I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the hyper-entanglement urn experiment. I restate first the Sleeping Beauty problem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the Sleeping Beauty experiment is best modelled with the hyper-entanglement urn. I draw then the consequences of considering that some balls in the hyper-entanglement urn have ontologically different properties from normal (...) ones. In this context, drawing a red ball (a Monday-waking) leads to two different situations that are assigned each a different probability, depending on whether one considers “balls-as-colour” or “balls-as-object”. This leads to a two-sided account of the Sleeping Beauty problem. (shrink)

The Sleeping Beauty problem—first presented by A. Elga in a philosophical context—has captured much attention. The problem, we contend, is more aptly regarded as a paradox: apparently, there are cases where one ought to change one’s credence in an event’s taking place even though one gains no new information or evidence, or alternatively, one ought to have a credence other than 1/2 in the outcome of a future coin toss even though one knows that the coin is (...) fair. In this paper we argue for two claims. First, that Sleeping Beauty does gain potentially new relevant information upon waking up on Monday. Second, his credence shift is warranted provided it accords with a calculation that is a result of conditionalization on the relevant information: “this day is an experiment waking day” (a day within the experiment on which one is woken up). Since Sleeping Beauty knows what days d could refer to, he can calculate the probability that the referred to waking day is a Monday or a Tuesday providing an adequate resolution of the paradox. (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)

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, 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 categories. 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 is involved. My solution is radically different and does not fall into either of these categories. 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 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)

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)

In this paper I defend the thirder solution to the sleeping beauty problem by considering the credence Beauty ought to have, upon first awakening, that it is Monday. This leads to problems for the double-halfer and halfer but not for the thirder. In the three cases the credences Beauty ought to have, upon first awakening, that it is Monday are 1, 3/4, and 2/3, respectively. The first value is implausible given that Tuesday awakenings are possible. The (...) second is implausible because Beauty's credence in the day of the week is linked to her credence in the result of the coin toss such that evidence to favor Monday over Tuesday is evidence that should affect her credence in the result of the coin toss. This is contrary to the halfers' claim that, upon first awakening, Beauty has no such evidence. However, the credence of 2/3 assigned by the thirder can be independently defended in a way that mirrors the thirders defense of assigning a credence of 1/3 to Heads. Moreover, recognizing the probabilistic connection between Beauty's credences in the days of the week and the results of the coin toss indicates the nature of Beauty's inadmissible information. Beauty's loss of information regarding the day is relevant to the credence she should assign to Heads. (shrink)

We present a new argument for the claim that in the Sleeping Beauty problem, the probability that the coin comes up heads is 1/3. Our argument depends on a principle for the updating of probabilities that we call ‘generalized conditionalization’, and on a species of generalized conditionalization we call ‘synchronic conditionalization on old information’. We set forth a rationale for the legitimacy of generalized conditionalization, and we explain why our new argument for thirdism is immune to two attacks (...) that Pust (Synthese 160:97–101, 2008) has leveled at other arguments for thirdism. (shrink)

In “Generalized Conditionalization and the Sleeping Beauty Problem,” Anna Mahtani and I offer a new argument for thirdism that relies on what we call “generalized conditionalization.” Generalized conditionalization goes beyond conventional conditionalization in two respects: first, by sometimes deploying a space of synchronic, essentially temporal, candidate-possibilities that are not “prior” possibilities; and second, by allowing for the use of preliminary probabilities that arise by first bracketing, and then conditionalizing upon, “old evidence.” In “Beauty and Conditionalization: Reply to (...) Horgan and Mahtani,” Joel Pust replies to the Horgan/Mahtani argument, raising several objections. In my view his objections do not undermine the argument, but they do reveal a need to provide several further elaborations of it—elaborations that I think are independently plausible. In this paper I will address his objections, by providing the elaborations that I think they prompt. (shrink)

This article is an attempt to use the insights of objective probability theory to solve the Sleeping Beauty problem. The approach is to develop a partial theory of direct inference and then apply that partial theory to the problem. One of the crucial components of the partial theory is the thesis that expected indefinite probabilities provide a reliable basis for direct inference. The article relies heavily on recent work by Paul D. Thorn to defend that thesis. The article’s (...) primary conclusion is that Beauty can by way of a justifiable direct inference from a statement of expected indefinite probability reach the conclusion that the epistemic probability that the relevant coin toss lands heads is 1/3. The article also provides an account of why the self-locating information that Beauty acquires on Monday is evidentially relevant to the question of whether the coin toss lands heads or tails. (shrink)

