But couldn't we imagine the A-times of events moving in the opposite direction, such that events become more future and less past? Probably not, since past and future are, on this view, distinguished by the different ways in which they “react” to the passage of time. Could we imagine time moving first in one direction and then in the opposite one (whichever direction we label as ‘past’ or ‘future’)? This seems to be a real problem for Tensers, one calling for some sort of asymmetry between past and future that explains the impossibility of such a reversal.
Would Growing Block Tensism (see Section 20.4) solve this problem? It could only if the growing block could not become a shrinking block. We see no principled way to rule out the shrinking block.
Dynamic modalities, of the kind proposed by Falling Branches Tensism (20.2T.2), are more promising. It seems plausible to think that what is impossible cannot become possible, and the necessary cannot become contingent, but that the contrary transformations are possible. If so, and if the future is associated with alternative possibilities and the past with a clear division into the impossible and the necessary, then we would have grounds for the impossibility of time reversal. This, however, merely raises the further question of why the impossible cannot become possible.
If we think of the B series as independent of the passage of time, Simple Tensism (20.2T.1), then Le Poidevin's refutation seems conclusive.
21.2 Truthmakers for Truths about the Past
Presentism (20.2T.4), although attractively common-sensical in many ways, has a number of problematic consequences concerning truthmakers for propositions about the past. According to Presentism, everything that exists exists in the present. There is nothing existing entirely in the past. Alexander the Great's horse Bucephalus, the Hanging Gardens of Babylon, dinosaurs: none of these exist according to Presentism. If Actualism (12.1T) is true, then no existing thing can make true such propositions as that Alexander once had a horse, that Babylon was once graced with beautiful hanging gardens or that dinosaurs once roamed the earth. Presentists have offered four accounts: (i) reductionist Presentism or Occurentism, (ii) sui generis past-tensed properties of present things, (iii) primitive past-tensed facts or states of affairs, and (iv) the wholesale rejection of Truthmaker Theory. Each has its difficulties.
21.2.1 Reductionistic Presentism or Occurentism
Occurentism is the thesis of the reducibility of the past and future to present-tensed facts. On this view, the past is wholly constituted by present memories and traces of it, and the future is wholly constituted by presently existing pre-determining conditions. This is the view of the logician Jan Łukasiewicz (1967: 38–39), Michael Dummett (1969), and Peter Ludlow (1999: 150–152). This view implies that aspects of the past literally cease to exist once all traces of them have disappeared. This seems a pretty crazy view and one that is dialectically unstable, since the argument for Tensism relies so heavily on a common-sense epistemology. Indeed, we can imagine situations in which all traces of some past event have disappeared. If this happens, the present underdetermines the past. But the past seems fully determinate, and so Occurantism is at least at odds with our common-sense view of what is possible. This violates Reidian Common Sense (PEpist 2).
There is a further intentionality objection. Statements about the past are simply not about present-day traces. Statements about dinosaurs are about dinosaurs, not about fossils and other vestiges of dinosaurs. Occurentism, therefore, seems to get facts about the contents of our language and mental states wrong.
21.2.2 Sui generis properties of present-day objects
Tensers might instead appeal to primitively tensed properties of eternal things like particles or parts of absolute space in order to ground truths about the past. This is John Bigelow's (1996) account, which follows the suggestions of ancient Stoics and Epicureans. The proposition that George Washington slept in this very bed is made true by the fact that this bed (or this part of space) has the property of having been slept in by George Washington. If one is a Presentist, one will need to appeal to something like the property of having been slept in by someone named ‘George Washington’, since George Washington is a past object. That there were once hanging gardens in Babylon is made true by some presently existing particles exemplifying the property of having composed some hanging gardens in Babylon. And so on.
If there is no matter or region of space handy, we could make the world the bearer of the property. It is true that dinosaurs once existed, and that there have never been unicorns, because of (1) and (2), respectively:
(1) The world has the property of having once contained dinosaurs.
(2) The world has the property of never having contained unicorns.
There are at least two objections to this view. First, these are just the wrong truthmakers. For example, some matter could be annihilated without annihilating all the facts about what it once composed. Second, there is again an intentionality objection. Statements about specific, localized past events are not about the whole world. To select anything short of the whole world would seem arbitrary.
21.2.3 Primitive past-tensed facts or states of affairs.
Arthur Prior (1968: 1–14) seemed to suggest that there were facts or states of affairs that are primitively past-tensed, and that these could be Presentist-friendly truthmakers for statements about the past. Theodore Sider (2001) argues that this amounts to metaphysical “cheating”, as it runs afoul of truthmaker principles. What Sider means is that Prior's primitive tensed-facts are somehow hypothetical, and the hypothetical ought to supervene on the non-hypothetical, the categorical. Prior would object to both premises, and Sider offers little by way of argument for his contentions.
The answer to these worries is given by careful attention to David Lewis (2002). Lewis's article is primarily a criticism of those (like Mark Johnston 1983, 1987) who would try to combine Eternalism (20.2A.1T) with enduring things, things that are wholly present at more than one time. Nonetheless, Lewis's central objection to Johnston can be turned to a different purpose by Presentists.
