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15 Non-Humeans who appeal to facts about the essences of natural properties are often called “dispositional essentialists”. For defenses of dispositional essentialism, see Chakravartty (2003) and Bird (2007). 16 In the Leibniz-Clarke correspondence, Leibniz justifies the PSR inductively in his Fifth paper to Clarke (see Alexander 1977). See Pruss (2006: 254-279) for a more detailed discussion. 17 Armstrong (1983), Ellis (2002), Bhogal (2021), and Builes (2022a) have argued that Humeans have a harder time than Non-Humeans with the problem of induction. 8 why the PSR is true is because of the first-order explanations for all other facts, then it is much harder to see how the PSR could be justified a priori in this way. I want to grant that these objections have some force, but they could also be resisted in various ways. In defense of the inductive argument for the PSR, the Humean Rationalist can appeal to the same kinds of considerations that Humeans about laws appeal to. Perhaps the kinds of metaphysical posits that Non-Humeans appeal to simply add metaphysical mysteries without helping the prospects of induction18, or perhaps the rationality of induction is a basic tenet of rationality that it would be misguided to provide any deeper justification for. In addition, perhaps other standard theoretical virtues, such as simplicity and non-arbitrariness, allow the Humean to rationally conclude that, when all observed Fs are Gs, the simplest and least arbitrary conclusion to draw is that all Fs are Gs. After all, it seems that even the Non-Humean has to appeal to such theoretical virtues in order to rationally conclude that there is a (Non-Humean) law that all Fs are Gs. Such a law seems to be the simplest and least arbitrary explanation for why all observed Fs are Gs, but it is conceivable that there could complicated gerrymandered laws (e.g. “it is a law that all Fs are Gs until tomorrow”) that similarly account for the fact that all observed Fs are Gs, yet do not support inductive inference.19 With respect to the fact that the PSR is allegedly highly intuitive or self-evident, the Humean Rationalist could deny that the intuitiveness or self-evidence of the PSR is undermined by the fact that the grounds of the PSR are not immediately intuitive or self-evident. For example, perhaps it is self-evident that 2+2=4, even though philosophers of mathematics sharply disagree about the grounds for such a truth.20 Lastly, even if these epistemological objections succeed, they aren’t reasons for thinking that Humean Rationalism is false. At best, these objections only show that, in the absence of a NonHumean explanation for the PSR, we should be less confident in some of the arguments in favor of the PSR. One might be tempted to strengthen this first epistemological objection to conclude that there couldn’t be any reason at all to endorse Humean Rationalism (at least until we have surveyed and successfully explained every fact). However, even if arguments from induction or intuition are undermined by the Humean PSR, there are a variety of arguments for the PSR that don’t seem to presuppose the Non-Humean PSR. For example, Pruss (2006) has argued that the rationality of inference to the best explanation depends on the PSR, and Koons and Pruss (2021) has argued that the falsity of the PSR leads to inductive skepticism. Combining these arguments 18 See Beebee (2011) for an influential argument that Non-Humean posits do not help with the problem of induction. 19 For more on this problem of complex/gerrymandered laws of nature, see Hildebrand (2013). Lastly, following Loewer (2023), the Humean can agree that in some sense physical events are “metaphysically” independent from one another, but they can deny the inference that they are therefore probabilistically independent from one another. 20 For example, some argue that “2+2=4” is true by convention (e.g. see Warren 2020), others argue that it is true because of the existence of certain abstract Platonic objects (e.g. see Linnebo 2018), others argue that it is true because of certain ontologically neutral modal claims (e.g. see Hellman 1989), etc. 9 with standard anti-skeptical premises directly leads to the PSR. To take another kind of example, Della Rocca (2010) and Dasgupta (2016: 409-412) argue that those who reject the PSR still need to endorse a strong and controversial view about exactly which facts must have explanations, and they argue in different ways that such a view ends up being no more antecedently plausible than the rationalist’s strong and controversial claim that all facts must have explanations. A second kind of objection to Humean Rationalism is that it would make the PSR a mere coincidence if it were true, but (allegedly) it would be very implausible if the PSR were simply true by coincidence. Although the relevant notion of coincidence here is a bit murky, a natural thought is that, according to Humean Rationalism, not only would there be no unifying reason as to why the PSR is true, but the grounds of the PSR would also be massively complicated and conjunctive.21 The Humean Rationalist could respond to this argument in several ways. First, they could point out that there are well-known arguments that the PSR implies that every