galilean, in compliance with (SPl). Now it might similarly be argued-though Earman does not do so-that a neo-Lorentzian theory also violates (SP1) in that it posits more structure to spacetime, such as hyperplanes of absolute simultaneity, than is necessary to explain the symmetries required by relativistic laws of motion, that is, the symmetries of the Lorentz-Poincare group. Therefore, such structures should be excised by Ockham's razor. Now Earman is lUldoubtedly on to something important here. One should like to have some SOrt of constraint upon the postulation of gratuitous spacetime structures. But the difficulty with (SPl) and (SP2) is that they are too restrictive, or to put the point another way, they can be overridden by considerations broader than the laws of motion. Indeed, the whole burden of this study has been to show that questions of time and space are metaphysical in character, so that such considerations cannot 69

70 71

72

lohn Earman, Warld Enaugh and Spacetime (Cambridge, Mass.: MIT Press, 1989), p. 48. Ibid., p. 486. Ibid., pp. 46-47. Ibid., p. 48.

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be ignored. As we have seen, the foundations of Newtonian time and space were laid in Newton's theism, as Earman acknowledges, but Earman simply ignores such theological considerations, choosing instead to put a "modem gloss" on Newton's views. 73 Newton's postulation of absolute space was not gratuitous but based, rightly or wrongly, in his conception of divine omnipresence. I think that Newton's conception of God's immensity was flawed; but it was not irrelevant, and I have argued at length that his position on divine temporality and, hence, absolute simultaneity, is eminently defensible. Such metaphysical considerations qualify any force which Earman's symmetry principles might possess. In any case, it needs to be understood that Earman's principles presuppose a spacetime ontology and therefore cannot be employed to justify aspacetime interpretation of SR over a neo-Lorentzian space and time interpretation. Earman employs aspacetime approach to all the theories he considers, speaking not only of Newtonian spacetime but even of Machian spacetime. This involves him in frequent anachronisms: he speaks ofNewton's "insistence that the structure of space-time is immutable;" he says that "If we take Newton at his word in the Scholium, the spacetime setting for the theory of motion and gravitation of the Principia is supposed to be a full Newtonian space-time ... ;" he explains that for Newton ''the space-time is given once and for all as an emanative effect of God .. ",,74 Of course, Newton himself insisted on and believed none of this, since his was a 3 + 1 ontology involving physical objects enduring through time. His laws of motion are not supported by various spacetime structures, as Earman assumes, for there are no such structures. Time and space have intrinsic structure, and motion is to be explained, not in terms of the geometrical structure of spacetime, but in terms of forces acting on bodies in space enduring through time. Earman's principles, then, take for granted aspacetime realism. At best, therefore, with respect to SR, Earman's symmetry principles could only serve to justify a Minkowskian spacetime realism over a neo-Lorentzian spacetime realism. But if only a single slice of spacetime actually exists, then the question becomes whether Einstein's original relativity interpretation is preferable to the neo-Lorentzian interpretation. And neoLorentzians and spacetime realists concur that the original, 3 + 1 relativity interpretation is deficient. In short, one's ontology may warrant postulating more structure to space and time than symmetry principles alone would allow. A possibly claimed advantage of aspacetime approach to Relativity Theory is that in GR gravitation is understood in terms of the geometry of spacetime. As Nerlich urges, " ... not only is spacetime curvature the fundamental explanatory concept of the theory, but the idea of spacetime geometry is actually used to reduce causal explanation by gravitational force in space during time.,,75 Nerlich gives the example of orbital planetary motion, which on the space and time ontology would have to be regarded as motion of an object under a gravitational force. But on a 7J 74

75

Ibid., p. 10. Ibid., pp. 35-36, 45, 48. Graham Nerlich, What Spacetime Explains (Cambridge: Cambridge University Press, 1994), p. 181.

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spacetime ontology we can still apply Newton's ftrst law to it in spacetime, seeing its trajectory as the geodesic path of a force-free body, thus reducing gravitation to spacetime curvature. The question raised by the geometrization of gravitation in GR is whether this is to be understood instrumentally or realistically. For what it is worth, most physicists are apparently content to take the theory instrumentally, interpreting spacetime curvature as a geometrical representation of gravitation. According to Arthur Fine, few working, knowledgeable scientists give credence to the realist existence claims for entities like the four-dimensional manifold and associated tensor ftelds in GR; rather GR is seen as "a magniftcent organizing tool" for dealing with certain gravitational problems in astrophysics and cosmology: "most who actually use it think of the theory as a powerful instrument, rather than as expressing a 'big truth,.,,76 I think we can safely say that no disadvantage arises from treating the geometrization of gravitation as a heuristic device only. On the contrary, it can be argued that a realist interpretation of spacetime actually obscures our physical understanding of nature by substituting geometry for a physical force, thereby impeding progress in connecting gravitational theory to particle physics. In the preface to his text Gravitation and Cosmology Steven Weinberg reflects, There was another, more personal reason for my writing this book. In learning general relativity, and then in teaching it to classes at Berkeley and M.I, T" I became dissatisfied with what seemed to be the usual approach to the subject. I found that in most textbooks geometrie ideas were given a starring role, so that a student who asked why the gravitationa/ field is represented by ametrie tensor, or why freely falling particles move on geodesics, or why the field equations are generally covariant would come away with an impression that this had something to do with the fact that spacetime is a Riemannian manifold, Of course, this was Einstein 's point of view, and his preeminent genius necessarily shapes OUT understanding of the theory he created, However, I believe that the geometrical approach has driven a wedge between general relativity and the theory of elementary particles, As long as it could be hoped, as Einstein did hope, that matter 16 Arthur Fine, The Shaky Game: Einstein. Realism. and the Quantum Theory (Chicago: University of Chicago Press, 1986), p, 123, See the statement of Steven Weinberg, Gravitation and Cosmology: Principles and Explications 01 the General Theory 01 Relativity (New York: John Wiley & Sons, 1972), p,147: """ the nonvanishing of the tensor R"~",, is the true expression of the presence of a gravitational field",. Riemann.,. introdueed the curvature tensor R,,~VK to genera/ize the eoncept of eurvature to three or more dimensions, It is therefore not surprising that Einstein and his sueeessors have regarded the effects of a gravitationa/ field as produeing a change in the geometry of spaee and time, At one time it was even hoped that the rest of physics eould be brought into a geometrie formulation, but this hope has met with disappointrnent, and the geometrie interpretation of the theory of gravitation has dwindled to a mere analogy, whieh lingers in our language in terms like 'metrie,' 'affine eonnection,' and 'eurvature,' but is not otherwise very useful. The important thing is to be able to make predietions about the images on the astronomers' photo graphie plates, frequeneies of speetral lines, and so on, and it simply doesn 't matter whether we aseribe these predietions to the physica/ effeet of gravitational fields on the motions of planets and photons or to a eurvature of spaee and time,"

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CHAPTER6 would eventually be understood in geometrical terms, it made sense to give Riemannian geometry a primary role in describing the theory of gravitation. But now the passage of time has taught us not to expect that the strong, weak, and electromagnetic interactions can be understood in geometrical terms, and too great an emphasis on geometry can only obscUfe the deep connections between gravitation and the rest of physics. 71

Weinberg believes that the theory of gravitational radiation provides "a cruciallink" between GR and the microscopic frontier of physics, since radiative solutions of Einstein's equations lead to the notion of a particle of gravitational radiation, the socalled graviton. 78 The geometrical approach of spacetime realism only impedes our gaining a more integral understanding of physics. Riemannian geometry, in Weinberg's view, should be understood "only as a mathematical tool" and ''not as a fundamental basis for the theory of gravitation.,,79 In sum, there do not seem to be compelling reasons to prefer aspacetime interpretation of SR over a neo-Lorentzian conception of space and time. On the other hand, I think we do have good reasons for rejecting spacetime realism and, therefore, aspacetime interpretation of SR. Inherent to the concept of spacetime is the indissoluble unification of space and time into a four-dimensional continuum. Hence, Minkowski' s pronouncement that "Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.,,80 It seems to me, however, that we have powerful metaphysical grounds for believing that time can exist independently of space. In making his pronouncement, Minkowski forgot Kant's

71 78

Weinberg, Gravitation and Cosmology, p. vii. Ibid., p. 251. Cf. Rovelli'sjudgement: "Einstein's identification between gravitational field and geometry can be read in two alternative ways: i. as the discovery that the gravitational field is nothing but a locai distortion of spacetime geometry; or ii. as the discovery that spacetime geometry is nothing but a manifestation 0/ a particular physical jield, the gravitational field. The choice between these two points of view is a matter of taste, at least as long as we remain within the realm of nonquantistic and nonthermal general relativity. I believe, however, that the first view, which is perhaps more traditional, tends to obscure, rather than enlighten, the profound shift in the view of spacetime produced by general relativity. *

*... The recent efforts to construct a quantum theory of gravity, or a unified theory of all

interactions (for instance, via string theory), or a thermodynamics of the gravitational field, and other efforts, suggest that the second point of view, namely viewing the metricfgravitational field as a field like any other, is the fruitful one" (Carlo Rovelli, "Halfway through the Woods: Contemporary Research on Space and Time," in The Cosmos 0/ Science, ed. 1. NOTton and J. Earman [Pittsburgh: University of Pittsburgh Press, 1998], pp. 193-194, 219). 79 Weinberg, Gravitation and Cosmology, p. viii. 80 H. Minkowski, "Space and Time," in The Principle 0/Relativity, by A. Einstein, et al., with Notes by A. Sommerfeld, trans. W. Perrett and G. B. Jeffery (1923; rep. ed.: New York: Dover Publications, 1952),

p.75.

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insight that time is a fonn applicable not only to the external world, but to consciousness as well. 8t Concerning Minkowski spacetime, Wenzl cautions: From the standpoint of the physicist, this is a thoroughly consistent solution. But the physicist will (doubtless) understand the objection, raised by philosophy, that time is by no means a merely physical matter. Time is, as Kant put it, the form not merely of OUT outer sense but also of our inner sense.... Should our experiences of successiveness and of memory be mere illusion ... ?82

Aseries of mental events alone is sufficient to set up a temporal sequence. 83 Thus, if we imagine God's counting down to the moment of creation: " ... , 3, 2, 1, Fiat lux!" then the beginning of spacetime would be preceded by a metaphysical time associated with the mental events of counting which would be wholly independent of space. Whether such a count-down can be beginningless or whether metaphysical time must itself have also had a beginning need not concern us here; the point is that physical events having spatial co-ordinates are clearly not a necessary condition of temporal events. This is especially evident in the case of God, since He is an unembodied Mind with whose mental states it is impossible to associate any brain states. If He experiences a succession of contents of consciousness, He is clearly in metaphysical time even if space does not exist. Pointing out that there are two percepts which give birth to the concept of time, one in the physical realm and one in the mental, E. A. Ramige contends, The spacetime concept is found to be ever more of a necessity in the theories of modem physics. However, necessary as it is in certain realms, that does not thereby rule out the separate concepts of space and time, any more than the concept of the area of a figure rules out the separate concepts of length and breadth. In the non-physical realm which we shall go into in taking up the concept of God it is time rather than space that is important. Descartes had stressed that thought is a separate attribute of reality from extension. 'What is conscious is not spatial and what is spatial is not conscious.' It is still held that in the mental realm space plays a less important role than time. 84

Indeed, time is more fimdamental than space, as Lucas is wont to emphasize. 85 For while aseries of mental events is a sufficient condition of time, it is not sufficient to constitute space. Since God is incorporeal, He would not be spatial prior to the Immanuel Kant, Immanuel Kant 's "Critique of Pure Reason, " trans. Norman Kemp Smith (London: Macmillan, 1970), A34; B51 (p. 77). 82 A. Wenzl, "Einstein's Theory of Relativity, Viewed from the Standpoint of Critical Realism, and its Significance fOT Philosophy," in Albert Einstein: Philosopher-Scientist, ed. P. A. Schilpp, Library of Living Philosophers 7 (LaSalle, Ill.: Open Court, 1949), pp. 587-588. 83 A point emphasized by Reichenbach: "An act of thought is an event and therefore defines a position in time. If my experiences are always produced within the framework of a 'now,' that means that each act of thought defines a point of reference. We cannot escape the 'now' because the attempt to escape signifies an act of thought and therefore defines a 'now'" (Hans Reichenbach, "Les fondements logiques de la mecanique des quanta," Annales de I 'Institut Henri Poincare 13 [1952]: 157). 84 Eldon Albert Ramige, Contemporary Concepts of Time and the Idea of God (Boston: Stratford, 1935), pp. iii-iv. 85 Lucas, Treatise, p. 3. 81

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creation of the universe even though He were temporal. Thus, on the orthodox view of God, time is more fimdamental than space, since God's mere thinking discursively is sufficient for the existence of time, but not of space. Reinforcing one's skepticism about spacetime realism is that fact that in Minkowski spacetime the spacetime interval between timelike separated events takes imaginary values. Christensen comments, This is disturbing in the first place because imaginary numbers seem like a paradigm of a convenient conceptual fiction. Tbey were originally invented to make it the case that all quadratic equations, not just some, would have two roots. Tbe serious question, however, is not whether there are imaginary numbers---numbers being a peculiar lot of entities to begin with-but whether there could really be such a thing as mathematically imaginary physical quantities .... No one doubts the convenience of computing with such quantities, even in an eminently practical field such as electrical engineering; but in the end the imaginary parts of the result are discarded. Could it be otherwise in SR, rationally?16

On the original relativity interpretation of SR, it is easy to dismiss this feature of Minkowski spacetime as a mathematical feature which does not correspond to any physical property in the world. But such arecourse is not open to the spacetime realist, who prides hirnself precisely on the interval as a luminous indication of space and time's unification. The spacetime interval is as real a magnitude-nay, more real, if Minkowski is to be believed-than the distance from New York to Los Angeles. But what sense is there in affirming that the spacetime separation of, say, my having lunch and my having dinner is imaginary? In addition to these difficulties, spacetime realism raises a host of problems due to its entailment of the doctrine of perdurance, or the existence of four-dimensional objects comprised of temporal parts. 87 Thus, with little to commend spacetime realism over a neo-Lorentzian conception of space and time and with powerful objections lodged against it, we may conclude that there is no reason to adopt a spacetime interpretation of SR rather than a neo-Lorentzian approach to the problems of Relativity Theory. I can only agree with David Bohm when he complains that a Minkowski diagram is ''misleading'' in showing the past and future as existent88 and with Max Black when he writes, ... this picture of a 'block uni verse, ' composed of a timeless web of 'world-lines' in a four-dimensional space, however strongly suggested by the theory of relativity, is a piece of gratuitous metaphysics.... Here, as so often in the philosophy of science, a useful limitation in the form of representation is mistaken for a deficiency in the uni verse. '9

F. M. Christensen, Spacelike Time (Toronto: University ofToronto Press, 1993), pp. 260-261. For this and other objections, see my Tenseless Theory ofTime. BI David Bohm, The Special Theory of Relativity, Lecture Notes and Supplements in Physics (New York: W. A. Benjamin, 1965), pp. 174-175. 89 Max Black, review of The Natural Philosophy of Time by G. 1. Whitrow, Scientific American 206 (April 1962), 181-182. 86 87

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Minkowski's four-dimensional, mathematical space serves as a convenient ca1culational and diagrammatical aid, a mathematical Hilfsmittel, but says absolutely nothing about ontology. As Arzelies states, "The four-dimensional continuum should therefore be regarded as a useful tool, and not as a physical 'reality,.,,90 Since time can exist independently of space, Minkowski's spacetime is at best a representation of physical time and space as described by the equations of SR and cannot pretend to imply a four-dimensional ontology. Minkowski spacetime is a mathematical space in which the Lorentz transformation of coordinates can be diagrammatically displayed. Since it is analytically connected with the propositions of the theory it displays, it cannot explain anything in the theory but only exhibit the theory's content graphically. Diagrams are useful in mathematics, as Plantinga says, because they enable us to see connections, entertain propositions, and resolve questions that would otherwise be seen, entertained, or resolved only with the greatest difficulty; but they do not serve as explanations. 91 In the same way, spacetime diagrams are indispensable aids in providing a visualization of the propositional content of the theory without serving as explanations of why time dilation and length contraction occur. 92 Sellars, noting that Minkowski spacetime is simply a metrical picture of the location of events, not a depiction of things which come to be and cease to be, conc1udes, "It has too often been supposed by philosophers (and physicists) who discuss the Special Theory of Relativity that the Minkowski mathematical apparatus automatically carries with it a commitment to an ontology of 'events.' This .. .is simply a mistake.,,93

90 Henri Arzelies, Relativistic Kinematics, rev. ed. (Oxford: Pergamon Press, 1966), p. 258; cf. Mary F. Cleugh, Time and Its Importance in Modern Thought, with a Forward by L. Susan Stebbing (London: Methuen, 1937), pp. 66-67; Herbert Dingle, The Special Theory 01 Re/ativity (London: Methuen, 1940), pp. 43-44. 91 Alvin Plantinga, "Reply to Robert Adams," in Alvin Plantinga, ed. James Tomberlin and Peter Van lnwagen, Profiles 5 (Dordrecht, Holland: D. Reidel, 1985), p. 378. 92 For a graphic explanation of how non-explanatory such accounts are, see C. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (San Francisco: W. H. Freeman, 1973), pp. 32-33. See also 1. D. North, 'The Time Coordinate in Einstein's Restricted Theory ofRelativity," Studium Generale 23 (1970): 222. 93 Wilfrid Sellars, "Time and the World Order," in Scientific Explanation, Space, and Time, ed. Herbert Feigl and Grover Maxwell, Minnesota Studies in the Philosophy of Science 3 (Minneapolis: University of Minnesota Press, 1962), p. 578. Robert Geroch says, "If you like, 'four dimensions' is just a convenient way of describing the world and thinking about the world, nothing more .... these pictures are merely a convenient way of looking at (not a necessary ingredient of) spacetime, while spacetime is merely a convenient way of looking at (not a necessary ingredient of) nature" (Robert Geroch, General Relativity from A to B [Chicago: University of Chicago Press, 1978], pp. 12-13). Dugas concludes, "Therefore it seems that Minkowski, carried away by a very natural enthusiasm for the remarkable geometrical synthesis that he had discovered, had to some extent gone beyond the relativistic doctrine, which does not in any way forbid that an observer should reason and calculate, as in daily life, in terms of space and time" (Rene Dugas, History 01 Mechanics, with a Foreword by Louis de Broglie, trans. 1. R. Maddox [New York: Central Book Company, 1955], p. 501).

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CONCLUSION It seems to me, therefore, that despite the widespread aversion to a neoLorentzian interpretation of Relativity Theory, such antipathy is really quite unjustified. Admitted on all sides to be empirically equivalent to the Einsteinian interpretation, the neo-Lorentzian interpretation is neither ad hoc nor more complicated than its riyal. The physical effects it posits are no less real in the received version, only there they appear as axiomatic deductions lacking causal explanations. Indeed, its fecundity in opening the question about physical causes is an important advantage of the neo-Lorentzian interpretation. Therefore, our pbilosopbically grounded preference for the neo-Lorentzian interpretation, however distasteful to the majority of physicists, cannot count against the truth of our argument concerning God's relationsbip to measured time. Of course, one could go on working within the theoretical framework of Einstein 's theory, being accustomed to so working and thereby retaining the advantage of using a received view of the scientific community, and yet consistently affirm what I have said concerning God, metaphysical time, and measured time simply by eschewing arealist understanding of SR. So long as one accords to bis theory a purely instrumentalist interpretation, one can employ it on pragmatic grounds without regarding it as even approximately true. But if one is interested in being a scientific realist on matters of time and space, then, in view of God's existence in metaphysical time and its implication of a set of absolutely simultaneous events being created by Him in the "now" of metaphysical time, one ought to affirm a neo-Lorentzian interpretation ofSR.

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f, as I have argued, God exists in time and there is some physical time which is the measure of God's time, as Newton believed, then the question arises as to whether we bave some idea of which measured time coincides with God's metaphysical time, or in other words, what clock time is the true time? The answer to this question will take us from Special into General Relativity, as we seek to gain a cosmic perspective on time. THE GENERAL THEORY OF RELATIVITY

The Special Theory is a restricted theory, since it concerns only reference frames which are in astate of uniform motion. Although the Special Theory can be adapted so as to analyze the notion of non-inertial (that is, accelerating or decelerating) frames of reference, it does not serve to relativize the motion of such frames by rendering them equivalent to inertial frames. As Einstein wrote, when we speak of the "special principle of relativity"-namely, that "If a system of co-ordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws also hold good in relation to any other system of co-ordinates K' moving in uniform translation relative to /C'-, then "The word 'special' is meant to intimate, that the principle is restricted to the case when K' bas a motion of uniform translation relatively to K, and that the equivalence of K' and K does not extend to the case of non-uniform motion of K' relatively to K."\ Troubled by the non-equivalence of inertial and non-inertial frames, Einstein labored for the decade subsequent to the publication of bis SR on a General Theory of Relativity, wbich bad as its aim the enunciation of a General Principle of Relativity wbich would serve, in turn, to render physically equivalent all inertial and non-inertial frames alike. He completed bis General Theory by 1915 and in the following year published bis definitive statement of it in bis article "The Foundations of General Relativity Theory," wbich appeared in Annalen der Physik. He boasted that bis theory "takes away from space and time the last remnant of physical objectivity."2 It was supposed to be, in effect, the final destruction of Newton's absolute space and time.

A. Einstein, "Tbe Foundations ofGeneral Re1ativity Tbeory," in General Theory ofRelativity, ed. C. W. Kilmister, Se1ected Readings in Physics (Oxford: Pergamon Press, 1973), pp. 141-172. Tbe original paper appeared in Annalen der Physik 49 (1916): 769. 2 Ibid., p. 148.

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In fact, however, Einstein was only partially successful in achieving his aims. He did not succeed in enunciating a tenable General Principle of Relativity after the pattern of the Special Principle, nor was he able to show the physical equivalence of all reference frames. He did succeed in drafting a revolutionary and complex theory of gravitation, which has been widely hailed as his greatest intellectual achievement. The so-called General Theory of Relativity is thus something of a misnomer: it is really a theory of gravitation and not an extension of the Special Theory of Relativity from inertial reference frames to all reference frames. 3 Since our interest is primarily in the conception of time in GR, we may forego an extensive exposition ofthe theory in favor offocusing on its implications for God's relationship to time. In a conscious effort to cast GR as parallel to SR, Einstein opens his paper with an epistemological analysis of the Postulate of Relativity and the need for an extension thereof to non-inertial frames. He begins, "In classical mechanics, and no less in the special theory of relativity, there is an inherent epistemological defect which was, perhaps for the first time, clearly pointed out by Ernst Mach.,,4 He illustrates this defect by means of the following Gedankenexperiment (Figure 7.1).

Figure 7.1. The sphere which becomes ellipsoidal is identified as the rotating sphere.

Two fluid spheres, SI and S2, of the same size and nature hover freely in space in a gravitation-free environment. Let either mass, as judged by an ob server at rest relative to the other mass, freely rotate with a constant angular velocity ab out a common axis. Let us now suppose that by means of measurements taken by See the very frank discussion by Hermann Bondi, "Is 'General Relativity' Necessary for Einstein's Theory of Gravitation?" in Relalivity, Quanta, and Cosmology in the Development of the Scientific Thought ofAlbert Einstein, ed. Francesco De Finis, 2 vols. (New York: Johnson Reprint Corp., 1979), pp. 179-186. According to Bondi, any notion of equivalence between inertial and accelerated observers is "physically meaningless," which goes to show "how void of significance any general principle of relativity must be." But because "a physically sound formulation of Einstein's theory of gravitation exists not involving the physically empty concept of general relativity," one may admire and embrace Einstein's theory of gravitation while rejecting his route to it. "It is perhaps rather late to change the name of Einstein 's theory of gravitation, but general relativity is a physically meaningless phrase that can only be viewed as a historical memento of a curious philosophical observation. " 4 Einstein, "Foundations ofGeneral Relativity," p. 143.

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instruments at rest relative to S\ and S2 respectively it is detennined that the surface of S\ is a sphere and the surface of S2 an ellipsoid of revolution. "What is the reason for this difference in the two bodies?" queries Einstein. ''No answer can be admitted as epistemologically satisfactory, unless the reason given is an observable fact of experience. The law of causality has not the significance of a statement as to the world of experience, except when observable facts ultimately appear as causes and effects."s This Gedankenexperiment is obviously inspired by Newton's own illustration of the two globes connected by a cord, revolving about their common center of gravity (Figure 7.2).

Newton's twin sphere experiment. The tension of the cord enables one to measure the absolute rotation ofthe system.

Figure 7.2.

Newton argues that even if this rotating system were placed "in any immense vacuum, where nothing external or sensible existed with which the balls could be compared," still we could by measuring the tension of the cord find "both the quantity and the direction of this circular motion.,,6 Thus, the rotating globes, like the more celebrated illustration in the Scholium two paragraphs earlier of the rotating bucket ofwater, serve to disclose to us absolute motion and, hence, absolute place (absolute motion being the translation of a body from one absolute place to another) and, hence, absolute space (absolute place being apart of absolute space which a body takes up). 7 But Einstein's Machian verificationism will not permit such an explanation of the difference between the spheres. He writes, Newtonian mechanies does not give a satisfactory answer to this question. It pronounces as follows:-The laws of mechanies apply to the space RI , in respect to which the body 8 1 is at rest, but not to the space R2, in respect to which the body 82 is at

lbid. lsaac Newton, The Principia, trans. I Bernard Cohen and Anne Whitman, with a Guide by I. Bernard Cohen (Berkeley: University ofCalifornia Press, 1999), p. 414. 7 Ibid., pp. 6-7.

