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According to Center Indifference, such an indifference principle is valid given Eternalism, but it is not valid given Presentism. Therefore, just like in the Boltzmann Brain case, the Presentist has resources to avoid this argument that are not available to the Eternalist.25 8. Modality and Inductive Skepticism Let us now turn to consider inductive skepticism. There are countless possible universes that contain agents like me, yet the inductive inferences of those agents go badly wrong. For example, there are countless possible universes that contain agents like me in which the sun will not rise 25 There are two caveats to make about the simulation argument in this dialectical context. First, it is unclear whether living in a simulation counts as a “skeptical hypothesis”. For example, Chalmers (2022) has argued that, so long as the simulation is sufficiently rich and “structurally” similar to the world that we believe that we inhabit, then most of our ordinary beliefs would still be true. Second, Bostrom (2003) defends the simulation argument both on the assumption that minds qualitatively exactly like ours will exist in the future and on the assumption that minds “similar” (but not qualitatively identical) to ours will exist in the future. In the latter case, Center Indifference might not directly apply, but the same reasons for thinking that Center Indifference is sensitive to one’s underlying metaphysics of time equally apply to the kind of indifference reasoning that Bostrom appeals to. 18 tomorrow. Given all of these possible agents in similar evidential situations to mine, how can I be sure that my inductive inferences will not go badly wrong? This is the classic problem of induction, and there is no agreed upon solution. Perhaps it is simply a brute fact about rationality that rational people ought to (defeasibly) believe that they are in inductively friendly worlds, or perhaps there is some deeper story to be told.26 However, at first glance, it seems like this problem has little to do with Center Indifference. Center Indifference only tells you to be indifferent over existing agents who share your same evidence, but as long as we are talking about merely possible agents who share your same evidence, Center Indifference does not apply. It is correct that Center Indifference is irrelevant to this skeptical argument so long as we think that these other possible universes don’t exist. However, according to Modal Realism, every possible universe is just as real as the universe that we actually inhabit. There are countless people out there, in a similar evidential situation to mine, whose inductive inferences go badly wrong. By Center Indifference, I’m required to be indifferent across all such people. Doesn’t that show that Modal Realism lands us in inductive skepticism? Lewis (1986) was aware of this problem to Modal Realism, because a similar problem had been raised by Forrest (1982).27 Lewis had two replies. First, he replied that the problem mistakenly assumes that Modal Realism implies that the actual world contains countless people who are inductively mistaken. However, as we saw before, Lewis argued that “worlds” should be identified with “universes”. So, for Lewis, the actual “world” was just the actual universe that we find ourselves in, rather than the collection of all existing universes. In effect, one could interpret this reply as Lewis advocating for 4-D Center Indifference rather than Center Indifference. According to Lewis, perhaps we should be indifferent across individuals who are spatiotemporally related to us, but we should not be indifferent across all individuals who exist (unrestrictedly speaking). In section 5, I argued that this is mistaken. We should accept Center Indifference rather than 4-D Center Indifference, and so I believe that this first reply fails. Lewis’ second reply was to question the technical details of such an argument. After all, although there are infinitely many individuals throughout modal space whose inductive inferences fail, there are also infinitely many individuals throughout modal space whose inductive inferences succeed. It’s therefore unclear whether Center Indifference has any unwelcome epistemological implications, even if Modal Realism is true. In what follows, I will try to fill in the technical details of an argument that does show that Center Indifference has unwelcome inductive consequences for Modal Realism. 26 For attempts at a deeper story, see White (2005b), Huemer (2009a), and Builes (2022a). 27 Forrest’s objection to Modal Realism was not targeted directly at inductive reasoning. Instead, Forrest argued that Modal Realism was in tension with Occam’s Razor. However, the problems are structurally analogous. 19 My target will be our knowledge of the fundamental laws of nature. Many of our best guesses of the fundamental laws of nature have been deterministic, where a law L is deterministic just in case it satisfies the following property: Determinism: For all metaphysical possible universes u and u* where L is true, if there is a time t at both u and u* such that t has the same intrinsic properties at both u and u, then u = u.28 Before the advent of quantum mechanics, all of our best guesses of the fundamental laws of nature were deterministic.29 In the case of quantum mechanics, the issue is more subtle. Certain interpretations of quantum mechanics imply that the world is deterministic (such as Everrettian quantum mechanics and Bohmain quantum mechanics), whereas other interpretations are indeterministic (such as objective collapse theories).30 Still, the history of physics suggests that we should regard it as a live epistemic possibility that we actually live in a deterministic universe. The question I want to focus on is the following: can it ever be rationally permissible for an agent to assign a non-zero credence that some particular deterministic law of physics holds? It seems to me that the answer is clearly “yes”. For example, consider a world governed by deterministic Newtonian Laws. Suppose the scientists in that world come up with Newton’s Laws, and for trillions of years Newton’s Laws are experimentally verified to arbitrary levels of precision, with no experimental anomalies. Surely it should at least be permissible to assign a non-zero credence in Newton’s Laws in such a situation! My worry, however, is that Center Indifference implies that it is never rationally permissible for any agent who believes in Modal Realism to assign nonzero credence in any deterministic law. Let’s first assume that in the relevant sense of “agent”, agents can only have evidence about the past and present state of the world. Perhaps there could be “agents” that can know the laws of physics by simply “seeing” the whole history of the universe through magical powers of clairvoyance, but we will be setting such agents to the side. Our question will be whether an agent 28 This definition follows the definition of “Full Determinism” in Teitel (2019: 353). 