A defense of objectivism about evidential support

Abstract

Objectivism about evidential support is the thesis that facts about the degree to which a body of evidence supports a hypothesis are objective rather than depending on subjective factors like one’s own language or epistemic values. Objectivism about evidential support is key to defending a synchronic, time-slice-centric conception of epistemic rationality, on which what you ought to believe at a time depends only on what evidence you have at that time, and not on how you were at previous times. Here, I defend a version of objectivism about evidential support on which facts about evidential support are grounded in facts about explanatoriness.

Keywords:

• Diachronic norms
• epistemology
• rationality
• evidence
• explanation

Notes

1 Note, however, that Uniqueness theorists may also simply deny that the facts about evidential support are so fine-grained. They might hold that the degree to which a body of evidence supports a hypothesis is sometimes to be represented by an interval of real numbers rather than by a single real number, for instance. Uniqueness theorists might also hold that it is sometimes indeterminate the degree to which a body of evidence supports a hypothesis, so that it is indeterminate what degree of belief an agent with that evidence should have in that hypothesis.

2 Of course, the opponent of diachronic norms could also deny the alleged datum. Perhaps, for instance, it is permissible to change one’s beliefs without a change in one’s evidence if this change is driven by the adoption of a different set of epistemic standards. For instance, it might be permissible to come to give greater weight to simplicity in evaluating evidence, and this will lead one to revise one’s beliefs without gaining or losing any evidence. Moss (2014) takes something analogous to this approach in discussing imprecise credences. She holds that an agent with imprecise credences (where her doxastic state is represented by a set of probability functions rather than by a single probability function) must identify with one member of that set of probability functions, and use that member as the basis for practical decision-making. She holds that it is permissible for that agent to come to identify with a different member of that set, where such a change is analogous to a rationally permissible change in her (practical) values. While Moss is discussing a change in which aspect of one’s doxastic state one uses for practical decision-making, rather than a change in one’s doxastic state itself (since she is assuming that one’s overall imprecise credal state remains constant absent changes in evidence), one could go further and say that it is also permissible to undergo a change in one’s doxastic state without a change in evidence due to a similar change of heart. Christopher Meacham (personal communication) tells me that he is sympathetic to this sort of position.

3 Note that on this sort of Permissivist picture, epistemic rationality isn’t all that much less demanding than on a Uniqueness picture. After all, maintaining the exact same evidential standards over time and always having the beliefs that those standards recommend is no mean feat!

4 See Meacham’s contribution to this volume for detailed discussion of subtleties involved in interpreting Conditionalization.

5 In earlier work (Hedden 2015a, b), I have defended a time-slice-centric picture of rationality on which all requirements of rationality are synchronic and impersonal. Obviously, this involves commitment to more than just Uniqueness, and hence objectivism about evidential support. For even if there are no diachronic norms governing what you ought to believe, there might be diachronic norms governing, say, the temporally extended process of reasoning, or evidence-gathering, or doxastic (as opposed to propositional) justification. Hlobil (2015) and Podgorski (forthcoming) argue that there may be diachronic requirements of rationality such as requirements governing the temporally extended process of reasoning, even if there are no diachronic norms governing what you ought to believe at a particular time. And even if there are no diachronic norms governing belief, there might be diachronic norms governing preferences, intentions, or actions, for instance. And even if there are no diachronic norms whatsoever, there might be norms that nevertheless fail to be impersonal, such as synchronic norms saying that you should defer to the attitudes that you now believe your early or later selves had or will have. Still, if objectivism about evidential support, or at least something close to it, is false, the whole edifice comes crashing down.

6 Indeed, this supervenience consideration is one of my main arguments for a time-slice-centric picture of rationality in Hedden (2015b, c).

7 This definition of ‘grue’ is slightly different from Goodman’s. His ‘grue’ applies to an object just in case it is green and was first observed before t (for some unspecified time t) or blue and first observed after t. I drop reference to t for simplicity.

8 It would go too far to say that observations of grue emeralds don’t support the claim that all emeralds are grue at all. After all, such observations rule out various hypotheses which are incompatible with the hypothesis that all emeralds are grue. For instance, they rule out the hypothesis that all emeralds are red. So they must support the claim that all emeralds are grue to at least some small degree.