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On the positivistic asswnption that a causal statement is meaningless unless the cause as weIl as the effect be an observable fact of experience, the Newtonian appeal to absolute space is ruled out of court, since absolute space is not a thing that can be observed. I shall not belabor the point how utterly untenable and outmoded such a positivistic outlook iso Let us rather look at Einstein's alternative explanation. As Friedman explains,9 Einstein was confronted with two possible routes of explaining non-symmetrical, differential effects, such as those evinced by the spheres, without recourse to absolute motion: (l) Extend the Principle of Relativity for inertial motions to the dass of all motions, so that no differential effects would appear. The Special Principle requires that no differential effects arise between two bodies in relative inertial motion; an extension of this principle would require that SI and S2 exhibit no such effects either. But (1) is untenable because such differential effects would in fact exist between SI and S2' This alternative would therefore fall into that dass of answers which, as Einstein puts it, ''may be satisfactory from the point of view of epistemology, and yet be unsound physically, if it is in conflict with other experiences."10 (2) Adopt Mach's Principle. Instead of regarding S2 as in absolute motion with respect to Rh we could regard S2 as in merely relative motion with respect to some third dass of objects, such as the fixed stars. According to Mach's Principle, Newtonian absolute motion is determined wholly by these distant masses. Were SI and S2 to exist in empty space, there would be no differential effects in them. This is the alternative which Einstein adopts, but in so doing he rnisconstrues it as an extension ofthe Principle ofRelativity. He writes, The satisfactory answer can only be that the physical system consisting of SI and S2 reveals within itself no imaginable cause to which the differing behavior of SI and S2 can be referred. The cause must therefore lie outside this system. We have to take it that the general laws of motion, which in particular deterrnine the shapes of SI and S2, must be such that the mechanical behaviour of SI and S2 is partially conditioned, in quite essential respects, by distant masses which we have not included in the system under consideration. These distant masses and their motions relative to SI and S2 must then be regarded as the seat of the causes (which must be susceptible to observation) of the different behaviour of our two bodies SI and S2. They take over the role of the factitious cause R I • Of all imaginable spaees RI, R 2, ete., in any kind of motion relatively to one another, there is none which we may look upon as privileged apriori without reviving the above-mentioned epistemologieal objeetion. The laws ofphysics must be of such a nature that they apply to systems of reference in any kind of motion. In this way we arrive at an extension of the postulate of relativity. 11

Einstein, "Foundations ofGeneral Relativity," pp. 143-144. See his lueid eornmentary in Michael Friedman, Foundations of Spacetime Theories (Prineeton: Princeton University Press, 1983), pp. 204-215. 10 Einstein, "Foundations ofGeneral Relativity," p. 143. 11

Ibid., p. 144.

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In this paragraph, Einstein makes a number of mistakes. First, Mach's Principle requires not just that the mechanical behavior of the spheres be partially conditioned by the distant masses, but that it be entirely determined by those masses insofar as effects relating to absolute acceleration and rotation are concemed. Second, even if such a strategy were successful, it would not yield an extension of the Principle of Relativity, for the differential effects remain real physical effects. Whether we take the mean matter of the universe to be at rest and 82 rotating relatively to it or 8 2 to be at rest and the average matter of the universe to be circling around it, the fact remains that there are produced in 82 differential effects as a result of the gravitation of the distant masses of the universe. Finally, Mach's strategy simply fails to eliminate absolute motion. For according to Mach's Principle, 82 's rotation is to be explained as a rotation relative to the mean matter distribution of the universe. But what if the average matter of the universe is not itself at rest? Nothing prevents the mean matter distribution of the universe from undergoing itself an absolute rotation. But then that rotation obviously cannot itself be explained as a rotation relative to the average matter of the universe. In the end Mach's Principle fails to eliminate absolute motion. These confusions are compounded by Einstein's confirmatory argument for a General Principle of Relativity, namely, the alleged physical equivalence of arbitrarily accelerated reference frames and frames under the influence of gravitational fields. He invites us to envision a reference frame K' which is moving in uniformly accelerated motion relative to the reference frame K. A mass sufficiently distant from other masses and moving uniformly relative to K will have an accelerated motion relative to K'. Einstein asks, Does this pennit an observer at rest relatively to K' to infer that he is on a 'really' accelerated system of reference? The answer is in the negative; for the above mentioned relation of freely movable masses to K' may be interpreted equally weil in the following way. The system of reference K' is unaccelerated, but the spacetime region in question is in a gravitational field, which generates the accelerated motion of the bodies relatively to K,.12

Tbis interpretation is possible, Einstein explains, because the gravitational field possesses the remarkable property of imparting the same acceleration to all bodies. The mechanical behavior of accelerated bodies is the same as that of stationary bodies in a gravitational field. Therefore, either K or K' can be regarded from the physical standpoint as being stationary. This well-known physical fact favors an extension ofthe Principle ofRelativity. In bis commentary on Einstein's use ofthe so-called Principle ofEquivalence as an argument for a General Principle ·of Relativity, Friedman notes that Einstein is perfectly correct that in the Newtonian Theory of gravitation, one cannot distinguish K from K,.13 One would be thus far justified in enunciating the Principle of Equivalence 12 IJ

Ibid., pp. 144-145. See Friedman, Spacetime Theories, pp. 191-204 for the following critique.

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E. All Galilean reference frames are physically equivalent (or physically indistinguishable). Ifwe supplement (E) with the Special Principle ofRelativity R2 • If two frames are indistinguishable according to aspacetime theory T, they should be theoretically identical according to T, then we should appear to have a General Principle of Relativity that relativizes acceleration just as the Special Principle relativized velocity. But, says Friedman, this argument fails for two reasons. First, even if CE) were true, it is still too restrictive to yield a General Principle of Relativity because Galilean reference frames do not include rotating frames of reference. Rotating frames of reference can be physically distinguished from non-rotating frames by the presence of Coriolis forces, which unlike gravitational or inertial forces, depend on the velocity of the particle acted upon. There is no Principle of Equivalence which govems rotating as well as arbitrarily accelerating frames. But secondly, CE) is in any case false because according to GR arbitrarily accelerating frames are not physically equivalent or indistinguishable. Only a certain class of accelerating frames within SR become physically indistinguishable within GR. This is because in GR the inertial frames in flat Minkowski spacetime are replaced with inertial trajectories of freely falling particles in curved Riemannian spacetime. GR introduces a variable curvature into the flat Minkowski manifold, the degree of curvature of a given region of spacetime being dependent on the distribution of mass and energy. Straight lines in this curved manifold are geodesics and are construed as the world lines of freely falling particles. There are no inertial frames within GR because bodies moving inertially are those which freely follow four-dimensional "straight lines" or geodesics. These inertial trajectories thus play the same role in GR as did inertial frames in SR. Freely falling frames are equivalent to inertial frames only at a single spacetime point or on a single trajectory. SR and GR are thus infmitesimally equivalent at every point of spacetime, but they differ in how those points are connected into aspacetime manifold. The difference between SR and GR is that in the latter inertially moving bodies follow geodesics of a non-flat spacetime connection instead of geodesics of a flat connection as in the former. The inertial trajectories serve as a standard which gives rise in the General Theory to an absolute distinction between inertial motion and non-inertial motion. Inertial motions are those whose trajectories in spacetime are geodesics of the postulated connection, and non-inertial motions are those whose trajectories deviate from the geodesics. Thus, the Principle of Equivalence does not eliminate privileged reference frames or states of motion within GR. Reference frames whose motions describe geodesics in spacetime are privileged in that their motion is natural, whereas motion which deviates from geodesic lines is accelerated. In particular GR permits an absolute, cosmic rotation of matter, as the Gödel and Ozsvath-Schücking

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models illustrate. 14 Hence, the Principle ofEquivalence does not serve to render all reference frames indistinguishable. Einstein's overstatement of his case seems to result from his conflation of physical equivalence and general covariance. But as Friedman points out, the inference that two reference frames are physically equivalent if the laws of nature take the same form in both is a non sequitur. 15 The notions of "sameness of form" and covariance correspond to the notions of physical equivalence and relativity only in flat spacetime theories, but in non-flat spacetime theories this correspondence breaks down because there is no standard formulation of the theory in the usual sense. The only standard formulation is the generally covariant formulation holding in all coordinate systems, and this is too weak a condition to guarantee physical equivalence of all reference frames. Friedman concludes, So Einstein ' s vision of a Leibnizian, or a relationalist, theory rests on a double confusion: a confusion of the strategy of Machianization with the strategy of relativization and a confusion of the notions of physical equivalence and relativity with the notions of sarneness of form and covariance. This double confusion is reinforced to the point of irresistibility by the principle of equivalence .... Clearly, then, general relativity realizes neither of OUf two strategies for relativizing motion. It does not satisfy a generalized or extended relativity principle, since inertially moving frarnes are just as distinguishable from accelerating and rotating frarnes as in all previous theories; and it does not conform to the strategy of Machianization, since absolute rotation has essentially the sarne status-narnely, independence from extemal masses-as in a11 previous theories. In the end, therefore, general relativity does not solve Einstein's problem of the rotating globes (or, equivalently, Newton's problem of the rotating bucket). General relativity, like all previous 'absolutist' theories, predicts that if SI and S2 were alone in the universe, it would still be possible for one and only one of them to experience distorting differential effects. 16

The failure of Einstein's epistemological and physical arguments aimed at relativizing acceleration and rotation does not, however, entail the existence of Newtonian absolute space and time. For within the context of GR these "absolute" motions are conceived to exist, not with respect to some absolute space and absolute time, but rather with respect to spacetime. All events are embedded in a fourdimensional spacetime manifold. Within this manifold a privileged class of inertial trajectories representing the world lines of freely falling particles exists. A particle whose world line deviates from one of these four-dimensional straight lines is moving non-inertially. "Thus, acceleration and rotation are essentially fourdimensional notions, whereas rest and velocity are essentially three-dimensional," explains Friedman. "In moving from a three- to a four-dimensional 'container' or embedding space, we eliminate the latter notions while retaining the former.,,17 This 14 Kurt Gödel, "A Remark about the Relationship between Relativity Theory and Idealistic Philosophy," in Albert Einstein: Philosopher-Scientist, ed. P. A. Schilpp, Library of Living Philosophers 7 (LaS alle, IIl.: Open Court, 1949), pp. 557-562; 1. Ozsvath and E. Schücking, "Finite Rotating Universe," Nature 193 (1962): 1168-1169. 15 Friedman, Spacetime Theories, pp. 207-214. 16 Ibid., pp. 208-209,210-211. 17 Ibid., p. 17.

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can be seen by recalling Galilean spacetime, in which absolute time exists but not absolute space. This theory distinguishes inertial from non-inertial motion, but concepts of absolute rest and absolute velocity fmd no place in the theory because a body which occupies the same spatial point on two planes of simultaneity relative to one reference frame will occuPY two different points at the relevant times relative to a different reference frame in motion with respect to the first. An ob server associated with the first reference frame would claim that the body is at rest, while an observer associated with the second would hold that it is in motion. Thus, the distinction between absolute rest and velocity is vanquished. But Galilean spacetime, while lacking absolute space, still makes sense of "absolute" motions like acceleration and rotation by interpreting these with respect to spacetime, rather than space. An object is accelerated just in case its world line deviates from a fourdimensional geodesic trajectory; an object is rotating just in case its world lines are "twisted" relative to the four-dimensional geodesic trajectories (Figure 7.3). I

! V

/

i

I

(FOUR- 01 MENSI ONAL) GEOOESIC TRAJ ECTORI ES

I I !

ACCELERATI NG WORLO-LINE

ROTATING OBJECT

Figure 7.3. Acceleration and rotation as four-dimensional motions.

In moving from Galilean to relativistic spacetime, we drop absolute time as weil as

absolute space, but acceleration and rotation are still defmable with respect to the four-dimensional spacetime manifold. Thus, although "absolute" motions"absolute" in the sense of ''non-relativized''-still exist within Relativity Theory, they do not guarantee the existence of absolute space and time, as Newton thought. Spacetime itself becomes, as Einstein held, a sort of relativistic ether which serves to defme such motions, but is not itself a reference frame. 18 Of course, such considerations do not prove that absolute space and time do not exist, for one may reject, as we have done, the spacetime realism underlying the above analysis. Still

18 A. Einstein, "Ether and the Theory of Relativity," in Sidelights on Relativity (New York: Dover Publications, 1903), pp. 16-17.

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this analysis does show that, pace Newton, non-relativistic motions do not of themselves necessitate the existence of absolute space and time. COSMICTIME It might appear, therefore, that GR has nothing more to contribute to the understanding of time than SR. They differ simply over the presence of curvature in spacetime; if one adds a condition of flatness to GR, then SR results. But such a conclusion would be hasty, indeed, for GR serves to introduce into Relativity Theory a cosmic perspective, enabling one to draft cosmological models of the universe governed by the gravitational field equations of GR. Within the context of such cosmological models, the issue oftime resurfaces dramatically. Einstein hirnself proposed the first GR-based cosmological model in his paper, "Cosmological Considerations on the General Theory of Relativity" in 1917. 19 The model describes a spatially finite universe which possesses at every time t the geometry of the surface of a sphere in three dimensions with a constant radius R. The model is characterized by the static metric di = _dt2 + R2 [dr 2 + sin2r (dfl + sin2 Bdl)]. Time, which is decoupled from space, extends from -00 to +00. Thus, spacetime takes on the form of a sort of four-dimensional cylinder, temporal crosssections of which are the 3-spheres. In order to bring such a model into conformity with his field equations, Einstein was compelled to adopt a term A, the so-called cosmological constant, which counteracted gravitation and so preserved the static three-dimensional space through time. By setting A > 0, one generates a weak repulsion between bodies, which keeps the universe equiposed between gravitational collapse and cosmological expansion. Kanitscheider draws our attention to the sort oftime coordinate which shows up in the metric ofEinstein's model: lt represents in a certain sense the restoration of the universal time which was destroyed by SR. In the static world there is a global reference frame, relative to which the whole of cosmic matter finds itself at rest. All cosmological parameters are independent of time. In the rest frame of cosmic matter space and time are separated. For fundamental observers at rest, all docks can be synchronized and a worldwide simultaneity can be defined in this cosmic frame. 20

Thus, cosmological considerations prompted the conception of a cosmic time which measures the duration of the universe as a whole. Nor was this cosmic time limited to Einstein's static model of the universe. Expansion models, which trace their origin to de Sitter's 1917 model of an empty

19 A. Einstein, "Cosmological Considerations on the General Theory ofRelativity," in The Principle of Relativity, by Albert Einstein, et al., with Notes by A. Sommerfeld, trans. W. PeITett and G. B. Jeffery (rep. ed.: New York: Dover Publications, 1952), pp. 177-188. 20 Bemulf Kanitscheider, Kosmologie (Stuttgart: Philipp Redam, Jun., 1984), p. 155. See also G. J. Whitrow, The Natural Philosophy ofTime, 2d ed. (Oxford: Clarendon Press, 1980), pp. 283-284.

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universe,21 mayaiso involve a cosmic time. De Sitter showed that Einstein's field equations may be satisfied by a gravitational field in the absence of any matter whatsoever in a world characterized by the metric ds 2 = -dr + e2tH [dr2 + r2 (df} + sin2 eal)]. The de Sitter universe also appears to be static, but that is only because it is empty. If particles of matter are introduced into it, one discovers that de Sitter space is in fact expanding because the distance between any two arbitrary points given by specific values of r, B, and t/J increases with time by a factor of etH due to the repulsive force of the cosmological constant A. De Sitter spacetime resembles a pseudo-sphere with three-dimensional cross-sections of positive curvature. Its geodesics were increasingly distant from each other in the past, approach each other to a minimal distance at t = 0, and then re-separate out toward infmity in the future. Thus, in 1917 two GR-based cosmological models had been drafted: one in which a material world exists, but is static, and another which is dynamic, but lacks a material world-a situation which inspired Eddington's crack: "Shall we put a little motion into Einstein's world of inert matter or shall we put a little matter into de Sitter's prim um mobile?,,22 It was the Russian physicist Aleksandr Friedmann who put together these elements in 1922 to produce a cosmological model of an expanding, material universe. 23 His model universe was characterized by ideal homogeneity and isotropy and set A = 0 (which was equivalent to omitting it, thus preserving the form of Einstein's original equation). Friedmann's solution to Einstein's field equation was

• 2

where R is the rate of increase of the scale factor R with time, G is the gravitational constant, pis the matter density, and k is the curvature constant which may take the values of 0, 1, or -1. The most startling implication of the Friedmann model is that as one traces the expansion back in time the universe becomes increasingly dense until one arrives at astate of infinite density before which the universe did not exist. Indeed, this state represents aspacetime singularity at which all spatial and temporal dimensions become zero, so that it marks the boundary to physical time itself. Cosmic time could not exist at or prior to the singularity, so that cosmic time must be finite in the past, thereby implying a defmite, fmite age of the universe. It is difficult to exaggerate how amazing such a prediction was, for it revealed that, in the

" Willem de Sitter, "On the Relativity of Inertia," in Koninldijke Nederlandse Akademie van Wetenschappen Amsterdam. Afdeling Wis- en Natuurkundige Wetenschappen. Proceedings ofthe Section ofScience 19(1917): 1217-1225. 22 Arthur S. Eddington, The Expanding Universe (Cambridge: Cambridge University Press, 1952), p. 46. 23

A. Friedmann, "Über die Krümmung des Raumes," Zeitschrift für Physik 10 (1922): 377-386.

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ideal case at least, the original GR equations implied the finitude of the past and creatio ex nihilo. In 1930, one year after Edwin Hubble's explanation ofthe observed red-sbift of galactic light as a Doppler effect due to a universal, isotropie galactic recession, Eddington demonstrated that the static Einstein model was radically unstable. 24 Even small changes in the density would upset the balance between gravitation and the cosmological constant, so that a cosmic expansion or collapse would result; moreover, so much as the mere transportation of matter from one part of the universe to another would cause the former region to expand and the latter to collapse. The following year Einstein recommended that the cosmologieal constant be dropped from the equations, later recalling it as ''the greatest blunder of my life.,,2s Thus, the Big Bang model of the universe-despite a later, temporary challenge from the Steady State model-came to be the controlling paradigm of GR-based cosmologieal models. The nature of the cosmic time wbich measures the duration of the universe in such models deserves our further scrutiny. In constructing a cosmological model, one overlooks the inhomogeneity of matter on the galactic and sub-galactie scales and takes instead an extremely large-scale viewpoint of the universe, on wbich these inhomogeneities become negligible. On this very large scale, galaxies and galaetie clusters can be viewed as partieies of a homogeneous and isotropie dust or gas filling the universe. We may even choose to ignore the particulate structure ofthis gas and treat it instead as an idealized, perfect fluid, characterized by a fourdimensional velocity u, a mass-energy density p, and apressure p. The 4-velocity U has reference to a hypothetical observer who is at rest relative to the material substratum in bis region and who therefore observes the immediately proximate galaxies to have no mean motion. Such an observer is frequently referred to, after the manner of E. A. Milne, as a "fundamental observer" and bis associated galaetic particle as a "fundamental particle." The mass-energy density p also has reference to such a fundamentalobserver, being the material density and radiation density of the cosmological fluid as observed by a fundamental observer in bis reference frame. The pressure p is the kinetic pressure of the galaxies determined by both matter and radiation. In the Friedmann model, the cosmological fluid is homogeneous and isotropic. But how are these notions to be understood? Intuitively, something is homogeneous if it is everywhere the same at a given moment of time. But when we take a cosmologieal perspective, this notion necessitates the existence of a cosmic time. Such a universal time can be constructed by assigning a time parameter to spacelike hypersurfaces wbich are distinguished by natural symmetries in the spacetime. A spacelike hypersurface is a three-dimensional spatial slice of spacetime, the prefix "hyper-" serving to alert us to the fact that the surfaces which dissect spacetime are 24 A. S. Eddington, "On the Instability of Einstein's Spherical World," Monthly Notices 0/ the Royal Astronomical Society 19 (1930): 668-678. 2' Albert Einstein, quoted in George Gamow, My World Line (New York: Viking Press, 1970), p. 44.

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not the two-dimensional planes which appear in our diagrams, but three-dimensional spaces. By foliating spacetime into such slices we can construct a cosmic time by ordering these slices serially according to a time parameter. The cosmic time so constructed will bear a special relationship to the fundamental ob servers, whose local planes of simultaneity, ca1culated by the standard SR clock synchronization procedure, will fit together to coincide with the cosmic hypersurface. Misner, Thome, and Wheeler explain, In Newtonian theory there is no ambiguity about the concept 'a given moment oftime.' In special relativity there is some ambiguity because of the nonuniversality of simultaneity, but once an inertial frame has been specified, the concept becomes precise. In general relativity there are no global inertial frames (unless spacetime is flat); so the concept of 'a given moment of time' is completely ambiguous. However, another, more general concept replaces it: the concept of a three-dimensional spacelike hypersurface. This hypersurface may impose itself on one's attention by reason of natural symmetries in thespacetime. Or it may be selected at the whim or convenience of the investigator.... At each event on a spacelike hypersurface, there is a local Lorentz frame whose surface of simultaneity coincides locally with the hypersurface. Of course, this Lorentz frame is the one whose 4-velocity is orthogonal to the hypersurface. These Lorentz frames at the various events on the hypersurface do not mesh to form aglobaI inertial frame, but their surfaces of simultaneity do mesh to form the spacelike hypersurface itself. The intuitive phrase 'at a given moment of time' translates, in general relativity, into the precise phrase 'on a given spacelike hypersurface.' The investigator can go further. He can 'slice up' the entire spacetime geometry by means of a one-parameter family of such spacelike surfaces. He can give the parameter that distinguishes one such slice from the next the name of 'time' .... The successive slices of 'moments of time' may shine with simplicity or may only do a tortured legalistic bookkeeping for the dynamies [ofthe geometry ofthe universe]. Which is the case depends on whether the typical spacelike hypersurface is distinguished by natural symmetries or, instead, is drawn arbitrarily.26

Several features of this explanation deserve comment. First, although one may slice spacetime into various hypersurfaces wholly arbitrarily, certain spacetimes have natural symmetries that guide the construction of cosmic time. 27 GR does not itself lay down any formula for dissecting the spacetime manifold of points; it has no inherent "layering." Theoretically, then, one may slice it up at one's whim. Nevertheless, certain models of spacetime, like the Friedmann model, have a dynamical, evolving physical geometry, a geometry that is tied to the boundary conditions of homogeneity and isotropy of the cosmological fluid, and in order to ensure a smooth development of this geometry, it will be necessary to construct a time parameter based on a preferred foliation of spacetime. For example, in 1935 H. P. Robertson and A. G. Walker independently showed that a homogeneous and isotropie universe requires that space be possessed of a constant curvature and be characterized by the metric:

26 Charles W. Misner, Kip S. Thome, and John Archibald Wheeler, Gravitation (San Francisco: W. H. Freeman, 1973), pp. 713-714. 27 See Kanitscheider, Kosmologie, pp. 182-197.

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dr 2 +r 2(d(}2 +sin 2 (}d,,2 (1+kr 2 /4)2 In the metric for spacetime, the spatial geometry is dynamic over time:

In this equation, called the Robertson-Walker line element, t represents cosmic time, the proper time of a fundamental ob server. It is detached from space and serves to render space dynamic. The geometry of space is thus time-dependent. The factor R(t) determines that all spatial structures of cosmic proportions, for example, a triangle demarcated by three galactic clusters or fundamental particles, will either shrink or stretch through the contraction or expansion of space, in this case into a similar smaller or larger triangle. The boundary condition ofhomogeneity precludes other geometrical changes such as shear, which would preserve the area but not the shape of the triangle. The condition of isotropy further precludes that the triangle should be altered in such a way as to preserve both its area and shape while nonetheless undergoing a rotational change of direction. Thus, in a Friedmann universe there are certain natural symmetries related to the dynamic geometry which serve as markers for the foliation of spacetime and the assigning of a cosmic time parameter. Of course, there are other cosmological models which do not involve homogeneity and isotropy and so may lack a cosmic time altogether. 28 Cosmic time is thus not nomologically necessary, and its actual existence is an empirical question. Secondly, cosmic time is fundamentally parameter time and only secondarily coordinate time. 29 Physical time can be related in two quite different ways to the manifold in which motion is represented. If it is part of that manifold, then it functions as a coordinate. If it is external to that manifold, then it functions as a parameter. In Newton's physics time functioned only as a parameter. Motion takes place in absolute space and is parameterized by absolute time. Similarly, in Einstein's original formulation of SR, relativistic time functions only as a parameter. Einstein rejected the existence of absolute space and a fundamental rest frame in favor of a plurality of relatively moving inertial spaces, each of which was characterized by a time parameter which registered the proper time for that inertial Kanitseheider eomments, "On the other hand it should also be emphasized eoneeming the geometrie side of this world model that the simple, form-preserving (dynamie), physieal geometry ean be traeed baek to the boundary eonditions whieh have been laid down and by no means possess either a logieally apriori or physieally neeessary eharaeter. If one eases the boundary eonditions, one obtains world models with shear and rotation, and they, too, ... ean be brought into harmony with the Einsteinian gravitational theory" (Ibid., p. 188). 29 See Peter Kroes, Time: Its Structure and Role in Physical Theories, Synthese Library 179 (Dordreeht: D. Reidel, 1985), pp. 60-96.

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frame. There was no absolute parameter time, only separate parameter times assigned to their respective inertial frames. The familiar spacetime formulation of SR used in virtually all contemporary expositions of the theory, according to which time is a co-ordinate (along with the three spatial co-ordinates) of an event in spacetime, derives from Minkowski. The spacetime formalism of Minkowski, in which time is part of the manifold in which motion is represented and so functions as a co-ordinate, was a wonderful aid to the visualization and comprehension of Relativity Theory; but even Newton's theory can be cast in terms of aspacetime formalism in which time functions as a co-ordinate of events in spacetime. 30 Both theories admit of either aspacetime formulation (in which spacetime is the manifold) or aspace and time formulation (in which the manifold is space(s), and time is a parameter). In the spacetime formulation, time functions as both a coordinate (locating events in the manifold) and as a parameter (recording the lapse of proper time along an observer's inertial trajectory), the chief difference between the two theories being that in SR parameter time loses the universality it possesses in Newtonian spacetime (that is, simultaneity becomes relative). When it comes to GR, it is unclear, according to Kroes, whether the theory could be formulated in terms of space and time rather than spacetime. He observes that differences in coordinate time values generally have no direct physical significance in GR (this is because of the variable spacetime geometry or gravitational fields which distort the co-ordinate grids laid on them). But insofar as time functions as a parameter in GR,31 it is a more fundamental notion oftime because it does possess direct physical significance. Parameter time can serve as a direct measure of the time elapsed between two events. Moreover, parameter time is well-suited, according to Kroes, for accommodating the tensed notion of temporal becoming. While there is no intrinsic difference between past and future in co-ordinate time, there exists such a distinction in parameter time. Thus, the "flow" of time could relate to parameter time. Kroes writes, In the space and time fonnulation of Newtonian physics, the increase of parameter time represents the objective flow of absolute time; for increasing values of parameter time, the distribution of the particles in space will be different, and therefore there is change and becoming with regard to parameter time. However, the same kind of reasoning,

30 Such is the treatment of Friedman, Spacetime Theories, for a11 the theories he diseusses, including Newtonian spaeetime (pp. 71-124). J\ There are three choices of time parameter available in GR, aecording to Misner, Thorne, and Wheeler: (i) the original time variable t. "This quantity gives direct1y proper time elapsed since the start of the expansion. It is the time available for the fonnation of galaxies. [t is also the time during which radioaetive deeay and other physieal processes have been taken plaee" (Gravitation, p. 730). (ii) the expansion factor R(t). Since this faetor grows with time, it serves to distinguish one phase of the expansion from another, thus serving as a parametrie measure oftime in its own right. The ratio of R(t) at two different times gives the ratio of the dimensions of the universe at those two times. (iii) the areparameter measure of time 7/(t). During the time interval dt, a photon traveling on hypersphere of radius R(t) covers an are in radians equal to drrdt/R(t). (In a model where the eurvature eonstant k=0 or-I, the words "hypersphere" and "are" should be replaeed with their appropriate analogues.) Small values of the are parameter indicate early times in the universe, large values later times.

