p21

So, for any proposition P, ChL(P | T) = ChL(P | Ht). Intuitively, the reason why Nomic Presentism entails Markovianism is because it entails that facts about the past must always be implicit in the present. Nomic Presentists think that there are already strong independent reasons to think this, having to do with the truthmaker objection. It is a surprising and elegant consequence of this response to the truthmaker objection that it automatically secures a striking aspect of our laws of physics. Before we move on, it’s helpful to see how this strategy compares with the previous one. We began with the intuition that the reason why Presentism might help secure Markovianism is because the past cannot place causal constraints on the future that go beyond the present if the past does not exist. However, this intuition faced the worry that there might be truths about the past that place causal constraints on the future that go beyond the present. Our first response to this objection was that the causal constraints on the future must supervene on the whole of concrete reality. This strategy was independently motivated by an Aristotelian view of natural necessity, according to which the causal constraints on the future are grounded in facts about the powers and potentialities of concretely existing physical entities. Our second response to this objection was that, insofar as there are truths about the past, such truths must nomically supervene on (present) being. This strategy is independently motivated by the view that all truths must be grounded in being, and it secures Markovianism by making all truths about the past implicit in the present. In sum, our first strategy involves the weaker claim that the causal16 constraints on the future must supervene on being, while our second strategy involves the stronger claim that all truths must supervene on being.18 5. Four Morals We have argued that certain versions of Non-Humean Presentism entail Markovianism, and hence Markovianism. We have also argued that there is no particular reason to believe that our universe should be Markovian given both Humean and Non-Humean versions of Eternalism, and in the absence of any such reason, it seems to us that one should be far from certain that our world is Markovian* a priori. Consequently, we think that a straightforward empirical argument can be given for (certain versions of) Non-Humean Presentism. The logic of this argument can be formalized in a Bayesian setting as follows. If we let “NHP” be the proposition that the relevant kind of Non-Humean Presentism is true, then we can formalize our central claim as follows: () For any rational prior Cr, Cr(Markovianism| ~NHP) << Cr(Markovianism| NHP) = 1.19 We have argued for the right hand side of this inequality by arguing that NHP entails Markovianism, and we have argued for the left hand side of this inequality by going through various different versions of “~NHP” (e.g. Humean Eternalism, Non-Humean Eternalism, and alternative versions of Presentism) and arguing that none of these views gives us reason to expect that Markovianism* should be true. Lastly, we have also argued that we have strong empirical reasons for thinking the actual world satisfies Markovianism. Applying standard Bayesian confirmation theory, we should substantially increase our confidence in NHP.20 We will close by discussing four morals of our overall argument. 18 It’s an interesting question whether other versions of the “A-theory” of time, according to which the present is somehow metaphysically privileged, can help secure Markovianism. We think that standard versions of non-Presentist A-theories have trouble securing Markovianism. For example, standard versions of the Growing Block theory and the Moving Spotlight theory accept the existence of independently existing, concrete past entities, so they cannot help themselves to the two Presentist strategies that we have defended here. However, there might be some non-standard versions of these other A-theories that can help secure Markovianism. For example, Sullivan (2012) has defended a version of the Moving Spotlight theory where only present things are concrete, spatiotemporally located, and have causal powers. Such a view may be able to secure Markovianism using the strategy discussed in section 4.1. 19 One way to resist () that entirely bypasses the metaphysical debate between Humeans and Non-Humeans is by way of Subjective Bayesianism, which is the claim that any probabilistically coherent prior is rationally permissible. So, for example, the Subjective Bayesian might claim that it is perfectly rational to set Cr(Markovianism| ~NHP) = 1, even if no reason can be given as to why Markovianism should be plausible given ~NHP. For a recent critique of Subjective Bayesianism, see Huemer (2017). 20 It is also worth noting that, in principle, this empirical argument cuts both ways. If one day physicists discover that our world is actually Non-Markovian, then we think this empirical discovery would falsify the relevant versions of Presentism. The fact that these versions of Presentism make precise falsifiable predictions is, we think, a virtue of these theories.17 The first moral concerns Presentism. As we’ve already noted, perhaps the central objection to Presentism is an empirical one: insofar as Presentism requires absolute simultaneity, it seems to be in tension with relativistic physics. However, because we think that Markovianism* provides strong empirical evidence in favor of Presentism, we think the empirical case for/against Presentism is much less clear cut. In light of both of these competing empirical arguments, which should we think is stronger? Although we think that reasonable people can disagree about how to weigh these two arguments, we are inclined to favor the argument from Markovianism. We have two main reasons for thinking this. First, it seems to us that the empirical case that our world is Markovian is stronger than the empirical case for thinking that physics does not require a relation of absolute simultaneity. While there are both historical pre-relativistic theories and contemporary quantum theories that require absolute simultaneity,21 every orthodox physical theory that has ever been seriously considered since Newton has been Markovian. Second, it seems to us that Presentists have two reasonable responses in light of the challenge from relativity. First, although relativistic theories don’t require absolute simultaneity, it