City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 5-2018 On A and B Theories of Time Edward Freeman The Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/2562 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] ON A AND B THEORIES OF TIME by Edward Freeman A dissertation submitted to the Graduate Faculty in Philosophy in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2018 ii ã2018 EDWARD FREEMAN All Rights Reserved iii This manuscript has been read and accepted for the Graduate Faculty in Philosophy in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy. Professor Steven Ross ___________________________ _______ ____________________________ Date Chair of Examining Committee Professor Iakovos Vasiliou ________________________ _________ _________________________ Date Executive Officer Professor Michael Levin (thesis adviser) ________________________ Professor Steven Ross _________________________ Professor Graham Priest __________________________ Professor John Lango __________________________ Professor Peter Simpson _________________________ Supervisory Committee THE CITY UNIVERSITY OF NEW YORK iv Abstract On A-and B-Theories of time by Edward Freeman Adviser: Professor Michael Levin Our metaphysical notion of temporality is exhausted by the concepts of fluid and static time. Following James Ellis McTaggart, philosophers refer to these times as the A-series and B-series respectively. To have a metaphysical argument against the reality of time as such, therefore, separate arguments against the reality of both temporal series are required. In the dissertation, I shall offer a number of both types of arguments. In the first chapter, McTaggart’s program is assessed. It is concluded that McTaggart has an argument against the reality of the A-series, but does not have one against the reality of the B-series. In the second chapter, additional arguments against the reality of the A-series, as well as against hybrid A/B series, are presented. In the third chapter, it is argued that the B-series is as unreal as its counterpart, the A-series, is. This outcome leaves us with the following philosophical predicament: on the one hand, our philosophical notion of time is exhausted by the concepts of fluid and static time; on the other hand, neither concept, nor any of their amalgamation, is adequate to give us a coherent metaphysical theory of time. The dilemma, I believe, is a sufficient reason for the conclusion that time, as it is conceived by philosophers, is not part of physical reality. v Preface The history of human knowledge presents us with many cases of reason going against our ordinary sense-experience and commonsense judgments. Take, for instance, the sun’s celestial movements. Even nowadays, when the knowledge that the sun does not rise and set is a commonplace, we still state with strait faces that the sun rises and sets at certain times of the day. Such is the binding force of our sensory experience that in our everyday goings our ancient geocentric bias totally eclipses our modern understanding of the cosmos. Analogously, I hold, time is an illusion stemming from our psychological predisposition to perceive things and events as necessarily temporally ordered. In actual fact, however, time is no more and no less than “a necessary representation given a priori.”1 That is my conviction. But my goal in this thesis is more modest. I do not argue that time as such is unreal (though I believe it is). My nonexistence claim is limited to two basic metaphysical concepts of time, viz. the notions of A-and B-time. I shall argue that neither the concept of A-time nor the concept of B-time nor, by extension, any of their various amalgamations, is theoretically viable. My arguments in these pages are only against these two metaphysical concepts of time. And since the metaphysics of time is in effect exhausted by these two concepts of temporality, I conclude that time, as it is conceived by philosophers, is nonexistent. 1 Immanuel Kant, Critique of Pure Reason (1781), Paul Guyer and Allen W. Wood (trans.), (Cambridge: Cambridge University Press, 1998), A31. vi Table of Contents: Preface……………………………………………………………..……………………………… iv Chapter I: McTaggart’s Argument 1.1 McTaggart’s A-series/B-series Distinction………………………….………...1 1.2 The Two Notions of Temporal Flow …………………………….…..………….13 1.3 The Essentiality Conjecture………………………………………………………...19 1.4 The Temporal Transience Paradox………………………………….…………...24 1.5 The General Structure of McTaggart’s Argument………………………..…38 Chapter II: A and A/B Theories of Time 2.1 Varieties of A and A/B theories…………………………………….…….…………43 2.2 The moving-now Model of Temporal Passage……………….………….….…46 2.3 The Burgeoning Universe Model of Temporal Passage……….