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applied to parameter time in the spacetime formalism of relativity theory, leads to the conclusion that parameter time has an objective flow (but with the proviso that the flow of parameter time is not universal). 32

Because parameter time in the Special Theory is the proper time of each inertial observer and because no inertial frame is preferred, the "flow" of parameter time is not universal. But insofar as cosmic time plays a role in GR-based cosmological models, that universality is restored. It is highly significant, then, that cosmic time appears fundamentally as a parameter time in GR, though it can be used to generate co-ordinate time as well, as we shall see. As a parameter, it is not part of the spacetime manifold, and it thus measures the duration of the universe in an observer-independent way, that is to say, the lapse of cosmic time is the same for all ob servers. Moreover, cosmic time supplies a physical time which is well-suited to accommodate the philosophical notion oftemporal becoming. Thirdly, cosmic time is intimately related to a dass of fundamentalobservers whose individual planes of simultaneity mutually combine to align with the hypersurface demarcating the cosmic time. 33 These hypothetical ob servers are conceived to be moving along with the cosmological fluid so that, although space is expanding and they are therefore mutually receding from each other, each is in fact at rest with respect to space itself. As time goes on and the expansion of space proceeds, each fundamental ob server remains in the same place-his spatial coordinates do not change-though his spatial separation from fellow fundamental observers increases. Because of this mutual recession, the dass of fundamental observers do not serve to define aglobai inertial frame, technically speaking, though aU of them are at rest. When each of them utilizes the light signal method of synchronization, interesting relativistic effects arise due to their relative recessional motio ll. Since the spatial distance between them grows with time, a light signal from fundamental ob server F to another such ob server F' wiU have farther to travel on its return leg of its journey than on its out-going leg (Figure 7.4).

F

F' Kroes, Time, p. 96. Dorato also maintains that "cosmic time would be an ideal candidate with respect to which to define a world-wide. mind-independent becoming" (Mauro Dorato, Time and Reality: Spacetime Physics and the Objectivity of Temporal Becoming, Collana di Studi Epistemologici 11 [Bologna: CLUEB, 1995]. p. 189). J2

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CHAPTER7 Figure 7.4. Because of the distance between fundamental observers F and F' increases with time, a light signal will have to travel a longer distance on its return trip than on its outbound trip in an exchange between F and F'.

F will therefore calculate that F"s clock is running sloW; but, of course, the converse is also the case. Here we do have "pure relativity" without absolute effects. It is purely a reciprocal measurement phenomenon. Fand F"s reciprocal observations of time dilation and length contraction have no absolute significance. They result merely from the manner of observation and are in fact similar to the familiar analogy of the mutual observation of diminishing size when two ob servers retreat from each other. Because F and F' will draw their planes of simultaneity orthogonal to their world lines, their surfaces of simultaneity will not be aligned. But since each is at rest with respect to space, his plane of simultaneity will coincide locally with the hypersurface of cosmic time. Were he in motion with respect to the cosmological fluid, then his plane of simultaneity would be at an angle with the local hypersurface. But in virtue of being at rest, he can be guaranteed that locally events which he judges to be simultaneous will lie on the hypersurface. Thus, the local regions of the planes of simultaneity of fundamentalobservers all blend together and coincide with the hypersurface, much as a circle is formed by the points of interseetion of all the straight lines which are tangents of its circmnference. This has two important implications: first, that the proper time of each fundamental observer coincides with cosmic time and, second, that all the fundamental observers will agree as to what time it iso By employing the notions explained above, one is now prepared to define "homogeneity" and "isotropy": Homogeneity ofthe universe means, then, that through each event in the universe there' passes a spacelike 'hypersurface ofhomogeneity' (physical conditions identical at every event on this hypersurface). At each event on such a hypersurface, the density, p, and pressure, p, must be the same; and the curvature of spacetime must be the same .... [sotropy of the universe means that, at any event, an observer who is 'moving with the cosmologicaljluid' cannot distinguish one ofhis space directionsfrom the others by any local physical measurement. 14

With these definitions in hand, one is now prepared to construct a cosmic coordinate time. 3S Choose any hypersurface of homogeneity S\ and to all the events on it assign the co-ordinate time (\. Next layout a grid of spatial co-ordinates (Xh X2, X3) on S\ and then, using the world lines ofthe fundamental particles project this grid through successive hypersurfaces, thus co-ordinating all of spacetime. The system of co-ordinates is thus co-moving with the fluid, so that the fluid is always at rest relative to the space co-ordinates. For the time co-ordinate of any event P, one uses t] plus the lapse of proper time, as measured along the world line of a fundamental

11 14

l'

See S. 1. Prokhovnik, Light in Einstein 's Universe (Dordrecht: D. Reidel, 1985), chaps. 4, 5, 6. Misner, Thorne, and Wheeler, Gravitation, p. 714. lbid., pp. 715-716.

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particle that passes through P, from SI to P. Letting ~Trepresent the lapse ofproper time, the time t of P will be t(P) = t 1 + ~ T. Milton K. Munitz explains, If we imagine observers attaehed to various particles of the homogeneous and isotropie eosmological fluid, then all such observers will be at rest with respect to any given hypersurface, yet they will move through a sequence of such hypersurfaces as the fluid itself moves through spacetime. The paths of timelike geodesics of free material particles in the cosmological fluid are orthogonal to the three-dimensional spatial hypersurface. Each observer measures proper time by his own dock along his own timelike geodesic. The intervals of each timelike geodesic of a material particle, orthogonal to a given hypersurface, will measure proper time along its own individual world line. Let various observers set their individual docks to a certain time when they observe the density of matter in their respective neighborhoods to have the same given value. Thus, if the galaxies are uniformly distributed throughout space, then at a given moment of cosmic time the same density of galaxies will hold at any region of space. The homogeneity of the model assures the retention of the synchronized clocks (and so of the measures of cosmic time) with change in density as the universe expands or contracts. (Any departures from the measurement of cosmic time-that is, any irregularities in time-keeping among different timekeepers-will be assigned to purely local or peculiar variations in velocity, and to local variations in gravitational fields associated with particular astronomical systems .... ) ... Allobservers situated on particles of the cosmological fluid can thus employ a common set of synchronous temporal coordinates. By adding the same interval of elapsed proper time to the coordinate time to of our present, initial, arbitrary hypersurface, we arrive at different hypersurfaces, each of which is identified by its distinctive value of the cosmic time t. The cosmic time coordinate will be constant for each hypersurface, but will change with changing hypersurfaces. Therefore, clocks attached to co-moving particles may be said to measure cosmic time t. 36

One thus supplements the cosmic parameter time with a cosmic co-ordinate time. It is noteworthy that deviations from this time are purely local effects to be explained due to velocity (SR) or to gravitation (GR). Thus, on a cosmic scale, we have that universality of time and absolute simultaneity of events which the Special Theory had denied. Whitrow asserts, " .. .in a universe that is characterized by the existence of a cosmic time, relativity is reduced to a local phenomenon, since this time is world-wide and independent ofthe observer.,,37 Kanitscheider explains, ... with the parameter t we can so order all slices through spacetime (the homogeneous hypersurfaces) that an unequivocal earlierllater relation can be set up worldwide. Within such a slice t = to (in a three-space) the material quantities p and p, as weil as the physical geometry, are everywhere the same. Isotropy implies, moreover, that a particle of the cosmological fluid traces a worldline that orthogonally intersects the hypersurfaee of homogeneity. One recognizes that there is here again a privileged reference frame; to an observer at rest relative to the substratum, who swims along with the fluid, the universe has a simple form in material structure and spacetime geometry .... The particular form of the motion of matter in this class of models suggests the utilization of a co-moving co-ordinate system, in which a worldwide, absolute simultaneity is defined. This is, however, no contradiction to the SR, since here the universe itself, with its limited possibility of movement, serves as an instrument of synchronization. The special relativistic time dilation, which we are acquainted with 36

37

Milton K. Munitz, Cosmic Understanding (Princeton: Princeton University Press, 1986), pp. 97-98. Whitrow, Natural Philosophy ofTime, p. 371.

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CHAPTER 7 through local experiments, still holeIs as before for docks moving relatively to the substratum. Nevertheless, the proper times of all observers who are at rest with respect to the flowing (expanding or contracting) substratum can be harmoniously fitted into a cosmic time. 38

Based on a cosmologieal, rather than a local, perspective, cosmic time restores to our intuitive notions of universal time and absolute simultaneity which SR denied. The question, then, becomes an empirical one: does cosmic time exist? The answer to that question comes from the evidence for large scale (scales of -10 8 light years or larger) homogeneity and isotropy in the universe. In models like Gödel's and Ozsvath and Schücking's, there is posited a worldwide rotation of the homogeneous sub stratum, so that the isotropy condition of the Friedmann model is violated and the proper times of fundamentalobservers cannot be fitted together into a universal time. However, the observational evidence for cosmic isotropy, partieularly for the isotropy of the cosmic microwave background radiation, which has been measured by the COBE satellite to an accuracy of one part in 100,000, makes it very likely that our actual universe does approximate a Friedmann universe. Martin Rees focuses on two important pieces of evidence that our universe is kinematieally described by a Robertson-Walker metric: (i) The Hubble Constant: (he Present Scale of the Observable Universe. The tight relation between the red shift and apparent magnitude of the brightest elliptical galaxies in clusters teIls us that their motions accord with those expected in a Robertson-Walker spacetime for a set of co-moving objects whose distances with respect to each other are smaller than the overall radius of curvature ofthe hypersurfaces ofhomogeneity. The constant of proportionality between recession velocity and distance, that is, the Hubble Constant, is thus the key parameter determining the scale of the observable universe and the time scale over which its properties can change. (ii) The Isotropie Microwave Background. According to the hot Big Bang model, the material in the early universe would constitute a hot plasma, strongly coupled to a radiation field. When adiabatic expansion had cooled the material to approximately 4,00ooK, the plasma would recombine and the radiation would no longer undergo scattering or absorption. The photons emitted then have been red-shifted to the microwave end of the spectrum and are now observed as a remarkably isotropie radiation background filling all of space. This radiation background establishes that the gross kinematies of the universe are exceedingly symmetrical with a greater precision than the data on which the Hubble Law is based. The measured isotropy implies that the observable universe can be very precisely described by a Robertson-Walker metrie. "Unless we adopt an anti-Copernican viewpoint, this forces us to adopt a RobertsonWalker metric.,,39 In addition to these kinematical considerations, Rees adds (iii) Evidence for large-scale homogeneity from radio, optical, and x-ray observations. The distribution of radio, optical, and x-ray sources on the sky supports large scale US

Kanitscheider, Kosmologie, pp. 186-187. Martin J. Rees, "The Size and Shape of the Universe," in Some Strangeness in the Proportion, ed. Harry Woolf(Reading, Mass.: Addison-Wesley Publishing Co., 1980), p. 293. 38

39

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isotropy, the x-ray radiation backgroWld supplying a particularly sensitive probe for large scale matter distribution. Rees concludes, ''The most remarkable outcome of fifty years of observational cosmology has been the realization that the universe is more isotropie and uniform than the pioneer theorists ofthe 1920's would ever have suspected. ,.40 "Consequently, we have strong evidence that the universe as a whole is predominantly homogeneous and isotropie," states Whitrow, "and this conclusion .. .is a strong argument for the existence of cosmic time.'.41 In fact, Hawking has shown that existence of stable causality, that is, the absence of any null or time-like closed causal paths, is a necessary and sufficient condition for the existence of cosmic time. 42 Thus, far from ''taking away from space and time the last remnant of physical objectivity," as Einstein thought at first, GR through its cosmological applications gives back what SR had purportedly removed. Whitrow concludes, The concept of the relativity of simultaneity on which, in 1905, Einstein based his Special Theory of Relativity at fIrst appeared to eliminate from physics any idea of an objective world-wide lapse of time according to which physical reality could be regarded as a linear succession of temporal states or layers. Instead each observer was regarded as having his own sequence of temporal states and none of these could claim the prerogative of representing the objective lapse of time. Nevertheless, a quarter of a century later, theoretical cosmologists who made use of the physical ideas and mathematical techniques associated with relativity theory were led ... to re-introduce the very concept which Einstein had begun by rejecting .... From the cosmological point of view ... it would therefore seem that neither the equivalence of all observers in uniform relative motion (Special Relativity) nor of a11 observers in any form of relative motion (General Relativity) can be accepted without restriction .... once the existence of a world-wide distribution of matter, albeit of extremely low mean density, becomes an essential feature of the problem under investigation, then certain frames of reference and observers must be specially distinguished, narnely those which move with the mean velocity of matter in their neighborhood. In the cosmological models which we have discussed ... , the local times of all these 'privileged' observers fit together, into one world-wide time called 'cosmic time. ,43

Relativity theory thus gives back with its right hand what it had taken away with its left. Gon AND COSMIC TIME Now it is my contention that since the inception of the universe and the beginning of physical time, this cosmic time plausibly coincides with God's Ibid., p. 301. See also now Martin Rees, Be/ore the Beginning: Our Universe and Others, with a Foreword by Stephen Hawking (Reading, Mass.: Addison-Wesley, 1997), p. 34: ''Tbe simple 'model universes' turn out, more than 60 years later, to fit extraordinarily well-they are more relevant to our real universe than Friedmann and other the pioneers would have dared to hope." 41 Whitrow, Natural Philosophy o/Time, p. 307. 42 S. W. Hawking, "The Existence of Cosmic Time Functions," Proceedings o/the Royal Society 0/ London A 308 (1968): 433-435. 43 Whitrow, Natural Philosophy o/Time, p. 302. 40

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metaphysical time, that is, with Newton's absolute time. It therefore provides the correct measure of God's time and thus registers the true time, in contrast to the multiplicity of local times registered by c10cks in motion relative to the cosmological sub stratum. Already in 1920, on the basis ofEinstein and de Sitter's cosmological models, Eddington hinted at a theological interpretation of cosmic time: In the first place, absolute space and time are restored for phenomena on a cosmical

scale. . .. The world taken as a whole has one direction in which it is not curved; that direction gives a kind of absolute time distinct from space. Relativity is reduced to a local phenomenon; and although this is quite sufficient for the theory hitherto described, we are inciined to look on the limitation rather grudgingly. But we have already urged that the relativity theory is not concemed to deny the possibility of an absolute time, but to deny that it is concemed in any experimental knowledge yet found; and it need not perturb us if the conception of absolute time turns up in a new fonn in a theory of phenomena on a cosmical scale, as to which no experimental knowledge is yet available. Just as each limited observer has his own particular separation of space and time, so a being co-extensive with the world might weil have a special separation of space and time natural to hirn. It is the time for this being that is here dignified by the title ·absolute.'44

A couple of items in this remarkable paragraph deserve comment. First, Eddington rather charitably interprets SR as positing merely an epistemic limitation on our temporal notions rather than an ontological limitation on time and space. But as friend and foe alike have emphasized,45 Einsteinian SR requires metaphysical, not merely epistemological, commitments concerning the non-existence of absolute space and time. Otherwise, one winds up with the Lorentz-Poincare interpretation ofthe theory, which is, in truth, the position which Eddington is describing. Second, Eddington is quite willing to call cosmic time "absolute" in view of its independence from space, that is to say, its status as a parameter. Relativistic time is, as Lorentz and Poincare maintained, only a local time, whereas cosmic time, being non-Iocal, gives the true time. Third, although in 1920 there was no empirical evidence for cosmic time, within a few short years astronomical evidence confmned the prediction of the Friedmann model of a universal expansion and, hence, of cosmic time. The veil of epistemic limitation had been tom away by empirical science. Finally, this cosmic time would be the time of an omnipresent being whose reference frame is the hypersurface of homogeneity itself. Is Eddington recalling here Poincare's "intelligence infinie", who c1assified everything according to his 44 Arthur Eddington, Space, Time and Gravitation, Carnbridge Science C1assics (Carnbridge: Carnbridge University Press, 1920; rep.ed.: 1987), p. 168. 45 Adolf GTÜnbaum asserts, "In short, it is because no relations of absolute simultaneity exist to be measured that measurement cannot disciose them; it is not the mere failure of measurement to disciose them that constitutes their non-existence, much as that failure is evidence for their non-existence" (GTÜnbaum, Philosophical Problems 0/ Space and Time, 2nd ed., Boston Studies in the Philosophy of Science 12 [Dordrecht: D. Reidel, 1973], p. 368). Richard Swinbume plumps for a neo-Lorentzian interpretation of SR, comrnenting, "One can describe the Universe of Special Relativity perfectly intelligibly by supposing that its equations show a limit to our knowledge of absolute simultaneity, not a limit to its existence" (Richard Swinbume, Space and Time, 2d ed. [London: Macmillan, 1981], p. 201).

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universal frame of reference, just as finite observers classify events according to their local frames? Cosmic time is not merely the "fusion" of all the proper times recorded by the separate fundamental ob servers, but, even more fundamentally, it is the time which measures the duration of the omnipresent being which co-exists with the universe. As the measure of the proper time of the universe, cosmic time also measures the duration of and lapse of time for a temporal being co-extensive with the world. For Eddington, it is the time of this being that deserves to be called "absolute. " The theological application is obvious. In Whitrow's interpretation, "Eddington endeavoured to explain away Einstein's re-introduction of cosmic time by regarding this concept as one of the prerogatives of Newton's ubiquitous Deity, and this is beyond the scope of experimental science.,,46 But the theistic philosopher need see nothing disingenuous about such an identification. It makes perfectly good sense to interpret the lapse of cosmic time as measuring the lapse of God's time. Thus, Fitzgerald, after asserting, "I see no way to save the idea of a worldwide surge of Absolute Becoming that would be intimately associated with God's temporal way of experiencing the world,,,47 recalls that some GR-based models have a cosmic time and admits that the theologian might take this to be a privileged time. He expresses hesitancy because Gödel showed that not all models have this cosmic time; still, he admits, this solution may not be a blind alley and he recommends that the theologian should explore it further. 48 Now God's metaphysical time cannot be said to be identical with cosmic time, since the former is capable of exceeding the latter, in that metaphysical time could precede physical time (recall God's counting down to creation). Nevertheless, since the inception of cosmic time, the moments of God's time would seem to coincide with the moments of cosmic time. When we reflect that God is causally related to the cosmos, sustaining it in being moment by moment, then it seems difficult to deny that the duration measured by cosmic time is also the duration of God's temporal being. If the duration of the universe measured in cosmic time is 15 billion years since the singularity, then is not the duration of God's creatorial activity in

Whitrow, Natural Philosophy ojTime, p. 284. Paul Fitzgerald, "The Truth about Tomorrow's Sea Fight," Journal oj Philosophy 66 (1969): 325. 48 Ibid., p. 326. See also the identification of cosmic time as God's time by Keith Ward, Religion and Creation (Oxford: Clarendon Press, 1996), pp. 301-303. Fitzgerald later rejected the identification of cosmic time with God's time because cosmic time, being a statistical matter based on mean matter density, allows a range of regions of the universe to be classed as simultaneous. "This means that strictly speaking, several mutually incompatible 'cosmic times' will be definable, each equally usable for the gross purposes of the astronomer, and none sufficiently preferable to the others to justify identifying it with 'God's time'" (Idem, "Relativity Physics and the God of Process Philosophy," Process Studies 2 [1972]: 256). The problem is that Fitzgerald is still operating with a reductionistic view oftime which equates time with physical time. But if God's time is metaphysical and cosmic time a sensible measure thereof, then it does not matter, as Newton saw, whether this measure is more or less equable. Cosmic time gives a rough measure ofGod's time. Moreover, as a result ofmeasurements made since the launch of the COBE satellite in 1989, we now have very precise measurements of the isotropy of the cosmic microwave background radiation, thereby honing the measure of cosmic time. 46

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metaphysical time also 15 billion years? In God's "now" the universe has (present tense) certain specific and unique properties, for example, a certain radius, a certain density, a certain background temperature, and so forth; but in the cosmic "now" it has all the identical properties, and so it is with every successive "now." Is it not obvious that these ''now's'' coincide and designate one and the same present? Perhaps we can state this consideration a bit more formally by means of the following proposed principle:

P: For any constantly and non-recurrently changing universe U and temporal intervals x, y large enough to permit change, if the physical description of U at x is the same as the physical description of U at y, then x and y coincide. Given that in metaphysical time there is a temporal interval or duration during which a certain physical description of the universe is true and that in cosmic time a similar interval exists, then it follows from P that those intervals of metaphysical and cosmic time coincide. It seems to me, therefore, that God's time and cosmic time ought naturally to be regarded as coincident since the inception of cosmic time. I do not mean to say that there are in fact two times rather than one; rather I mean simply to reaffinn Newton's distinction between absolute (=metaphysical) time and relative (=physical) time. The latter is merely a sensible measure of the former, and my suggestion is that cosmic time is a sensible measure ofGod's time since creation. Such an affIrmation will be typically met with passionate disclamations. Such protestations strike me, however, as being for the most part misconceived. In our weighing this issue, two questions need to be kept distinct: (i) Does cosmic time provide a sensible measure of God's metaphysical time? (ii) Is cosmic time in some sense absolute? COSMIC TIME AS A MEASURE OF GOD'S TIME The first question is scarcely ever directly addressed. But very frequently assertions are made ab out the nature of cosmic time which would seem to imply that cosmic time enjoys no special status such that we should be warranted in identifying it as a sensible measure of God's time any more than we should be warranted in picking out some arbitrary inertial frame and identifying the time associated with it as privileged. The choice of cosmic time as a measure of God's time could be said to be arbitrary because nothing in GR requires that we slice up spacetime in one way rather than another. The theory allows one's three-dimensional hyper-surfaces to dissect spacetime in any arbitrary way, so that the selection of one foliation over another is a conventional choice. Kroes explains, If cosmic time functions are considered in abstracto, i.e., without relating them to the notion of the evolution of the universe, it is immediately clear that the existence of these functions does not contradict the basic principles of RT. If aspacetime M admits the definition of one cosmic time function f, then infinitely many other cosmic time functions can be defined; f is by no means unique. But this infinity of different cosmic time functions contains members wh ich generate different total temporal orders of the

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events. RT does not, however, prescribe such a choice; it does not specify which is the 'real' cosmic time function with its corresponding 'real' total temporal order. The foregoing can be stated in a different way. The choice of a particular cosmic time function introduces a family of simultaneity planes in the spacetime manifold; each simultaneity plane consists of all those events m of M for which j{m) has the same value. But the simultaneity of events defmed by / in the neighbourhood of a point of such a simultaneity plane will coincide only for a special observer, in the appropriate state of motion, with the simultaneity of events defined by the Einstein convention for synchronizing docks. Thus to each cosmic time functionf, there corresponds a special group of observers for whom the standard defmition of simultaneity gives locally the same result as simultaneity defined by the cosmic time functionf Therefore, if it were possible to single out on the basis of objective physical principles, a unique cosmic time function as the 'real' one, then it would also be possible to single out a preferred group of observers. In that case, however, there would clearly be a dash with GTR, according to which allobservers, in whatever state of motion, are equivalent horn a physical point ofview. Since it is impossible to single out, on physical grounds, a dass of preferred observers for whom the definition of simultaneity has objective physical significance, it is impossible to determine which cosmic time function is the 'real' one. 49

Eddington graphically expressed this point in drawing our attention to the difference between a pile of sheets of paper and a solid paper block. "The solid block is the true analogy for the four-dimensional combination of spacetime; it does not separate naturally into a particular set of three-dimensional spaces piled in time order. It can be redivided into such a pile; but it can be redivided in any direction we please."so The implication would seem to be that the identification of our cosmic time as the sensible measure ofGod's time is wholly conventional. But the shortcoming of this answer to our question is that such a response is not based on the whole story. It is true that the General Theory itself does not mandate a specific foliation of spacetime; but this is only to consider the theory, as Kroes puts it, in abstracto, apart from any de facto boundary conditions arising from the nature ofmaterial reality. The answer explicitly ignores ''the notion ofthe evolution of the universe" and considers just a manifold of points. Once we introduce, however, considerations concerning the de facto distribution of matter and energy in the universe, then certain natural symmetries emerge which discIose to us the preferential foliation of spacetime and the real cosmic time in distinction from artificial foliations and contrived times. Michael Shallis, reflecting on the relativity of simultaneity in SR, writes, It is also possible, however, to take a single clock as standard, taking it to define a universal time coordinate, and to relativize everytbing to it.... Of course, the choice of

Kroes, Time, pp. 15-16. Eddington, Space, Time and Gravitation, p. 34. Cf. Graves's comment that it makes no difference to the validity of the (tensor) initial value equations how we define a hypersurface or what sort of coordinates we use on it. The choice of an initial hypersurface is "who11y arbitrary" (John Cowpertbwaite Graves, The Conceptual Foundations 0/ Contemporary Relativity Theory, with a Foreword by John Archibald Wbeeler [Cambridge, Mass.: MIT Press, 1971], pp. 250-252). So also Vesselin Petkov, "Simultaneity, Conventionality, and Existence," British Journal/or the Philosophy o/Science 40 (1989): 75, who argues that a11 events are therefore equally real. 49

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a coordinate time is, to a certain considerable extent, arbitrary-in principle one could take any dock as one' s standard. But in a cosmological context, it is natural to take as standard a dock whose motion is typical or represen/a/ive of the motion of matter in general---Qne which simply 'rides a1ong', so to speak, with the overall expansion ofthe universe. SI