Johnston's solution to the paradox of intrinsic change was to suggest that the copula linking subject and property involves essentially a relation to a time. The stick is-at-t bent, but the stick is-at-t′ straight. Lewis objects that such a copula “alienates” the stick from its properties. The stick is never straight or bent simpliciter but only bears some relation or other to straightness or bentness. If one retorts that there is, in any case, a relation of instantiation between a thing and its properties, then one faces the onslaught of Bradley's Regress (see Section 7.2.1.3): if a's being F depends on a real relation of instantiation holding between a and F, then it follows that a's instantiating F-ness depends on a real relation of instantiation holding between the pair
Lewis appears to be right. A tensed-copula is inherently alienating. Ironically, this fact provides the Presentists with a solution to Sider's truthmaker objection: a past-tensed fact consists in something's bearing a tensed-copula (was or will-be) relation to some property or cluster of properties, while the corresponding present-tensed fact consists in that thing's having that property simpliciter (without any alienating copula). Thus, the stick is straight simpliciter (no alienation), but it has the is-at-t relation to the property of bentness (alienation) for some past time t. The alienation of objects from their past-tensed properties is exactly what Presentists want! The contrast between alienation toward past-tensed properties and no alienation toward present-tensed ones secures the uniqueness of the present.
This solution, like the rejection of Truthmaker Theory we consider below, has a problematic feature, namely, necessary connections between distinct facts. If a is now F, then at all future times, a will bear the is-at-t relation to F-ness, where t is the time that will hereafter correspond to the present moment. (We're imagining Presentists who believe that there are only past times. We can speak about the present moment, but only loosely, si
nce strictly speaking by the time has uttered such a phrase there is no longer the relevant moment, although another will immediately begin to exist that corresponds to the facts that presently obtain.) This connection between present and future past facts is a necessary one, even though the two facts involve different relations. The past-in-the-future fact involves a time-relativized copula that does not yet exist. Such necessary connections violate the Second Corollary of Ockham's Razor (PMeth 1.2).
This account is different from Growing Block Tensism, since the present isn't simply the leading edge of the past according to Presentism. There is a clear metaphysical difference between the present and any past moment. Only present predications are predications simpliciter. Past predications, in contrast, introduce an intermediate relation between a thing and its quondam properties.
There's an alternative approach that works but that seems much less attractive. One could postulate that corresponding to every n-place relation, there is an n+1-place relation that takes a time as its last relatum. So, corresponding to the one-place property bentness, there is a two-place relation bent-at-ness that holds between things and times. If a is now bent, then in the future it will be the case that a bears the bent-at-t relation to the time t that will correspond to the present moment.
Michael Tooley (1997) argues that all these views are burdened by a large number of unexplainable brute necessities, such as the incompatibility between pastness and futurity (or between one degree of pastness and another) and the systematicity of time flow (the synchronicity with which the relevant modalities are stepped up as time passes). Again, such necessities are costs of these views (PMeth 1.2).
Here are two responses to Tooley. First, it's not easy to say which theory of time postulates the greatest number of brute facts. All of them seem to require many, and so it may be that Ockham's Razor doesn't tell in favor of one over the others. Second, Ockham's Razor has a proviso: we don't multiply entities without necessity. If alternative accounts fail or are incredible or have decisive disadvantages, we could well be justified in positing the brute necessities Tooley lists.
21.2.4 Rejection of Truthmaker Theory
Presentists can circumvent these problems by rejecting Truthmaker Theory tout court. This would leave Presentists without any account of the metaphysical and logical independence of atomic facts about the past. But it is not clear how much this matters.
21.2.5 Truthmaker problems for Growing Block Tensism
Growing Block Tensism avoids most of the truthmaker objections lodged against Presentism, since Growing Block Tensers acknowledge the reality of the past, as well as that of the present. There is, however, a truthmaker problem for Growing Block Tensism. Consider the proposition that the battle of Hastings is at the leading edge of reality. This proposition was once true (in 1066), so, presumably, it had then a truthmaker. According to Growing Block Tensism, however, once a fact comes into existence, it stays in existence. Therefore, the truthmaker of this proposition must still exist. And yet the proposition is now clearly false! Either reality is incoherent because it includes truthmakers for both the proposition and its negation, or the size of the growing block of time is irreducibly a matter of one's perspective.
To avoid this conclusion, the defender of Growing Block Tensism must distinguish between those facts that endure and those that do not. B-facts endure, but total-block-relational facts, like how far a given event is from the leading edge, do not. Thus, Growing Block Tensism seems committed to at least a moderate analogue of Presentism about the total-block-relational facts. It thus faces truthmaker problems pertaining to past-tensed growing-block propositions of exactly the sort that Presentism faces. It's unclear what has been gained. Growing Block Tensism appears, therefore, to be dialectically unstable.