9 I owe this term to Jonathan Weisberg, who recently used it in a lecture on objective Bayesianism.

10 Titelbaum (2010) holds that his proof shows that the naturalness proposal, or something very close to it, is a necessary condition for objectivism to be true. The reason is that if a substantive evidential support relation cannot treat evidential support as invariant under permutations of predicates, it can seem that any such evidential support relation must treat some predicates (or the properties to which they refer) as special, whether we call this specialness ‘naturalness’ or something else. But in my view, the fact that the evidential support relation cannot be invariant under permutations of predicates does not entail that it must treat some predicates (or properties) as special in and of themselves, such that the appearance of certain predicates in the evidence and hypothesis always makes for greater evidential support. Instead, it could be that the evidential support relation cares about the relationship between the predicates and the object terms of which they are predicated; that is, it must care about the meaning of the proposition as a whole (and about the relationship between the evidence proposition and the hypothesis proposition). This is akin to the Moore (1903) notion of an organic unity. Consider the fact that chocolate and strawberries (together) taste better than chocolate and salmon. This doesn’t mean that the presence of strawberries in and of itself makes for a better dish than does the presence of salmon. After all, salmon and greens tastes better than strawberries and greens. It’s the relationship between the two that matters. For this reason, naturalness isn’t the only game in town when it comes to objective evidential support. In fact, as I will argue shortly, it isn’t even the most promising approach.

11 As Titelbaum (2010, 485) puts the point, the problem is that any substantive evidential support relation ‘displays a bias toward certain properties that is prior to and independent of the influence of any evidence. But supplying such a bias was the job the natural properties were supposed to do! In order for the list of natural properties to play its envisioned role in shaping the evidence favoring relation, it cannot be determinable from an agent’s evidence.’ One might attempt to invoke reference magnetism to escape Titelbaum’s circle. According to one interpretation of the idea of reference magnetism, it is a brute constraint on interpreting the meanings of terms in a language that they tend to refer to natural rather than unnatural properties. So, if you just project the predicates that are already in your language, you’re likely to be projecting a natural property. Now, Titelbaum worries that there is still a problem, since despite a general preference for natural properties to serve as the referents of predicates, one’s language is still likely to contain plenty of predicates referring to unnatural properties as well. So one will still need empirical evidence to know which of the predicates in one’s language to project. Of course, the naturalness theorist might respond that in any case most of one’s predicates will refer to natural ones due to the general constraints imposed by reference magnetism, and so by adopting a general policy of projecting any and all predicates in one’s language, one makes it likely that in any particular instance one will be projecting natural properties. Even so, there is a deeper problem with this escape route. For arguably, it is in virtue of facts about rationality, and in particular about evidential support, that predicates in one’s language tend to refer to natural rather than unnatural properties. Weatherson (2012) makes a compelling case that this is the order of explanation in Lewis’ philosophy of language, at least. There, the idea is that facts about mental content are explanatorily prior to facts about linguistic meaning, and facts about mental contents are themselves determined in part by facts about rationality. It’s easier to have rational attitudes toward propositions involving natural properties, so there’s pressure to interpret agents as having attitudes toward such propositions rather than propositions involving unnatural properties. And that’s why linguistic predicates tend to refer to natural rather than unnatural properties. But this Lewisian picture is one we can’t endorse if we hold that the fact that one’s terms tend to refer to natural properties is itself what explains how and why it is rational to project natural properties.

12 Titelbaum considers this possibility in Section 5 of his 2010.

13 These two quotes are highlighted in Schaffer (2004).

14 Another representative quote: Lewis (1986, 60) writes that ‘What physics has undertaken ... is an inventory of the sparse [i.e. natural] properties of this-worldly things.’

15 There may also be grounds for ditching or demoting the supervenience role of the natural/unnatural distinction. For as Schaffer (2004, 99) argues, there may be possible worlds in which there is no minimal supervenience base, and instead, ‘properties might be endlessly supervenient upon lower level properties.’

16 Lewis himself certainly thought that it was a non-contingent matter which properties are possibly natural, though it is unclear whether he thought this was also a priori. He writes that, ‘The name [natural] has proved to have a drawback: it suggests to some people that it is supposed to be nature that distinguishes the natural properties from the rest; and therefore that the distinction is a contingent matter, so that a property might be natural at one world but not at another. I do not mean to suggest any such thing. A property is natural or unnatural simpliciter, not relative to one or another world’ (1986, 60, fn 44).