Kroes himself admits that when we turn from the theory considered in abstracto to describing the actual evolution of the universe, "certain 'natural' cosmic time fimctions force themselves upon uso ,,52 In universes with fimdamental ob servers one may introduce a special co-ordinate system which "distinguishes itself from all the other coordinate systems by the fact that the spacelike hyperplanes of constant t coincide with the hyperplanes of homogeneity;" relative to this group of observers, we can "speak properly of 'the' evolution of the universe.,,53 To return to Eddington's analogy of the paper block, suppose that only by foliating the block into a stack of sheets do we discover that on each sheet is a drawing of a cartoon figure and that by flipping through the sheets successively, we can see this figure, thus animated, proceed to pursue some action. Any other slicing of the block would result merely in a scrambled series of ink marks. In such a case, it would be silly to insist that any arbitrary foliation is just as good as the foliation which regards the block as a stack of sheets. But analogously, the Robertson-Walker metric discloses to us the natural foliation of spacetime for our universe. It would, indeed, be disingenuous to insist that the universe is not really expanding homogeneously and isotropically in approximation of the Friedmann model, that it does not really have a certain spacetime curvature, density, and pressure, that it has not really been about 15 billion years since the singularity, but that any arbitrary foliation and contrived time will yield equally appropriate descriptions of the way the universe actually is and evolves. 54 Eddington realized this, of course, and we have seen that he recognized the privileged status of our cosmic time, though he emphasized that no experimental knowledge of it was as yet available. Today, however, the situation has considerably changed, as P. C. W. Davies explains: At any given place in the uni verse, there is only one reference frame in which the universe expands isotropically. This privileged reference frame defines a privileged time scale (the time as told by a dock at rest in that frame). Two separated places have their privileged reference frames in mutual motion, because of the expansion of the universe. Nevertheless, the time measured by the entire collection of imaginary standard docks are obviously correlated such that the global condition (e.g. average separation of!Wo galaxies) of the universe appears the same at equal times as registered Michael Shallis, "Time and Cosmology," in The Na/ure ofTime, ed. Raymond Flood and Michael Lockwood (Oxford: Basil Blackwell, 1986), pp. 68-69. Cf. Asghar Qadir and John Archibald Wheeler, "York's Cosmic Time Versus Proper Time as Relevant to Changes in the Dimensionless 'Constants,' KMeson Decay, and the Unity of Black Hole and Big Crunch," in From SU(3) /0 Gravity, ed. Errol Gotsman and Gerald Tauber (Cambridge: Cambridge University Press, 1985), pp. 383-394. 52 Kroes, Time, p. 16. 53 Ibid., p. 17. 54 Of course, as Dorato points out, the existence of a plurality of cosmic times which is merely the resuIt of a change of origin or a change of scale within the global time function does nothing to underrnine the objectivity of cosmic time (Dorato, Time and Reality, p. 201; cf. p. 192, n.12). SI

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by every privileged clock (assuming they are all properly synchronized). Happily, the earth is moving very slowly relatively to the loeal privileged frame in our vicinity of the uni verse, so that Earth time is a fairly accurate measure of cosmic time. 55

Thus, not only do we know that a privileged cosmic time in which the universe evolves exists, but because the earth is approximately at rest with respect to our galactic fimdamental particle, we also have a fair idea ofwhat time it ist Thus, it is possible to single out on physical grounds-not from the theory alone, but from de facto material conditions in the universe---a special group of preferred observers, the fimdamental observers, that serve to define a privileged cosmic time, which deserves to be called the real cosmic time in counterdistinction to other mathematically possible fimctions. Nor does this conclusion in any way clash with GR. That theory does not, pace Kroes, succeed in establishing the equivalence of all observers from a physical point of view, as we have seen, and there simply is no General Principle of Relativity that requires that no privileged time exists from the cosmological point of view. In view of the importance of this answer to our first question, it seems worthwhile to underscore it by means of two supporting arguments. First, a fondamental frame for li~ht propagation is plausible in view of modern cosmology. As Prokhovnik explains, 6 the Robertson-Walker metric is expressed in such a way that every fimdamental particle has a fixed set of co-ordinates which do not vary with time. The particles are not conceived to be moving through space but to be each at the same place in space, as space itself expands with time. In view of the equivalence of all fimdamental observers with respect to their view of the universe and the laws of nature, the interval d-r, signifying proper time, is invariant for all such observers. The invariance of the interval is restricted to the set of reference frames associated with the fimdamental observers, and each such observer can be considered at the origin of such a frame. Therefore, the ensemble of fimdamental observers serves to define a unique cosmological frame which may properly be referred to as the fondamental reference frame. The members of the ensemble of equivalent frames are merely representations of the fimdamental frame in terms of different points of origin of the coordinate system. Hubble's Law w = rlt (velocity equals radius over time) manifests itself isotropically only to fimdamental observers and thus provides an observable criterion for distinguishing any representation ofthe fimdamental frame. The constant c represents the velocity of light with respect to the reference system defined by the Robertson-Walker metric, namely, that associated with the set of fimdamental observers. "Hence, the formulation of the 55 P. C. W. Davies, "Spacetime Singularities in Cosmology and Black Hole Evaporations," in The Study 0/ Time [II, ed. 1. T. Fraser, N. Lawrence, and D. Park (Berlin: Springer Verlag, 1978), p. 76. I have corrected the spelling errors in the quotation. 56 Prokhovnik, Light in Einstein 's Universe; idem, "The Logic ofthe Clock Paradox," paper presented at the International Conference of the British Society for Philosophy of Science, "Physieal Interpretations of Relativity Theory," Imperial College of Science and Technology, London, 16-19 September, 1988; idem, "The Twin Paradoxes of Special Relativity-Their Resolution and Implications," Foundations 0/ Physics (preprint). Cf. Swinbume, Space and Time, chaps. 11, 12.

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Robertson-Walker metric implies that the propagation of light takes place relatively to a unique cosmological reference frame associated with the large scale distribution of matter in the universe. ,,57 The existence of a unique fimdamental reference frame also has important implications for our interpretation of SR as weH. For the existence of a fimdamental reference frame for light propagation implies that the speed of light is isotropie only with respect to observers which are stationary relative to the fimdamental frame (the fimdamental observers). With respect to an observer which is moving with a velocity v relative to the fimdamental frame, light will approach such an observer with the speed of c + v in the line of v and overtake it with a speed of c - v in the line of v. These departures from constant c will not, however, be detectable to such observers due to length contraction and time dilation. Length contraction results from the endeavor of a moving system of particles to maintain its internal equilibrium. Time dilation foHows as a result of the anisotropy of the velocity of light and length contraction. Einstein's Light Postulate is now seen to concern the measurement of light's velocity in various inertial frames, and the relativity of simultaneity which results from his synchronization procedure becomes intelligible in view of observers who are in motion relative to the fimdamental frame's regarding their inertial systems as being at rest for the purpose of clock synchronization. Prokhovnik concludes, The anisotropy consequences ... , whieh affect moving bodies and the observations of moving observers, provide a complete physieal interpretation, free of any ambiguity, of Speeial Relativity. They show how and why the Light Prineiple operates in respect to all inertial frames, they explain why any loeal experiment designed to detect an absolute veloeity is bound to yield a null-effeet. The existence of a fundamental reference frame provides a physica1 basis for the absolute anisotropy effects, and their interaction produees the (Ioeal) observational equivalence of a11 inertial frames in respect to the laws of nature.. .. Only by cosmologieal astronomieal observations ean we discern the existence of the fundamental frame and our movement relative to it. SI

Given the existence ofthis unique fimdamental reference frame, one thus arrives at a perspicuous neo-Lorentzian interpretation of Special Relativity Theory. The unpopularity of such an interpretation no doubt accounts for the widespread resistance to the notion of a unique fimdamental reference frame; nonetheless, the existence of such a frame is implied by the existence of the ensemble of fimdamental observers and is disclosed in observational astronomy. Secondly, modern equivalents of the aether serve to establish a preferred reference frame. In a remarkable about-face of science, the old, despised aether of classical physics has been replaced by modem ethers, which serve a similar fimction in distinguishing a privileged rest frame co-extensive with space itself. According to DufIy, " ... in recent years there are many signs that the aether concept is playing

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Prokhovnik, Light in Einstein 's Universe, p. 53. Prokhovnik, "Twin Paradoxes," pp. 8-9.

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an ever increasing role in physieS."S9 There are several plausible candidates, each of which will serve nicely as an ersatz-ether for the nineteenth century aether: (i) The cosmological fluid. The "gas" of fundamental partieies is itself a sort of ether in that it is co-extensive with and at rest with respect to space. It therefore serves to single out a universal frame of reference and thereby asswnes the function ofthe classieal aether. Heller, Klimek, and Rudnicki remark, We may talk of symmetries in the energy-mass distribution ... only after distinguishing a eertain universal frame of referenee in whieh these symmetries appear in a natural way. The existence of such a particular frame of reference resembles the eoncept of the aether in c1assical eleetrodynamies. 60

These three authors therefore refer to the universal reference frame as the "neo-ether of Relativistic Cosmology." Prokhovnik points out that this universal reference frame can be regarded as a sort of inertial frame (though it is expanding), in the sense that a fundamental partic1e stationary with respect to this frame remains SO.61 A material body will maintain its motion relative to the expanding cosmological substratwn in the absence of any extraneous causes, thus satisfying Newton's ftrst law. So although the cosmological fluid is radieally different from the classieal aether in that it exists in a systematically expanding frame, still it has a universal connotation and is able to fulftll a nwnber of important roles for which the classieal aether was invented. Speciftcally, this modem ether allows in a natural way for the existence of (1) universal cosmic time, (2) 3-spaces of constant curvature orthogonal to the time lines, and (3) a frame of reference co-moving with the substratwn. 62 Therefore, just as the c1assieal aether was regarded as the physical realization of the fundamental reference frame, so the gas of fundamental partieies serves to distinguish physically an equally fundamental frame. (ii) The microwave background radiation. The cosmic microwave background radiation ftlls all of space and is remarkably isotropie for any observer at rest with respect to the expansion of space. The radiation background will be anisotropie for any ob server in motion with respect to an ob server whose spatial coordinates remain ftxed. It is therefore a sort of ether, serving to distinguish physieally a fundamental

59 Michael Ciaran Duffy, "The Modified Vortex Sponge: a Classieal Analogue for General Relativity," paper presented at the International Conferenee of the British Society for the Philosophy of Seien ce, "Physieal Interpretations of Relativity Theory," London, 16-19 September, 1988. According to the eminent Italian physicist Franco Selleri, "the absence of the notion of an ether has important, negative eonsequences for the possibility of our rationally understanding the world of physies and notably the nature oftime" (Franeo Selleri, "Le principe de la relativite et la nature du temps," Fusion 66 [1997]: 54). SeIleri's articIe is strikingly confirmatoryofthe understanding ofSR defended in this book. 60 Michael Heller, Zbigniew K1imek, and Konrad Rudnicki, "Observation al Foundations for Assumptions in Cosmology," in Confrontation ojCosmological Theories with Observational Data, ed. M. S. Longair (Dordreeht: D. Reidel, 1974), p. 3. 61 Prokhovnik, Light in Einstein 's Universe, pp. 76-78, 126; so also Geoffery Builder, "Ether and Relativity," Australian Journal oj Physics 11 (1958): 279-297, reprinted in Speculations in Science and Technology 2 (1979): 230-242. 62 Heller, et al., "Foundations for Assumptions in Cosmology," pp. 4-5.

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universal reference frame. 63 What is especially astounding is that recent tests have actually been able to detect the earth's motion relative to the radiation background, thus fulfilling nineteenth century physics' dream of measuring the aether wind! Smoot, Gorenstein, and Muller discovered that the earth is moving relative to the radiation background with a velo city of 390 ± 60 km/sec in the direction of the constellation Leo. They comment, Thus, exceptfor a component that varies as cos (8, ij), the cosmic blackbody radiation is isotropie to I part in 3,000. The eosine anisotropy is most readily interpreted as being due to the motion of the earth relative to the rest frame of the cosmic blackbody radiation-what Peebles calls the 'new aether drift'. 64

Commenting on this result, Kanitscheider remarks, "The cosmic background radiation thereby furnishes a reference frame, relative to which it is meaningful to speak of an absolute motion. ,,65 What Michelson and Morley failed to detect using visible light radiation, twentieth century physicists discovered using microwave radiation. Mansouri and Sexl comment, "The discovery of the cosmic background radiation has shown that cosmologically a preferred system of reference does exist. This system is defmed and singled out much more unambiguously to be a candidate for a possible 'ether frame' than was the solar rest frame in Einstein's days.,,66 By means of this empirically distinguished frame of reference one can, in Stapp's words, "defme an absolute order of coming into existence.,,67 One can only speculate whether, had this microwave background radiation and the measure of our motion relative to it been known to Einstein prior to 1905, he would have claimed that no fundamental frame exists relative to which all local inertial frames are in motion. 68 Ibid., p. 4. G. F. Smoot, M. Y. Gorenstein, and R. A. Muller, "Detection of Anisotropy in the Cosmic Blackbody Radiation," Physical Review Letters 39 (1977): 899. 65 Kanitscheider, Kosmologie, p. 256. 66 Reza Mansouri and Roman U. Sex!, "A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization," General Relativity and Gravitation 8 (1977): 497-498. 67 Henry Pierce Stapp, "Quantum Mechanics, Local Causality, and Process Philosophy," Process Studies 7 (1977): 176. In order to rescue the relativity of simultaneity, Stapp is driven to decouple temporal order from the order of coming into existence. Not only is this expedient counter-intuitive; it is ultimately futile, since in some frame temporal order will coincide with the absolute order of becoming, and thereby that frame will be distinguished. 68 Consider Arthur I. Miller's paper, "On Some Other Approaches to Electrodynamics in 1905," in Strangeness in the Proportion, pp. 66-91, in connection with P. A. M. Dirac's remark in discussion that "In one respect Einstein went far beyond Lorentz and Poincare and the others, and that was in asserting that the Lorentz transformation would apply to the whole of physics and not merely to the phenomena based on electrodynamics ... , which is going far beyond what the people who were working with electrodynamics were thinking about. And, of course, in a way Einstein was wrong, because the Lorentz transformation does not apply to everything. There is the microwave radiation, which does provide an absolute velocity. It provides an ether, but the real importance of Einstein's work was to show how Lorentz transformations dominate physics" (p. A. M. Dirac, "Discussion," Strangeness in the Proportion, pp. 110-111). 63

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(iii) The quantum mechanical vacuum: Underlying all of physical reality is the quantwn mechanical vacuwn, which is not "nothing," but rather a sea of evanescent particles fonning by fluctuations of the energy field and returning to it almost at once; as Hönl and Dehnen explain: The vacuum of modem physics is not identical with empty space-with Democritus' IlTJ ov; it is to be taken for the 'ground state of the universe' and it possesses structure. That means that it contains all elementary particles virtually, in consequence ofwhich it is polarizable and able to produce real particles and antiparticles after sufficient supply of energy. Therefore the vacuum is to be considered as its own substratum besides the classical matter and the metrical field. 69

All physical reality is ultimately a manifestation of this quantwn mechanical substratwn. The quantwn realm supplies the grounds for a modern equivalent ofthe ether in various ways, among which we may mention two: (a) Quantum electrodynamics. In the classical electrodynamics of Maxwell, radiation was thought of as waves in the all-pervasive aether. But with the triwnph of Special Relativity Theory, electromagnetic energy was regarded as traveling through the empty vacuwn, and the aether mediwn was regarded as non-existent. As quantwn theory penetrated electrodynamics, however, the vacuwn was discovered to be anything but empty and to be the seat of fluctuating electromagnetic fields. P. A. M. Dirac, who pioneered the development of relativistic, quantwn electrodynamics, regarded the idealized state of the quantwn vacuwn as a suitable candidate for an ether, commenting, Physical knowledge has advanced very much since 1905, notably by the arrival of quantum mechanics, and the situation has again changed. If one re-examines the question in the light of present day knowledge, one finds that the aether is no longer

Cf. Elie Zahar, "Why Did Einstein's Programme Supersede Lorentz's? (ll)," British Journal/or the Philosophy o/Science 24 (1973): 243-244. Cf. Nathan Rosen's comrnent: "In view of the existence of the Hubble effect, it appears that the universe is expanding. It also appears that there exists a frame of reference-nearly coinciding with that of the solar system-in which the universe presents isotropie appearance. This holds for the Hubble effect and also the microwave background radiation. In other words there exists a fundamental frame in the universe. From the equations ofthe general relativity theory one can also show that, in such an expanding universe, an observer carrying out mechanical and optical experiments in his laboratory in principle can determine the motion ofthe laboratory with respect to this fundamental frame ofreference. One cannot help wondering what would have happened had Einstein been aware of the existence of this fundamental reference frame at the time he was looking for a generalization of the special relativity theory that would describe gravitation. Would he have developed the same general relativity theory that he actually did?" (Nathan Rosen, "Bimetric General Relativity and Cosmology," General Relativity and Gravitation 12 [1980]: 494.) 69 H. Hönl and H. Dehnen, "The Aporias of Cosmology and the Attempts at Overcoming Them by Nonstandard Models," in Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, ed. Alwyn van der Merwe (New York: Plenum Press, 1983), p. ISO.

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ruled out by relativity, and good reasons can now be advanced for postulating an aether. 70

Dirac's ether is the quantwn vacuwn considered in abstraction from matter and field but wbich serves as the dynamical arena in wbich virtual events OCCUf. It differs from the classical aether in that it is not amenable to a mechanical description; but it nonetheless plays a role similar to that of its classical predecessor, as Rompe and Treder explain: Dirac's quantum vacuum ... is a physical entity for which one cannot define a magnitude of motion and even not the velocity zero, but which defines an inertial system within special relativity. And, furthermore, a11 particles, the whole substantial world of atomism and the real physical fields connected according to Einstein and de Broglie with atomism, represent excitations of the vacuum. 71

As a physically real, universal, all-pervasive, inertial system, Dirac's quantwn vacuwn deserves, according to Sir Edmund Whittaker in bis monwnental History 0/ the Theories 0/ Aether and Electricity, to be regarded as the modem equivalent of the classical aether, which Relativity Theory had cast away: As everyone knows, the aether played a great part in the physics of the nineteenth century; but in the first decade of the twentieth, chiefly as a result of the failure of attempts to observe the earth's motion relative to the aether, and the acceptance ofthe principle that such attempls must always fai!, the word 'aether' fell out offavour, and it became customary to refer to the interplanetary spaces as 'vacuous'; the vacuurn being conceived as mere emptiness, having no properties except that of propagating electromagnetic waves. But with the development of quantum electrodynamics, the vacuum has come to be regarded as the seat of the 'zero-point' oscillations of the electromagnetic field, of the 'zero-point' fluctuations of electric charge and current, and of a 'polarization' corresponding to a dielectric constant different from unity. It seems absurd to retain the name 'vacuum' for an entity so rich in physical properties, and the historical word 'aether' may fitly be retained. 72

Tbis modem quantwn mechanical ether thus serves to delineate a fundamental reference frame with respect to which, like the classical aether, privileged velocities OCCUf and, hence, privileged spatial and temporal relations may be established. Ironically, due to an ether compensatory mechanism, no 'ether wind' can be detected due to an observer's motion through the vacuwn. 73 In this respect it 70 P. A. M. Dirac, "Is There an Aether?" Nature 168 (29 November 1951), 906-907; cf. P. A. M. Dirac and L. Infeld, "Is There an Aether?" Nature 169 (26 April 1952), 772. 71 R. Rompe and H.-J. Treder, "Is Physics at the Threshold of a New Stage of Evolution?" in Quantum, Space and Time-The Quest Continues, ed. Asim O. Bamt, A1wyn van der Merwe, and Jean-Paul Vigier, Cambridge Monographs on Physics (Cambridge: Cambridge University Press, 1984), pp. 603-604. See also Alexander W. Stern, "Space, Field, and Ether in Contemporary Physics," Science 116 (November 1952) 493-496. 72 Edmund Whittaker, A History ol/he Theories 01 Aether and Eleclricity, 2 vols. (rep. ed.: New York: Humanities Press, 1973), I:v. 73 I. D. Novikov explains, "When an observer starts moving in this medium, the oncoming energy flow does meet hirn and it may seem that the observer could measure this flow (this would be the 'wind'). However, another oncoming energy flow, due to negative pressure, will also

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resembles even more closely the classical aether. This new ether, in the words of Igor Novikov, "can restore the concepts of absolute rest and absolute motion. Indeed, the motion relative to this medium would be the motion ... with respect to absolute space.,,74 (b) The EPR experiment and Bel/'s Inequalities: A second way in which quantum physics serves to disclose a privileged reference frame and absolute simultaneity concerns the startling experimental results obtained on what was originally a thought experiment aimed at exposing the deficiencies of Bohr's Copenhagen Interpretation of quantum measurement situations. According to one recent commentator, the experimental verification ofviolations ofBell's Inequalities "constitutes the most significant event of the last half-century" for those interested in the fundamental structure of the physical world. 7S Let us first look at the original thought experiment before examining recent findings and their implications. As is well-known, Einstein staunchly opposed the indeterminist interpretation of quantum physics in favor of a "hidden variables" interpretation, according to which elementary particles actually do possess complementary properties like position and momentum, even if these are incapable of being simultaneously measured by us; and between 1927 and 1935, in a prolonged dispute with Niels Bohr, he proposed a' number of thought experiments, each aimed at demonstrating that the quantum physical description of a particle is really incomplete. 76 The most celebrated of these thought experiments was proposed in 1935 in collaboration with Boris Podolsky and Nathan Rosen and, hence, bears the initials of its concocters as the EPR experiment. The EPR thought experiment is based on a reality criterion, which supplies a sufficient condition for some physical quantity's being real: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.',77 Thus, if one could predict be there. Tbis flow has negative sign, its magnitude equal to that of the former flow and exactly canceling it. As a result, no 'wind' is produced, Whatever the motion of the observer by inertia, he always measures the same energy density of the vacuum (if it is nonzero) and the same negative pressure, so no 'wind' will be created by the motion, Tbe vacuum is the same for allobservers moving by inertia with respect to one another..." (lgor D. Norikov, The River of Time, trans. Vitaly Kisin [Cambridge: Cambridge University Press, 1998], p. 175). 14 Ibid., p. 174. 15 Tim Maudlin, Quantum Non-Locality and Relativity, Aristotelian Society Series \3 (Oxford: Blackwell, 1994), p. 4. 16 The reader may note that Einstein's attitude toward quantum mechanicaI descriptions in quantum theory was thus the precise opposite of his positivistic attitude toward absolute simultaneity in Relativity Theory! This strange inconsistency was not lost on others, who queried Einstein about it, only to receive the reply, "A goodjoke should not be repeated!" 11 A. Einstein, B. Podolsky, and N. Rosen, "Can Quantum Mechanical Description ofPhysical Reality Be Considered Complete?" Physical Review 47 (1935): 777, reprinted in Quantum Theory and Measurement, ed. John Archibald Wheeler and Wojciech Hubert Zurek, Princeton Series in Physics (Princeton: Princeton University Press, 1983), p. 138.

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accurately, say, the position of a particle without in any way disturbing it via a measurement process, the particle must actually have a position. Accordingly, Einstein, Podolsky, and Rosen imagine the following scenario: two photons are frred in opposite directions along the line of motion. Complementarity forbids that both the momentum and position of one ofthe photons be measured simultaneously. But because the photons are identical, we know that if we determine the momentum of photon 1, then photon 2 must possess precisely the same momentum, even though no measurement is carried out on photon 2. Nor can our measurement of photon 1's momentum be said to disturb photon 2, for causal influences cannot propagate faster than the speed of light. Yet at the very instant that the momentum of photon 1 is established, photon 2 must have an identical momentum. Therefore, according to the EPR reality criterion, photon 2 must really possess a momentum. But, quite evidently, we could just as easily have chosen to measure photon 1's position instead of its momentum. But then by parity of reasoning, photon 2 would also have to possess a real position. So whether we choose to measure photon 1's momentum or position, photon 2, while remaining causally isolated, must also possess at the same time the relevant property, as really as does photon 1. But since the EPR reality criterion expresses a modal proposition, photon 2 must possess these properties not merely whenever measurements are carried out on photon 1, but whenever such measurements-and corresponding predictions-can be carried out. So long as we can predict photon 2's position and momentum without disturbing it, photon 2 must actually possess those properties. The quantum mechanical description of the system is therefore essentially incomplete: any description of the system will include specific values of only one of the complementary properties, even though the EPR experiment shows that the particles actually possess both. There must therefore exist hidden variables in any quantum mechanical situation which we are incapable of determining. The EPR thought experiment remained just that until 1964, when J. S. Bell showed that any hidden variables theory which preserved locality-that is to say, prohibited action at a distance-must make statistical predictions which disagree with those made by quantum mechanics. 78 Suddenly, the EPR experiment had been seen to lead to testable results. In his paper, Bell notes that David Bohm's hidden variables interpretation of quantum mechanics escapes Von Neuman's alleged proof that no such theory is possible due to the fact that Bohm's interpretation has a grossly non-Iocal structure. Bell's Theorem is the proof that any theory which reproduces exactly the quantum mechanical predictions must be non-local. In place of EPR's use of the complementary properties of position and momentum, Bell borrows Bohm's example of spin Y2 particles moving freely in opposite directions and so correlated that if the measurement by use of magnets of the spin component in one particle yields the value + 1, then measurement of the spin component in the other particle must yield the value -1, and vice versa. He then assumes ''that if the 78 J. S. Bell, "On the Einstein Podolsky Rosen Paradox," Physics I (1964): 195-200, reprinted in Quantum Theory and Measurement, pp. 403-408.

