Don’t stop believing

Abstract

It’s been argued that there are no diachronic norms of epistemic rationality. These arguments come partly in response to certain kinds of counterexamples to Conditionalization, but are mainly motivated by a form of internalism that appears to be in tension with any sort of diachronic coherence requirements. I argue that there are, in fact, fundamentally diachronic norms of rationality. And this is to reject at least a strong version of internalism. But I suggest a replacement for Conditionalization that salvages internalist intuitions, and carves a middle ground between (probabilist versions of) conservatism and evidentialism.

Keywords:

• Epistemology
• conditionalization
• diachronic norms
• evidentialism
• evidence

Notes

No potential conflict of interest was reported by the authors.

1 That is, an rational agent’s credences conform to the following axioms: where is the set of all worlds under consideration (which I suppose throughout this paper to be finite):

(1)	Nonnegativity: for all propositions ,
(2)	Normalization:
(3)	Finite additivity: if A and B are disjoint, then

2 is usually defined as follows:

3 Indeed, while I will defend conditionalization against the time-slice internalist’s objections, it seems to me obvious that de se information of the sort discussed in Arntzenius (2003)s Shangri-La case are successful objections to conditionalization. Note, however, that these cases are not counterexamples to the norm I call ‘diachronic evidentialism.’

4 Note that while Meacham argues that there is a conflict between conditionalization and internalism, and provides a synchronic alternative to conditionalization, he is (at least in his (2010) not committed to the denial of traditional diachronic conditionalization.

5 These interpretations depend on a non-tensed reading of the principles, which I take to be charitable (since otherwise their synchronic commitments would be undefended).

6 Christensen’s objection to diachronic norms, which I discuss in Section 3, doesn’t require appeal to either mentalist or access internalism. Williamson and Moss both explicitly reject access internalism. Note: if evidence need not be accessible, then it’s no longer clear what motivates restricting the evidence an agent’s belief states should respect to evidence that is internal to a time-slice. Moss (p.c.) suggests that this restriction is not motivated by any more general principle and is normatively primitive.

7 Meacham (forthcoming) distinguishes sequential and interval updating rules. A sequential updating rule tells an agent how to adjust her doxastic attitudes whenever she receives a piece of new information. An interval updating rule tells an agent how her credences should harmonize over arbitrary intervals, given the cumulative information that she receives during an interval. Conditionalization has both sequential and updating interpretations. Both are properly diachronic. Interval conditionalization is a stronger norm than sequential conditionalization, since the latter doesn’t rule out changes in belief that aren’t responses to new evidence: for example, forgetting.

8 Hedden (2015) accepts that such an agent is rational.

9 Of course, it’s entirely appropriate that an agent’s beliefs should continuously change a little all the time: she should update on new information about, e.g. the passage of time, new events that she encounters, etc. But in the example I’m concerned with, a much greater proportion of her beliefs change, and not simply because she’s exposed to new evidence.

10 See Williamson (2000) for the canonical defense of this identity.

11 On conceptions of evidence where one’s own beliefs aren’t evidence, there need be no epistemic norms on evidence possession – only on doxastic responses to evidence.

12 In a 2012 AAP talk (no manuscript currently exists), Wolfgang Schwarz argued, similarly, that the motivation for rejecting diachronic norms derives from the idea that they cannot be action-guiding, and this turns on an illicit conflation of the practical with the epistemic.

13 Agents can take actions to induce beliefs, e.g. gathering evidence, or take actions to slowly indoctrinate themselves over time. But there is an important sense in which one cannot believe a proposition merely by trying.

14 In Bayesian terms, this would amount to obeying conditionalization with respect to every past time-slice. This is a simplification: again, de se information and its effects on de dicto information make clear that lifelong conditionalization is not epistemically ideal. I will (temporarily) speak as though conforming to lifelong conditionalization is epistemically better than not doing so for ease of exposition (and because it’s not obvious what the best update rule for de se information is).

15 I don’t specify which diachronic constraints in the interest of generality (but at the possible expense of clarity).

16 It’s consistent with this hypothesis that we treat final epistemic value as, e.g. true or comparative gradational accuracy.

17 As Titelbaum (2006) pointed out, the Greaves and Wallace (2006) defense of conditionalization isn’t properly understood as diachronic. Rather, it provides a justification for planning or intending to update by conditionalization in light of future evidence. But imagine we are programming our robot to be an ideal information gatherer. We have the option of programming it to plan to update by conditionalization and the option of programming it actually to update by conditionalization. We will choose the latter. Programming our robot to update by conditionalization is the best means of gathering information, from the (third personal) perspective of us, the theorists.

18 Fuller discussion of Arntzenius’ counterexample to conditionalization would require framework for de se belief update, which would take the present discussion too far afield.

19 Carr (1997) argues against the conception of expected accuracy used by epistemic utility theorists. For the purposes of addressing this objection to diachronic rationality, though, I will take the appeal to accuracy at face value.

20 Namely, that epistemic utility functions must be proper in the sense that they yield the result that any coherent credence function maximizes expected accuracy by its own lights.

21 See Joyce (2009) and Leitgeb and Pettigrew (2010) for plausible constraints on epistemic utility functions.

22 One might make the case that clutter avoidance is a more psychologically realistic version of an informational tradeoff; see Harman (1986).