17 Of course, if one cannot refer to uninstantiated but possibly natural properties, this complicates matters. Take one of Titelbaum’s central examples, that of phlogiston theory at a time when it was still a live possibility. On some views, phlogiston necessarily doesn’t exist. It wouldn’t exist even if the Ramsey sentence corresponding to phlogiston theory were true. If that is right, the same difficulties arise in modeling the doxastic states of phlogiston theories and interpreting their language that arise for fictional terms like ‘Santa Claus.’ I won’t go into these matter here.

18 A caveat: Hawthorne and Dorr (2013) mention the possibility of evaluating entire probability functions for naturalness, with the result that facts about evidential support boil down to facts about which probability functions are most natural. I won’t pursue this possibility here.

19 Note that the fact that gruesome properties are counterfactually dependent on observation is independent of whether we start with non-gruesome predicates and define gruesome ones therefrom, or if we instead start with gruesome predicates and define non-gruesome ones therefrom. Even if we define ‘green’ as ‘grue if observed and bleen if unobserved,’ if remains the case that an unobserved green thing (which is therefore bleen) would still have been green had we observed it (in which case it would have been grue).

20 What about cases where it isn’t wholly arbitrary which emeralds we’ve observed? Consider a different property grue+, where something is grue+ just in case it is green and first observed before AD 2500 or blue and first observed (if ever) after AD 2500. Suppose also that for any given emerald we don’t observed AD 2500, the reason it doesn’t get observed until then it that it’s on an exoplanet, and we don’t get the technology to mine on exoplanets until after AD 2500. Then, the hypothesis that all emeralds are grue+ provides a fairly stable explanation of why we’ve observed only grue+ emeralds. If all emeralds are grue+, then even if we’d made somewhat different observations than we in fact did, this wouldn’t involve our mining on exoplanets in the twenty-first century, and so we still would have observed only grue+ emeralds. I think there are three things to say about this sort of case. First, even if the hypothesis that all emeralds are grue+ is a rather stable explanation of our evidence, it is still a bit a less stable explanation than the hypothesis all emeralds are green. If the former hypothesis is true, then it is still possible for us not to have gotten the evidence that we’ve observed only grue+ emeralds, even if we have to go to fairly dissimilar possible worlds to get cases where we lack this evidence. So the grue+ hypothesis may be a lot better than the standard grue hypothesis in terms of explanatory stability, but it’s still not as good as the green hypothesis. Second, we know that by around the late twenty-fifth century, we (i.e. later humans) will start heavily favoring the green hypothesis over the grue+ hypothesis (and White’s story explains why this would be justified), so reflection-style reasoning suggests we should favor the green hypothesis now. Third, even if there are gruesome property where While’s explanationist story breaks down (consider the property grue++, which applies to things that are green unless they’re in some causally inaccessible region of the universe), we can still fall back on an appeal to naturalness, provided that it’s a priori which properties are possibly natural, as I have suggested. This would amount to a retreat from a monolithic picture of evidential support, on which explanatory considerations do all the work, to a pluralist approach on which there are a variety of substantive factors that together determine the evidential support relation.

21 One might worry that facts about simplicity will depend on facts about naturalness, for the reason given by Lewis in his discussion of laws of nature. If simplicity is a matter of, say, the number of symbols needed to state the hypothesis, then how simple a hypothesis is will depend on the language used to express it. So we need to fix on a canonical language in which to evaluate the simplicity of different hypotheses, and one option would be for the canonical language to be one in which the predicates refer to natural properties. But if facts about which properties are possibly natural-to-such-and-such-degree are a priori, as suggested above, then this doesn’t threaten to make facts about simplicity, and hence explanatoriness, empirical. An alternative option, which I won’t pursue here, would be to conceive of simplicity in non-syntactic terms.

22 See Field (2009) for a defense.

23 Perhaps no evidence could simultaneously call into question the preference for simplicity, unification, and stability (or whatever one’s candidate basic explanatory standards are). In that case, at least one such explanatory standard would be treated as empirically indefeasible in that particular situation, and would be used to determine how to modify the methodological principles that are called into question. This would amount to a picture on which at least one methodological principle is treated as a priori relative to a given body of evidence, even though no methodological principle is treated as a priori relative to all possible bodies of evidence. (Compare citeauthorbib2 (citeyearbib2) on the law of contradiction in logic.) Of course, provided that there is a uniquely rational way to determine which principles to treat as indefeasible for present purposes, and how to revise those principles that are called into question, it is tempting to say that really, the most basic methodological principles are those that determine this uniquely rational way to proceed with methodological change, even if we find it difficult or impossible to actually articulate those most basic principles.