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two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other.,,79 and then attempts to elicit a contradiction with quantum mechanical predictions, thereby falsifying the locality assumption. Most contemporary discussions of Bell's Theorem utilize measurements on the polarization of photons rather than their spin orientation. Light which is polarized possesses an electric field which is orthogonal to the direction of motion and which is oriented in a certain direction (for example, vertically or horizontaHy). Polarization can characterize not only wavelengths of light, but individual photons as weH. In the EPR situation, the individual photons are so correlated that once one of them is measured and so acquires a polarization, both have the same polarization. The polarization detectors A and B are constructed to measure photon polarization either along or across the axis ofthe detector. Ifthe two detectors are oriented at the same angle, their polarization correlation equals 1, a perfect match in the distribution of photons detected vertically or horizontally polarized with respect to the axis. If, on the other hand, B is set at a 90° angle to A's orientation, then their polarization correlation is 0, a perfect mismatch in the distribution of photons detected to be vertically or horizontally polarized. The rub comes when the angle between the settings of the detectors varies between zero and ninety degrees: here statistical correlations known as Bell's Inequalities emerge. For example, we may set A such that its directional setting differs from B's by some angle () such that for every four photon pairs measured, A and B agree on the verticallhorizontal polarization of only three; for one photon pair out of four A will measure it as vertical and B as horizontal or vice versa. Recalling then the locality condition presupposed by Bell and beginning with the settings of A and B aligned, let us turn the setting of B such that it is at the angle () with respect to A and then turn A in the opposite direction such that the angle between the settings of A and Bis 2(}. Since the rate of mismatches at () is one out of four, the rate at 2(} cannot be greater than two out of four (though it could be less, since a pair of deviations from the detectors' aligned value could coincide to produce a match). This ratio is an example of a Bell Inequality. Quantum mechanics, however, predicts that at the angle 2(}, the mismatches would be greater than two out offour. Since Bell's Theorem was explicated, a number of EPR-type experiments have been run, and the most precise of these, notably the experiments of Alain Aspect at the Institut d'Optique d'Orsay and the long distance tests of Tittel, Brendel, Gisin, and Zbinden of the University of Geneva, have fully vindicated the predictions of quantum mechanics. 80 The breaching of the Bell Inequalities therefore necessitates Ibid., p. 403 . See Alain Aspect and Philippe Grangier, "Experiments on Einstein-Podolsky-Rosen-type correlations with pairs of visible photons," in Quantum Concepts in Space and Time, ed. R. Penrose and C. 1. Isham (Oxford: Clarendon Press, 1986), pp. 1-15; W. Tittel, 1. Brendel, N. Gisin, and H. Zbinden, "Long Distance Bell-type Tests Using Energy-Time Entangled Photons," Physical Review A 59/6 (1999): 4150-4163. 79

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abandonment of the locality asswnption which underlay the EPR thought experiment. According to Bell, "It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."SI Therefore, according to Rae, "nearly everyone working in this area" has been convinced ''that all local hidden-variable theories can now be discounted."S2 And it is worth emphasizing that abandonment of locality is not dependent upon a realist interpretation of quantwn physics: the breaching of the Bell Inequalities can be demonstrated on the macro-Ievel, so that even if quantwn physics is someday superseded, we seem to be stuck with non-Iocality.s3 The demonstration that reality is non-Iocal seems to leave us in a dilemma, either horn of which has, in turn, important implications for the existence of an ether. Dur first alternative is to hold that adjustments in the polarization at A have a causal effect on the polarization at B. Since the collapse of the wave function occurs instantaneously over arbitrarily large distances, ''Quantwn theory suggests that measurement at A, say, causes an instantaneous change at B, and this seems to be confumed by experiment."S4 But such an instantaneous influence establishes absolute simultaneity and thus requires are-interpretation of quantwn theory along neo-Lorentzian lines. In his 1964 paper, Bell concluded, " ... there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrwnent, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant."S5 Such instantaneous causal connections serve to establish an absolute reference frame in which the events at A and B are simultaneous. Hence, Bell, later pondering the implications of Aspect's experiments, comments, I think it' s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something Iike going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether-a preferred frame of reference--but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether .... that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. ... what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether-that is a perfectly coherent point of view.... The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent,

Bell, "On the Einstein Podolsky Rosen Paradox," p. 403. A1astair I. M. Rae, Quantum Physics: Illusion or Reality? (Cambridge: Cambridge University Press, 1986), p. 45. 83 See Nick Herbert, Quantum Reality (Garden City, N. Y.: Doubleday, 1985), pp. 234-236. 84 Euan Squires, The Mystery olthe Quantum World (Bristol: Adam Hilger, 1986), p. 100; cf. p. 102. " Bell, "On the Einstein Podolsky Rosen Paradox," p. 107. 81

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that also means that things can go backward in time .... [this1introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is areal causal sequence which is defined in the aether. 86

If, then, we allow for causal connections between the events at A and B, the EPR experiment implies the existence of absolute simultaneity and an ether frame. And, in fact, such a theory exists in the form of de Broglie-Bohm pilot wave model. Bohmian quantum mechanics is mathematically consistent and consonant with all experimental results but is a deterministic theory featuring super-lumina! causal influences. According to Henry Stapp, The simplest pieture of nature compatible with quantum theory is the model of David Bohm. It explains all of the empirical facts of a relativistic quantum theory, including, in particular, the impossibility of transmitting 'signals' (i.e., controlled messages) faster than light. In spite of this complete agreement with relativistic quantum theory at the level of observed phenomena, and the strict prohibition of all observable faster-thanlight effects, Bohm's model is based explicitly on the postulated existence of an advancing sequence of preferred global 'nows,' which single out a preferred reference frame for defining absolute sirnultaneity.87

Bohm's interpretation thus demotes SR from ''the status of absolutely universal foundational theory and instead demands relativistic invariance only of the 'observational' content of a physical theory"-precisely Lorentz's approach. 88 Unfortunately, the same epistemological positivism which underlay Einstein's SR also served to torpedo Bohm's interpretation of the formalism of quantum mechanics. Bohm ascribed the indifference to his theory to "a general philosophical point of view containing various branches such as 'positivism,' 'operationalism,' 'empiricism,' and others and which began to attain widespread popularity among physicists during the twentieth century.,,89 In fact, as we have seen, Einstein's verificationist-operational approach to problems of time and space actua11y served to engender a similar approach to quantum physics.90 The strategy ofthe defenders of 86 "John Bell," interview in P. C. W. Davies and 1. R. Brown, The Ghost in the Atom (Cambridge: Cambridge University Press, 1986), p. 48-49. Cf. 1. S. Bell, "The paradox of Einstein, Podolsky, and Rosen: action at a distance in quantum mechanies?" Speculations in Science and Technolog)! 10 (1987): 279. According to Vigier, ..... far from destroying the Einstein-de Broglie causal point of view, it may very weil turn out that quantum non-Iocality would act in their favor, provide evidence of the 'aether's' existence, strengthening (instead of weakening) their basic idea that our universe is a causal, deterministic machine-and show that Einstein was basically right in the Bohr-Einstein controversy" (Jean-Paul Vigier, "Louis de Broglie-Physicist and Thinker," in Quantum, Space and Time, pp. 9-10). See also 1. S. Bell, "On the Impossible Pilot Wave," in Quantum, Space and Time, pp. 66-76. 87 Henry Stapp to D. R. Griffm, April 16, 1992, cited in David Ray Griffm, "Hartshome, God, and Relativity Physics," Process Studies 21 (1992): 109-110. 81 James T. Cushing, Philosophical Concepts in Physics (Cambridge: Cambridge University Press, 1998), p. 337. 89 David Bohm, Causality and Chance in Modern Physics (London: Routledge, Kegan & Paul, 1957), p.97. 90 Cushing remarks, "The prevalence of an empiricist-operationalist philosophical tendency among Heisenberg, Pauli, and Bohr can be traced in part (somewhat ironically, given Einstein's later view) back

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Copenhagen orthodoxy was simple: Simply postulate that what cannot be measured-does not exist. By defining concepts operationally through a procedure for their measurement, and then applying the quantum formalism to the anal ysis of the measurement procedure, we will obtain nothing less but deductions from the quantum formalism (such as, for example, the uncertainty relations). In this way an illusion is created that the features of the theory (such as uncertainty) belong to the very definitions of the concepts used, and that they inevitably follow from a logical analysis of conditions of experience. 91

In fact the triwnph' of the Copenhagen Interpretation was secured only by the "dictatorial help" of operationalism.92 With the collapse of positivism, a Bohmian approach to quantwn physics is receiving renewed attention. 93 Callender and to Einstein 's 1905 relativity papers. This operationalist approach, one aspect of which was an eschewal of unobservable entities in a theory, seems to have made a great impression and to have exerted a profound influence upon young German physicists" (Cushing, Philosophical Concepts in Physics, p. 287). In fact, Heisenberg described his abandonment ofthe "Kantian category of causality" as the natural continuation of Einstein's overthrow of Kantian space and time as forms of intuition! (Mara Beller, "Bohm and the 'lnevitability' of Acausality," in Bohmian Mechanics and Quantum Theory: An Appraisal, ed. James T. Cushing, Arthur Fine, and Sheldon Goldstein, Boston Studies in the Philosophy of Science 184 [Dordrecht: K1uwer Academic Publishers, 1996], p. 214). 91 Beller, "Bohm," p. 220.

Ibid., p. 221. See, e.g., Antony Valentini, "Pilot-Wave Theory ofFieids, Gravitation and Cosmology," in Bohmian Mechanics and Quantum Theory, pp. 45-66; Tim Maudlin, "Space-Time in the Quantum World," in Bohmian Mechanics and Quantum Theory, pp. 285-307. Valentini points out that the pilot wave model naturally singles out a preferred rest frame. "The nonlocality acts instantaneously across a true 3-space, defining an absolute simultaneity and a true time t" (Valentini, "Pilot-Wave Theory," p. 56). What emerges "is not Einstein's special relativity but Lorentz's earlier interpretation of the Lorentz transformations" (Ibid.). Such an absolute 3+ I approach to electrodynamics is simpler and therefore preferable to the relativistic approach. Valentini extends the absolute 3+ 1 approach into general relativity as weil, postulating an absolute, curved 3-space which evolves in absolute time. Nonlocality distinguishes and maintains the absolute slicing of spacetime into 3-D hypersurfaces. Maudlin argues that if we are to avoid backward causation, we must either postulate a foliation of spacetime into spacelike hyperplanes which serve to define a preferred synchronization between widely separated events or else posit directly a synchronization parameter. The most straightforward route to integrating quantum theory with relativity theory, he states, is to add some structure to spacetime and, hence, to reject relativity as the complete story. He asserts, "lndeed, given that this is the most obvious way to frame Bohmian or collapse theory in a non-c1assical space-time, we ought to take it as a benchmark. What Bohm's theory and the collapse theories seem to need is something like the c1assical notion of simultaneity: a fundamental physical relation between events at space-Iike separation. In effect such a relation would induce a joliation of spacetime, a division of the spacetime manifold into a stack of space-like hyperplanes. Putting a measure over those hyperplanes yields an absolute time function in terms of which the Bohmian dynamics or the collapse dynamics can be framed. If there is something objectionable about adding a foliation to space-time, we should consider just how objectionable it is, since there is no point in doing something even more objectionable just to retain the relativistic account of space-time" (Maudlin, "Space-Time in the Quantum World," p. 295). See Maudlin' s ensuing, interesting discussion about what would be so terrible, after a11, about positing such structure. He indicts contemporary theorists for an "obsessive attachment to Relativity" (Ibid., p. 305). 92

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Weingard have applied Bohmian quantum mechanics cosmologically and report that "when cosmological factors are considered, the de Broglie-Bohm interpretation remains the only satisfactory interpretation of quantum theory. ,,94 This model enables one to resolve the problem of time without having to split worlds, multiply minds, or even worry about observers collapsing wavefunctions, in contrast to the Many Worlds Interpretation, the Many Minds Interpretation, or the Copenhagen Interpretation. Time in the Bohmian model remains essentially the immutable, external, unobservable, unique time ofNewtonian mechanics, in which the dynamic variables of cosmology, like the radius of the universe and the scalar field, evolve. This implies that Bohmian cosmology is not generally covariant: "The laws defme a preferred time.,,95 Callender and Weingard recognize that the admission of a preferred time may be upsetting to some, but they note that the goal of cosmology is to watch the evolution of physical quantities over time, which Bohmian cosmology, in contrast the infinite number of possible time parametrizations (most of which are pathological) compatible with SR, permits. Earlier I alluded to a "sea-change" in the attitude toward Bohmian quantum mechanics which has occurred in the foundations of physics community largely as a result of EPR and the Bell Inequalities. Adoption of such an interpretation would require abandonment of an EinsteinianlMinkowskian approach to Relativity Theory in favor of a non-relativistic approach. But an increasing number of theorists today are willing to give a serious look at Bohm's interpretation. Even ifthe details ofhis theory undergo revision and development, the commitment to a preferred time will remain one of the defining features of such an approach. Suppose, on the other hand, that we reject a causally deterministic interpretation in favor of some interpretation according to which wave function collapse occurs, the photons at A and B being somehow correlated, but not causally connected. On this interpretation, the composite state consisting of the two photons with their respective polarization detectors constitutes a single system, which is in adefinite state. 96 To affect the behavior of one photon via measurement is to disturb the whole system. When the wave function of a photon at A collapses, there is an immediate and correlated collapse of the wave function of its counterpart at B. But clearly, even though this interpretation denies the superluminal causal influence from A to B posited by the hidden variables theory, it still just as effectively abrogates the relativity of simultaneity, since the collapse of the paired wave functions is simultaneous. Therefore, asseverations that such an interpretation would not run contrary to the received interpretation of SR because that theory prohibits only signals of superluminal velocities, not instantaneous correlations, are 94 Craig Callender and Robelt Weingard, "The Bohmian Model of Quantum Cosmology," in PSA 1994, ed. David Hull, Micky Forbes, and Richard M. Burian (East Lansing, Mich.: Philosophy of Science Association, 1994), p. 218. 95 Ibid., p. 224. 96 See Niels Bohr, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Physical Review 48 (1935): 696-702, reprinted in Quantum Theory and Measurement, pp. 145-151.

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quite beside the point. 97 The point is that such correlations fumish the means of establishing relations of absolute simultaneity and a fundamental frame. 98 In bis acc1aimed Quantum Non-Locality and Relativity, Tim Maudlin repeatedly underscores this point. Although Maudlin interprets the counterfactual dependence relation wbich exists between the separated polarization events in EPR as a causal connection, bis emphasis lies on the fact that relativity cannot make physical sense ofinstantaneous collapse ofthe wave function. He writes, The c1assical formulations of non-relativistic quantum theory also posit an instantaneous non-Iocal change: wave collapse. When our two photons leave the source each is in an indefinite state of indefmite polarization (or each is not in any state of polarization). At the moment that the first photon is observed the wave function describing the pair undergoes a sudden change such that the unobserved partner assurnes adefinite state of polarization which matches its partner. In this way the perfect correlations of the EPR experiment are maintained (and the correlations which violate Bell' s inequality generated). In Minkowski spacetime this theory of wave collapse no longer makes sense. The collapse can be instantaneous in at most one reference frame, leading to two possibilities: either some feature of the situation picks out a preferred reference frame, with respect to which the collapse is instantaneous, or the collapse is not instantaneous at all. 99

The problem posed by instantaneous collapse of the wave function for Relativity Theory can be clarified by realizing that since, according to SR, simultaneity is relative to reference frames, the collapse of the wave function for spatially separated photons will itselfbecome relative to a reference frame, as Figure 7.5 illustrates.

Such assertions may not even be true. It is very difficult to see why the entanglement-based quantum cryptography suggested by the experiments of the Geneva Group (see note 80) would not involve the instantaneous transmission of information even in the absence of superluminal propagation of causal influences. James Franson of Johns-Hopkins, when asked how identical random-number sequences generated simultaneously by widely separated particles differs from information, could only say, "That's a difficult question, and I don't think anyone could give you a coherent answer. Quantum theory is confirmed by experiments, and so is relativity theory, which prevents us from sending messages faster than light. I don't know that there's any intuitive explanation of what that means" ("Far Apart, 2 Particles Respond Faster than Light," New York Times [22 July 1997], p. CI). 98 See Henry P. Stapp, "Are Faster-Than-Light Influences Necessary?" in Quantum Mechanics versus Loeal Realism, ed. Franco Selleri, Physics of Atoms and Molecules (New York: Plenum Press, 1988), pp. 71-72, who points out that Bohr and Heisenberg themselves effectively reject the EPR locality assumption. See the very interesting statement by Wemer Heisenberg, The Physical Principles 0/ the Quantum Theory (New York: Dover, 1930), p. 39. 99 Maudlin, Quantum Non-Loeality, p. 196; cf pp. 137-138,144.

97

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('= 5

(= 5

('= 4

(=4

('= 3

(= 3

('= 2

(= 2

('= 1

(= 1

t'= 0

t= 0

detector 1

source

detector 2

Figure 7.5. The EPR experiment in two reference frames. For the unprimed frame, the right photon strikes the detector first, and instantly the left photon acquires a defmite polarization be/ore it strikes detector 1; but for the primed frame the left photon is detected first and at the same time the right photon acquires a defmite polarization be/ore it strikes detector 2.

Whether a photon is defmitely polarized before striking its detector depends upon one's reference frame. In some frames a photon is in an indefinite state until measured by a c1assical apparatus and its interaction with it will be stochastic; but relative to other frames that same photon is fully determinate before it reaches the detector and its interaction with it wholly deterministic. Thus, the determinacy or indeterminacy of a photon at the same spacetime point is hyperplane dependent. The problem, as Maudlin points out, is that polarization is not such an intrinsically relational matter. In a uni verse with only one photon, the photon could have adefinite state of polarization. Indeed, one has the strong intuition that whether or not a photon is polarized should be a matter purely of the intrinsic state of it, independent of considerations about hyperplanes. 100

The theory of the hyperplane dependence of quantum states achieves Lorentz invariance only by exacting an exorbitant price: It does so via a fundamental rejection of the ontological foundations of both common sense and of classical physics. Indeed, the rejection is more radical than either Relativity or non-relativistic quantum theory suggest. Photons in non-relativistic quantum theory may be in strange states of indefmite polarization, but at least they are perfectly determinate strange states. Photons in [the hyperplane dependence] theory can be both polarized and not polarized. Measurement events can be both deterministic and

100

Ibid.,p.210.

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The problems attending hyperplane dependence in SR are magnified when we move to GR. Due to the curvature of spacetime, one must make quantum states dependent upon any spacelike hypersurface. Maudlin points out that the quantum state of a partic1e may differ relative to two hypersurfaces even though they coincide where they intersect the partic1e (Figure 7.6).

A B

detector 1

source

detector 2

Figure 7.6. The left photon intersects hypersurfaces A and Bat a place where they constitute a common surface. Yet relative to A the photon has adefInite polarization, whereas relative to B it does not.

After surveying various attempts to integrate Bell's Inequalities with Relativity Theory, Maudlin conc1udes that these theories "entail such severe dislocations of our physical view that one must seriously consider whether our grounds for adhering to relativity are really strong enough to justify such extreme measures."I02 "Indeed, the cost exacted by those theories which retain Lorentz invariance is so high that one might rationally prefer to reject relativity as the ultimate account of spacetime structure. ,,103 The postulation of preferred hyperplanes of simultaneity in the structure of spacetime is, in fact, the only position discussed by Maudlin which does not face severe objections. The only objection to such an approach to quantum

Ibid., p. 212. Ibid., p. 239. Cf. P. H. Eberhard, "Bell's Theorem and the Different Concepts ofLocality," 11 Nuovo Cimento 46B (1978): 392-419; Luis Carlos Ryff, "Gedanken Experiments on Duality," in Wave-Particle Duality, ed. Franco Selleri (New York: Plenum Press, 1992), p. 249. 103 Maudlin, Quantum Non-Locality, p. 220. 101

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theory and EPR is that it requires one to reject Einsteinian Relativity. Maudlin writes, If a preferred family of hyperplanes is part of the intrinsic structure of spacetime then the fundamental postulate of the Theory of Relativity is false. Relativity postulates that the metrical structure is the only intrinsic spatio-temporal structure and that, more specifically, nothing intrinsic to spacetime picks out a preferred reference frame. A family of hyperplanes distinguishes one frame over all others, namely the frame in which the hyperplanes are simultaneity slices. This would not demand the elimination of any relativistic structure, but would undercut the relativistic democracy of frames. In a relativistic milieu, absolute simultaneity implies a unique privileged frame, a1lowing the definition of Absolute Motion and Rest. So option I can be adopted only by those who are willing to throw out the relativistic world-view. 104

In light of the above, it is little wonder that Karl Popper regards the Aspect experiments as the ftrst crucial experiments between Lorentz's and Einstein's interpretations ofthe formalism ofSpecial Relativity. He remarks, The reason for this assertion is that the mere existence of an infinite velocity entails that of an absolute simultaneity and thereby of an absolute space. Whether or not an infmite velocity can be attained in the transmission 0/signals is irrelevant for this argument: the one inertial system for which Einsteinian simultaneity coincides with absolute simultaneity ... would be the system at absolute rest-whether or not this system at absolute rest can be experimentally identified. lOS

If there is action at a distance, advises Popper, "it would mean that we have to give up Einstein's interpretation of special relativity and return to Lorentz's interpretation and with it to Newton's absolute space and time.,,106 Popper goes on to observe that none ofthe formalism of SR need be given up, but only Einstein's interpretation of it. "If we now have theoretical reasons from quantum theory for introducing absolute simultaneity, then we would have to go back to Lorentz's interpretation."I07

Ibid., p. 202. Karl Popper, "A Critical Note on the Greatest Days of Quantum Theory," in Quantum, Space and Time, p. 54; cf. idem, Quantum Theory and the Schism in Physics, ed. W. W. Bartley, m(Totowa, N. J.: Rowan & Littlefield, 1982), pp. xviii, 20. Cf. Penrose's judgement: The EPR results "pose a profound challenge to any 'realistic' space-time picture of what is going on consistently with the tenets ofrelativity theory" (R. Penrose, "Is Conscious Awareness Consistent with Space-Time Descriptions?" in Philosophy, Mathematics, and Modern Physics, ed. Enno Rudolf and 1.-0. Stamatescu [Berlin: Springer Verlag, 1994], p. 43). Popper's use of the expression "infinite velocity" is misleading, since the salient point is the simultaneous collapse of the correlated two wave functions, as if they were joined by an influence of infinite velocity. See Abner Shimony, "Metaphysical Problems in the Foundations of Quantum Mechanics," International Philosophical Quarterly 18 (1978): 13. 106 Popper, Quantum Theory, p. 29. Actually, as Maudlin points out, one may either return to a Newtonian spacetime and show how electromagnetic effects in rods and clocks conceal the fundamental Newtonian structure or else one can retain the relativistic metric at the fundamental level and add some spacetime structure, such as preferred foliation, to it. Maudlin hirnself prefers to abandon relativity by means of the latter route because it is more straightforward. (Maudlin, "Space-Time in the Quantum World," p. 297; cf. pp. 295, 306). On either account, as Callender notes, temporal becoming "could occur either with respect to this extra structure or with respect to the underlying neo-Newtonian structure" (CalIender, "Shedding Light on Time," p. 8). 107 Ibid., p. 30. 104

lOS

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The above three physical realities-the cosmologieal fluid, the microwave background radiation, and the quantum mechanical vacuum-all serve to revitalize in a new guise the concept ofthe ether. James T. Cushing, after arguing on the basis of Bohm's quantum mechanies for the existence of a preferred frame, remarks, "As a curious point, there does today seem to be a universal preferred frame defmed by the asymmetry of the cosmic background radiation.... Today ... the aether has reemerged through quantum phenomena!"I08 Bohm himself, maintaining that there is "a unique spacetime frame, in terms of which 'simultaneous contact' would be specified," comments, "Empirically, this should be elose to the frame in which the mean velocity of the 3°K radiation background in space is zero."I09 Since the microwave background radiation is isotropie only with respect to the frame in which the fundamental partieies of the expanding universe are at rest, the fundamental frame of the cosmic expansion fills the role of the preferred frame required by quantum theory.l \0 According to Prokhovnik, "The notion of non-Iocal causality, discussed by Bell, requires a criterion of simultaneity which has some absolute significance; it is seen that a cosmological basis for a universal measure of (cosmic) time resolves this problem .... the existence of an observationally-based fundamental frame is invaluable not only for the understanding of our universe and of Special Relativity, but also to make sense of quantum theory along the lines proposed, for example, by Dirac ... and John Bell."lll While differing markedly from the elassieal aether, the newethers play the same essential role in marking off a fundamental reference frame, the frame of expanding physical space itself, in which privileged relations of simultaneity may be established. Lorentz's prediction has been fuHy vindieated: "In my opinion it is not impossible that in the future this road, indeed abandoned at present, will once more 108 James T. Cushing, "What Measurement Problem?" in Perspectives on Quantum Reality, ed. Rob Clifton, University of Western Ontario Series in Philosophy of Science 57 (Dordrecht: K1uwer Academic Publishers, 1996), p. 175; cf James T. Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony, Science and Its Conceptual Foundations (Chicago: University ofChicago Press, 1994), pp. 188-192. Popper also points out that there are "independent arguments" for areturn to Lorentz's approach, as required by EPR, "especially since the discovery of the microwave background radiation" (popper, Quantum Theory, p. 30). 109 David Bohrn to D. R. Griffin, May 17, 1992, cited in Griffin, "God and Relativity Physics," p. 110. When Callender and Weingard contrast the cosmic time of Bohmian cosmology with "the arbitrary parameter found in general relativity," the contrast concerns the arbitrariness permined by GR taken in abstracto (Callender and Weingard, "Bohmian Model," p. 227). GR cosmic time and Bohmian cosmic time may weil be extensionally equivalent, even though intensionally diverse. 110 According to Valentini, " ... the absolute 3-space along which subquantum nonlocality acts ... will necessarily coincide with the observed rest-frame defined by the uniform microwave background. We therefore predict that, if the nonlocality ever becomes directly observable, it will be found to propagate a10ng the hypersurface defined by the observed cosmological rest frame. (Note that York slicing coincides with cosmological rest for a Friedmann modeL)" (Valentini, "Pilot-Wave Theory," p. 63). 111 S. J. Prokhovnik, "A Cosmological Basis for Bell's Views on Quantum and Relativistic Physics," in Bell's Theorem and Foundations 0/ Modern Physics, ed. A. van der Merwe, F. Selleri, and G. Tarozzi (Singapore: World Scientific, 1992), pp. 388-396.