…….….….61 2.4 Presentism…………………………………………………………...…….………………….65 2.5 B-Accounts of the Phenomenology of Temporal Passage………………….70 Chapter III: Eternalism 3.1 The Argument against Object-Eternalism..……………………..……………….82 3.2 The Argument against Event-Eternalism…………………………………….…...97 3.3 The Notion of Temporal Dimension …………..….…………………..……..….....119 3.4 The Argument against Eternalism from Change...………………….…..…..…132 3.5 The Argument against Eternalism from Persistence………………….….….146 Afterword……………………………………………………………..…..……………………….….158 vii Bibliography …………………………………………………………………………..163 List of Figures Figure 1 p. 9 Figure 2 p. 17 Figure 3 p. 28 Figure 4 p. 29 Figure 5 p. 32 Figure 6 p. 44 Figure 7 p. 45 Figure 8 p. 47 Figure 9 p. 48 Figure 10 p. 53 Figure 11 p. 56 Figure 12 p. 58 Figure 13 p. 63 Figure 14 p. 77 Figure 15 p. 86 Figure 16 p. 87 Figure 17 p. 98 Figure 18 p. 103 Figure 19 p. 122 Figure 20 p. 124 Figure 21 p. 125 Figure 22 p. 134 Figure 23 p. 150 Figure 24 p. 151 1 Chapter I: McTaggart’s Argument 1.1 McTaggart’s A-series/B-series Distinction 1.1.1 At the outset of the last century, an article appeared in Mind. Despite its overall sophistic tenor and a number of technical shortcomings, it would exert a strong sway over the subsequent generations of analytical metaphysicians. The article was James Ellis McTaggart’s “The Unreality of Time.”2 As its title implies, McTaggart argues that time is not part of concrete reality. Specifically, he argues that since our metaphysical notion of time is constituted by two fundamental concepts of temporality, the concepts of fluid and static time; he dubbed them the A-series and the B-series respectively, and since on his view neither concept is theoretically viable, he concludes that time as such is nothing but an illusion arising from our perception of essentially atemporal reality, “Whenever we perceive anything in time – which is the only way in which, in our present experience, we do perceive things – we are perceiving it more or less as it really is not” (NE, §333).3 2 J. M. E. McTaggart, “The Unreality of Time,” Mind 17 (1908), 457-74. A somewhat augmented version of the essay makes up Chapter XXXIII of McTaggart’s unfinished magnum opus The Nature of Existence, C. D. Broad (ed.) (Cambridge: Cambridge University Press, 1927). I will be quoting primarily from The Nature of Existence, abbreviated as NE, and indicating section numbers instead of page numbers. I will abbreviate “The Unreality of Time” as UT, followed by page number. 3 This is essentially a Hegelian view of time as opposed to Kantian one according to which time is nothing but a cognitive construct superimposed on reality. McTaggart is explicit about that his idea of temporal order resembles that of Hegel rather than that of Kant: “Hegel regarded the order of temporal series as a reflection, though a distorted reflection, of something in the real nature of the timeless reality, while Kant does not seem to have contemplated the possibility that anything in the nature of the noumenon should correspond to the time-order which appears in the phenomenon” (NE, §350). 2 Nowadays, almost no philosopher endorses this sweeping metaphysical thesis.4 Most do see fluid time as entirely illusory. The rest is split between those who believe to the contrary and those who hold fluid and static times to be equally real.5 Yet, as I shall argue in this study, McTaggart is essentially right; the truth is that neither concept of time, nor any of their amalgamations, is grounded in reality. McTaggart begins his argument for the unreality of time with his celebrated distinction between two fundamental concepts of time. On the one hand, we envisage time as the flow from the future, through the present, and into the past, this is McTaggart’s A-series.6 On the other hand, we conceptualize time as a static sequence of moments standing in earlier than/later than relations; this is McTaggart’s B-series: 4 T. L. S. Sprigge, “The Unreality of Time,” Proceedings of the Aristotelian Society 92 (1992), pp. 1-19 and present undertaking, at least as far as the two metaphysical conceptions of time are concerned, are rather rare exceptions. Mathematicians and physicists, on the other hand, are more open to the idea of the unreality of time. Consult, for instance, Gödel’s “A Remark about the Relationship between Relativity Theory and Idealistic Philosophy” in Albert Einstein: Scientist-Philosopher, P. A. Schilpp (ed.) (Evanston, Ill: Library of Living Philosophers, 1949), and more recent J. Barbour, The End of Time (Oxford, New York: Oxford University Press, 1999). 5 The most prominent B- time theorists are: B. Russell, “On the Experience of Time,” The Monist 25 (1915), pp.