Presentism and the Space-Time Manifold* Dean Zimmerman, Rutgers University I. Introduction: Presentism Among the A-Theories The A-Theory of Time and the B-Theory of Time McTaggart gave the name “A-series” to “that series of positions which runs from the far past through the near past to the present, and then from the present through the near future to the far future, or conversely”; and the name “B-series” to “[t]he series of positions which runs from earlier to later, or conversely”.1 McTaggart’s rather bland labels have stuck, and been put to further use. The “determinations” (his word), or properties, being past, being present, and being future are generally called the “A-properties”. The relations of being earlier than, being later than, and being simultaneous with, are the “B-relations”. These days, philosophers are said to hold an “A-theory of time” or a “B-theory of time”, depending upon their attitudes to these properties and relations. Some philosophers suppose that there are objective distinctions between what is present and what is past and what is future. In order to tell the full truth about time, they think, one must advert to the A-properties. Naturally enough, such philosophers are called “A-theorists”. Although A-theorists disagree about many details, they agree that the present is distinguished from past and future in a deep and important way. Exactly how to describe this difference is a vexed question, and some philosophers have argued that would-be A-theorists inevitably fail to stake out a coherent position.2 I shall not attempt a full-scale defense of the coherence of the A- theory here; but hopefully the following characterization will suffice to convey, in a rough-and- ready way, the nature of the A-theorists’ convictions about time: The A-theorist grants that every thing in time (setting aside the possibility of a beginning or end of time itself) is “past relative to” some things, “future relative to” others, and “present relative to” itself — just as every place on earth (setting aside the poles) is south relative to some places, north relative to others, and at the same latitude as itself. But the A-theorist insists that this attractive analogy between spatial and temporal dimensions is misleading; for, of any time or event that is past, present, or future in this merely relative way, one can also ask whether it is, in addition, past, present, or future in a non-relative way — past, present, or future simpliciter. The A-theorist takes the merely relative A-determinations to be based upon facts concerning which times and events are really past, present, or future, not merely relatively so. “B-theorists”, by contrast, deny the objectivity of the division of time into past, present, and future; they regard the spatial north-south analogy as deeply revelatory of the purely relative nature of this division (though many B-theorists admit that there is some intrinsic difference between spatial and temporal distances). To arrive at more objective facts about time, one must turn to relations like being earlier than, being later than, and being simultaneous with — the “B-relations”.3 The A-theory is almost certainly a minority view among contemporary philosophers with an opinion about the metaphysics of time.4 Nevertheless, it has many defenders — Ian Hinckfuss, J. R. Lucas, E. J. Lowe, John Bigelow, Trenton Merricks, Ned Markosian, Thomas Crisp, Quentin Smith, Craig Bourne, Bradley Monton, Ross Cameron, William Lane Craig, Storrs McCall, Peter Ludlow, George Schlesinger, Robert M. Adams, Peter Forrest, and Nicholas Maxwell, to name a few.5 Several of the most eminent 20th century philosophers were A- theorists, notably C. D. Broad, Arthur Prior, Peter Geach, and Roderick Chisholm.6 2 The B-theory can claim support from two of the founders of the analytic movement in philosophy: Gottlob Frege and Bertrand Russell.7 In the years since, it has achieved broad acceptance. D. C. Williams, W. V. O. Quine, Adolf Grünbaum, J. J. C. Smart, David Lewis, D. H. Mellor, Paul Horwich, Tim Maudlin, Frank Arntzenius, Theodore Sider, Robin Le Poidevin, Nathan Oaklander, Steven Savitt, and Thomas Sattig are just the tip of the B-theorist iceberg.8 B-theorists have raised many kinds of objections to the A-theory and to the particular kind of A-theory I find most attractive, namely, presentism.9 What follows is a defense of presentism in the face of just one of these: that the view has been refuted or at least badly undermined by discoveries in physics. The rejection of Newton’s substantival space by the natural philosophers and physicists of the nineteenth century had already created an environment somewhat hostile to presentism, as shall emerge in my discussion of one of Theodore Sider’s objections to presentism (the objection described near the end of Section III, based on cross- temporal relations involving motion). Einstein’s Special Theory of Relativity (SR) and General Theory of Relativity (GR) seem only to have made things worse. Both imply the “relativity of simultaneity”; and this raises obvious questions for all A-theorists. If, as A-theorists believe, there is an objective fact about what is presently happening, there must be an objective fact about which events are simultaneous with one another — in other words, a fact about simultaneity that is not relative to anything, including the frames of reference of SR, or the local frames of GR. But, on the face of it, these scientific theories require that simultaneity be frame-relative. Before launching into description of the variety of A-theories, and defense of the kind I prefer, I should mention some things that will not be discussed in this essay. The first is a philosophical debate that is sometimes conflated with the A-theory-B-theory dispute: namely, the question whether time has an intrinsic direction to it; that is, whether the relation being 3 earlier than holds between moments or space-time locations independently of the contents of space-time. No one, to my knowledge, has defended the following combination of views: time lacks an intrinsic direction but includes objective distinctions between past, present, and future. The idea is not completely incoherent: one might attempt to reconstruct the difference between distance-into-the-past and distance-into-the-future on the basis of facts about what is present and “direction-neutral” temporal distance facts.10 But the project will probably seem quixotic to most A-theorists (I know it does to me!). B-theorists, however, are sharply divided on the question whether time has an intrinsic direction. Two temporal directions are distinguishable from the spatial ones in the space-time of SR and in manifolds compatible with GR — at least, in the less bizarrely shaped ones. But some philosophers of physics deny that one direction is more deserving of the label “forward in time”, when considered all by itself, in abstraction from space- time’s material contents. These deniers of intrinsic direction claim that the actual difference between forward and backward in time does not supervene upon facts about intrinsic structure alone, but only upon such facts plus contingent facts about the contents of space-time, such as the distribution of matter. Both A-theorists and the friends of intrinsic temporal direction are often said to believe that “time flows”, or to believe in “objective passage”; and their opponents may be said to champion a more “static” conception of time. But the two controversies are obviously quite different. Only the bona fide A-theory–B-theory debate shall figure in this chapter; for an up-to-date discussion of the question whether time has an intrinsic direction, see Huw Price, “The Flow of Time”, in this volume.11 Many other important issues will be set aside, including the allegation that A-theorists and B-theorists are simply talking past one another. Some philosophers claim not to be able even to understand the A-theory–B-theory debate; and they cannily manage to extend this 4 inability so that it includes all the terms that might be used to explain it to them.12 Fortunately, a number of effective therapies have been developed for those who find themselves losing their grip on the nature of the disagreement between A-theorists and B-theorists, or between presentists and non-presentists. The best treatment for the condition is something I discuss elsewhere.13 Other issues to be set aside include the majority of the objections that have been raised against the A-theory in general and presentism in particular. Chief amongst these is the argument that truths about the past need “truthmakers” (where a truthmaker for a proposition is some part of the world in virtue of which the proposition is true), and that the presentist lacks the resources to provide them.14 In the face of this challenge, some presentists cast about for present states of the world that will ground truths about the past15; while others question the legitimacy of the demand for truthmakers.16 I shall take it for granted that presentists can appeal, unproblematically, to facts about what was the case at each instant in the past — at least, that purely qualitative facts about each past moment are well-grounded. Even granting so much as that, presentism’s critics can raise serious objections based on what physics seems to say about the nature of space-time. The two problems upon which I focus are these: (1) Determinate facts about the state of the universe at each instant may fail to provide an adequate basis for certain cross-temporal facts that are physically important and objective.