Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

What is it to know someone? Epistemologists rarely take up this question, though recent developments make such inquiry possible and desirable. This paper advances an account of how such interpersonal knowledge goes beyond mere propositional and qualitative knowledge about someone, giving a central place to second-personal treatment. It examines what such knowledge requires, and what makes it distinctive within epistemology as well as socially. It assesses its theoretic value for several issues in moral psychology, epistemic injustice, and philosophy of mind. (...) And it offers an account of the complex content in play if interpersonal knowledge is to be understood in terms of its mental states and their functions. (shrink)

We start by presenting three different views that jointly imply that every person has many conscious beings in their immediate vicinity, and that the number greatly varies from person to person. We then present and assess an argument to the conclusion that how confident someone should be in these views should sensitively depend on how massive they happen to be. According to the argument, sometimes irreducibly de se observations can be powerful evidence for or against believing in metaphysical theories.

A number of cases involving self-locating beliefs have been discussed in the Bayesian literature. I suggest that many of these cases, such as the sleeping beauty case, are entangled with issues that are independent of self-locating beliefs per se. In light of this, I propose a division of labor: we should address each of these issues separately before we try to provide a comprehensive account of belief updating. By way of example, I sketch some ways of extending Bayesianism in order (...) to accommodate these issues. Then, putting these other issues aside, I sketch some ways of extending Bayesianism in order to accommodate self-locating beliefs. Finally, I propose a constraint on updating rules, the "Learning Principle", which rules out certain kinds of troubling belief changes, and I use this principle to assess some of the available options. (shrink)

The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an (...) important assumption, necessary for its generation, has been overlooked. My aim in this paper is to identify this assumption. Since what it claims turns out to be prima facie problematic, I will urge that the burden of proof now shifts to the objectors to PI; they have to provide reasons why this assumption holds. (shrink)

Can self-locating beliefs be relevant to non-self-locating claims? Traditional Bayesian modeling techniques have trouble answering this question because their updating rule fails when applied to situations involving contextsensitivity. This essay develops a fully general framework for modeling stories involving context-sensitive claims. The key innovations are a revised conditionalization rule and a principle relating models of the same story with different modeling languages. The essay then applies the modeling framework to the Sleeping Beauty Problem, showing that when Beauty awakens her degree (...) of belief in heads should be one-third. This demonstrates that it can be rational for an agent who gains only self-locating beliefs between two times to alter her degree of belief in a non-self-locating claim. (shrink)

The central claim of this essay is that many deflationary theories of truth are variants of the correspondence theory of truth. Essential to the correspondence theory of truth is the proposal that objective features of the world are the truthmakers of statements. Many advocates of deflationary theories (including F. P. Ramsay, P. F. Strawson and Paul Horwich) remain committed to this proposal. Although T-sentences (statements of the form “ s is true iff p ”) are presented by advocates of deflationary (...) theories of truth as truisms or analytic truths, T-sentences are often understood as entailing commitment to the central proposal of the correspondence theory. (shrink)

This paper considers fair betting odds for certain bets that might be placed in the situation discussed in the so-called Sleeping Beauty Problem. This paper examines what Thirders, Halfers, and Double Halfers must say about the odds as determined by various decision theoretic approaches and argues that Thirders and Halfers have difficulties formulating plausible and coherent positions concerning the relevant betting odds. Double Halfers do not face this problem and that is an important consideration in favor of Double Halfers.

Darren Bradley has recently appealed to observation selection effects to argue that conditionalization presents no special problem for Everettian quantum mechanics, and to defend the ‘halfer’ answer to the puzzle of Sleeping Beauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about Sleeping Beauty. This result is doubly good news for Everettians: they can endorse Bayesian confirmation theory without qualification, but they are not thereby compelled to adopt the (...) unpopular ‘halfer’ answer in Sleeping Beauty. These considerations suggest that objective chance is playing an important and under-appreciated role in Sleeping Beauty. 1 Introduction2 Confirmation in Everettian Quantum Mechanics3 Sleeping Beauty4 The Selection Model5 Bradley’s Argument6 The Right Route to ⅓7 The Breakdown of the Analogy8 Alternative Diagnoses9 God’s Gambling Game10 Non-chancy Sleeping Beauty Cases11 Conclusion. (shrink)

Darren Bradley has recently appealed to observation selection effects to argue that conditionalization presents no special problem for Everettian quantum mechanics, and to defend the ‘halfer’ answer to the puzzle of Sleeping Beauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about Sleeping Beauty. This result is doubly good news for Everettians: they can endorse Bayesian confirmation theory without qualification, but they are not thereby compelled to adopt the (...) unpopular ‘halfer’ answer in Sleeping Beauty. These considerations suggest that objective chance is playing an important and under-appreciated role in Sleeping Beauty. (shrink)

I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis's Principal Principle. The problem, put roughly, is that in scenarios like Elga's `Sleeping Beauty' case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy.

