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Humeanisms: metaphysical and epistemological

“It is, surely, not difficult to see that this theory of uniformities, far from helping to establish the validity of induction, would be, if consistently admitted, an insuperable objection to such validity. For if two facts, A and B, are entirely independent in their real nature, then the truth of B cannot follow, either necessarily or probably, from the truth of A.” (emphasis mine)

“Uniformity” C.S. Peirce (1995)

Abstract

Classic inductive skepticism–the epistemological claim that we have no good reason to believe that the unobserved resembles the observed–is plausibly everyone’s lot, whether or not they embrace Hume’s metaphysical claim that distinct existents are “entirely loose and separate”. But contemporary advocates of a Humean metaphysic accept a metaphysical claim stronger than Hume’s own. I argue that their view plausibly gives rise to a radical inductive skepticism–according to which we are downright irrational in believing as we do about the unobserved–that we don’t otherwise have reason to accept. The Metaphysical Neo-Humean is in an epistemological quagmire all her own.

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Notes

  1. See, inter alia, (Read and Richman 2008; Strawson 2013; Beebee 2013).

  2. If that interpretation turns out to be wrong, then what I say in this section should be understood as being about the views of Hume’s counterpart, who composed works at least morphologically identical to the Enquiry and Treatise, and whose actual views are those that the traditional interpretation attributes to Hume himself.

  3. For other sharpenings in the literature, see, inter alia (Efird and Stoneham 2008; Cameron 2010; Wilson 2010a, 2015; Segal 2015; Russell and Hawthorne 2018).

  4. Although, he does say, in §4.2, nt. 7, that “The word power is here used in a loose and popular sense. The more accurate explication of it would give additional evidence to this argument. See Section 7.” That’s why I said that on Hume’s view “Metaphysical Humeanism might give us a reason to believe Epistemological Humeanism”. But he gives no indication that the addition of that other evidence is needed in order to have reason enough to accept Epistemological Humeanism, and he gives every indication otherwise.

  5. Beebee (2011) mentions each of the following responses, but focuses on the two in the next paragraph.

  6. Others disagree. Here’s Huemer (2009, §3.4): “For this reason, given the Explanatory Priority Proviso, Humean views of causation and laws induce a different sort of probability distribution from non-Humean, realist views. On a Humean view, the appropriate application of the Principle of Indifference is to assign equal probabilities to the possible sequences of particular events, resulting in the inductive skeptic’s probability distribution. On a realist view, on the other hand, causal and nomological facts, including facts about objective chances, are explanatorily prior to facts about sequences of particular events, and the resulting interpretation of the Principle of Indifference, as we have seen, yields an inductivist probability distribution.” (Note: in this passage, ‘probability’ means ‘credence’.)

    But Huemer doesn’t explain how it is that assigning “equal probabilities to the possible sequences of particular events, result[s] in the inductive skeptic’s probability distribution”. After all, as Huemer is of course aware, there are infinitely many (indeed, given certain plausible assumptions, uncountably many) possible sequences of particular events, so each such sequence, if assigned an equal probability, will have to be assigned a probability of 0. But then the question of what probabilities to assign to various (uncountably infinite) sets of such sequences—roughly, to certain propositions that are less-than-maximally-detailed—won’t be settled by the individual probabilities of their members. When it comes to non-Humeans assigning probabilities to objective chances between 0 and 1, Huemer can sensibly claim, on the basis of his qualified Principle of Indifference, that the probability density function for the chances is uniformly 1. And so we get probabilities not only for individual chances (each probability of which is 0), but for any measurable set of chances, and in particular for intervals of chances (the probabilities for which will be nonzero). But that makes sense only because objective chances, if they are in fact representable by real numbers, come with their own measure. The measure of the interval [a,b] is just b – a. When it comes to Humeans assigning probabilities to possible sequences of particular events, on the other hand, it makes no sense at all to say that the probability density function for the possible sequences is uniformly 1, without supplying some measure function on the space of possible sequences. And for all Huemer has said or shown, nothing in Metaphysical Humeanism is incompatible with the claim, which contemporary Humeans make, that the relevant measure function assigns higher numbers to those sets of sequences in which Nature is more Uniform.