truth (including itself) is a necessary truth, and these arguments do not depend on whether Humean or Non-Humean Rationalism is true.22 So, if these arguments work, they would establish that the PSR is metaphysically necessary. Although one could still object that the PSR would be a metaphysically necessary coincidence, it at least seems that the necessary status of the PSR makes it less of a “coincidence” then it otherwise might be. For example, it is natural to think that if something is a coincidence, then it could have easily been false. However, if the PSR is metaphysically necessary, then there are no nearby possible worlds in which it is false.23 Second, the Humean Rationalist could try to reduce the apparent massive complexity of the grounds of the PSR. For example, suppose the Humean Rationalist claims to have an (autonomous) explanation for the particular initial conditions of the universe and an (autonomous) explanation for the particular deterministic laws of nature. Then, the Humean Rationalist could use these two explanations to explain everything else about the physical world. What this example shows is that the Humean Rationalist is not committed to finding infinitely many separate and independent explanations for everything: they might be able to find an elegant, simple, and unified explanation that ultimately explains 21 For further discussion of the nature of coincidences, see Lando (2017) and Bhogal (2020a). 22 Van Inwagen (1983: 202-204), Bennett (1984), Dasgupta (2016), and McDaniel (2019) have argued that the PSR implies that every truth is a necessary truth. See Dasgupta (2016) for further discussion of why this consequence should not be regarded as absurd. 23 The fact that the PSR might imply that every truth is a necessary truth also threatens to trivialize some contemporary accounts of coincidence. For example, Bhogal’s (2020a) account of coincidence appeals to a notion of “explanatory goodness”, which requires looking at the space of possible worlds where an explanandum is true and comparing it to the space of possible worlds in which an explanans is true. However, if there is only one possible world, such an account of explanatory goodness becomes trivial and can’t be used to distinguish coincidences from non-coincidences. In response, one could point out that there is some precedent for thinking that there might be metaphysically necessary coincidences in the form of mathematical coincidences. For example, Lange (2010) argues that some mathematical facts are coincidental if they don’t have a “unified” explanation. However, as I’m about to argue, Humean Rationalism is compatible with the view that the PSR has a (non-immediate) unified explanation. 10 everything else. In other words, although the Humean Rationalist is committed to the view that the immediate grounds of the PSR are massively complicated and disunified (since the immediate grounds of the PSR will include every fact), the Humean Rationalist is perfectly free to think that there is a simple and unified non-immediate ground for the PSR. The disagreement between the Humean and the Non-Humean Rationalist is not about whether there is a simple and unified ultimate explanation for everything. They can both agree that there is. Their disagreement is only about the structure of the explanation of the PSR. Lastly, even if Humean Rationalism does imply that the PSR is a “coincidence” (in some sense), it is not clear why this would be so problematic. After all, everyone agrees that there are plenty of true coincidences. Moreover, when comparing Humean and Non-Humean Rationalism, the alleged coincidental nature of Humean Rationalism must be weighed against the fact that there doesn’t seem to be any plausible account of how Non-Humean Rationalism could be true in the first place. 5. Explanatory Differences Having given a preliminary defense of Humean Rationalism, it is worth highlighting an important “first-order” explanatory difference between Humean and Non-Humean Rationalism. There are many historically influential examples of rationalist arguments with the following general structure: 1) If P, then the PSR would be false. 2) The PSR is true. 3) Therefore, not-P. One famous example of such an argument is Leibniz’ argument against substantivalism about space. If space were an infinite and homogeneous substance, then there would be no reason why material objects should be oriented one way with respect to space rather than another way. So, no matter how material objects are oriented with respect to substantival space, the PSR would be violated. Therefore, given that the PSR is true, space must be relational rather than substantival. To take another historical (but controversial) rationalist argument, one can also argue for the “Principle of the Identity of Indiscernibles” (PII) on the basis of the PSR. There are many formulations of the PII, but according to one formulation, any two objects that share all of the same qualitative properties and relations must be identical.24 Given this formulation, we might argue as follows. If the PII were false, then there could be two objects that share all the same qualitative properties and relations but were nonetheless distinct. However, in such a situation there would be no explanation for why such objects were