I defend the suggestion that the rational probability in the Sleeping Beauty paradox is one third. The reasoning in its favour is familiar: for every heads-waking, there are two tails-wakings. To complete the defense, I rebut the reasoning which purports to justify the competing suggestion – that the correct probability is half – by undermining its premise, that no new information has been received.

I defend the suggestion that the rational probability in the Sleeping Beauty paradox is one third. The reasoning in its favour is familiar: for every heads-waking, there are two tails-wakings. To complete the defense, I rebut the reasoning which purports to justify the competing suggestion – that the correct probability is half – by undermining its premise, that no new information has been received.

The Sleeping Beauty Problem attracts so much attention because it connects to a wide variety of unresolved issues in formal epistemology, decision theory, and the philosophy of science. The problem raises unanswered questions concerning relative frequencies, objective chances, the relation between self-locating and non-self-locating information, the relation between self-location and updating, Dutch Books, accuracy arguments, memory loss, indifference principles, the existence of multiple universes, and many-worlds interpretations of quantum mechanics. After stating the problem, this article surveys its connections to all (...) of these areas. (shrink)

I begin by discussing a conundrum that arises when Bayesian models attempt to assess the relevance of one claim to another. I then explain how my formal modeling framework manages this conundrum. Finally, I apply my modeling methodology to respond to Namjoong Kim’s objection to my framework.

“Double-halfers” think that throughout the Sleeping Beauty Problem, Beauty should keep her credence that a fair coin flip came up heads equal to 1/2. I introduce a new wrinkle to the problem that shows even double-halfers can't keep Beauty's credences equal to the objective chances for all coin-flip propositions. This leaves no way to deny that self-locating information generates an unexpected kind of inadmissible evidence.

The traditional solutions to the Sleeping Beauty problem say that Beauty should have either a sharp 1/3 or sharp 1/2 credence that the coin flip was heads when she wakes. But Beauty’s evidence is incomplete so that it doesn’t warrant a precise credence, I claim. Instead, Beauty ought to have a properly imprecise credence when she wakes. In particular, her representor ought to assign \(R(H\!eads)=[0,1/2]\) . I show, perhaps surprisingly, that this solution can account for the many of the intuitions (...) that motivate the traditional solutions. I also offer a new objection to Elga’s restricted version of the principle of indifference, which an opponent may try to use to collapse the imprecision. (shrink)

The Sleeping Beauty puzzle has dramatized the divisive question of how de se beliefs should be integrated into formal theories of rational belief change. In this paper, I look ahead to a related question: how should de se beliefs be integrated into formal theories of rational choice? I argue that standard decision theoretic frameworks fail in special cases of de se uncertainty, like Sleeping Beauty. The nature of the failure reveals that sometimes rational choices are determined independently of one’s credences (...) in the kinds of ‘narrow’ de se propositions that Sleepy Beauty has set in relief. Consequently, in addition to pinpointing a failure of standard decision theoretic frameworks, this result casts doubt on a large class of strategies for determining principles for the rationally updating de se beliefs in cases like Sleeping Beauty, and also calls into question the importance of making such a determination at all. (shrink)

Indexical beliefs pose a special problem for standard theories of Bayesian updating. Sometimes we are uncertain about our location in time and space. How are we to update our beliefs in situations like these? In a stepwise fashion, I develop a constraint on the dynamics of indexical belief. As an application, the suggested constraint is brought to bear on the Sleeping Beauty problem.

The puzzle of the absentminded driver combines an unstable decision problem with a version of the Sleeping Beauty problem. Its analysis depends on the choice between “halfing” and “thirding” as well as that between “evidential” and “causal” decision theory. I show that all four combinations lead to interestingly different solutions, and draw some general lessons about the formulation of causal decision theory, the interpretation of mixed strategies and the connection between rational credence and objective chance.

When an agent undergoes fission, how should the beliefs of the fission results relate to the pre-fission beliefs? This question is important for the Everett interpretation of quantum mechanics, but it is of independent philosophical interest. Among other things, fission scenarios demonstrate that ‘self-locating’ information can affect the probability of uncentred propositions even if an agent has no essentially self-locating uncertainty. I present a general update rule for centred beliefs that gives sensible verdicts in cases of fission, without relying on (...) controversial metaphysical or linguistic assumptions. The rule is supported by the same considerations that support standard conditioning in the traditional framework of uncentred propositions. (shrink)

Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...) in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma. (shrink)

