Reflection and conditionalization: Comments on Michael Rescorla

Rescorla explores the relation between Reflection, Conditionalization, and Dutch book arguments in the presence of a weakened concept of sure loss and weakened conditions of self-transparency for doxastic agents. The literature about Reflection and about Dutch Book arguments, though overlapping, are distinct, and its history illuminates the import of Rescorla's investigation. With examples from a previous debate in the 70s and results about Reflection and Conditionalization in the 80s, I propose a way of seeing the epistemic enterprise in the light of practical requirements to be met by demands for synchronic coherence and probability updating policies. This includes a defense of principles rejected by Rescorla, while allowing for the value of his results in the borderland between theories of cognition and formal epistemology.     

Diachronic Dutch Books and Evidential Import

A handful of well‐known arguments (the ‘diachronic Dutch book arguments’) rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not ‘diachronically Dutch book‐able’) if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non‐trivial assumptions about which evidence you might acquire—in the case of conditionalization, the assumption is that, if you might learn that e, then it is not the case that you might learn something else that is consistent with e. These assumptions may not be relaxed. When they are, not only will non‐(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid.     

The Coherence Argument Against Conditionalization

I re-examine Coherence Arguments (Dutch Book Arguments, No Arbitrage Arguments) for diachronic constraints on Bayesian reasoning. I suggest to replace the usual game–theoretic coherence condition with a new decision–theoretic condition ('Diachronic Sure Thing Principle'). The new condition meets a large part of the standard objections against the Coherence Argument and frees it, in particular, from a commitment to additive utilities. It also facilitates the proof of the Converse Dutch Book Theorem. I first apply the improved Coherence Argument to van Fraassen's (1984) Reflection principle. I then point out the failure of a Coherence Argument that is intended to support Conditionalization as a naive, universal, update rule. I also point out that Reflection is incompatible with the universal use of Conditionalization thus interpreted. The Coherence Argument therefore defeats the naive view on Bayesian learning that it was originally designed to justify. This revised version was published online in August 2006 with corrections to the Cover Date.     

Beauty and the Bets

In the Sleeping Beauty problem, Beauty is uncertain whether the outcome of a certain coin toss was heads or tails. One argument suggests that her degree of belief in heads should be 1/3, while a second suggests that it should be 1/2. Prima facie, the argument for 1/2 appears to be stronger. I offer a diachronic Dutch Book argument in favor of 1/3. Even for those who are not routinely persuaded by diachronic Dutch Book arguments, this one has some important morals.     

Objective Bayesianism,Bayesian conditionalisation and voluntarism

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief. One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief.     

Conditionalization,Reflection, and Self-Knowledge

Van Fraassen famously endorses the Principle of Reflection as a constraint on rational credence, and argues that Reflection is entailed by the more traditional principle of Conditionalization. He draws two morals from this alleged entailment. First, that Reflection can be regarded as an alternative to Conditionalization – a more lenient standard of rationality. And second, that commitment to Conditionalization can be turned into support for Reflection. Van Fraassen also argues that Reflection implies Conditionalization, thus offering a new justification for Conditionalization. I argue that neither principle entails the other, and thus neither can be used to motivate the other in the way van Fraassen says. There are ways to connect Conditionalization to Reflection, but these connections depend on poor assumptions about our introspective access, and are not tight enough to draw the sorts of conclusions van Fraassen wants. Upon close examination, the two principles seem to be getting at two quite independent epistemic norms. My thanks to Frank Arntzenius, Barry Loewer, Chris Meacham, John Hawthorne, and an anonymous referee for their helpful discussion and criticism. Special thanks to Bliss Kern for bringing the topic to my attention.     

The puzzle of the hats

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty.     

Qeauty and the books: a response to Lewis’s quantum sleeping beauty problem

In his 2007 paper “Quantum Sleeping Beauty”, Peter Lewis poses a problem for the supporters’ of the Everett interpretation of quantum mechanics appeal to subjective probability. Lewis’s argument hinges on parallels between the traditional “sleeping beauty” problem in epistemology and a quantum variant. These two cases, Lewis argues, advocate different treatments of credences even though they share important epistemic similarities, leading to a tension between the traditional solution to the sleeping beauty problem (typically called the “thirder” solution) and Everettian quantum mechanics. In this paper I examine the metaphysical and epistemological differences between Lewis’s two cases, and, in particular, I show how diachronic Dutch book arguments support both the thirder solution in the traditional case and the Everettian’s solution in the variant case. These Dutch books, I argue, reveal an important disanalogy between Lewis’s two cases such that Lewis’s argument does not reveal an inconsistency in either the Everettian’s or the thirder’s assignment of credences.     

Holistic Conditionalization and Underminable Perceptual Learning

Seeing a red hat can (i) increase my credence in the hat is red, and (ii) introduce a negative dependence between that proposition and potential undermining defeaters such as the light is red. The rigidity of Jeffrey Conditionalization makes this awkward, as rigidity preserves independence. The picture is less awkward given ‘Holistic Conditionalization’, or so it is claimed. I defend Jeffrey Conditionalization's consistency with underminable perceptual learning and its superiority to Holistic Conditionalization, arguing that the latter is merely a special case of the former, is itself rigid, and is committed to implausible accounts of perceptual confirmation and of undermining defeat.     

