How can self-locating propositions be integrated into normal patterns of belief revision? Puzzles such as Sleeping Beauty seem to show that such propositions lead to violation of ordinary principles for reasoning with subjective probability, such as Conditionalization and Reflection. I show that sophisticated forms of Conditionalization and Reflection are not only compatible with self-locating propositions, but also indispensable in understanding how they can function as evidence in Sleeping Beauty and similar cases.

Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen's Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new "Qualified Reflection" principle, which states that an agent should obey Reflection only if he or she is (...) certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a "Distorted Reflection" principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence—some dramatize a less blameworthy sort of epistemic frailty that the essay calls "self-doubt." The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt. (shrink)

How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment (the manner in which she responds to her evidence), then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle-a version amended to handle cases of information (...) loss. When you count an advisor as an epistemic peer, you should give her conclusions the same weight as your own. Denying that view-call it the "equal weight view"-leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well-informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors. (shrink)

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. (shrink)

I bring together social ontology and social epistemology by consideringsocial entities (``epistemic unities'') that are constituted by the holdingof epistemic relations between their members. In particular, I focus onthe relation of taking someone as an expert. Among the types of structuresexamined are ones with a single expert and one or more non-experts whomay or may not know of each other's situation; and ones with more thanone expert, including cases in which the relation between the experts ishierarchical and cases in which (...) it is symmetrical. These structures modela variety of social situations which can thus be given a unified treatment.Among the cases I discuss are persons, which I argue are multiple-expertunities of persons at times. Taking a person as a social unity like this offersa clear sense in which some groups can also be person-like. (shrink)

In Belief and the Will, van Fraassen employed a diachronic Dutch Book argument to support a counterintuitive principle called Reflection. There and subsequently van Fraassen has put forth Reflection as a linchpin for his views in epistemology and the philosophy of science, and for the voluntarism (first-person reports of subjective probability are undertakings of commitments) that he espouses as an alternative to descriptivism (first-person reports of subjective probability are merely self-descriptions). Christensen and others have attacked Reflection, taking it to have (...) unpalatable consequences. We prescind from the question of the cogency of diachronic Dutch Book arguments, and focus on Reflection's proper interpretation. We argue that Reflection is not as counterintuitive as it appears — that once interpreted properly the status of the counterexamples given by Christensen and others is left open. We show also that descriptivism can make sense of Reflection, while voluntarism is not especially well suited to do so. (shrink)

The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle ([1984]), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach, (...) and without eliminating this inconsistency, the approach cannot be regarded as scientific. The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three <span class='Hi'>categories</span>. The first two share the view that new evidence is absent, but differ about the conclusion of whether Sleeping Beauty should change her belief or not, and why. The third category is characterized by the view that, after all, new evidence (although hidden from the initial view) is involved. My solution is radically different and does not fall into either of these <span class='Hi'>categories</span>. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e., there is no need to explain the (un)change of belief. The Sleeping Beauty Problem The Problem Deflated 2.1 From contradiction to consistency 2.2 The inanimate version 2.3 Back to SB Summary CiteULike Connotea Del.icio.us What's this? (shrink)

How far, if at all, do our intrapersonal and our interpersonal epistemic obligations run in parallel? This paper treats the question as addressing the stability of doxastic commitment in the two dimensions. In the background lies an analogy between doxastic and practical commitment. We’ll pursue the question of doxastic stability by coining a doxastic analogue of Gregory Kavka’s much-discussed toxin case. In this new case, you foresee that you will rationally abandon a doxastic commitment by undergoing a shift in the (...) context in which you doxastically deliberate. The case reveals an important stability condition on doxastic commitment that plays no role in cases modeled on Ulysses and the Sirens, the scenario that has shaped previous attempts to draw an analogy between doxastic and practical commitment. The stability condition thereby revealed is not diachronic -- it does not involve a shift in belief -- but we can construct specifically diachronic cases that reveal an important intrapersonal epistemic obligation. This obligation arises when you expect the shift in belief by ‘projecting’ yourself into a future doxastic context -- thus vindicating a restricted, but only this restricted, application of Bas van Fraassen’s Reflection Principle. Despite some important differences, we can use these diachronic cases as a model for interpersonal cases that reveal an important role for doxastic context in the epistemology of disagreement. But the roles played by projection and context in disagreement ensure that there is no general obligation to be responsive to the opinion of an epistemic peer who disagrees with you. (shrink)