Terence Horgan defends the thirder position on the Sleeping Beauty problem, claiming that Beauty can, upon awakening during the experiment, engage in “synchronic Bayesian updating” on her knowledge that she is awake now in order to justify a 1/3 credence in heads. In a previous paper, I objected that epistemic probabilities are equivalent to rational degrees of belief given a possible epistemic situation and so the probability of Beauty’s indexical knowledge that she is awake now is necessarily 1, precluding such (...) updating. In response, Horgan maintains that the probability claims in his argument are to be taken, not as claims about possible rational degrees of belief, but rather as claims about “quantitative degrees of evidential support.” This paper argues that the most plausible account of quantitative degree of support, when conjoined with any of the three major accounts of indexical thought in such a way as to plausibly constrain rational credence, contradicts essential elements of Horgan’s argument. (shrink)

With the notable exception of David Lewis, most of those writing on the Sleeping Beauty problem have argued that 1/3 is the correct answer. Terence Horgan has provided the clearest account of why, contrary to Lewis, Beauty has evidence against the proposition that the coin comes up heads when she awakens on Monday. In this paper, I argue that Horgan’s proposal fails because it neglects important facts about epistemic probability.

“Double-halfers” think that throughout the Sleeping Beauty Scenario, Beauty ought to maintain a credence of 1/2 in the proposition that the fair coin toss governing the experimental protocol comes up heads. Titelbaum (2012) introduces a novel variation on the standard scenario, one involving an additional coin toss, and claims that the double-halfer is committed to the absurd and embarrassing result that Beauty’s credence in an indexical proposition concerning the outcome of a future fair coin toss is not 1/2. I argue (...) that there is no reason to regard the credence required by the double-halfer as any less acceptable than the one deemed required by Titelbaum. (shrink)

Horgan and Mahtani (Erkenntnis 78: 333–351, 2013) present a new argument for the 1/3 answer to the Sleeping Beauty problem resting on a principle for updating probabilities which they call “generalized conditionalization.” They allege that this new argument is immune to two attacks which have been recently leveled at other arguments for thirdism. I argue that their new argument rests on a probability distribution which is (a) no more justified than an alternative distribution favoring a different answer to the problem, (...) and (b) ultimately unjustified. I go on to show that generalized conditionalization cannot be applied in the manner suggested, given the cogency of the aforementioned attacks on thirder arguments. Hence, the new argument fails to advance the case for the 1/3 answer. (shrink)

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. (shrink)

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 (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

Since the publication of Elga's seminal paper in 2000, the Sleeping Beauty paradox has been the source of much discussion, particularly in this journal. Over the past few decades the Everettian interpretation of quantum mechanics 1 has also been much debated. There is an interesting connection between the way these two topics raise issues about subjective probability assignments.This connection is often alluded to, but as far as we know Peter J. Lewis's ‘Quantum Sleeping Beauty’ is the first attempt to examine (...) it explicitly. Lewis claims that the two debates are not independent: to be specific, he argues that accepting the Everettian interpretation of quantum mechanics requires you to be a ‘halfer’ about Sleeping Beauty, in opposition to the more widely accepted ‘thirder’ solution.This paper will argue that Lewis is wrong. Everettians do not have to be halfers. It is perfectly cogent to be both an Everettian and a thirder. (shrink)

Adam Elga takes the Sleeping Beauty example to provide a counter-example to Reflection, since on Sunday Beauty assigns probability 1/2 to H, and she is certain that on Monday she will assign probability 1/3. I will show that there is a natural way for Bas van Fraassen to defend Reflection in the case of Sleeping Beauty, building on van Fraassen’s treatment of forgetting. This will allow me to identify a lacuna in Elga’s argument for 1/3. I will then argue, however, (...) that not all is well with Reflection: there is a problem with van Fraassen’s treatment of forgetting. Ultimately I will agree with Elga’s 1/3 answer. David Lewis maintains that the answer is 1/2; I will argue that cases of forgetting can be used to show that the premiss of Lewis’s argument for 1/2 is false. (shrink)

The moral commonly drawn from Zhuangzi’s butterfly dream is that there is no distinction between the subjectivity of the dreamer and the awake. It is, however, tenuous to incorporate this insight into an overall view of Zhuangzi, whether as a perspectival relativist, a mystic, or an anti-rationalist, just to name the more popular positions. The parable, despite its brevity and clarity, is difficult because the assertion about metaphysical distinction in the last two lines does not cohere with the preceding text (...) about knowledge. To cope with this problem, there are recent interpretations that advocate textual revision or adumbrate a non-skeptical Zhuangzi. In this article, I shall evaluate these strategies and explain the discrepancy in understanding the butterfly dream. Besides employing the concept of self-locating belief to account for the paradox of waking and not-knowing, I shall also argue for an epistemic grounding of the metaphysical distinction. (shrink)