distinct rather than identical, since there would be 24 See Forrest (2020) for further discussion of different formulations of the PII. 11 (qualitative) difference between them. So, if the PII were false, then the PSR would be false. But, since the PSR is true, the PII must be true. One can certainly question whether such an argument is sound, but it is another example of a historically influential argument that shares the same argumentative structure.25 Both the Humean and Non-Humean Rationalist are able to endorse the soundness of these kinds of arguments. However, the Non-Humean Rationalist can use these arguments to explain their conclusions, while the Humean Rationalist cannot. To take the example of the nature of space, it would be objectionably circular for the Humean Rationalist to explain why space is relational rather than substantival in terms of the PSR, because the PSR is explained in virtue of the fact that everything else (including the nature of space) can be explained! Intuitively, the PSR comes “late” in the explanatory order for the Humean Rationalist: the only reason why the PSR is true is because of the independent explanations that exist for everything else. However, the Non-Humean Rationalist is able to explain why space must be relational rather than substantival using the above argument. More precisely, the Non-Humean Rationalist can explain why space cannot be substantival by appealing to whatever it is that grounds the PSR. For example, suppose the NonHumean Rationalist appeals to a “law of metaphysics” to ground the PSR. Then, that law of metaphysics would be able to explain why space is not substantival: after all, if space were substantival, the laws of metaphysics would be violated. Similarly, a Non-Humean about laws could (for example) explain why some particular object does not move faster than light by means of the fundamental laws of nature. After all, if an object did move faster than light, the laws of nature would be violated.26 This explanatory difference between Humean and Non-Humean Rationalism can be seen from different perspectives. On the one hand, this difference seems to favor Non-Humean Rationalism, because it shows that the Non-Humean Rationalist has an easier time explaining things than the Humean Rationalist. The Non-Humean Rationalist can appeal to the PSR itself (or whatever is the Non-Humean ground of the PSR) in order to explain why things are the way they are, while the Humean Rationalist must explain things without appealing to the PSR. However, this feature of Non-Humean Rationalism can also be seen as a bug. The Humean Rationalist claims that there are “neutral” explanations for why things are the way they are, where neutral explanations are 25 For more on how to explain facts about identity and distinctness, and the relationship between the PSR and the PII, see Shumener (2017, 2020). Contemporary “anti-arbitrariness” arguments, such as in Builes (2022b), could also be seen as presupposing (at least a restricted) version of the PSR. 26 The fact that Humean Rationalists seem to face an explanatory circularity problem if they use the PSR to explain particular first-order facts parallels a similar debate between Humean and Non-Humean accounts of the laws of nature. In particular, many Non-Humeans about laws have argued that if Humean laws were capable of explaining particular physical events, then because Humean laws are themselves explained by (the totality of) particular physical events, this would result in an explanatory circle. Some of the responses that Humeans about laws have made to this challenge (e.g. distinguishing different kinds of explanation) could also be made by the Humean Rationalist. For more on this debate, see Loewer (2012), Lange (2013, 2018), Shumener (2019), and Bhogal (2020b). 12 explanations that are in principle acceptable to everyone, regardless if they are antecedently committed to the PSR. As a consequence, the rationalist project of the Humean Rationalist is in a sense more ambitious than the rationalist project of the Non-Humean Rationalist. Only the Humean Rationalist claims to be able to explain everything in ways that we can all appreciate. 6. Conclusion Upon hearing the view that everything must have an explanation, it is very natural to ask why that should be so. Although those who reject the PSR don’t always have to answer every why-question, rationalists don’t have that luxury. My goal here has been to challenge a presupposition that has been common to all attempts at explaining the PSR: that rationalists must be Non-Humean Rationalists. If such a presupposition were true, then the failure of (Non-Humean) attempts at explaining the PSR would show that the PSR is self-refuting. However, this presupposition is false. Even if every version of Non-Humean Rationalism is mistaken, that does not imply that the PSR is mistaken. Instead, rationalists are free to be Humean Rationalists.27

