1 Introduction There are two traditions in the philosophy of time that, while op- posing one another, are locked in a mutual embrace. The embrace is cemented by two shared assumptions: first, that time presupposes Thoroughly Modern McTaggart change; and, second, that genuine change requires Becoming. Both traditions have ancient roots. One, which takes its inspiration from Parmenides, denies the reality of change and time by rejecting Be- coming; the other, which can be traced to Aristotle, upholds the real- Or ity of change and time by claiming to find Becoming at work in the What McTaggart Would Have Said If He world. What complicates an already complex discussion is that there are at least two distinct senses of Becoming in play. One sense is ex- Had Read the General Theory of Relativity emplified in McTaggart’s (1908, 1927) infamous A-series, in which events are ordered as to past, present, and future. In capsule form, McTaggart’s argument for neo-Parmenideanism goes as follows: (P1) There must be real change if there is to be time. (P2) There must be temporal passage (i.e. a continual change in John Earman events of the non-relational properties of presentness, past- ness, and futurity) if there is to be real change. (P3) Temporal passage is incoherent. (C) Therefore, time is unreal. While the majority of philosophers agree with McTaggart’s (P3), there is a significant minority that finds his alleged demonstration of the incoherency of the A-series less than convincing.1 McTaggart’s brand of Becoming is property-based: that an event becomes present means for him that it loses the (non-relational) Philosophers’ Imprint property of futurity and takes on the (non-relational) property of <http://www.philosophersimprint.org/002003/> nowness. A non-property-based form of Becoming was articulated Vol. 2 No. 3 in modern form by C. D. Broad (1923) and has been championed August 2002 1 (c) John Earman 2002 See, for example, Savitt (2001a) and the exchange between Smith and Oak- lander, Essays 14-18, in Oaklander and Smith (1994). John Earman Thoroughly Modern McTaggart more recently by Michael Tooley (1997). Both Broad and Tooley both of the venerable traditions alluded to above: let them remain subscribe to a form of Aristotle’s doctrine that the future is unreal locked in their mutual embrace of Becoming and sink from view and/or does not exist and that events become real by coming into into the metaphysical mire. Becoming, in either McTaggart’s sense existence. If we follow convention and call a universe stripped of or Broad’s sense, is part of the manifest image. The scientific image its A-series properties a block universe, then what Broad and Tooley knows nothing of either, and yet science does describe a rich and present us with can be called a dynamic or growing block universe robust sense of change.3 Relinquishing the A-series and eschewing that continually adds new layers of existence. As Broad put it: the metaphor of the piling up of thin slices of existence leaves what has been called the non-dynamic block universe in which events are Nothing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the ordered only by the earlier-than relation (a.k.a. the B-series). To world. The past is thus as real as the present. On the other hand, be sure, the non-dynamic block universe is itself unanimated; but the essence of a present event is, not that it precedes future events, (to quote Savitt (2001b)) to have a picture of animation, one doesn’t but that there is quite literally nothing to which it has the relation of precedence. The sum total of existence is always increasing, and have to provide an animated picture. The animation that is pictured it is that which gives the time-series a sense as well as an order. A is B-series change–at different moments of time different proper- moment t is later than a moment t0 if the sum total of existence at ties are instantiated, the instantiation of all of which at any single t includes the sum total of existence at t0 together with something more. ... [W]hen an event becomes, it comes into existence; and moment of time would be contradictory. it was not anything at all until it had become. ... Whatever is has Needless to say, the adequacy of the B-series account of change become, and the sum total of existence is continually augmented by needs to be defended against a number of objections, but the de- becoming. (1923, 66-69) fense will not be mounted here.4 For present purposes I can as- Although the text of Gödel’s (1949) essay “A Remark About the Re- sume that this account of change is adequate, for my main aim is lationship Between Relativity Theory and Idealistic Philosophy” is to call to the attention of philosophers the fact that coupling this open to various interpretations, a plausible reading sees Gödel as at- assumption to one of the fundamental theories of modern physics– tempting to derive the ideality of time by coupling an acceptance of Einstein’s general theory of relativity (GTR)–revives McTaggart’s Becoming in Broad’s sense as a necessary condition for real change worries. For GTR–appropriately interpreted–seems to imply that, if with the claim that Einstein’s special and general theories of relativ- the B-series account of change is accepted, then there is no physical ity are incompatible with this sense of Becoming.2 change since–under the appropriate interpretation–GTR implies that The issues surrounding change and Becoming are revisited over no genuine physical magnitude takes on different values at differ- and over again in the philosophical literature, with each generation 3 adding new layers of wisdom. Since I do not aim to contribute to This cavalier attitude glosses over the problem of reconciling the manifest and scientific images; in particular, the problem of how science, if it eschews Be- this literature, I will take a cavalier and callous attitude towards coming, can give an adequate account of the phenomenology of experience which does involve a transient ‘now’. See Shimony (1993). 2For various interpretations and evaluations of Gödel’s argument, see Earman 4The most thoroughgoing defense of the B-series conception of change is to (1995, Ch. 6), Yourgrau (1991, 1999), and Belot (2001). be found in Mellor (1981, 1998). 2 John Earman Thoroughly Modern McTaggart ent times. This implication naturally raises the question of whether sting of this reaction can be drawn by showing both that it does not McTaggart’s conclusion that time is unreal can be avoided in GTR. entail McTaggart’s conclusion of the unreality of time and that it is The plan of the paper is as follows. In section 2 I discuss the compatible with preserving much of the common sense talk about logic of B-series change. The application of this logic to the actual change, albeit in an altered form. My conclusions are presented in universe, as described by textbook versions of GTR, seems to con- section 12. I emphasize especially that these issues are not merely firm the common sense conclusion that there is change in the world. playthings of academic philosophers since the stance taken on them In section 3 we meet modern McTaggart who accepts the B-series influences the direction of current research in physics. account of change but who rejects the common sense conclusion on the grounds that it rests on taking the surface structure of GTR too literally and that B-series change disappears in the deep structure 2 The logic and existence of B-series change of the theory. Section 4 describes in detail the considerations that On the B-series conception of change, change and the Heraclitean appear to support modern McTaggart’s claim that in the deep struc- role of time go hand in hand: the different moments of time sep- ture of GTR the dynamics is “frozen,” wherein all genuine physical magnitudes or “observables” are “constants of the motion.” Since arate what would otherwise be contradictories, transforming them into the temporal alteration that constitutes real change. There are familiar physical quantities do not count as observables in GTR, one must ask what the observables of the theory are and how they can be two ways to understand how time performs its Heraclitean function– the temporal stage view and the relational view.5 According to the used to express the results of observation and measurement. These first, if Jeremy changes from slim to portly, it is because of the matters are taken up in section 5. Section 6 is devoted to some stock taking. I indicate why GTR does not imply a flat-out no change conjunction of three facts: Jeremy is composed of temporal parts, Jeremy-at-t for variable t; Jeremy-at-t is slim; and Jeremy-at-t is view: it is compatible with an ontology consisting of a time ordered 1 2 t < t series of occurrences or events, with different occurrences or events portly, where 1 2. It is crucial, of course, that the temporal occupying different positions in the series. But GTR does not, I stages are stages of the same continuant. But even with this proviso in place, some philosophers remain unsatisfied. Thus, Mellor once claim, sanction an interpretation of this D-series (as I dub it) that restores B-series or property change. Section 7 contains a digres- complained that “different entities differing in their properties do not amount to change even when ..