29 There are several subtleties though. First, classical theories are only deterministic if the values of certain vector quantities (like velocity or momentum) are specified, which may require the intrinsic state of an arbitrarily small temporal interval, rather than a mere instant of time (e.g. see Arntzenius 2000 and Builes and Teitel 2020). Second, there are some exotic situations (e.g. “space invaders”, “Norton’s dome”, and certain situations involving supertasks) where classical mechanics might not be deterministic, depending on exactly what assumptions are built into “classical mechanics” (e.g. see Fletcher 2012). Third, whether determinism is true in General Relativity depends on certain “physically reasonable” assumptions such as global hyperbolicity (e.g. see Smeenk and Wüthrich 2022). Lastly, some have argued that determinism should be restricted to merely “qualitative” facts, but see Builes and Teitel (2022) for arguments against this restriction. 30 See Maudlin (2019) for an introduction to these three different approaches to quantum mechanics. 20 who only has access to the past and present (i.e. an agent like us) can permissibly assign a nonzero credence in some deterministic law. Let’s consider the best case scenario for such an agent, where we let the agent have access to the entire history of the universe up until the present time. We can formulate the hypothesis that such an agent can permissibly have non-zero credence in some deterministic law as follows: The Viability of Determinism: There is some possible universe u, with some initial segment of history H up to time t, and some agent a in u at t, such that it is rationally permissible for a at t to set Cr(L | H) > 0, for some deterministic law L. A surprising fact is that, given Center Indifference, The Viability of Determinism fails for any agent a that believes in Modal Realism. The reasoning behind this claim is a bit technical. It starts with the observation that there is only a single universe uLH where L and H are true, since L is deterministic. So, since the agent knows that L and H are true if and only if they live in uLH, the agent is rationally required to assign Cr(L | H) = Cr(uLH | H). However, according to Lewis’ version Modal Realism, there are uncountably many different universes where H holds. For example, for every positive real number r, there is a universe whose last moment of time is r seconds after t. Each of these uncountably many universes will contain an agent at t whose evidence is compatible with a’s evidence (i.e. an evidential twin), since each of these uncountably many universes share an initial history up to t. Therefore, given Modal Realism, there will be uncountably many evidential twins of a who live in universes distinct from uLH. So, as long as there are only countably many evidential twins of a that live in uLH, Center Indifference will entail that, if a is a Modal Realist, a is rationally required to set Cr(uLH | H) = 0. I will leave the proof of this claim to a footnote.31 Although there is a caveat here that there are only countably many evidential twins of a that live in uLH, this assumption is certainly satisfied in our universe.32 Insofar as we ultimately care about drawing conclusions about our own epistemic predicament, this caveat is no caveat at all. Center Indifference therefore implies that there can be no Modal Realist for which any hypothesis about the deterministic laws of nature is a viable hypothesis. Even if such a law was breathtakingly 31 Let a1, a2, a3, … be the (finitely many or countably many) agents located in uLH compatible with a’s evidence. Since a lives in uLH if and only if a is one of a1, a2, …, a is rationally required to set Cr(uLH | H) = Cr(a1 or a2 or … | H). Using an instance of Finite Additivity or Countable Additivity, Cr(a1 or a2 or … | H) = Cr(a1 | H) + Cr(a2 | H) + … . So, it suffices to show Cr(ai | H) = 0 for all i. This is true because H is true in uncountably many epistemically possible centered worlds, and by Center Indifference each pair of such epistemically possible centered worlds must be assigned equal credence by a (since a’s evidence is exhausted by H). This can only be true if a assigns Cr(c | H) = 0, for all centered worlds c compatible with H, as desired. 32 From the fact that there is a countable dense subset of space-time points in our space-time manifold, it follows that, so long as “agents” need to occupy some finite volume of space-time, uncountably many agents cannot fit inside our space-time manifold. 21 elegant and simple, and even if could be conclusively verified that such a law had been perfectly followed for trillions of years, and even if the entire scientific community unanimously agreed that such a law must be true, the Modal Realist is rationally required to assign a credence of zero that the law is true.33 Therefore, given Center Indifference, Modal Realism seems highly implausible. 9. Conclusion Principles of indifference are powerful principles. Left unchecked, they can easily lapse into contradiction, just as Naive Indifference clearly does. However, if a suitably restricted principle of indifference can be defended, it can potentially lead us to a wide variety of interesting epistemological consequences. I have tried to defend a restricted principle of indifference here, namely Center Indifference, and I have explored some of its surprising consequences. In particular, I have argued that Center Indifference implies that both Eternalists and Modal Realists face distinctive skeptical challenges that are not faced by Presentists and Actualists.34 One might have thought that debates in the metaphysics of time and modality would be insensitive to debates in epistemology, but if I’m right, then perhaps another way we could make progress on these metaphysical debates is by looking at their epistemological consequences.