is consistent to supplement these theories with a privileged relation of simultaneity (e.g. by way of a privileged inertial reference frame or a privileged foliation of space-time).22 It is true that supplementing these theories with a privileged relation of simultaneity goes beyond what physics requires, but metaphysicians commonly take themselves to have good reasons to believe in all sorts of facts that go beyond what physics requires: various kinds of abstract objects, non-natural moral facts, fundamental properties or substances associated with consciousness, concrete possible worlds, etc.23 Second, some philosophers have even developed versions of Presentism that don’t require a relation of absolute simultaneity at all, sidestepping the objection from relativity altogether.24 However, in the case of Markovianism, we don’t think it is a reasonable response to say that Markovianism* is just an unexplained coincidence. At least to us, the truth of Markovianism* seems far too simple, precise, and elegant a theoretical principle to think it is just a matter of luck that our universe happened to be Markovian. We think the best way to resist the empirical argument from Markovianism isn’t to say that it is merely a coincidence, but rather to do the hard work of developing an alternative Eternalist account of why Markovianism* should be true. Insofar as the prospects of such an account seem dim, we are inclined to think that the balance of empirical considerations favors Presentism over Eternalism. 21 For example, some interpretations of Quantum Mechanics (e.g. Bohmian Mechanics) require absolute simultaneity, and there are some speculative theories of Quantum Gravity that are formulated using absolute simultaneity as well (e.g. see Monton 2006). 22 As we noted before, there are some physically unrealistic solutions to the equations of General Relativity that do not admit of any global foliation into times, but precisely because they are physically unrealistic, the Presentist can safely assume that they do not accurately describe the actual world. 23 In the case of absolute simultaneity, Builes and Teitel (forthcoming) have argued that there are reasons for believing in a relation of absolute simultaneity that are entirely independent of one’s views on temporal ontology. 24 For examples of such theories, see Emery (forthcoming) and Balaguer (MS).18 Our second moral concerns Non-Humeanism. Many Non-Humeans have argued that Humeanism is implausible on the grounds that it would be extraordinarily unlikely for the world to be regular if Humeanism were true. Here is how Strawson (2014) makes the point: According to [Humeanism], then, the regularity of the world’s behaviour is, in a clear sense, a complete and continuous fluke. It is not just that we don’t know whether or not there is any reason for it in the nature of things. According to [Humeanism], there is definitely no reason for it in the nature of things. It is … an objective fluke, in the simple sense that there is, objectively or in the nature of things, absolutely no reason at all why regularity rather than chaos occurs from moment to moment.25 (23) In probabilistic terms, we might understand this kind of argument as implicitly appealing to the following claim (where “Regular” is the proposition that the world is a regular place): () For any rational prior Cr, Cr(Regular | Humeanism) << Cr(Regular | Non-Humeanism). If we combine () with the empirical discovery that our world is in fact a regular place, this would give us strong empirical evidence against Humeanism.26 However, justifying (*) has proven difficult, and Humeans have remained unconvinced. One major difficulty is that it is far from clear how to understand the claim that our world is “regular” in a precise way. Another major difficulty is that, while it may be unclear why we should expect our world to be regular given Humeanism, it is also unclear why we should expect our world to be regular given Non-Humeanism. Why should we expect (say) that metaphysically fundamental laws of nature are simple and regular rather than complicated and irregular? The structurally similar empirical argument for (Presentist) Non-Humeanism that we have defended avoids both of these objections. First, it appeals to a perfectly precise datum about our universe, namely Markovianism, and second, we have argued that certain versions of (Presentist) Non-Humeanism predict this datum with certainty. We therefore hope to have strengthened the overall case for Non-Humeanism, independently of any of our conclusions about the metaphysics of time. Our third moral concerns the connection between Presentism and Non-Humeanism. In practice, these views tend to be discussed and defended independently of one another. Moreover, opinions greatly differ about their relative plausibility: Non-Humeanism seems to be a much more popular 25 It is also worth noting that, as a historical matter, Strawson (2014) argues that David Hume himself rejected “Humeanism”. 26 For different discussions of this kind of schematic argument, see Foster (1982), Tooley (2011), Hildebrand (2013), Filomeno (2019), Bhogal (2021), Builes (2021), and Hildebrand and Metcalf (2021).19 position than Presentism.27 However, there is intuitively a close connection between them: both views imply that our world is in some sense a “dynamic” place. Roughly speaking, Non-Humeanism implies that the material world “inside” time is dynamic, whereas Presentism implies that time itself is dynamic.28 We hope to have provided some more concrete reasons for thinking that Non-Humeanism and Presentism are at their most plausible when defended together. Our fourth and last moral concerns the meta-metaphysical dispute about whether debates over temporal ontology are substantive in the first place. Some philosophers have argued that such debates are merely verbal, and others have argued that there is no fact of the matter about the correct temporal ontology of the universe. Views of this kind have been defended in different ways by Callender (2000), Meyer (2005), Dorato (2006) Savitt (2006), Norton (2015), and Balaguer (2016).29 However, if different views in temporal ontology make different empirical predictions (e.g. if certain versions of Presentism predict that Markovianism must be true while other views in temporal ontology do not), then it seems to us that even the most hardcore logical positivist should think that debates over temporal ontology are substantive.30,31