    (N.B. Filomeno (2019, §4.4) like Huemer, argues that the Metaphysical Humean is committed to a probability assignment that makes the set of non-uniform sequences much more likely than the set of uniform ones, and attempts to sidestep the problem I’ve noted by “opt[ing] to stick to [a] finite model”. This is an approach well worth considering, but I am less sanguine that Filomeno that the finite toy model “does not leave out any relevant feature that would alter the conclusion.”)

  7. See Maudlin (2007), who notes that empiricism (or an “empiricist stance”), together with contemporary physics, would seem to militate against the Humean Supervenience that Lewis endorses. See also MacBride (2005) and Wilson (2010a), who note that contemporary Humeans about metaphysics have abandoned Hume’s empiricist theory of ideas, and yet cling to Hume’s metaphysical views.

  8. The rest of Epistemological Humeanism—regarding our beliefs about the laws, causation, and dispositions—can be established likewise, when the considerations are conjoined with what Metaphysical (Neo)-Humeanism implies about the nature of laws, causation, and dispositions—in particular, that no law or causal fact or disposition is intrinsic to any region of spacetime. (For two possible definitions of ‘P is intrinsic’, each of which can serve my purposes, see nt. 14. There are natural and by-now familiar ways to extend those definitions in order to define the term ‘P is intrinsic to x’.)

  9. On Objective Bayesianism in general, see inter alia, Strevens (1999) and Bradley (2020). Note: the term ‘Objective Bayesianism’ is used differently by different authors; some (e.g. Easwaran (2011)) use it to refer to the view that there is exactly one set of rational initial priors, while others (e.g. Talbott (2016), Bradley (2020)) use it to refer to the view that there are some constraints on rational initial priors beyond probabilistic coherence. To be clear, I mean it only in the latter, weaker sense: I nowhere assume that there is exactly one set of rational initial priors. See nt. 29.

  10. This function need not be total, i.e. it need not specify this for every proposition/set of worlds, not even for every “measurable” proposition/set of worlds. Also, it might be interval-valued rather than real-valued, giving us imprecise or mushy logical probabilities.

  11. For classical defenses of the existence of logical probability, see Keynes (1921) and Carnap (1962). (Though, strictly speaking, Carnap put forward a measure over a space of state descriptions, rather than the space of possible worlds, it being a purely syntactic matter whether a set of sentences is a state description or not. This latter feature of state descriptions is responsible for one of the serious difficulties confronting Carnap’s program, i.e. that a single measure function defined on a space of state descriptions “translates” into different measure functions on the space of possible worlds (understood as maximal possible propositions), given different models of the language. And, to be sure (if we ignore the previous point) Carnap’s logical probability is “inductively friendly”, unlike what I claim about logical probability. But that’s only because he ignores the Humean denial of necessary connections.) See also Plantinga (1993, 150) and Van Inwagen (1998). For my own defense of its existence and its role in explaining constraints on rational initial priors, see Segal (2020) and my discussion in §3.3.

  12. I don’t mean that Metaphysical Neo-Humeans are explicitly committed to the claim I go on to make about the independence of logical probabilities. I mean that their ban on brute necessities, together with other plausible principles, implies such a claim of independence.

  13. One might object that the fact of probabilistic independence–if it be a fact–is likewise going to be an inexplicable necessity. It’s a necessity, after all, and the relevant properties are all intrinsic. My reply is that it won’t be inexplicable; the explanation is precisely the fact that any departure at all from such independence would be a brute necessity, and there are no brute necessities. (Just as the explanation of the (necessary) fact that all possible situations can be freely patched together is that any departure from such freedom—any necessary tie—would be a brute necessity, and there are no brute necessities.)