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be followed with good results, if only because it can lead to the thinking out of new experimental results. ,,112 It seems to me, therefore, that we have quite convincing grounds for holding that cosmic time is, indeed, a privileged time. Its privileged status is implied by the existence of a fundamental reference frame for light propagation in line with modem cosmology and by the existence of modem ethers wbich serve to demarcate a preferential reference frame. Cosmic time is the time of the duration of the universe. Therefore, according to the argument presented above based on principle P, cosmic time and God's metaphysical time now coincide. The lapse of cosmic time measures the lapse of God's time, and the "now" of God's time coincides with the "now" of cosmic time. About the only way to avoid tbis conclusion would be to claim that our physical, expanding space does not coincide with absolute space, but is in motion relative to it, so that God's metaphysical time does not coincide with cosmic time either. The question is not whether our 3-space is embedded in some bigher dimensional space, but rather whether our physical 3-space coincides with metaphysical 3-space. But the problem with such an objection is that wbile God's existence (if He is changing) entails the existence of metaphysical time, His existence in no wise implies the existence of metaphysical space. While Newton correct1y inferred the existence of metaphysical time from God's eternity, bis deduction of metaphysical space from God's omnipresence is a non sequitur. Ifwe thus reject Newton's curious doctrine that absolute space is God's sensorium, then we simply have no grounds for positing some metaphysical space wbich is non-coincident with physical space. After all, the objection under consideration does not spring from Relativity Theory; it could have been pressed with equal force against classical aether theories: maybe the aether itself was moving with respect to absolute space! It was simply assumed that the aether was at rest with respect to space itself and so served as its physical embodiment. In the context ofmodem cosmology, it is not clear that it even makes sense to speak of our expanding 3-space moving relative to a metaphysical 3space. ll3 The proper question is not whether physical space is moving in some metaphysical space, but rather whether any physically defmable reference frame should be thought of as privileged and thus coincident with metaphysical space. On tbis score it must be said that the same Robertson-Walker metric that serves to distinguish a privileged time serves equally to demarcate a privileged reference frame that may be taken to coincide with metaphysical space as squarely as did the

H. A. Lorentz, The Einstein Theory of Relativity (New York: Brentano's, 1920), pp. 61-62. In Milne's kinematic theory of relativity, the material universe is viewed as expanding into a static, empty 3-space. But even here, it is not physical space which is expanding in metaphysical space. And Milne's theory preserves a cosmic time. In any case, such a move on our objector's part would mean his abandoning Einsteinian Relativity Theory, which was supposed to be the basis for the whole objection to absolute becoming which is at issue here. For Milne's theory see E. A. Milne, Kinematic Relativity (Oxford: Clarendon Press, 1948); idem, Modern Cosmology and the Christian Idea of God (Oxford: Clarendon Press, 1952). For discussion, see Grünbaum, Space and Time, chap. 13. 112 113

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aether, except that this privileged frame is now seen to be expanding. 114 Maudlin observes that it is difficult to imagine what evidence for the existence of Newton's absolute space and time could be stronger than the occurrence of velocity tenns in fundamental laws of nature, velocity tenns which do not seem to refer to velocities relative to any material. 115 Hence, it seems to me that the objection is quite groundless and that there is no good reason to think that the isotropically expanding space of modern cosmology is not coincident with space itself. Therefore, I conclude, in answer to our first question, that God's metaphysical time does coincide with cosmic time. THE ABSOLUTENESS OF COSMIC TIME That leads us on to our second question: is cosmic time in some sense absolute? Wehave already had occasion to say something about this in our answer to the previous question. Since cosmic time coincides with God's metaphysical time since the moment of creation, it records, in effect, Newton's absolute time. We have seen that several thinkers are therefore quite willing to speak of cosmic time as absolute. John Barrow, for example, asserts, ... whereas Einstein taught us that in the world of special relativity (where gravity is ignored) there is no absolute standard of time that is better than any other, and by use of which everyone in the universe can agree on the time unambiguously, this is no longer true in general relativity. In relativistic cosmology there exist absolute times. For example, in an expanding Universe of uniform density, anyone in the Universe could use the local measure of that density to determine the absolute time since the beginning of the expansion. 116

Park therefore concludes, "Special Relativity questions absolute simultaneity, but relativistic cosmology reestablishes an absolute frame of reference (that of the universe as a whole) relative to which Aristotle's statement about a universal present makes sense.,,117 Agazzi also asserts that "cosmic time .. .is essentially an equivalent of the old absolute time, and in particular it allows one to speak of the past, present,

114 See Fitzgerald's critique of Swinbume's failure to posit a privileged space as weil as a privileged time on the basis of the Robertson-Walker metric. Swinbume cannot have it both ways, he asserts. "Either the Robertson-Walker frame ... gives us privileged cosmic instants and also privileged places lasting through time, or it gives us neither" (paul Fitzgerald, Critical notice of Space and Time, by R. Swinburne, Philosophy ofScience 43 [1976]: 631). 115 Maudlin, Quantum Non-Locality, p. 192. 116 lohn Barrow, The World within the World (Oxford: Oxford University Press, 1988) p. 234. Barrow's further discussion ofwhich is the fundamental cosmic time has to do more with cosmic timekeeping and, despite his disclairners, treats cosmic time on the pattern of Zeno's paradoxes, as is pointed out by Andreas Barteis, Kausalitätsverletzungen in allgemeinrelativistischen Raumzeiten, Erfahrung und Denken 68 (Ber1in: Duncker & Humboldt, 1986), p. 112. lI7 David Park, "What Is TimeT' in Time, Creation, and World Order, ed. Mogens Wegener, Acta lutlandica 74: I, Humanities Series 72 (Aarhus, Denmark: Aarhus University Press, 1999), p. 22.

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and future of the universe."U8 Frank Tipler concurs: ''this unique foliation of spacetime by constant mean extrinsic curvature hypersurfaces defmes absolute space and time in general relativity: the hypersurfaces are absolute space, and the timelike trajectories which are everywhere normal to the hypersurfaces are absolute time.,,119 In answer to the question, "Why should we exalt this foliation of spacetime above all others?" Tipler gives three reasons: (1) It is a natural foliation, in the sense that it is defmed by the global distribution ofmatter and gravitational waves. (2) We adopt the constant mean extrinsic curvature foliation as the standard of space and time for the same reason we require elocks to measure universal time in Newtonian spacetime, namely, we adopt the time and space standard so that motion looks simple. (3) In a universe which is very elose to the Friedmann case ofhomogeneity and isotropy (as our universe is) the rest frames of the foliation will coincide with the rest frames of the Cosmic Background Radiation. Tipler concludes, "The development of physics ... has proven that absolute space and time do in fact exist, and we have succeeded in measuring our absolute motion. Newton's magnificent intuition, as shown in the Principia, has been fully vindicated.,,120 But the suggestion that cosmic time is comparable to Newton's absolute time is likely to be met with heated resistance. Unfortunately, much of the disagreement seems due simply to the failure to keep elearly in mind Newton's distinction between absolute and relative time. Virtually all the objections are based on showing that cosmic time is in some way relative time and then coneluding that it cannot therefore be absolute time-as if Newton had not himself distinguished the two! The pertinent question is whether the relative time kept by the ideal elock of a fundamental ob server provides a measure of absolute time and so in that derivative sense can be said to share its absoluteness. Most critics have failed to keep elear the sense in which cosmic time can be said to be "absolute," and have compounded that failure by failing to appreciate the notion of the coincidence of cosmic time with metaphysical time. For example, it is frequently said that cosmic time does not represent areturn to Newtonian absolute time because cosmic time would not exist independently of all

118 Evamlro Agazzi, "The Universe as a Scientific and Philosophical Problem," in Philosophy and the Origin and Evolution ofthe Universe, ed. Evandro Agazzi and Alberto Cordero, Synthese Library 217 (Dordrecht: K1uwer Academic Publishers, 1991), p. 29. 119 Frank 1. Tipier, "The Sensorium of God: Newton and Absolute Space," in Newton and the New Direction of Science, ed. G. V. Coyne, M. Heller, and J. Zyncinski (Vatican City: Specola Vaticana, 1988), p. 222. 120 Ibid., p. 224. Prokhovnik offers a more qualified endorsement: "Of course, cosmic time has no absolute connotation-it relates directly to the apparent nature of the cosmos-but it does provide a universal measure of time which 'f1ows' uniformly and independently of any local phenomena, and so fulfills Newton's desideratum for the nature ofthe ultimate variable associated with a11 physical changes" (Prokhovnik, Light in Einstein 's Universe, p. 127). On the basis of cosmic time's universality, Michael Shallis is also willing to say that it is Iike Newton's absolute time (Shallis, "Time and Cosmology," p. 71).

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physical events as would absolute time. 121 But such an objection only reminds us that cosmic time is physical time rather than metaphysical time. One can reject cosmic time's absoluteness in the sense of "non-relational" without repudiating the absoluteness of cosmic time in the sense that cosmic time represents the true time (in the Lorentz-Poincare sense) as opposed to the merely local time. The objection is impotent against the claim that cosmic time and metaphysical time are presently coincident, though not identical. Because these times are not identical, cosmic time need not share all the properties of absolute time, such as its allegedly non-relational character, and yet its moments still coincide with the moments ofmetaphysical time. In virtue of that coincidence, cosmic time may be quite properly said to be absolute in the sense that it gives the true time. Or again, it is frequently objected that cosmic time is contingent and therefore cannot be regarded as absolute. We saw, for example, that Fitzgerald is worried about the existence of GR-based models which lack a cosmic time. 122 Since cosmic time does not exist in such models, it cannot be said to represent the true time. But all that follows from the existence of models lacking a cosmic time is that cosmic time contingently coincides with metaphysical time. 123 In virtue of that coincidence, it records the true time in this world. Our world is characterized by cosmic time, and its absence in other cosmological models is wholly irrelevant to whether it coincides with God's time in the actual world. The contingency of cosmic time thus says nothing against its privileged status in this world; in fact, a relationalist can consistently maintain that even metaphysical time exists contingently, for if God had chosen to exist absolutely changelessly permanently from etemity and never created a world, there would be no events at all and, hence, not even metaphysical time. The existence of both metaphysical and physical, cosmic time is thus a contingent fact dependent upon God's will. Again, it is sometimes objected that cosmic time is not a vindication of Newton's absolute time because it is itself the by-product of relativity and is bound up with space. Munitz, for example, explains, One should not think, therefore, ofwhat we are here calling 'cosmic time' as in any way equivalent to Newton's concept of absolute time. For relativity theory, time is not an independent continuum whose properties can be determined apart from space. Therefore, the assignment of a temporal structure to the uni verse as a physical system is intertwined with adetermination of its spatial structure. Cosmic time is one dimension ofthe spacetime structure ofthe universe as a whole.\24

But the fact that cosmic time is a formulation within aspacetime theory says nothing in and of itself against its absoluteness, since even Newtonian theory Can be given such a formulation. Moreover, Munitz is not sufficiently discriminatory between cosmic parameter time and cosmic coordinate time. Only the latter is a dimension \2\ Whitrow, Natural Philosophy ofTime, pp. 34-36,283-302. \22 Fitzgerald, "Truth about Tomorrow's Sea-Fight," p. 326; see also Alan Padgett, God, Eternity and the Nature ofTime, (New York: St. Martin's, 1992), pp. 128-129. \23 Dorato also makes this point (Dorato, Time and Reality, p. 204). \24 Munitz, Cosmic Understanding, p. 96.

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of the spacetime structure; but as a parameter cosmic time is independent of space. In the Robertson-Walker line element, the striking thing about the cosmic time parameter is precisely its independence from space. Of course, the parameter is assigned to certain hypersurfaces in spacetime, but then so is Newtonian time in a spacetime formulation of Newtonian theory. The point in saying that the cosmic time parameter is independent of space is not that it is unrelated to space, but that a mere change in spatial coordinates is not a sufficient condition for a change in the cosmic time. In any case, the objection becomes irrelevant once it is recalled that we are claiming, not the identity of Newtonian metaphysical time and cosmic time, but their coincidence since creation. For even if cosmic time were bound up with space, that fact says nothing against its coinciding with God's time and so being the privileged physical time. A related objection is that cosmic time cannot be the basis for the construction of an absolute Newtonian time because cosmic time is observer-dependent and, hence, relativistic. Thus, Kroes admits that in universes in wbich fundamentalobservers exist one may introduce a special co-ordinate system wbich is distinguished by the fact that the spacelike hypersurfaces of constant t coincide with the hypersurfaces of homogeneity, so that relative to the group of fundamental ob servers, one may speak properly of ''the'' evolution of the universe. But, he insists, this temporal order is still observer-dependent: "it is based upon a preferred group of observers, viz., the group of fundamental ob servers. ,,125 Without this group of observers, the total temporal order has no physical meaning whatsoever. Therefore, one cannot construct an absolute Newtonian time on the basis ofthis cosmic time. But Kroes's objection merely trades on the ambiguity of the expression "observer-dependent." Co-ordinate cosmic time does rely on the use of certain fundamentalobservers to establish origins of the co-moving coordinate system and in that sense can be said to be observer-dependent. But the time so constructed is the same for aH observers, in whatever inertial frame they find themselves, and so is observer-independent. Every observer, whatever bis state of motion, will measure events as occurring at the same values of cosmic time. Therefore, as Kroes says, the fundamentalobservers are a preferred group of observers. Cosmic time is privileged, and relativity is thereby overcome. The fact that cosmic time is relative to a reference frame, namely, the fundamental frame, is not incompatible with its coincidence with absolute time. Otherwise one might as weH charge that the time of nineteenth century physics was not absolute either, since it was relative to the aether rest frame! The point is that in both cases, the reference frame in question is preferred and therefore the time kept with respect to it measures absolute time. Another way of putting this is to affirm that cosmic time and metaphysical time are extensionally equivalent, but intensionally diverse. Both concem the same duration, at least since creation, but do so under different definitions. To use an analogy, we might speak of Jan Craig as ''the woman who has properties x, y, z" or, 11S

Kroes, Time, pp. 17-18.

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altematively as "the wife of the man who has properties a, b, c." Obviously the definitions are not the same; one is relational, while the other is not. Nonetheless, they pick out the same entity under different descriptions. Similarly, cosmie time and metaphysical time, while radically different in that one is physical and the other is hot, pick out the same duration under different names. They pick out the same referent, but constitute different means of fixing the referent. They thus differ de dicta, but pick out the same duration de re. Hence, objections aimed at showing that eosmic time is not absolute are quite misconceived. Defmitionally, it is not absolute in the sense that it is, after all, physical time, and so relative to a reference frame. But that frame is, Iike the aether frame of nineteenth century physics, privileged, and so the time relative to it is, as Lorentz and Poincare saw, the true time as opposed to merely loeal time. But de re, eosmic time coincides with God's metaphysical time and so measures the lapse of metaphysical time. Therefore, eosmie time is absolute in the Lorentz-Poincare meaning of that term, and, furthermore, it eoincides de re with metaphysical time since creation and thus measures absolute time and so can be properly said to be absolute in that sense as well. One of the most intriguing indications that cosmie time is the physical equivalent of Newtonian absolute time is the surprising demonstration by E. A. Milne and W. H. McCrea that all the results of GR-based, Friedman cosmology ean be recovered by Newtonian physics and in a way that is simpler than Einstein's cumbersome tensor ealculus! Milne and McCrea were able to reproduce all the results of Big Bang cosmology by means of a material universe expanding in empty, cIassical space through cIassical time. 126 Comparing relativistic and Newtonian cosmology, Kerszberg observes, "as far as the prediction of the overall history of the universe is concemed, the equivalence seems to be total.,,127 This implies, in Bondi's words, that GR "cannot be expeeted to explain any major features in any different or better way than Newtonian theory.,,128 In particular the concept of cosmic time in GRbased models corresponds to absolute time in the Newtonian model. Schücking points out that the main asset of the Milne-McCrea formulation was that it gave exactly the same equations for the time development of the universe as the Friedman theory and yet allowed a much simpler derivation. 129 The history of the universe described by the variation of the scale factor R(t) in the Robertson-Walker line element is identieal in the two theories, even though in the one the scale factor R(t) is determined by Einstein's gravitational field equations, while in the other only

126 E. A. Milne, Relativity, Gravitation and World Structure (Oxford: Clarendon Press, 1935); idem, "A Newtonian Expanding Universe," Quarterly Journal of Mathematics 5 (1934): 64-72; W. H. McCrea, "On the Significance of Newtonian Cosmology," Astronomical Journal 60 (\955): 271-274. For discussion see Peter T. Landsberg and David A. Evans, Mathematical Cosmology: An Introduction (Oxford: Clarendon Press, 1977). 127 Pierre Kerszberg, "On the A1leged Equivalence between Newtonian and Relativistic Cosmology," British Journalfor the Philosophy ofScience 38 (\ 987): 349. 128 H. Bondi, Cosmology, 2d ed. (Cambridge: Cambridge University Press, 1960), p. 89. 129 E. L. Schücking, "Newtonian Cosmology," Texas Quarterly 10 (\967): 274.

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Newtonian absolute time and Euclidian geometry come into play.130 All this is not to suggest that Newtonian theory is correct after an; we have already seen how Lorentz was forced to modify Newtonian physics on the local level. But the equivalence of Milne-McCrea Newtonian cosmology with GR-based, Friedman cosmology is a convincing demonstration that cosmic time is, indeed, the physical equivalent of Newtonian absolute time. Thus, Bondi compares cosmic time with Newton's uniform, omnipresent, and even-flowing time, which enables an observers to synchronize their clocks to a single time. 131 Kerszberg concludes, "On the whole, the equivalence between Newtonian and relativistic cosmology only reinforces the conviction that cosmic time is indeed a necessary ingredient in the formalisation of a relativistic cosmology, however alien to general relativity and congenial to Newton's theory the notion ofuniversal synchronisation might seem.,,132 CONCLUSION In conclusion, then, we have seen that when one moves from SR into GR, the application of the latter theory to cosmology yields a cosmic time, which is plausibly regarded as being the physical time which measures God's time and therefore registers to a good degree of approximation the true time. Although the theological significance of cosmic time is rarely discussed, sometimes contemporary thinkers come close. Consider, for example, Milne's notion of a world map. Munitz comments, Let us imagine a superhuman observer-a god-who is not bound by the limitations of the maximum velocity of light. Such an observer could survey in a single instant the entire domain of galaxies that have already come into existence. His survey would not have to depend on the fmite velocity of light. lt would not betray any restriction in information of the kind that resuits from the delayed time it takes to bring information about the domain of galaxies to an ordinary human observer situated in the universe, and who is therefore bound by the mechanisms and processes of signal transmission. The entire domain of galaxies would be seen instantaneously by this privileged superhuman observer. His observational survey of all galaxies would yield what Milne calls a 'world map. ,13l

A world map gives precisely the content of what God knows to be happening at any moment of cosmic time. It lays out, in effect, His perspective on the world. Kanitscheider proceeds, rhe theorist. .. would like to draw up, as Milne put it, a world map. On it the state of the world at a specific moment of cosmic time is indicated. All points of space on a hypersurface of spacetime are at once grasped and physically described. Such a slice through the happening of events corresponds, of course, to no datum of observation; rather it concems a theoretical construction. Only a hypothetical, spiritual observer, who could visit all points on the hypersurface without any delay, would be able to Bondi, Cosmology, p. 105; Kerszberg, "Equivalence," p. 349. Bondi, Cosmology, pp. 70-71. 132 Kerszberg, "Equivalence," p. 376. m Munitz, Cosmic Understanding, p. 157.

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CHAPTER 7 achieve such an overview and could confinn the statement that H(t) does in fact possess the same value at every place. 114

Kanitscheider explains that we earthbound observers have only a world picture, in which distant parts of the world actually belong to earlier moments of cosmic time. Only an omnipresent, cosmic observer, he concludes, who sees the world sub specie aeternitatis, can be in the position to draw up a world map.135 Here the relevance of cosmic time to the theological doctrine of divine eternity becomes explicit. One final point should be made to avert possible misunderstanding. Padgett intimates that God could not be in cosmic time, or indeed, any measured time, because God would also then have to be spatial as weIl as temporal. 136 For in order to have cosmic time co-ordinates, God would also have to have spatial co-ordinates as weIl. Indeed, as we have seen above, He would have to be present at all points on any given hypersurface correlated with a cosmic time t. But then God would be extended physically throughout space, being Himself a sort of divine aether! But such a conception ofGod's omnipresence contradicts God's transcendence. Such a conception of omnipresence is, indeed, flawed, but fortunately no such notion is implied by the doctrine of divine eternity which I have explicated. In the first place, the objection does not distinguish between cosmic time as a parameter and as a co-ordinate. Insofar as cosmic time functions as a parameter, God's being in cosmic time does not imply His having spatial co-ordinates. Therefore, God could be in measured time while transcending space. But secondly, and more importantly, the claim is not that God exists in cosmic time as such; rather He exists in metaphysical time as such, but since creation the moments of cosmic time coincide with the moments of metaphysical time. It is in virtue of this coincidence that cosmic time measures God's metaphysical time. God thus exists in metaphysical time per se, but He exists in cosmic time per accidens. God does not exist in cosmic time in virtue of existing at all points on a three-dimensional hypersurface of spacetime, but rather because all the events on a given hypersurface are causally related to God as simultaneous and present. Cosmic time t corresponding to that hypersurface is ''now'' for Hirn. In virtue of this coincidence of the moments of cosmic time with the moments of His metaphysical time, God can be said to be in cosmic time in the sense that it is true for any cosmic time t that "God exists at t," and at t God believes "t is now." His omnipresence should be explicated in terms of His being aware of and causally active at every point in space.

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m 136

Kanitscheider, Kosmologie, p. 193. lbid., p. 194. Padgett, "Divine Etemity and the Nature ofTime," pp. 203-205.

SECTION 2: GOD, TIME, AND CREATION CHAPTER8 CREATIO EX NIHILO

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f God exists in time, then God, since He can neither begin nor cease to exist, exists omnitemporally, that is to say, He exists at every time which ever exists. But is God's duration infinite? Has He arrived at the present moment only after enduring through an infinite succession of prior moments? If the universe is sempitemal, that is, infmite in its past as weil as future duration, then the answer must be in the affIrmativ(~. But suppose that the universe began to exist. Would time in that case also have a Ibeginning? Or would there be an infInite duration prior to the inception of the world? To set the stage for a consideration of these questions, we turn to a discussion ofthe traditional doctrine of creatio ex nihilo. THE BIBLICAL BASIS OF CREATIO EX NIHILO "In the beginning God created the heavens and the earth." With that terse and majestic statement, the author of Genesis 1 differentiated his outlook from all the ancient creation myths of Israel's neighbors. The expression "the heavens and the earth" denotes the totali~y of physical reality or, more simply, the universe. No preexistent material seems presupposed, no warring gods or primordial dragons are present-only God, who simply "creates" (barah, a word used only with God as its subject and which does not presuppose a material sub stratum) the world. As Robert Jenson points out, "the whole point of this story is that there was nothing before this event.... God and only God is the creature's antecedent."t At face value, the opening line ofthe Bible seems to teach creatio ex nihilo. It was certainly understood as such by later biblical authors, as we shall see, but many modem commentators have denied this prima facie reading. Usually their claim is that v. 1 should be read as a sub ordinate circumstantial c1ause modifying v. 2: "When in the beginning God created the heavens and the earth, the earth was without form and void .... " In this way, it would appear that God's creation of the world consisted simply in fashioning a cosmos out of apre-existent chaotic state. This issue has been long discussed, and it seems to me that Westermann in his thorough and disinterested discussion of this text has convincingly discredited the

Rober! Jenson, "Aspects 01' a Doctrine of Creation," in The Doctrine ofCreation, ed. Colin Gunton (Edinburgh: T. & T. Clark, 1997), pp. 20, 22.

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interpretation of v. as a sub ordinate clause. To summarize his main points: (i) There is no evidence that bereshith (in the beginning) cannot be used in the absolute state at the beginning of a sentence to indicate a point in time. For example, Isaiah 46.10 appears to use bereshith to denote an absolute beginning, which shows that a deftnite article is not necessary to indicate a deftnite beginning point. Confrrmation of this conclusion comes from the oldest textual witnesses: the Massoretic punctuation, the oldest translations, and the New Testament took v. 1 as a main clause and bereshith as designating an absolute beginning. (ii) The syntax of v. 1 does not prove that bereshith is part of an adverbial construct chain. A strong argument in favor of taking v. 1 as a subordinate clause would seem to be the fact that an identical construction appears in Hosea 1.2 to express a circumstantial idea: "When the LORD spoke at ftrst through Hosea .... " Genesis I, however, must be read in the context of Genesis, not of Hosea. In Gen. 5.1, when the author wishes to express a circumstantial idea, he uses the infinite construct, which is the usual form for circumstantial clauses, "When God created man, he made him .... " It is Hosea's syntax, therefore, that is unusual, and provides no ground for reinterpreting Gen. 1.1, whose author, had he wished to express a circumstantial idea, would have used the normal infinite construct. (iii) Theological arguments alone cannot resolve the issue simply because this presupposes that we already understand vv. 1-3. We cannot avoid an exegesis ofthese verses to determine their meaning, an exegesis which must be carried out within the context of the chapter and the wider context of ancient creation narratives. (iv) When this is done, one discovers that Gen. 1.1 is without parallel in ancient creation myths. The usual form of these myths was "When _ _ was not yet, then God made .... " The ftrst clause expressed the state ofthings prior to God's action, the second clause God's subsequent activity in making something out ofthat state. We ftnd this typical form in Genesis 2: "When no plant ofthe fteld was yet in the earth and no herb ofthe fteld had yet sprung up ... , then the LORD God formed man .... " According to Westermann, the author ofGenesis 1 took the typical "When _ _ was not yet" and made it v. 2 and then took the typical ''then God" and made it v. 3; then he preftxed both ofthese by his own sentence in v. 1. Hence, v. I is not a temporal subordinate clause; it lies "completely outside" the typical structure and is the author's own formulation-"It acquires a monumental importance which distinguishes it from other creation stories.,,2 " ... v. 1 has no parallel in the other creation stories, while all three sentences of v. 2 are based on traditional material. The tradition history of the creation stories provides us with an answer to the question about the inter-relationship of the ftrst verses of Genesis which is certain.,,3 (v) The style of the author of Genesis 1 favors taking v. 1 as a main clause. "It would be completely out of harmony with P's style in Gen. I to arrange the ftrst three verses into one complete sentence.,,4 For these reasons, the Claus Westermann, Genesis 1-11, trans. lohn 1. Scullion (Minneapolis: Augsburg, 1984), p. 97. Ibid. Ibid.

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most plausible interpretation of v. 1 is that it is not a subordinate circumstantial clause, but a main clause asserting God's creation of everything there iso Important as this conclusion is, however, it does not decide the question decisively in favor of creatio ex nihilo. For now the relation of V. 1 to VV. 2-3 must be considered. It might be thought that V. 1 describes God's creation of the raw material wbich then supplies the stuff ofv. 2. But against this, it may be objected: (i) "heaven and earth" in V. 1 designates not just the totality of things, but an ordered cosmos, and (ii) creation of chaos is a contradiction in terms. Hence, V. 1 might be construed to be a sort of title or heading to the chapter which summarlzes the contents ofwhat is described in VV. 2ff. On this reading, creation really begins at V. 3 and may be thought not to entail creatio ex nihilo. Against this understanding ofv. 1, it may, however, be objected that the grammatical relation ofv. I to V. 2 becomes an insuperable problem. For as Delitzsch pointed out long ago, V. 1 cannot be merely a heading, since it is connected with V. 2 by waw (and), indicating a relation of connection between God's prlmary and subsequent acts of creation. 5 What Delitzsch sensed intuitively from bis mastery of the Hebrew language may be more rigorously proved by computer-aided grammatical analysis, which shows that whenever one has a construction of waw plus a non-predicate plus a predicate, then the preceding clause furnishes either background or circumstantial information, depending on the relation of this construction to the main verb. 6 Whenever this construction precedes the main verb, as it does in V. 2, then it is background information which is given. Accordingly, V. 1 is not simply a heading, but a bistorical statement wbich constitutes the background to V. 2. As for the tension between V. 1 and V. 2, this may simply be the result of the author's prefixing V. 1 to the traditional material of VV. 2-3 out of bis desire to express creatio ex nihilo, thereby creating a tension which he does not resolve. When one reflects that P is usually given a post-exilic date, critical scholars can hardly consistently object that P's theological thinking could not have been sufficiently developed to entertain this doctrine. Indeed, the level of theological retlection in Genesis 1 is of such a degree that one wonders whether a more consistent interpretation ofthe chapter might not be forthcoming. For example, V. 1 could be taken as universal in its scope and V. 2 as focusing particularly on God's formation of the earth. The description of the earth as tohuwabohu does not connote a prlmordial chaos in the Greek sense; rather it means the earth was a desert waste or In the succeeding verses God's transforming this an uninhabitable place. uninhabitable waste into a paradise for man to dweIl in is described. It might be thought that the creation of the heavenly bodies in V. 14 indicates that a more universal creation is after all in view, but the construction used here is not the same as that used in God's previous creatorial aets such as in VV. 3,6. The construction C. F. Keil and F. Delitzsch, Commentary on the Old Testament, 10 vols., vol. I: The Pentateuch, trans. James Martin (rep. ed.: Grand Rapids, Mich.: Wm. B. Eerdmans, 1973), p. 46. 6 My former colleague lohn Sailhammer has carried out such an analysis.