The Smith-Walley Interpretation of Subjective Probability: An Appreciation

The right interpretation of subjective probability is implicit in the theories of upper and lower odds, and upper and lower previsions, developed, respectively, by Cedric Smith (1961) and Peter Walley (1991). On this interpretation you are free to assign contingent events the probability 1 (and thus to employ conditionalization as a method of probability revision) without becoming vulnerable to a weak Dutch book. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Dutch Books,Coherence, and Logical Consistency

In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff (s)he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of whether we have a Dutch Book Argument for Conditionalization is left open.     

Sleeping Beauty and shifted Jeffrey conditionalization

In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule.     

A forward looking decision rule for imprecise credences

Adam Elga (Philosophers’ Imprint, 10(5), 1–11, 2010) presents a diachronic puzzle to supporters of imprecise credences and argues that no acceptable decision rule for imprecise credences can deliver the intuitively correct result. Elga concludes that agents should not hold imprecise credences. In this paper, I argue for a two-part thesis. First, I show that Elga’s argument is incomplete: there is an acceptable decision rule that delivers the intuitive result. Next, I repair the argument by offering a more elaborate diachronic puzzle that is more difficult for imprecise Bayesians to avoid.     

Diachronic agency and practical entitlement

As diachronic agents, we deliberate and decide in the present to perform future courses of action. Such future‐directed decisions normally enjoy a distinctive species of rational authority over subsequent thought and action. But what is the nature of this authority, and what underwrites its normative force? In this paper, I argue that our answer to this question must begin by situating future‐directed deciding within an intrapersonal model of cross‐temporal influence. The role of future‐directed deciding (and intending), then, is not to generate a novel decision‐based reason for action, but instead to preserve a certain positive normative status over time. I develop an entitlement approach to decisional authority, according to which an agent who rationally decides to ? enjoys a practical entitlement, rather than a reason‐based practical justification, to ? at the appointed time. This entitlement is underwritten, I argue, by the warrant‐preserving nature of the sequence taking an agent from deliberation to subsequent action.     

Credal imprecision and the value of evidence

This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost-free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry, an inquiry where they revise their beliefs using an updating rule that doesn't satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost-free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision.     

Personhood and future belief: two arguments for something like Reflection

This paper offers two new arguments for a version of Reflection, the principle that says, roughly, that if one knew now what one would believe in the future, one ought to believe it now. The most prominent existing argument for the principle is the coherence-based Dutch Strategy argument advanced by Bas van Fraassen (and others). My two arguments are quite different. The first is a truth-based argument. On the basis of two substantive premises, that people’s beliefs generally get better over time and that being a person requires having knowledge of this fact, it concludes that it is rational to treat your future selves as experts. The second argument is a transcendental one. Being a person requires being able to engage in plans and projects. But these cannot be meaningfully undertaken unless one has Reflection-like expectations about one’s future beliefs. Hence, satisfaction of Reflection is necessary for being a person. Together, the arguments show that satisfaction of Reflection is both rational and necessary for persons.

The Self in Early Nyāya: A Minimal Conclusion

In this paper I revisit the early Nyāya argument for the existence of a self. In section 1, I reconstruct the argument in Nyāya-sūtra 1.1.10 as an argument from recognition following the interpretation in the Nyāyasūtra-Bhā?ya and the Nyāya-Vārttika. In Section 2, I reassess the plausibility of the Nyāya argument from memory/recognition in the Bhā?ya and the Vārttika in the light of recent empirical research. I conclude that the early Nyāya version of the argument from recognition can only establish a minimal conclusion that self is a unitary and persisting conscious agent, in contrast to the ontological conclusion that the self is distinct a substance qualified by consciousness. In the final section, I address the tension between the two conclusions in Nyāya and suggest how it might be resolved.     

Moral Judgement and Moral Motivation

I criticize an important argument of Michael Smith, from his recent book The Moral Problem (Oxford: Blackwell, 1994). Smith's argument, if sound, would undermine one form of moral externalism – that which insists that moral judgements only contingently motivate their authors. Smith claims that externalists must view good agents as always prompted by the motive of duty, and that possession of such a motive impugns the goodness of the agent. I argue (i) that externalists do not (ordinarily) need to assign moral agents such as a motive, and (ii) that possession of this motive, when properly understood, is morally admirable.     

Response to Abrusán,Shaw, and Elbourne

In my book Category Mistakes (OUP 2013), I discuss a range of potential accounts of category mistakes and defend a pragmatic, presuppositional account of the phenomenon. Three commentators discuss the book: Márta Abrusán focuses on a comparison between my book and Asher’s Lexical Meaning in Context, suggesting that Asher’s theory has the advantage of accounting not only for category mistakes, but also for additional phenomena such as so-called ‘coertion’ and ‘co-predication’. I argue that Asher’s account of all three phenomena is deficient, and, moreover, that it is far from clear that the latter two phenomena are related to that of category mistakes. James Shaw challenges two of my arguments against the MBT view. I respond to these challenges. Paul Elbourne provides a novel argument in support of my account of category mistakes, involving multi-sentence discourses and ERP experiments. I show that it is not entirely straightforward for my account to explain this data, but that his argument does ultimately provide support for my view.