The Sleeping Beauty problem has attracted considerable attention in the literature as a paradigmatic example of how self-locating uncertainty creates problems for the Bayesian principles of Conditionalization and Reflection. Furthermore, it is also thought to raise serious issues for diachronic Dutch Book arguments. I show that, contrary to what is commonly accepted, it is possible to represent the Sleeping Beauty problem within a standard Bayesian framework. Once the problem is correctly represented, the ‘thirder’ solution satisfies standard rationality principles, vindicating why (...) it is not vulnerable to diachronic Dutch Book arguments. Moreover, the diachronic Dutch Books against the ‘halfer’ solutions fail to undermine the standard arguments for Conditionalization. The main upshot that emerges from my discussion is that the disagreement between different solutions does not challenge the applicability of Bayesian reasoning to centered settings, nor the commitment to Conditionalization, but is instead an instance of the familiar problem of choosing the priors. (shrink)

I argue that the theory of chance proposed by David Lewis has three problems: (i) it is time asymmetric in a manner incompatible with some of the chance theories of physics, (ii) it is incompatible with statistical mechanical chances, and (iii) the content of Lewis's Principal Principle depends on how admissibility is cashed out, but there is no agreement as to what admissible evidence should be. I proposes two modifications of Lewis's theory which resolve these difficulties. I conclude by tentatively (...) proposing a third modification of Lewis's theory, one which explains many of the common features shared by the chance theories of physics. (shrink)

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 (...) account also leads to counterintuitive consequences, but they’re not as bad as those of Elga’s account, and no worse than those of Lewis’ account. (shrink)

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.

Hintikka and Sandu’s independence-friendly logic is a conservative extension of first-order logic that allows one to consider semantic games with imperfect information. In the present article, we first show how several variants of the Monty Hall problem can be modeled as semantic games for IF sentences. In the process, we extend IF logic to include semantic games with chance moves and dub this extension stochastic IF logic. Finally, we use stochastic IF logic to analyze the Sleeping Beauty problem, leading to (...) the conclusion that the thirders are correct while identifying the main error in the halfers’ argument. (shrink)

The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the problem (...) I address in this article. I suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well defined; such is the main contribution of this article. 1The Sleeping Beauty Game2Groisman’s and Peter Lewis’s Approaches3Discussing Beauty’s Credences4The Principle of Equivalence's Failure5Making Sense of the Principle of Equivalence's Failure6Elga’s and Lewis’s Approaches7ConclusionAppendix. (shrink)

The Sleeping Beauty paradox in epistemology and the many-worlds interpretation of quantum mechanics both raise problems concerning subjective probability assignments. Furthermore, there are striking parallels between the two cases; in both cases personal experience has a branching structure, and in both cases the agent loses herself among the branches. However, the treatment of probability is very different in the two cases, for no good reason that I can see. Suppose, then, that we adopt the same treatment of probability in each (...) case. Then the dominant ‘thirder’ solution to the Sleeping Beauty paradox becomes incompatible with the tenability of the many-worlds interpretation. (shrink)

All parties to the Sleeping Beauty debate agree that it shows that some cherished principle of rationality has to go. Thirders think that it is Conditionalization and Reflection that must be given up or modified; halfers think that it is the Principal Principle. I offer an analysis of the Sleeping Beauty puzzle that allows us to retain all three principles. In brief, I argue that Sleeping Beauty’s credence in the uncentered proposition that the coin came up heads should be 1/2, (...) but her credence in the centered proposition that the coin came up heads and it is Monday should be 1/3. I trace the source of the earlier mistakes to an unquestioned assumption in the debate, namely that an uncentered proposition is just a special kind of centered proposition. I argue that the falsity of this assumption is the real lesson of the Sleeping Beauty case. (shrink)

I argue that the Doomsday argument fails because it fails to take into account the lesson of the Sleeping Beauty puzzle.

I argue that a recent variation on the Sleeping Beauty case due to Titelbaum [2012a] puts significant pressure on Lewis's theory of doxastic content—the theory of content that Titelbaum and others presuppose. In particular, that theory cannot make sense of the rational constraints on credences imposed by the Principal Principle, as ordinarily understood. I then argue more generally that any theory on which contents of credences are sets of centered worlds cannot adequately represent all of the rational constraints on credences.

In his “Relevance of Self-locating Belief”, Titelbaum suggests a general theory about how to update one’s degrees of self-locating belief. He applies it to the Sleeping Beauty problem, more specifically, Lewis’s :171–176, 2001) version of that problem. By doing so, he defends the Thirder solution to the puzzle. Unfortunately, if we modify the puzzle very slightly, and if we apply his general updating theory to the thus modified version, we get the Halfer view as a result. In this paper, we (...) will argue that the difference between the two versions of Sleeping Beauty isn’t sufficient for justifying the different verdicts on them. Since this is a counter-intuitive result, we should reject Titelbaum’s theory of de se updating. (shrink)