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here (hayah [to bel plus infinitive) means "Let the lights in the firmament be for the separating of day and night;" unlike the earlier "let there be---" this c1ause specifies what something is to be for. It presupposes that the lights already exist and specifies their purpose. It might be countered, however, that vv. 16-18 still go to show that God had not until then made the heavenly bodies. This objection, however, ignores the interesting duplex nature of the narrative in chapter one. Many commentators have observed that Genesis 1 seems to combine two patterns of creation: one by God's creative word (vv. 3, 6, 9,11, ete.) and one by God's action (vv. 7,12,16,21, ete.). This could be due to the author's interbraiding two different traditions. On the other hand, the coherence and unity of the chapter would be more satisfactorily maintained if we take this duplex pattern to be one of report/comment on the author's part. For example, v. 12 does not actually describe something God does, nor is it meant to follow temporally v. 11, for this would seem to be prec1uded by the "and it was so" conc1uding v. 11; rather v. 12 is the author's parenthetical comment on the report given in v. 11. Similarly, v. 15 conc1udes "and it was so," suggesting that vv. 16-18 are the author's comment on God's creation ofthe heavens, a creation which is not necessarily at that point in time. Indeed, the previous presence of light and particularly day and night suggests that the sun and moon were created by God prior to the fourth day. Hence, vv. 14ff do not indicate God's creation of the heavens at that time. If we understand v. 1 as universal in its scope and vv. 2ff as narrowing in on God's creation of life on earth, then the tension between vv. 1 and 2 is resolved. There thus seems to be no compelling reason to interpret Genesis other than as it has been traditionally interpreted: that God's creation of the spacetime universe ex nihilo marked the inception of its existence. This is the natural interpretation of the passage, and if we are to take it in a weaker sense, then that interpretation must be proved to be more plausible than the prima fade reading. The same may be said ofthe many other Old Testament passages which speak of God as the Creator ofall things. Isaiah, for example, dec1ares, '''I am the LORD, who made all things, who stretched out the heavens alone, who spread out the earth-who was with me'?" (Is.44.24). This prophecy, usually dated as exilic, asserts that God made everything. Isaiah envisions God existing alone and then bringing into being all that exists besides. He could never have countenanced the idea that something existed alongside God which God did not create: "For thus says the LORD, who created the heavens (he is God!), who formed the earth and made it (he established it; he did not create it a chaos, he formed it to be inhabited!)" (Is. 45.18; cf. 24). In the various creation Psalms, the impression is never given that God's creation is not ex nihilo. "For he spoke, and it came to be; he commanded, and it stood forth" (Ps. 33.9). God's eternity is contrasted with the temporal finitude of creation: "Before the mountains were brought forth, or ever thou hadst formed the earth and the world, from everlasting to everlasting thou art God" (Ps. 90.2). It would be unthinkable that there should have also existed some co-eternal, uncreated stuff along with God. Creatio ex nihilo is the implicit assumption. Job is more explicit: "He stretches out the north over the void, and hangs the earth upon nothing" (Job 26.7, cf. Ps. 89.11,

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12). And God's creatorial acts are but "a whisper" of His power (Job 26.14)! Proverbs 8.22-31 seems to be an especially interesting reflection on Genesis 1. God's wisdom is personified and speaks: "The LORD created me at the beginning of his work, the first of his acts of old. Ages ago I was set up, at the first, before the beginning of the earth. When there were no depths I was brought forth ... " (Prov. 8.22-24). Especially significant is the claim that God's wisdom was with the LORD even when the depths were not yet in existence, for it is precisely the depths which Gen. 1.2 describe. It is God who created the depths and who then took their measure and prescribed their limits (Prov. 8.27-29; cf. Ps. 104.5-9). The doctrine of creatio ex nihilo, it is generally agreed, comes to clear expression during the inter-testamental period. II Maccabees 7.28 enjoins, " ... observe heaven and earth, consider all that is in them, and acknowledge that God made them out of what did not exist, and that mankind comes into being in the same way." Among the Dead Sea scrolls preserved from the Essene community at Qumran, we read, "From the God of Knowledge comes all that is and shall be. Before ever they existed He established their whole design, and when as ordained for them, they accomplish their task without change" (IQS 3.l5). When the first century rabbi Gamaliel was told by a philosopher that "Your God was indeed a great artist, but he had good materials [unformed space/void, darkness, water, wind, and the depths] to help him," Gamaliel corrected him, "All of them are explicitly described as having been created by him.,,7 The New Testament also extols the God who is Maker ofheaven and earth and understands the Old Testament doctrine as creatio ex nihilo. After citing Isaiah 40.13, 14, Paul declares, "For from him and through him and to him are all things" (Rom. 8.36). The God of Abraham is the God ''who gives life to the dead and calls into existence the things that do not exist" (Rom. 4.17). In the same vein, the writer to the Hebrews states, "By faith we understand that the world was created by the word of God, so that what is seen was made out of things which do not appear" (Heb. 11.3). The beatified in heaven are said to sing to God: "Worthy art thou, our Lord and God, to receive: glory and honor and power, for thou didst create all things, and by thy will they existed and were created" (Rev. 4.11). But the most notable contribution of the New Testament is its ascription of creatio ex nihilo to the preincarnate person of Jesus Christ, who is the Father's agent in creating the world. "There is one God, the Father, from whom are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist" (I Cor. 8.6). Indeed, Christ is God, since he is the Creator of all things. In words reminiscent of Gen. 1.1, John writes, "In the beginning was the Word and the Word was with God, and the Word was God. He was in the beginning with God; all things were made through him and without him was not anything made that was made" (Jn. 1.1-3). Paul reflects, "For in him all things were created, in heaven and on earth,

42.

Jacob Neusner, Confronting Creation (Columbia: University of South Carolina Press, 1991), pp. 41-

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visible and invisible, whether thrones or dominions or principalities or authoritiesall things were created through bim and for him. He is before all things, and in him all things hold together" (Col. 1.16, 17). Similarly, the author of the Epistle to the Hebrews asserts, "In these last days [God] has spoken to us by a Son, whom he appointed the heir of all things, through whom also he created the world. He reflects the glory of God and bears the very stamp of bis nature, upholding the universe by bis word ofpower" (Heb. 1.2,3; cf. 2.10). The similarity ofthese passages suggests that the notion of the cosmic Christ was a common motif in the theology of the primitive church. The New Testament writers not only Wlderstood the Old Testament to be teaching creatio ex nihilo, but went further in identifying the preincamate Christ as the principal agent of creation. The biblical conception ofGod's relation to the world is therefore one ofCreator to creature. Dualistic conceptions of God confronted with a co-eternal, Wlcreated material wbich He fasbions into a cosmos are alien to the biblical writers, who think of God as all-powerful and the source of all reality external to Himself. He speaks, and the universe springs into being, created out of nothing by His incomparable power. "Before" the beginning, so to speak, only God existed, and creation, we leam from the New Testament, results from His Word, wbich is the pre-incamate Christ. Thus, it is not only inadequate to conceive of creation as a mere fasbioning, but also even as a conserving of the universe in being. The biblical doctrine of creation is inextricably bOWld up with temporal considerations and asserts that the universe began to exist at a point in the finite past at which it sprang into being out ofnothing by God's almighty Word. 8 UnfortWlately many contemporary theologians evince an Wlseemly timorousness conceming the biblical affinnation of creatio ex nihilo. Claiming that "creation is concerned with ontological origin, not temporal beginning,,,9 John Polkinghorne states, "The doctrine of creation is not an assertion about what God did in the past to set things going; it is an assertion of what he is doing in the present to maintain the

It was 50 understood by the vast majority of early Church Fathers (e.g., Tatian Oratio ad graecos 5.3; cf. 4.1ff, 12.1; Theophilus Ad Autolycum 1.4; 2.4,10,13; Irenaeus Adversus haeresis 3.10.3) and was finally promulgated as official Church teaching at the Fourth Lateran Council (1215), which dec1ared God to be "Creator of a11 things, visible and invisible, ... who by his almighty power, from the beginning of time has created both orders in the same way out of nothing." 9 lohn Polkinghorne, critical notice of Cosmos as Creation, ed. Ted Peters, Expository Times 101 (1990): 317. According to Polkinghorne, "To speak of God as Creator is not to attempt an answer to the question Who lit the blue touch paper ofthe Big Bang? To talk in that way belongs to deism and not to Christi an theology" (John Polkinghorne, "Cosmology and Creation," address at Trinity Hall, Cambridge, undated photocopy). "There is general agreement that the Big Bang is nothing special from a theological point of view.... The idea of creatio ex nihilo asserts the total dependence of the universe upon the sustaining will of its Creator" (polkinghorne, critical notice of C osmos as Creation, p. 317). Whether the Big Bang represent5 the moment of creation is, however, irrelevant to the conceptual content of the doctrine of creatio ex nihilo. The biblical doctrine, like Deism, affirrns a temporal beginning of the universe; moreover, Deists did not in fact deny God's conservation ofthe world in being, but rather His supernatural action in the world.

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universe in being."IO In fact, however, nearly the opposite is the case, biblically speaking. Creation in the Bible virtually always involves the notion of a temporal beginning (as is evident simply from the ubiquitous past-tense, rather than presenttense, verbs with respect to God's creating), and one will have to search for passages supporting the notion of the on-going ontological dependence of the universe upon God's sustaining will. Those passages are there to be found (Heb. 1.2); but we are everywhere confronted with the idea that at some point in the past God created the world. After surveying the data, George Hendry concludes that "Creation in the language of the Bible unquestionably connotes origination ... , the bringing into existence of something that did not previously exist. ,,11 A robust doctrine of creation therefore involves both the affirmation that God brought the universe into being out of nothing at some moment in the flnite past and the affirmation that He thereafter sustains it in being moment by moment. 12 CREATION AND THE NATURE OF TIME Now the theorist (lf tenseless time can only ingenuously make the flrst affirmation. For on a tenseless theory oftime temporal becoming is not an objective feature of the physical world, but a mind-dependent phenomenon. As Grünbaum explains, "coming into being (or 'becoming') is not a property of physical events themselves but only of human or conscious awareness of these events.,,13 Objectively speaking, events occur tenselessly at their respective times; but their coming into being is purely subjective: Since an event comes into being by occurring now, the coming into being or becoming of an event, as distinct from its mere tenseless occurrence at a certain time, is thus no more than the entry of some of its temporally proximate effects into the immediate awareness of a conceptualizing organism (man). 14

\0 Polkinghorne, "Cosmology and Creation." So also Langdon Gilkey, Maker of Heaven and Earth (Garden City, New York: Doubleday, 1959); Ian Barbour, Issues in Science and Religion (New York: Harper & Row, 1971), p. 384; Arthur Peacocke, Creation and the World ofScience (Oxford: Clarendon Press, 1979), pp. 78-79; Keith Ward, Religion and Creation (Oxford: Clarendon Press, 1996), pp. 289290. This watered-down doctrine of creation is the legacy of the father of modern theology, F. D. E. Schleiermacher, The Christian Faith, 2d ed., ed. H. R. Mackintosh and J. S. Stewart (Edinburgh: T.& T. Clark, 1928), sec. 36-41. While acknowledging that the biblical conception of creation involves a temporal beginning (sec. 36.2), Schleiermacher held that this component of the doctrine could be safely suppressed in favor of the absolute dependence of the creation on God (sec. 41). See remarks by Nelson Pike, God and Timelessness, Studies in Ethics and the Philosophy of Religion (New York: Schocken Books, 1970), pp. 107-110. I1 George S. Hendry, "Eciipse of Creation," Theology Today 28 (1972): 420. So also Paul Copan, "Is Creatio ex nihilo a Post-biblic211Invention?" Trinity Journal 17 (1996): 77-93. 12 For more on this distinctJion, see William Lane Craig, "Creation and Conservation Once More," Religious Studies 34 (1998): 177-188. 13 AdolfGrünbaum, "The Anisotropy ofTime," in The Nature ofTime, ed. T. Gold (Ithaca, N. Y.: CorneU University Press, 1967), p. 153. 14 Ibid.

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Hence, Grünbaum denies that at the Big Bang the universe comes into being or becomes actual. ls Rather ''we can describe the situation as follows: The big bang models feature a world whose past time is unbounded (open) but metrically fInite in years. ,,16 Thus, creatio ex nihilo for the theistic advocate of tenseless time means only that the world depends immediately upon God for its existence at every moment. The affIrmation that God brought the universe into being out of nothing at some moment in the fInite past can at best mean that there is (tenselessly) a moment which is separated from any other moment by a fInite interval of time and before which no moment of comparable duration exists and that whatever exists at any moment, including the moments themselves, is tenselessly sustained in being immediately by God. All this adds to the doctrine of ontological dependence is that the tenselessly existing block universe has a front edge. It has a beginning only in the sense that a yardstick has a beginning. There is in the actual world no state of affairs of God existing alone without the spacetime universe. God never really brings the universe into being; as a whole it co-exists timelessly with Him. Leftow, whose theory of divine eternity entails a tenseless theory of time, admits as much. He writes, So if God is timeless and a world or time exists, there is no phase of His life during which He is without a world or time or has not yet decided to create them, even if the world or time had a beginning. . . . God need not begin to do anything, then, in order to create a world with a beginning. That action that from temporal perspectives is God's beginning time and the universe is in etemity just the timeless obtaining of a causal dependence or sustaining relation between God and a world whose time has a first moment. ... in etemity, God is changelessly the Lord: He timelessly coexists with His creatures. 17

Leftow never addresses the theological objection that such an emasculated doctrine of creatio ex nihilo does not do justice to the biblical data, which give us clearly to understand that God and the universe do not timelessly co-exist, but that the actual world includes astate of affairs which is God's existing alone without the universe. Typically such astate is described in the ordinary language of the biblical authors as obtaining "before" the world began (Jn 17.24; Eph. 1.4; I Pet. 1.20; cf. Mt 13.35; 24.21; 25.34; Lk 11.50; Heb 9.6; Rev 13.8; 17.8) or, even more boldly, "before all time" (11 Tim. 1.9; Tit 1.2 [pro chronon aionion]; Jude 25 [pro pantos tou aionos]). To quote again the Psalmist's words: "Before the mountains were brought forth, or 15 AdolfGrünbaum, "Some Comments on William Craig's 'Creation and Big Bang Cosmology'," Philosophia naturalis 31 (1994): 229. 16 AdolfGrünbaum, "A New Critique ofTheological Interpretations ofPhysical Cosmology," British Journaljor the Philosophy ojScience (forthcoming). 17 Brian Leftow, Time and Eternity, ComeIl Studies in Philosophy of Religion Othaca, N. Y.: ComeIl University Press, 1991), pp. 290-291, 310; cf. p. 322, where he affirms that God is etemally incamate in Christ. Cf. also p. 239, where he affirms that in etemity events are "frozen" in an array of B-series positions. See also Yates's chapter on timeless creation in John C. Yates, The Timelessness oj God (Lanham, Md.: University Press of America, 1990), pp. 131-163.

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ever thou hadst fonned the earth and the world, from everlasting to everlasting thou art God" (Ps. 90.2). Judle's doxology is especially interesting: "to the only God ... be glory, majesty, dominion, and authority, be/ore al! time and now and/orever" (Jude How these ordinary language expressions are to be fonnulated 25). philosophically-the Bible is not, as Paul Helm reminds us, a philosophy book from which a doctrine of divine eternity may simply be read off the surface-will be addressed in the sequel; but their intent is dear and must be taken seriously. The notion that God and the universe timelessly co-exist in an asymmetrical relation of ontological dependence is not only foreign to, but actually incompatible with, the biblical writers' conception of creatio ex nihilo, of God's existing alone and bringing the world into being out of nothing. If, on the other hand, we adopt a tensed theory of time, then we are able to affmn a full-blooded doctrine of creation. For on such a theory, the universe is not merely metricaUy finite in its past temporal extension. Rather it came into being at the first moment of its existence. That coming to be, the doctrine of creation tens us, was not a spontaneous, uncaused event but was the result of God's causal action. It was creation. The doctrine of creatio ex nihilo thus raises a nest of intriguing and difftcult questions: Did God exist in time prior to His creation of the universe? Does creatio ex nihilo imply the creation of time itself? Can God's priority to time be understood in some way other than chronological? These are questions, an adequate answer to which must be given from the perspective of a tensed theory of time. CONCLUSION Essential to the biblical doctrine of creatio ex nihilo is the dual affmnation that God brought the universe into being out of nothing at some moment in the finite past and that He sustains it inunediately in being moment by moment. The first part of this afftnnation implies that there obtains in the actual world astate of affairs which may be described as God's existing alone without the universe. The theorist of tenseless time cannot afftnn this, since on his theory of time the block universe coexists timelessly with God, perhaps having tenselessly a first moment but never really coming into being out of non-being. The advocate of tenseless time thereby reduces the first component of the doctrine of creation to the second-tenseless ontological dependence·-and thereby emasculates creatio ex nihilo. His only escape route would be the metaphysically extravagant postulation of a hyper-time in which the 4D universe originates, a view which requires a (hyper-)temporal deity. A robust, biblical doctrine of creatio ex nihilo thus presupposes a tensed theory of time, and its conundrums must be addressed from that viewpoint.

CHAPTER9 GODANDTHEBEG~GOFTIME THE INFINITUDE VS. FINITUDE OF THE PAST

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reatio ex nihilo is a biblical doctrine affinned by the Church and confinned by modem cosmology. But if the universe began to exist, what shall we say of God's temporal status sans the world? The Christian doctrine of creation requires that the actua1 world includes astate of affairs which consists of God existing alone without any created realm, a doctrine remarkably consonant with the worldview of contemporary cosmology, which posits an absolute beginning of physical space and time. Is God sans the universe timeless or temporal? According to current cosmological theory, time and space came into existence with the Big Bang. As the British physicist P. C. W. Davies explains, If we extrapolate this prediction to its extreme, we reach a point when a11 distances in the universe have shrunk to zero. An initial cosrnological singularity therefore fonns a past temporal extremity to the universe. We cannot continue physical reasoning or even the concept of spacetime, through such an extremity. For this reason most cosmologists think of the initial singularity as the beginning of the universe. On this view the big bang represents the creation event, the creation not only of a11 the matter and energy in the universe, but also of spacetime itself I

On such an understanding, the universe did not spring into being at a point in a previously existing empty space. Rather space and time themselves come into being along with the universe, which implies creation out of absolutely nothing. Thus, Barrow and Tipler assert, "At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo."z This feature of the standard Big Bang model has appeared especially baftling to philosophically-minded cosmologists, particularly those with an atheistic bent. For example, the Russian astrophysicist Andrei Linde acknowledges quite frankly the problem the standard model poses for him: "The most difficult aspect of this problem is not the existence of the singularity itself, but the question of what was be/ore the singularity.... This problem lies somewhere at the boundary between physics and metaphysics.,,3 In order to avoid this question, Linde therefore Paul Davies, "Spacetime Singularities in Cosmology and Black Hole Evaporations," in The Study 01 Time III, ed. J. T. Fraser, N. Lawrence, and D. Park (Berlin: Springer Verlag, 1978), pp. 78-79. 2 John Barrow and Frank Tipier, The Anlhropic Cosmological Principle (Oxford: Oxford University

Press, 1986), p. 442. 'Andrei Linde, "The Inflationary Universe," Reports on Progress in Physics 47 (1984): 976.

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proposed an etemal inflationary model of the universe, according to which our observable universe was birthed by a prior universe, and so on ad irifinitum. But in 1994, two other cosmologists Arvind Borde and Alexander Vilenkin showed that inflationary scenarios like Linde's cannot avoid an initial singularity. They conclude, "A physically reasonable spacetime that is etemally inflating to the future must possess an initial singularity.... The fact that inflationary spacetimes are past incomplete forces one to address the question of what, if anything, came before?,,4 Other cosmologists have tried to eliminate the initial space-time singularity by introducing speculations about quantum gravity, as in Stephen Hawking's famous theory. On such models, imaginary numbers are assigned to the time variable in the equations, which has the effect of suppressing the singular point. But as Hawking hirnself acknowledges, such models in "imaginary time" are not realistic descriptions of the universe but have mere instrumental value. 5 "When one goes back to the real time in which we live," Hawking admits, ''there will still appear to be singularities.,,6 In any case, as Barrow emphasizes, such models still involve a merely finite past and so imply the beginning of space and time: ''This type of quantum universe has not always existed; it comes into being just as the classical cosmologies could, but it does not start at a Big Bang where physical quantities are infinite .... ,,7 Thus, the beginning oftime is not avoided. So today, in Hawking's words, "almost everyone now believes that the universe, and time itself, had a beginning at the big bang."s This consensus seems to lend strong support to the view that neither events nor time exists prior to creation. As physicist David Park says, "It is deceptively easy to imagine events before the big bang ... , but in physics there is no way to make sense ofthese imaginings.,,9 The fly in the ointrnent, however, is Park's phrase "in physics." For we have been wont to emphasize throughout this study that time as it plays a role in physics is at best a measure of time, not time itself. It is perfectly coherent to imagine nonphysical events prior to the Big Bang, whether mental events in God's stream of consciousness or events in angelic realms created by God prior to the physical universe. At most, then, the physical evidence proves that physical time had a beginning at the Big Bang, not that time itself so began. Of course, it is possible to take the origin of physical time as coincident with the origin of time itself; indeed, if time did begin to exist, such a conception is simpler than taking time to have begun at a moment prior to th~~ Big Bang by some finite interval. But if we are to decide

Arvind Borde and A1exander Vilenkin, "Etemal Inflation and the Initial Singularity," Physical Review Letters 72 (1994): 3305,3307. 5 Stephen Hawking and Roger Penrose, The Nature of Space and Time (Princeton: Princeton University Press, 1996), pp. 3-4, 121; cf. pp. 53-55. 6 Stephen Hawking, ABriefHistory ofTime: From the Big Bang to Black Holes, with an Introduction by Carl Sagan (New York: Balltarn Books, 1988), p. 139. 1 John Barrow, Theories of Everything (Oxford: Clarendon Press, 1991), p. 68. Hawking and Penrose, Nature of Space and Time, p. 20. David Park, "The Beginning and End ofTime in Physical Cosmology," in The Study ofTime IV, ed. J. T. Fraser, N. Lawrence, and D. Park (Berlin: Springer Verlag, 1981), pp. 112-1 I3.

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whether God endured through infinite time prior to His creation of the world or whether God sans the universe is timeless, we shall have to have recourse to metaphysical, not physical, arguments. ARGUMENTS FOR THE PASrS INFINITUDE What reasons, then, might be adduced in favor of the view that past time is infinite? Newton's view that time is an emanent effect or necessary concomitant of God's being and therefore infinite appears to presuppose that the idea ofthe timeless existence of an entity is broadly logically incoherent. But Newton gives no argument for bis position, and the willingness of a good many pbilosophers-even empiricists like Quine---to entertain timeless abstract objects in their ontologies suggests that there is nothing demonstrably incoherent about timeless existence as such. Of course, in order to exist in such astate, God would have to exist changelessly (though not immutably), and many regard this as impossible for a personal being like God. But in Chapter 2 we considered and rejected the claim that a personal being like God could not exist timelessly. I am unaware of any other arguments that God sans the universe must be temporal and therefore the past infinite. There are, however, a good number of traditional arguments for the past infInity of time,10 and one of these, stemming from Aristotle, has been defended by Swinbume. According to Aristotle, "since time cannot exist and is unthinkable apart from the now, and the now is a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time ... ,.. 11 that is, that time is beginningless and endless. Swinbume similarly argues that time is of logical necessity unbounded: After every period of time which has at some instant an end, there must be another period of time, and so after every instant another instant. For either there will be swans somewhere subsequent to aperiod T, or there will not. In either case there must be a period subsequent to T, during which there will or will not be swans. By an analogous argument any period which has a beginning must have been preceded by another period, and hence time is necessarily unbounded. 12

Since the same instant oftime never recurs, time's unboundedness implies that time is of logical necessity infinite. To say that the universe began to exist is to say that a finite time ago there were no physical objects. As it stands, this argument is not very compelling. Even if every instant of time is the boundary of an earlier and a later interval of time, it only follows that there is no first or last instant of time, not that there is no first or last moment (nondegenerate interval) of time and that therefore time is infinite. The flnitude of past See the marvelous review in Thomas Aquinas Summa contra gentiles 2.32-37. Aristotle Physics 8.1.25 I b 19-23. (Revised Oxford trans.) 12 Richard Swinbume, Space and Time, 2d ed. (London: Macmillan, 1981), p. 172. So also J. R. Lucas, A Treatise on Time and Space (London: Methuen & Co., 1973), pp. 10-11; Raja Bahlul, "Ghazali on the Creation vs. Etemity of the World," Philosophy and Theology 6 (1992): 269. 10

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time is not abrogated by cutting out the initial instant of time. 13 Moreover, it is not clear that every instant of time is the boundary of both earlier and later temporal intervals. Why may not a temporal instant be simply first, the boundary of a later interval only? Or if one prefers to treat time as discrete, why must any moment of time be preceded by a prior moment? There seems to be no conceptual difficulty in the notion of a first chronon not preceded by another, distinct chronon. But perhaps we are overlooking the role played by tense in the argument. Aristotle does not contend that there cannot be a first instant or moment, but a first "now." The claim is that any time which is present implies the existence of past time and future time, since the present is the end of the past and the beginning of the future. In such a case, it is the tensed time theorist alone who is committed to the infmitude of time. Perhaps we can interpret Aristotle to mean that if there were a first "now," then, just as there are present-tense statements which are true or may be truly asserted at that point, so also are there past-tense statements which enjoy a similar status, which fac:t implies the reality of the past after all. Sorabji interprets Aristotle's cryptic remark in Metaphysics 12.6 ''Nor can time come into being or cease to be; for there could not be a before or an after if time did not exist,,14 to assert that "You cannot say time began, for that would imply that previously (proteron) there was no time, and the word 'previously' implies that there was time after all.,,15 Actually, it is not the tenseless term "previously" which occasions the problem, but the tensed word "was." The theorist of tenseless time can at the first moment of time assert truly and without fear of incoherence that there is no previous or earlier time. But the advocate of tensed time may seem to be faced with having to assert at the first moment of time that there was no earlier time, which is incoherent. Any number ofpast-tense truths, like "There were no stars before now," seem to confront the defender of tensed time at the first moment of time. Indeed, as Swinburne suggests, it is logically necessary that either stars existed or stars did not exist, so that the Law ofExcluded Middle requires the truth ofpast-tense statements at the first moment oftime. But the tensed time advocate can properly retort that the surface grammar of such statements is misleading. 16 Past-tense statements should be analyzed along the lines oftense logic as being ofthe form pcp), for example, "It was the case that stars exist." The statement that "There were no stars before now," when asserted at the 13 See Quentin Smith, "On the Beginning ofTime," NoUs 19 (1985): 579-584. In fact, in contemporary cosmological models the absence of an initial temporal instant does not even imply that time as a whole is unbounded, since the initial cosmological singularity, while not an instant of time, nevertheless constitutes a boundary of time. In this case there is a beginning point to time but no first instant of time. It is, however, not evident that these conceptions of physical spacetime can be carried over successfully to metaphysical time. In the case of metaphysical time, one could say that the first moment of time simply lacks a first instant. 14 AristotieMetaphysics 12.6.1071b8. 15 Richard Sorabji, Time, Creation, and the Continuum (lthaca, N. Y.: Cornell University Press, 1983), p.279. 16 See A. N. Prior, "The Logic of Ending Time," in Papers on Time and Tense (Oxford: Clarendon Press, 1968), pp. 98-115.