Tooley (1997) argues that there is a great difference between an event's having different intrinsic A-properties at different times and an event's having different A-relational properties (such as the distance to the edge of the growing block of time) at different times. We're unclear as to how this difference is supposed to be decisive. Presumably, relational propositions require truthmakers just as much as intrinsic-property facts do. Perhaps this is not the case, but more needs to be said by way of explanation, and Tooley offers no help on that score.
21.2.6 Further truthmaker problems: Cross-temporal spatial relations (Motion)
Sider (2001) argues that Presentists cannot account for cross-temporal spatial relations, like being in the same place at different times or being in a different place at different times, and so cannot account for such features of the world as velocity, acceleration, and continuous and discontinuous motion. On the Presentist picture, we have two kinds of facts. First, there are those that make up the present moment; these obtain simpliciter. Second, there are those that once made up past moments; these can be spoken of only via instantaneous temporal operators like ‘once upon a time’ or ‘n units of time ago’. Thus, Presentism's world consists of an infinite collection of snapshots. The problem of cross-time relations is that of defining the correct 4-dimensional geometry of kinematics, of characterizing locomotion (accelerated vs. un-accelerated, continuous vs. discontinuous). We could line up the snapshots in such a way that each enduring thing jumps discontinuously from one location to another at each moment. Presentists need an account of why only certain arrangements of these snapshots are appropriate.
The first thing to notice is that if Presentists follow postulate absolute, substantival space, then the problem disappears. We can use the standard, Russellian At/At Theory of Motion (24.5A.1T), according to which something moves in so far as it is located at different places at different times. This allows us to construct a unique function, assigning each object's absolute spatial location at each moment of time, which in turn will supply the needed kinematic geometry. So, let's assume that Presentists don't go that way, instead adopting some version of the minimalist reinterpretation of special relativity described in the next section.
This is certainly a non-trivial problem for Presentists, but we shouldn't lose sight of the fact that there are comparable problems for Eternalists who reject the existence of absolute space. Without absolute space, we cannot ask whether a particle's absolute motion is continuous or discontinuous (since there is no such thing) but only whether the relative motions of two or more particles are continuous or discontinuous. It seems that Presentists and Eternalists are in the same situation here: both can assert that relative motions are discontinuous just in case the relative spatial positions of the particles change discontinuously over time. This answer is available to Presentists as much as to Eternalists, since Presentists have access to all of the facts about the relative spatial positions of particles at times (the synchronic spatial relations).
However, this objection to Sider overlooks the affine and topological structure of spacetime, as discussed by Lawrence Sklar in Space, Time and Spacetime (Sklar 1974). In neo-Newtonian and Minkowski spacetime, there is a level of structure that is intermediate between old-fashioned Newtonian absolute motion and the merely relative motions recognized by Leibnizians. We can distinguish between continuous and discontinuous paths of particles, even when the relative positions of the two paths vary continuously over time. Similarly, we can distinguish between accelerated and un-accelerated paths, even when all the relative velocities are constant (as in the case of distinguishing Newton's rotating bucket from a stationary bucket, which we discussed in Section 17.3). The distinction could be based (for Eternalists) on a primitive relation of linear betweenness holding among triples of spacetime points (including cases in which the three points occur at different times).
For Eternalists, this affine structure can be fixed by metaphysically primitive features of four-dimensional paths. This solution would seem to be unavailable to Presentists, since it involves the obtaining of primitive diachronic facts, that is, facts that span an interval of time.
Sider considers two families of solutions for Presentists,
holistic and atomistic. Holistic solutions involve assigning the properties of continuity and of constant-velocity to particle-paths in a way that maximizes some holistic feature of the assignment. For example, we could maximize the number of paths that are continuous or un-accelerated. As Sider points out, this has counterintuitive consequences, especially with respect to small-world thought experiments. Suppose Newton's rotating bucket constituted the entire world. It is still possible for it to follow an accelerated path through space, even though assigning it such an accelerated path would violate the proposed holistic constraint.
A better version of the holistic strategy would be to maximize the applicability of simple laws of motion, including force laws, like gravity and electromagnetism. If no force is acting on the bucket, then the preferred assignment would give it an un-accelerated path; in contrast, if the bucket is under the influence of some force, then the preferred assignment would give it an appropriately accelerated path. This still doesn't eliminate all plausible counterexamples. We could imagine a world that accidentally satisfies some very simple laws of motion. The holistic assignment would then assign accelerations inappropriately, in accordance with merely apparent laws of motion.
Perhaps, then, Presentists should take the holding of the laws of motion and the force laws to be a metaphysically brute fact, as Nomists (4.4A.2), Powerists (4.4A.3), and Hypotheticalists (4.4A.1) might believe. If the laws of nature dictate continuous motion, then the correct assignment of affine structure should assign continuous paths to all particles, and it should assign the appropriately accelerated paths, given the configuration of forces, to each particle. This will work, however, only if a violation of a world's laws of motion is metaphysically impossible. If there are worlds containing miracles, then Presentists will be unable to find a suitable assignment to that world of affine structure.
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