Center Indifference and Skepticism David Builes Forthcoming in Noûs Abstract Many philosophers have been attracted to a restricted version of the principle of indifference in the case of self-locating belief. Roughly speaking, this principle states that, within any given possible world, one should be indifferent between different hypotheses concerning who one is within that possible world, so long as those hypotheses are compatible with one’s evidence. My first goal is to defend a more precise version of this principle. After responding to several existing criticisms of such a principle, I argue that existing formulations of the principle are crucially ambiguous, and I go on to defend a particular disambiguation of the principle. According to the disambiguation I defend, how we should apply this restricted principle of indifference sensitively depends on our background metaphysical beliefs. My second goal is to apply this disambiguated principle to classical skeptical problems in epistemology. In particular, I argue that Eternalism threatens to lead us to external world skepticism, and Modal Realism threatens to lead us to inductive skepticism. 1. Introduction When a range of different hypotheses are compatible with your evidence, how should you distribute your confidence between them? Life would be very simple if we just had to follow a naive version of the principle of indifference: Naive Indifference: If H1, H2, …, Hn are mutually exclusive and jointly exhaustive epistemic possibilities that are compatible with your evidence, then you are rationally required to assign a credence of 1/n to each of them. Unfortunately, Naive Indifference is inconsistent. Suppose I am about to roll a die. According to Naive Indifference, I should assign a credence of 1/2 that I will roll a ‘1’, since either I will roll a ‘1’ or I won’t. At the same time, I should also assign a credence of 1/6 that I will roll a ‘1’, since there are six possible numbers that I could roll. 2 Even if we set aside these contradictions, a major flaw of Naive Indifference is that it assumes that we can never have reasons to favor one hypothesis over another if both hypotheses are compatible with our evidence. The clearest counterexamples to this assumption involve objectively chancy processes. For example, since there is an objective chance of 1/6 that I will roll a ‘1’ with a fair die, I shouldn’t be indifferent between my rolling a ‘1’ and my not rolling a ‘1’.1 Other philosophers have argued that we should favor hypotheses that conform to various theoretical virtues over ones that don’t. For example, perhaps we should favor simpler theories over more complex theories, or perhaps we should favor more explanatory theories over less explanatory ones, etc.2 In spite of these problems with Naive Indifference, there are still some contexts where it is very natural to apply the principle. Consider the following case: Two Rooms: There are two indistinguishable rooms: R1 and R2. Each room contains a single agent, and both agents are duplicates of each other at any given time. Given that they both know that this is happening, how confident should any one of them be that they are in room R1? The obvious answer is “1/2”. While it may be perfectly consistent for them to assign a credence of (say) 0.281 that they are in room R1, it seems like the only non-arbitrary answer is 1/2. The first goal of this paper is to defend a restricted version of Naive Indifference, which generalizes the intuition that one should assign a credence of 1/2 in Two Rooms. After introducing and defending a principle inspired by Elga (2004) that is meant to accomplish this purpose (section 2), I argue that such a principle is ambiguous (section 3), and I defend a particular disambiguation (sections 4 and 5). My second goal will be to argue that resolving this ambiguity has far reaching consequences for a number of independently interesting epistemological questions, such as the epistemology of metaphysics (section 6), external world skepticism (section 7), and inductive skepticism (section 8). 2. Center Indifference We begin with the familiar notion of an (epistemically) possible world, which is roughly a maximal way that reality might be that is compatible with your evidence.3 Following Lewis (1979), we will 1There is disagreement about whether ordinary cases like this are cases of “objective chance”, or whether the only objective chances are to be found in indeterministic quantum theories (e.g. see Schaffer (2007), Glynn (2010), and Emery (2017). Either way, the example could be modified to be one of indeterministic quantum mechanics. 2For different perspectives on the uses of simplicity in science and philosophy, see Huemer (2009b), Sober (2015), and Bradley (2018). For the case of explanation, see Hedden (2015) and Lange (forthcoming). 3I only say “roughly” because we will be exploring exactly what is meant by a possible world in future sections. 3 also need the notion of a centered possible world, which is a possible world together with a designated individual and time.4 Lastly, let us say that two centered worlds are similar just in case they are associated with the same possible world. We can now formulate the following principle, which is meant to generalize our verdict in Two Rooms: Center Indifference: For any two similar centered worlds c1 and c2, if both c1 and c2 are compatible with your evidence, then it is rationally required to set Cr (c1 | c1 or c2) = 1/2.5 The main intuition behind Center Indifference is supposed to be the same one that motivated the “1/2” verdict in Two Rooms. Conditional on c1 or c2, you can know exactly which possible world you inhabit.