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first moment of time, should be understood to be of the form -P(P), rather than P(-p). The Law ofExcluded Middle may then be understood to be ofthe form P(P) v -P(P) and to be valid for past-tense statements, all ofwhich turn out to be false at the first moment of time. Thus, the partisan of a tensed theory of time can provide a coherent account of the apparent truth of past-tense statements at the first temporal moment. 17 Swinburne questions whether the statement "It is not the case that there was an earlier time" differs more than verbally from the objectionable "Earlier there was no time.,,18 But clearly it does, for only the latter implies that a past moment of time existed. ARGUMENTS FOR THE PAST'S FINITUDE Absent any cogent argwnents that time must be beginningless, it behooves us to ask whether there is any reason to think that the past is, in fact, finite. Again there is a long philosophical history of argwnentation for the finitude of the past, especially in Islamic Kalam,19 and I have elsewhere defended two such argwnents: the argwnent based on the impossibility of an actual infinite and the argwnent based on the impossibility of the formation of an actual infinite by successive addition. 20 I shall not repeat what I have said there, as I believe no compelling defeaters have been offered for those argwnents. It is worth noting, however, that the argwnents are independent of each other and that only the second presupposes a tensed theory of time. If successful, these argwnents demonstrate that the past is of metaphysical necessity finite. Why Did Not God Create the World Sooner?

Here I should like to examine two additional considerations that tell in favor of the fmitude of the past. The first arises from the conundrum posed by Leibniz to Clarke in their famous correspondence: Why did not God create the world sooner?21 Leibniz had presented this challenge as an objection to Newton's substantival view oftime, but it is, in fact, an objection to time's past infinity. On Leibniz's preferred relational view of time, there are no instants of time in the absence of changing things; hence, time begins at creation and the question as to why God did not create

17 So also W.-H. Newton-Smith, The Structure of Time, International Library of Philosophy (London: Routledge, Kegan & Paul, 1980), p. 98. 18 As reported from personal conversation by Sorabji, Time, Creation, and the Continuum, p. 280. 19 Again, see Aquinas's survey in Summa contra gentiles 2.38. 20 See, for example, William Lane Craig, The Kalam Cosmological Argument, Library of Philosophy and Religion (London: Macmillan, 1979); William Lane Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Clarendon Press, 1993). 21 G. W. Leibniz, "Mr. Leibniz's Third Paper," in The Leibniz-Clarke Correspondence, ed. with an Introduction and Notes by H. G. Alexander (Manchester: Manchester University Press, 1956), p. 27.

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the world sooner is simply misconceived. 22 But the substantivalist who believes in the finitude of the past will also find the question inappropriate, since there are no empty instants of time preceding creation, as Newton believed. The question why did God not create the world sooner is thus irrelevant to the substantivalismlrelationalism debate; it is rather a challenge to the infinitude of the past. 23 It asks what possible reason God could have had for delaying for infinite time His creation of the world. Whether time is construed substantivally or relationally, since, according to Judaeo-Christian doctrine, God created all reality outside Himself ex nihilo at some time in the ftnite past, it follows, if past time is infinite, that God endured through an infinite period of creative idleness up until the moment of creation. Why did He wait so long?

On Leibniz's relational view, since God is irnmutable, " ... ifthere were no creatures space and time would be only in the ideas of God" (G. W. Leibniz, "Mr. Leibniz's Fourth Paper," in Correspondence, p. 42). Hence, "".once it has been shown, that the beginning, whenever it was, is a1ways the same thing; the question, why it was not otherwise ordered, becomes needless and insignificant" (Ibid., pp. 38-39). Cf. his later explanation: "If there were no creatures, there would be neither time nor place, and consequently no actual space. The immensity of God is independent upon space, as his eternity is independent upon time. These attributes signify ooly [with regard to those two orders of things] that God would be present and co-existent with aU the things that should exist. And therefore I don't admit what's here a1leged, that ifGod existed a1one, there would be time and space as there is now: whereas then, in my opinion, they would be only in the ideas of God as mere possibilities" (G. W. Leibniz, "Mr. Leibnitz's Fifth Paper," p. 80). A Christian relationalist who holds to the infinitude of God's past would have to regard God as being in immemorial change, for example, counting down the negative numbers, which Leibniz would reject due to his commitment to divine immutability. The question why God did not finish His countdown sooner remains unabated for the relationalist who regards God as being in immemorial change. The substantivalist could see God as either changing or changeless prior to the moment of creation. 23 That this is the case is clear from the historical provenance of the question. In the debate between medieval Islamic philosophers and practitioners of kalam over the world's eternity, philosophers championing eternal emanation of the world opposed adherents of temporal creation by defying them to explain why God did not create the world sooner. Defenders of creatio ex nihilo like a1-Ghazali responded by arguing that time begins at creation, so that the question is meaningless (AI-Ghazali, Tahafut al-Falasifah, trans. S. A. Kamali [Lahore: Pakistan Philosophical Congress, 1963], pp. 35-36; cf. p. 23). Leibniz himself hints at the real issue when he remarks, "It is a". fiction, (that is) an impossible one, to suppose that God might have created the world some millions of years sooner. Those who run into such kind of fictions, can give no answer to one that should argue for the etemity of the world" (Leibniz, "Fourth Paper," p. 38). The wider context in which the question at issue arose was the emanationist philosophers' challenge to creationists to explain how a first temporal effect could originate from an eternal, changeless cause (Ghazali, Tahafut, p. 14). Ghazali argues that (i) God as a free agent cause can initiate new effects in time without any determining conditions, (ii) God wills etemallythatatemporallyfiniteeffectappear.so that the appearance of the effect involves no change in God and, hence, does not compromise divine timelessness, and (iii) that since time begins at the moment of creation, it is senseless to ask why God did not create sooner. I have found Ghazali's discussion enormously stimulating and profitable. In my own work I have defended both (i) and (iii), but I have argued against (ii) in chap. 3 of the present work, because even if no intrinsic change in God occurred at creation, He would at least change extrinsically and, hence, become temporal. 22

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It might be said that given inftnite past time, it is simply logically impossible for God to have a sufftcient reason for choosing one moment rather than another to create the world and that God can hardly be blamed for not doing what is logically impossible. 24 God's choices are limited to refraining from creation, creating from eternity past, or choosing arbitrarily some moment of inftnite time at which to create. But far from resolving Leibniz's challenge, such a response serves only to underline the difftculty. The problem may be formulated as folIows, where t ranges over times prior to creation:

1. If the past is inftnite, then at t God delayed creating until t + n.

(P)

2. If at t God delayed creating until t + n, He must have had a good reason for doing so.

(P)

3. If the past is inftnite, God cannot have had a good reason for delaying at t creating until t + n.

(P)

4. Therefore, if the past is inftnite, God must have had a good reason for delaying at t creating until t + n. (HS,1 ,2) 5. The past is inftnite.

(P)

6. Therefore, God must have had a good reason for delaying at t creating until t + n. (MP,4,5) 7. Therefore, God cannot have had a good reason for delaying at t creating until t + n. (MP,3,5) 8. Therefore, God must have had a good reason for delaying at t creating until t + n, and God cannot have had a good reason for delaying at t creating until t + n. (Conj.,6,7) 9. Therefore, if the past is inftnite, God must have had a good reason for delaying at t creating until t + n, and God cannot have had a good reason for delaying at t creating until t + n. (CP,5-8) 10. Therefore, the past is not inftnite.

(RAA,9)

The claim that it is logically impossible for God to have any reason for preferring one moment over another as the moment at which to create does nothing to undermine the crucial premiss (2) but rather undergirds the truth of premiss (3). In an inftnite, empty time prior to the existence of any reality, physical or spiritual, outside of God, there can be no reason for God to wait longer to create the world. At any time t, after all, He has already waited for inftnity! Why delay any longer?

24

This objection has been suggested to me in conversation by Quentin Smith.

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In his interesting analysis of this problem,2s Brian Leftow observes that if God acquires at some moment a sufficient reason to create the world, this reason must come from some change either within God or outside of God. The only change going on outside of God is the absolute becoming of time itself. If, from eternity past, God has willed to create the world at t, then the arrival of t as present could give God a new reason to create. But, says Leftow, it is at least initially plausible that a perfectly rational God could not have from all eternity a reason to create at one particular instant rather than another. For there is nothing about the position of any particular instant which makes it an especially appropriate point for the beginning of the universe. So if God is to have a new reason to create, it must come from within Himself. But since God is from time immemorial perfectly good, omniscient, and omnipotent, no change within Himself can occur which should prompt Him to create at some time rather than earlier. Thus, God cannot acquire at some moment a sufficient reason to create the world. But by the same token neither could He have had some reason from eternity past to create at some particular time, as already seen. Leftow's analysis goes to support (3) above, that God could not have had any good reason at any time t in the infinite past for delaying at t His creation of the world until t + n. Leftow seeks to av:ert the force of the argument by claiming that God's reason for delaying creating is the joy of anticipation of creating. He says, "So (I submit) God can delay creating to enjoy anticipating a universe and/or desiring to create one. Parents can find joy in the anticipation of a child. ... So God a fortiori can savour in advance the coming-to-be of a universe whose precise nature He foreknows. ,,26 Such a portrait of God may seem overly anthropomorphic; but Leftow argues that a person of overflowing love delights in the goodness of a gift he will give and in the joy ofthe receiver in getting it and that God's nature's being agape makes Him such aperson. The real rub with Leftow's proposal, I think, lies in whether his proposed solution provides an answer to the question of why God would delay for infinite time His creation ofthe world. Leftow sees no problem in God's waiting for infinite time, since God is infmitely patient. But the question remains of why God, having anticipated from eternity past the creation of the world, would at t delay creating until t + n. ür, obversely, why did He ce ase waiting and anticipating at t + n instead of earlier or later? Leftow answers that there is a time tat which one's anticipation over bestowing a gift begins to wane and so reaches a point of diminishing returns. So a rational person concerned to maximize his or her overall happiness would have some reason to give his or her gift at t.... [But if] this is God's concern, then God will not want 10 wait beyond t if after t He will no longer enjoy His maximal slate of anticipatory happiness and will enjoy greater happiness if He gives at t. Now if God foresees His own fhture states, He knows from a11 eternity precisely when His

25

26

Brian Leftow, "Why Didn't God Create the World Sooner?" Religious Studies 27 (1991): 157-172. Ibid., p. 163.

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CHAPTER9 anticipation 's point of diminishing retum will fall. If so, He can resolve to create at just this point. 27

Leftowenvisions a sort of "Gaussian curve" representing God's rising and falling anticipatory pleasure (Figure 9.1): y = leasure

x=time Figure 9.1. God's anticipatory pleasure rises from a minimal value at t to a peak value before declining to a minimal value at t = +00 again

=--00

God will create at the moment His anticipatory pleasure peaks, and that is t, the time of creation. Again, one might reasonably object that such a portrayal of God's anticipatory pleasure is grossly anthropomorphic; but let that pass. The more saHent difficulty is that Leftow's Gaussian curve must be logically prior to the fact of the curve's peaking specifically at t if it is to provide some rationale for God's choosing to create at t. But then why, if the past is infinite, did God's anticipation peak at t rather than sooner? Leftow's reply is faltering: ... let us imagine a curve irifinite a10ng the x-axis inscribed in a two-dimensional space. There is no empty space along the x-axis into which to shift such a curve. The equation whose values that curve expresses generates a value of y for each point a10ng the x-axis. Thus we cannot even speak of the curve's nature and its location as two independent factors determining its highest point. Such a curve cannot be ·shifted'. Rather, where its highest point falls clearly is a function ofthe nature ofthe curve a1one. The curve's nature suffices to determine where a10ng thex-axis the curve's greatesty-value occurS. 28

This reply fails to take account of the paradoxical nature of the actual infinite. Just as the infamous Hilbert's Hotel (each of whose infinitely many rooms are occupied) can accommodate infinitely many new guests simply by shifting each guest into a room with a number twice his own (thereby freeing up all the oddnumbered rooms), so God's pleasure curve, though infinitely extended, can be shifted backward in time simply by dividing every value of the x-coordinate by two. Since the past is, ex hypothesi, actually infinite, there is no danger of "scrunching up" the front of the curve by such a backward shift. If such a shift seems impossible, what is called into question is the possibility of an infinite past. But given the past's infinity, there is no problem in shifting such a curve: its shape could Ibid., pp. 166-167. Ibid., p. 169. It is not clear to me that God's having waning anticipation is consistent with Leftow's claim that God is infmitely patient. 27

28

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remain unchanged and yet peak anywhere in the inftnite past or future. Therefore, Leftow has not provided a cogent argument for thinking that God's anticipating creation for inftnite time provides a reason as to why God creates at t instead of t + n (or t - n). Thus, we have good grounds for affmning premise (3) of the argument. Premiss (1) of our argument seems incontestable. If the past is inftnite, then at any moment prior to creation, God existed at that moment and could, at that moment, have brought the universe into being. But He did not. He waited. He deliberately delayed creating the world until some later moment should arrive. The most controversial premiss will therefore be (2), that God must have had a good reason for delaying until t + n. Notice that (2) does not depend on the truth of some broader Principle of Sufftcient Reason. It states merely that in this speciftc case God, existing alone at t, but deciding to refrain from creating at t and to delay creating until t + n, must have had a good reason for waiting. Notice, too, that (2) does not presuppose the infmity of time. Hence, it is doubly irrelevant to protest that given an inftnite past God's decision when to create must be arbitrary. Not only does that merely underscore (3), but (2) does not postulate the infmitude ofthe past. It asserts that if God at some moment prior to creation consciously defers creating until a later moment, then He surely has a reason for doing so. A perfectly rational agent does not delay some action he wills to undertake apart from a good reason for doing SO.29 Thus, (2) strikes me as eminently plausible. Accordingly, the Leibnizian challenge seems to me to furnish a cogent and persuasive argument for thinking that the past is ftnite. God's idling awayeternity, continually delaying His creation of the world throughout infmite past time, seems to be an unintelligible conception. Why Is It Now?

A second, but less perspicuous, reason for denying the infmitude of the past derives from 1. 1. C. Smart's question to the theorist of tensed time: why is the present date present?30 This question might appear to embody a mere tautology; but if we take "the present event" to refer de re, then we are asking of the moment in time so picked out why it is present. Even so construed, the question may appear trivial, for the "is" must be present-tense, in which case it becomes obvious that the only time at which a moment has presentness is when it is present. So it is wrongheaded to ask why a certain moment has (present-tense) presentness. Still, in a difftcult to articulate way, it does seem unintelligible why, say, 2000 is present ifthe past is inftnite. If time had a beginning, then a ftrm foothold is gained which makes 2000's being present more intelligible. For a certain number of years earlier than 2000, a ftrst moment was present, and it makes no sense to ask of it at that time why 29 For this reason, Quentin Smith's claim in "Kant and the Beginning ofthe World," New Scholasticism 59 (1985): 345 that " ... something can come to be at one time rather than another accidentally" is irrelevant, since Smith does not consider the case of theistic creation. 30 1. 1. C. Smart, Philosophy and Scientific Realism (London: RoutIedge, Kegan & Paul, 1963), p. 135.

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it, as the first, was present. For it could not have occurred earlier (since there was no earlier), nor could it have occurred later (since it was the first moment). But if the fIrst moment of time is thus anchored in place, then so is the second moment, and the third, and the fourth, and so on. We can say of any time that the reason it is present is because n years earlier there was a beginning of time and a first moment which was present. The location of the present is thus founded upon the platform of the first moment of time. By contrast, an infInite past is a bottomless quicksand which affords no foothold for the determination of the present. If we say that 2000 is present because n years ago some earlier time was present, our question can be asked again of that earlier time: why was it present? It becomes unintelligible why it has taken until now for 2000 to arrive or, on the other band, why it has not taken longer. Why did 2000 not become present two years ago? This is not to ask why 2000 is not 1998, but rather why, to borrow Leftow's terminology, the temporal series of events is not shifted into the past. Not that we could tell any difference; but there is a difference between 1998's being present, and we may ask why one is in fact the case rather than the other. A relationalist might try to avert this conundrum by holding that the temporal series just is the series of events, so that it is meaningless to speak of a shift toward the past ofthe series of events. But Smith has shown convincingly that the series of times cannot be plausibly identifIed with the series of events (if this were not intuitively obvious of itself).31 Nonetheless, the relational view is helpful, since it fumishes an analogue to our question which is perhaps more perspicuous: why is the present event occurring? Given the fInitude of the past, it is not hard to understand why certain events rather than others are occurring, since a causal chain stretches back to the first event n years ago which was then occurring. But if the past is infInite, it seems wholly mysterious why the present events are elapsing now, why they have not already occurred or have yet to occur. One cannot say it is because an infInite number of years ago a certain event was then occurring, for (if the events of the past correspond to the natural number series) there was no event an infInite number of years ago, and for every event n years ago the same question can be asked. To give a scientifIc illustration: P. C. W. Davies has argued that the universe must have had a beginning due to the fact that it is not in astate of thermodynamic equilibrium. According to Davies the thermodynamic properties of the universe have two profound implications: The first is that the universe will eventually die, wallowing, as it were, in its own entropy. This is known among physicists as the 'heat death' of the universe. Tbe second is that the universe cannot have existed for ever, otherwise it would have reached its equilibrium end state an infmite time ago. Conclusion: the universe did not always exist. 32

11 Quentin Smith, "The New Theory of Reference Entails Absolute Time and Space," Phil080phy 0/ Science 58 (1991): 411-416. 32 Paul Davies, God and the New Physics (New York: Simon & Schuster, 1983), p. 11.

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This reasoning is a clear instance of the problem we are examining. Even if the universe's energy were infinite, it would in infinite time come to equilibrium; but since at every point in an infinite past an infinite amount of time has already elapsed, what determines the time at which the universe reaches equilibrium? Davies's own answer is that at every point in the past it would have already reached equilibrium (or, as he puts it, would have reached equilibrium an infinite time ago). Davies' sanswer implies that just as the universe must have begun to exist, so also in the case of Smart's conundrum time must have begun to exist. Even if we do not take Davies's line in response to the problem, it remains the case that the finitude of the past can be avoided only by making it unintelligible why the events of 2000 are occurring now. To return to our original, non-relational formulation of the problem, someone might say that even if time had a beginning, still we could ask why it is not, say, 1900 instead of 2000. But insofar as such a question is non-trivial, there does seem to be a more intelligible answer given the finitude, as opposed to the infinitude, of the past: it is 2000 because n years ago it was then t = 0, the first moment of time, of which it cannot be meaningfully asked why it was present. If it be said that we can ask, "Why is t = 0 past?" it can be answered, "Because t = 0 was present n years ago." If at t = 0 someone were to have asked, "Why is t = 0 not past?" the answer could have been given, "Because no time has elapsed since t = 0 was (or is) present." These answers may seem almost silly until we reflect on the fact that no answer of even comparable merit can be given to questions about why some time is present rather than past on the assumption of the infmitude of the past. In summary, Smart's question, insofar as it can be given a non-trivial sense, seems to receive a more intelligible answer given the finitude of the past than given the past's infinity. The more intelligible answer is to be preferred. Therefore, the past is finite. Thus, it seems to me that we have good grounds for affirming the finitude of the past and the beginning of time. TEMPORALITY Vs. ATEMPORALITY OF GOD SANS CREATION Now if time had a beginning at some moment in the finite past, it follows that God sans the universe exists atemporally, even if subsequent to the moment of creation He is temporal. Now prima facie such a conclusion seems bizarre, even incoherent. For on such a view there seem to be two phases of God's life, which stand to each other in a relation of earlierl/ater than. But a timeless phase can hardly be coherently said to exist earlier than a temporal phase of God's life. Leftow has stated the objection forcefully: If God is timeless, there is no before and after in His life. No phase of His life is earlier or later than any other phase, for ooly temporal durations and their phases stand in these relations. As it lacks earlier and later parts, an etemal life has no phases, even if it is somehow extended. So if God is timeless and a world or time exists, there is no phase of His life during which He is without a world or time or has not yet decided to create them, even if the world or time had a beginning. For a life without phases cannot have one phase that is without the world or time and another phase that is with it. The whole

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CHAPTER9 of God's life is identical with the 'phase' of it during which the universe or time exists and during which God has decided to create them.))

Leftow's characterization of God's timeless life is an apt description of God's atemporal existence on a tenseless theory of time, since the four-dimensional spacetime manifold is as extrinsically timeless as God and never came into being. But I have argued that given a tensed theory oftime, God's temporal status cannot remain unaffected by His creation of a temporal universe. Given God's real relation to the world, God must, subsequent to creation, be temporal. But then, if a timeless phase of one's life is, as Leftow puts it, a phase co-extensive with the whole of one's life, it follows that God, having a temporal phase of His life, cannot also have a timeless phase of His life. Hence, God must also be temporal prior to creation; indeed, given God's beginningless existence, time must be beginningless as well. Metrically Amorphous Time sans Creation

How are we to escape this apparent antinomy? One possibility is suggested by a closer examination of the arguments I presented for the finitude of the past. Strictly speaking, none of the arguments I have defended implies that time itself had a beginning. Rather what they entail is that time which is divisible into distinct intervals must have had a beginning. But the arguments would not be incompatible with the existence of an undifferentiated "before" followed by the beginning of time as we know it. Such a view of divine eternity sans the universe has been defended by Padgett and Swinbume. 34 Both of them endorse metric conventionalism with respect to time and so regard God existing prior to creation as enduring through a metrically amorphous time, astate which Padgett calls ''relative timelessness." Now I have criticized the conventionalist thesis elsewhere;3s but perhaps we could say that metric time begins only at the moment of creation. If God is changeless prior to creation, perhaps the time which characterized such an existence was radically different from metric time. In a metrically amorphous time, there is no difference between a minute, an hour, or an aeon; more exactly, such measured intervals of time do not exist at alt. Thus it is a mere chimera to imagine God existing, say, one hour before He created the world. Swinburne argues that on such an understanding, God's time is beginningless but cannot be said to be infinite (or finite): ... think of God, the temporal being, existing by himself, not having created a universe in which there are laws of nature. There would then ... be no 'cosmic clock' which )) Brian Leftow, Time and Etemity, (New York: Comell University Press, 1991), pp. 290-291; cf. Idem, "Etemity," in A Companion to Philosophy 0/ Religion, ed. Philip Quinn and Charles Taliaferro, Blackwell Companions to Philosophy (Oxford: Blackwell, 1997), p. 259. )4 A1an G. Padgett, God, Etemityand the Nature o/Time (New York: St. Martin's, 1992), pp. 122-146; Richard Swinbume, "God and Time," in Reasoned Faith, ed. Eleonore Stump (Ithaca, N. Y.: Comell University Press, 1993), pp. 204-222. See also endorsements by Lucas, Treatise, pp. 311-312 and Bahlul, "Creation vs. Etemity," p. 272 and discussion in Prior, "Logic ofEnding Time," pp. 109-115. lS See my Time and the Metaphysics 0/ Relativity (Dordrecht: K1uwer Academic Publishers, 2001), chap.2.

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GoD AND THE BEGINNING OF TIME ticked unstoppably away, that is, there would be no temporal intervals of any definite length. There would just be an event or sequence of events in the divine consciousness. Think of hirn too as the subject of just one mental event, a conscious act without qualitatively distinguishable temporal parts Ce.g., conscious act that does not consist of one thought followed by a different thought). Now ... any event has to take time, but there wouldn't be a truth that this event Cthis act) had lasted any particular length oftime rather than any other. There would be no difference between a divine act of selfawareness which lasted a millisecond and one that lasted a million years .... Would there be difference between a divine conscious act which was God's only conscious act and was qualitatively identical throughout which was of finite length, and one which was of infinite length? No-so long as the former really is qualitatively identical throughout and thus contains no experience of a beginning or end; and so long as there is no time at which God is not. 36

Such a view has considerable attraction: it enables us to speak literally of God's existing before creation without affmning the problematic claim that God has endured through infinite time prior to creation. We can also conceive of God's literal foreknowledge of future events subsequent to creation, including His own acts. And we encounter no problems arising from the principle that a cause must be temporally prior to its effect. Nonetheless, the Padgett-Swinburne doctrine of divine eternity is demonstrably defective as it stands and so needs revision. 37 Metric conventionalism is the thesis that there is no fact of the matter concerning the comparative lengths of non-nested temporal intervals. What metric conventionalism does not assert is that no intervals at all exist in metrically amorphous time or that nested intervals cannot be compared to each other with respect to length. So in a metrically amorphous time, it is meaningful to speak of factual differences of length of certain temporal intervals (Figure 9.2). d

c

b

a

(=

0

Figure 9.2. Intervals in metrically amorphous time prior to creation at ( = O.

According to the conventionalist, there is no fact of the matter concerning the comparative lengths of dc and cb or db and ca. But there is an objective difference in length between da and ca or cb and ca, namely da>ca and cb