  14. By ‘intrinsic property’ I mean ‘a property that necessarily is never instantiated in virtue of its bearer’s relations, or lack thereof, to anything other than its bearer’s parts’. For a more precise definition along these lines, see Rosen (2010). This analysis lends itself most naturally to our argument from brute necessities: For if an intrinsic property is necessarily never instantiated in virtue of its bearer’s relations, or lack thereof, to anything other than its bearer’s parts, then nothing could possibly explain why its instantiation by one thing raises or lowers the probability that it is instantiated by something that does not overlap it.

    But the same point could be made if we understand ‘intrinsic property’ as ‘a property that never differs between possible duplicates’ and ‘x and y are duplicates’ is understood as ‘there is an isomorphism from x’s parts to y’s parts that preserves fundamental (or perfectly natural) properties and relations’ (Lewis (1986, 61–62), Sider (1996)). For then every intrinsic property is equivalent to a disjunction of fundamental natures, where a fundamental nature specifies the fundamental features of its bearer’s parts and the fundamental relations in which those parts stand. And so any such necessary connection between intrinsic properties is equally well a necessary connection between fundamental natures; and a necessary connection between fundamental natures is inexplicable because they’re fundamental.

  15. Disjoint regions, by definition, are regions that have no subregion in common. But it’s at least conceptually possible that they still have other parts in common. (See Segal (2014).) That is why I flag the non-trivial assumption that disjoint regions share no parts whatsoever in common.

  16. See nt. 16.

  17. They are in fact somewhat less general than their Possibilities-counterparts, as they don’t bear on the probabilistic independence of a thing’s fundamental/intrinsic features from the relations in which it stands. There are generalizations of these that do, and further generalizations to any number of non-overlapping beings (see Segal (2020) for details). But the substantially simpler (and less general) principles that I delineate do all the work we need for the purposes of my argument in this paper, while the more complex (and general) ones introduce complications that are at best distracting, and at worse barriers to employment in the present context.

  18. Treating the conditional probabilities in this and subsequent principles as straightforward ratios of unconditional probabilities encounters a well-known difficulty in cases where the event upon which it is conditional has probability 0. This very general difficulty and proposed solutions are beyond the scope of this paper; for very helpful discussion, see Hájek (2003), Fitelson and Hájek (2017), and Easwaran (2019).

  19. Henceforth I will drop the qualifier, ‘initial’, but it should be understood throughout that when I speak of an agent’s prior, I have in mind her initial prior, i.e. the credences the agent has before learning anything.

  20. What follows is an elaboration of my brief remarks in Segal (2020).

  21. For a comprehensive discussion of such refinements, see Pettigrew (2016). The principle, in some form or other, has very widespread acceptance. See Eagle (2019): “There is thus widespread agreement that the Principal Principle, or something close to it, captures a basic truth about chance.”

  22. Cf. Hoefer (2007). Strevens (1999) is focused on the question of justification rather than explanation—i.e. whether we have any non-circular reason to believe the principle—but his objections to previous attempts at justification carry over to analogous attempts at explanation.

  23. I’m ignoring pragmatic justifications. As Pettigrew points out, those are justifications for the analogous claims about pragmatic rationality, while our discussion is about epistemic rationality.

  24. This might be because that’s just what objective chance is, but it might not.

  25. If chances were just actual frequencies—the least sophisticated reductionist account—then they’d also be just good-old proportions. But for familiar reasons, they can’t be.

  26. Or, at least all the propositions that have logical probabilities.

  27. The difficulty is usually put in terms of different partitions of the space of possibilities, over which we can be indifferent. But if, as we are assuming, the rational prior function is uniformly distributed over a maximally fine-grained partition—i.e. a partition into possible worlds—then the difficulty is just that it’s not clear which measure on that space is such that rational priors are supposed to be uniform with respect to it: a measure function that assigns the same size to the set of worlds in which the edge lengths are between 0 inches and 1 inch as it does to the set of worlds in which the edge lengths are between 1 inch and 2 inches, or, alternatively, a measure function that assigns the same size to the set of worlds in which the face areas are between 0 square inches and 2 square inches as it does to the set of worlds in which the face areas are between 2 square inches and 4 square inches?

