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A plea: If you're going to propose a Bayesian framework for updating self-locating degrees of belief, please read this piece first. I've tried to survey all the extant formalisms, group them by their general approach, then describe challenges faced by every formalism employing a given approach. Hopefully this survey will prevent further instances of authors' re-inventing updating rules already proposed elsewhere in the literature. |
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In “Judy Benjamin is a Sleeping Beauty” (2010) Bovens recognises a certain similarity between the Sleeping Beauty (SB) and the Judy Benjamin (JB). But he does not recognise the dissimilarity between underlying protocols (as spelled out in Shafer (1985). Protocols are expressed in conditional probability tables that spell out the probability of coming to learn various propositions conditional on the actual state of the world. The principle of total evidence requires that we not update on the content of the proposition (...) |
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The best arguments for the 1/3 answer to the Sleeping Beauty problem all require that when Beauty awakes on Monday she should be uncertain what day it is. I argue that this claim should be rejected, thereby clearing the way to accept the 1/2 solution. |
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Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) |
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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 (...) |
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The question of diachronic coherence, coherence of degrees of belief across time, is investigated within the context of Richard Jeffrey’s radical probabilism. Diachronic coherence is taken as fundamental, and coherence results for degrees of belief at a single time, such as additivity, are recovered only with additional assumptions. Additivity of probabilities of probabilities is seen to be less problematic than additivity of first-order probabilities. Without any assumed model of belief change, diachronic coherence applied to higher-order degrees of belief yields the (...) |
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In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...) |
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In addition to being uncertain about what the world is like, one can also be uncertain about one’s own spatial or temporal location in the world. My aim is to pose a problem arising from the interaction between these two sorts of uncertainty, solve the problem, and draw two lessons from the solution. |
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Argues for the "thirder" solution to the Sleeping Beauty puzzle. The argument turns on an analogy with a variant case, in which a coin-toss on Monday night determines whether one's memories of Monday are permanently erased, or merely suspended in such a way that they will return some time after one wakes up on Tuesday. |
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This paper examines three accounts of the sleeping beauty case: an account proposed by Adam Elga, an account proposed by David Lewis, and a third account defended in this paper. It provides two reasons for preferring the third account. First, this account does a good job of capturing the temporal continuity of our beliefs, while the accounts favored by Elga and Lewis do not. Second, Elga’s and Lewis’ treatments of the sleeping beauty case lead to highly counterintuitive consequences. The proposed (...) |
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I hear the patter of little feet around the house, I expect Bruce. What I expect is a cat, a particular cat. If I heard such a patter in another house, I might expect a cat but no particular cat. What I expect then seems to be a Meinongian incomplete cat. I expect winter, expect stormy weather, expect to shovel snow, expect fatigue---a season, a phenomenon, an activity, a state. I expect that someday mankind will inhabit at least five planets. (...) |
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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 (...) |
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The Snow White problem is introduced to demonstrate how learning something of which one could not have learnt the opposite (due to observer selection bias) can change an agent’s probability assignment. This helps us to analyse the Sleeping Beauty problem, which is deconstructed as a combinatorial engine and a subjective wrapper. The combinatorial engine of the problem is analogous to Bertrand’s boxes paradox and can be solved with standard probability theory. The subjective wrapper is clarified using the Snow White problem. (...) |
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How should rational beliefs change over time? The standard Bayesian answer is: by conditionalization (a.k.a. Bayes’ Rule). But conditionalization is not an adequate rule for updating beliefs in “centred” propositions whose truth-value may itself change over time. In response, some have suggested that the objects of belief must be uncentred; others have suggested that beliefs in centred propositions are not subject to diachronic norms. Iargue that these views do not offer a satisfactory account of self-locating beliefs and their dynamics. A (...) |
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Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, self-locating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “ur-priors”. But different authors have understood the rule in different ways, and (...) |
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This paper is about the standard Reflection Principle :235–256, 1984) and the Group Reflection Principle :478–502, 2007; Bovens and Rabinowicz in Episteme 8:281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124:449–491, 2015). I argue that these principles are incomplete as they stand. The key point is that deference is an intensional relation, and so whether you are rationally required to defer to a person at a time can depend on (...) |
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In the context of the Sleeping Beauty problem, it has been argued that so-called “halfers” can avoid Dutch book arguments by adopting evidential decision theory. I introduce a Dutch book for a variant of the Sleeping Beauty problem and argue that evidential decision theorists fall prey to it, whether they are halfers or thirders. The argument crucially requires that an action can provide evidence for what the agent would do not only at other decision points where she has exactly the (...) |
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The aim of this paper is to provide a case for the double-halfer position in the sleeping beauty. This case relies on the use of the so-called imaging rule for probabilistic dynamics as a substitute for conditionalization. It is argued that the imaging rule is the appropriate one for dealing with belief change in sleeping beauty and that under natural assumptions, this rule results in the double-halfer position. |
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The Puzzle 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 (...) |
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The Sleeping Beauty problem is presented in a formalized framework which summarizes the underlying probability structure. The two rival solutions proposed by Elga and Lewis differ by a single parameter concerning her prior probability. They can be supported by considering, respectively, that Sleeping Beauty is “fuzzy-minded” and “blank-minded”, the first interpretation being more natural than the second. The traditional absent -minded driver problem is reinterpreted in this framework and sustains Elga’s solution. |
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I consider the puzzles arising from four interrelated problems involving `anthropic' reasoning, and in particular the `Self-Sampling Assumption' (SSA) - that one should reason as if one were randomly chosen from the set of all observers in a suitable reference class. The problem of Freak Observers might appear to force acceptance of SSA if any empirical evidence is to be credited. The Sleeping Beauty problem arguably shows that one should also accept the `Self-Indication Assumption' (SIA) - that one should take (...) |
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If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. (...) |
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I defend a general rule for updating beliefs that takes into account both the impact of new evidence and changes in the subject’s location. The rule combines standard conditioning with a shifting operation that moves the center of each doxastic possibility forward to the next point where information arrives. I show that well-known arguments for conditioning lead to this combination when centered information is taken into account. I also discuss how my proposal relates to other recent proposals, what results it (...) |
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In this paper I show that Elga’s argument for a restricted principle of indifference for self-locating belief relies on the kind of mistaken reasoning that recommends the ‘staying’ strategy in the Monty Hall problem. |
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Robert Stalnaker opposes the traditional view that knowledge of one's own current thoughts and feelings is the unproblematic foundation for all knowledge. He argues that we can understand our knowledge of our thoughts and feelings only by viewing ourselves from the outside, by seeing our inner lives as features of the world as it is in itself. |
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