We discuss the cable guy paradox, both as an object of interest in its own right and as something which can be used to illuminate certain issues in the theories of rational choice and belief. We argue that a crucial principle—The Avoid Certain Frustration (ACF) principle—which is used in stating the paradox is false, thus resolving the paradox. We also explain how the paradox gives us new insight into issues related to the Reflection principle. Our general thesis is that principles (...) that base your current opinions on your current opinions about your future opinions need not make reference to the particular times in the future at which you believe you will have those opinions, but they do need to make reference to the particular degrees of belief you believe you will have in the future. (shrink)

This is an essay in the Bayesian theory of how opinions should be revised over time. It begins with a discussion of the principle that van Fraassen has dubbed "Reflection". This principle is not a requirement of rationality; a diachronic Dutch argument, that purports to show the contrary, is fallacious. But under suitable conditions, it is irrational to actually implement shifts in probability that violate Reflection. Conditionalization and probability kinematics are special cases of the principle not to implement shifts that (...) violate Reflection; hence these principles are also requirements of rationality under suitable conditions, though not universal requirements of rationality. (shrink)

The Story of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but (...) ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable. (shrink)

It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a complete one (...) are established. (shrink)

This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...) rationality and prudence. The sensible lover imitates the older literary example of Ulysses' tying himself to the mast. (The example belongs therefore to the class of problems treated in Elster (1979)). Both this lover and Ulysses foresee that under certain possible future conditions, their opinions, values and preferences will or would differ from what they are now, in a very definite fashion. To what extent is such foresight possible? Correspondingly (when we do not claim foreknowledge) to what extent is such opinion reasonable, rational, coherent, or consistent in some suitably broad sense? It is not easy to understand exactly what is possible or even logically permissible in this respect. In an earlier paper, "Belief and the Will", I argued for a principle ("Reflection") to govern such deliberation. Here I will both generalize the treatment of opinion in "Belief and the Will" and respond to criticism. Critical examples mainly resembled the story of Ulysses who foresaw a period of dysfunction (at the sound 2 of the sirens) in his epistemic and/or doxastic future. Other criticism focused on the model of opinion used (precise numerical subjective probability) and on the merits of Dutch Book arguments. The present argument will not rely on Dutch Book arguments and strategies, and the Reflection principle will be formulated so as to apply also to vague opinion. (shrink)

We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that for (...) all sentences φ $I\Delta_0 + \Omega_1 \vdash \forall x \operatorname{Prov}(\ulcorner \forall y \leq \bar{x} (\operatorname{Prf} (y. \overline{\ulcorner \varphi \urcorner}) \rightarrow \varphi)\urcorner).$ The proof hinges on the use of definable cuts and partial satisfaction predicates akin to those introduced by Pudlak in [Pu86]. Finally, we give some applications of the small reflection principle, showing that the principle can sometimes be invoked in order to circumvent the use of provable Σ-completeness for witness comparison formulas. (shrink)

Conditionalization is an intuitive and popular epistemic principle. By contrast, the Reflection principle is well known to have some very unappealing consequences. But van Fraassen argues that Conditionalization entails Reflection, so that proponents of Conditionalization must accept Reflection and its consequences. 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. I (...) also propose a replacement for Reflection that accounts for the intuitions that made Reflection appealing, but doesn’t lead to Reflection’s bad consequences. (shrink)

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)