  28. White (2009) contends that in the cube factory case (he speaks of a square factory case, but no matter), only one of the partitions (according to length of the edges, or according to area of the faces) is one that gives rise to “evidential symmetry,” though we don’t know which. I have no handle on what this could mean, unless what’s meant is that one of the partitions is such that each member of the partition has the same logical probability.

    If I understand Huemer (2009) correctly, he thinks our priors ought to be distributed uniformly over the explanatorily basic hypotheses—and Bradley (2020) attempts to generalize this to take account of the relative naturalness of hypotheses. But, again, why think that these metaphysical features of propositions give rise to the epistemic feature of demanding equal priors, unless the former give rise to the corresponding feature of having equal logical probabilities?

  29. As with logical probabilities (nt. 10), the rational prior function need not be total, i.e. it need not specify a value for every proposition, not even for every “measurable” proposition. Likewise, the function might be interval-valued rather than real-valued, giving us imprecise or mushy rational priors.

  30. Here I take a logically stronger, but cleaner, position than I did in Segal (2020).

  31. Here and in the next principle ‘\(\alpha \)’ and ‘\(\beta \)’ are to be replaced by expressions formed in the usual way from propositional variables, truth-functional connectives, and the conditionalization symbol.

    Note: since I’ve said that neither function needs to be total, we might need to add the proviso that they are both well-defined.

  32. As long as L(\(\alpha \)) and L(\(\beta \)) are defined.

  33. The literature on this relationship is now quite extensive. See inter alia, Buchak (2014), and Jackson (2018, 2019).

  34. Remember (nt. 23), our topic is epistemic rationality, not pragmatic rationality, so Jamesian Will to Believe considerations are neither here nor there.

  35. If there’s more than one, arbitrarily pick any. Hyperintensional distinctions won’t matter here.

  36. Where ‘property P entails property Q’ = \({}_{df}\) necessarily, anything that instantiates P instantiates Q.

  37. I am implicitly assuming a certain connection between what Sue ‘learns’ and what Sue ‘knows by observation’. The notion of learning in terms of which I (following others) have characterized Bayesianism is a somewhat murky and contested one, and one might suggest that Sue learned something at some point that goes beyond what she observed and that raises the likelihood that Tomorrow instantiates Freezing. (Thanks to an anonymous referee here.) But here I note the following: for any proposition p that Sue has learned, it must be rationally permitted for Sue to have a credence greater than 0.5 in p, conditional upon Hitherto instantiating Observed. And for exactly parallel reasons to the argument from (1), (2), and (4), no such proposition can say anything about the intrinsic properties of any region disjoint from Hitherto. But then any proposition Sue has learned will, like the proposition that Hitherto instantiates Observed, be a proposition that is equivalent to some proposition about the intrinsic character of Hitherto.

  38. See Segal (2014).

  39. I presented a version of this paper at the 2018 Bucharest-Budapest Workshop on Humeanisms, and an earlier version at the 2016 Hebrew University/UNC-Chapel Hill Joint Philosophy Workshop on Metaphysics and History of Metaphysics. I am indebted to participants at both workshops for helpful comments. I also received invaluable feedback from a number of anonymous referees, for which I am most grateful. Research for this paper was supported by the Israel Science Foundation (grant no. 932/16) and was facilitated by Tom Baz and Yonatan Eisenstein.

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Segal, A. Humeanisms: metaphysical and epistemological. Synthese 199, 905–925 (2021). https://doi.org/10.1007/s11229-020-02741-w

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Keywords

  • Metaphysical humeanism
  • Epistemological humeanism
  • Problem of induction
  • Denial of necessary connections