In “Generalized Conditionalization and the Sleeping Beauty Problem,” Anna Mahtani and I offer a new argument for thirdism that relies on what we call “generalized conditionalization.” Generalized conditionalization goes beyond conventional conditionalization in two respects: first, by sometimes deploying a space of synchronic, essentially temporal, candidate-possibilities that are not “prior” possibilities; and second, by allowing for the use of preliminary probabilities that arise by first bracketing, and then conditionalizing upon, “old evidence.” In “Beauty and Conditionalization: Reply to (...) Horgan and Mahtani,” Joel Pust replies to the Horgan/mahtani argument, raising several objections. In my view his objections do not undermine the argument, but they do reveal a need to provide several further elaborations of it—elaborations that I think are independently plausible. In this paper I will address his objections, by providing the elaborations that I think they prompt. (shrink)

Next SectionAn attempt to resolve the controversy regarding the solution of the Sleeping Beauty Problem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum Sleeping Beauty Problem. We apply the concept of a measure of existence of a world and reach the solution known as ‘thirder’ solution which differs from Peter Lewis’s ‘halfer’ assertion. We argue that this method provides a simple and powerful tool for analysing rational decision theory problems.

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)

Several philosophical problems are based on an analogy between a real situation and a probabilistic model. Such problems are based on urn analogies. The present dissertation aims to describe and implement a methodology oriented towards the resolution of philosophical problems based on an urn analogy. This methodology is based on the use of the n-universes. To this end, I describe first the n-universes in a detailed way. I also discuss the difficulties of the theory of n-universes related to the demultiplication (...) of the criteria and to the relation one/many between the objects and a given criterion. On the one hand, I present an application of the framework of n-universes to the Doomsday argument and to the problems recently appeared in the literature in keeping with the Doomsday argument. My concern is also with showing how the application of the framework of n-universes to several problems and thought experiments related to the Doomsday argument helps clarifying the problem data and making disappear the associated ambiguity. I present then an analysis of the following problems related to the Doomsday argument: the two urn case, God's Coin Toss, the Sleeping Beauty Problem, the Presumptuous Philosopher, Lazy Adam, and the Shooting-Room Paradox. I present lastly a solution to the Doomsday argument, based on a third route, by contrast to two types of solutions classically described. On the other hand, I present an application of the framework of n-universes to Goodman's paradox. I replace first Goodman's statement in the framework of n-universes. I propose then a solution to the paradox, based on a distinction between two different modelizations of Goodman's statement in two structurally different n-universes. (shrink)

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)

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. Sample spaces for all three problems are presented. The conclusion is that subjectivity plays no irreducible role in solving the Sleeping Beauty problem and that no reference to centered worlds is required to provide the answer. (shrink)

A group of philosophers led by the late John Pollock has applied a method of reasoning about probability, known as direct inference and governed by a constraint known as Reichenbach's principle, to argue in support of ‘thirdism’ concerning the Sleeping Beauty Problem. A subsequent debate has ensued about whether their argument constitutes a legitimate application of direct inference. Here I defend the argument against two extant objections charging illegitimacy. One objection can be overcome via a natural and plausible (...) definition, given here, of the binary relation ‘logically stronger than’ between two properties that can obtain even when the respective properties differ from one another in ‘arity’; given this definition, the Pollock group's argument conforms to Reichenbach's principle. Another objection prompts a certain refinement of Reichenbach's principle that is independently well-motivated. My defense of the Pollock group's argument has epistemological import beyond the Sleeping Beauty problem, because it both widens and sharpens the applicability of direct inference as a method for inferring single-case epistemic probabilities on the basis of general information of a probabilistic or statistical nature. (shrink)

I maintain, in defending “thirdism,” that Sleeping Beauty should do Bayesian updating after assigning the “preliminary probability” 1/4 to the statement S: “Today is Tuesday and the coin flip is heads.” (This preliminary probability obtains relative to a specific proper subset I of her available information.) Pust objects that her preliminary probability for S is really zero, because she could not be in an epistemic situation in which S is true. I reply that the impossibility of being in (...) such an epistemic situation is irrelevant, because relative to I, statement S nonetheless has degree of evidential support 1/4. (shrink)

Currently, it appears that the most widely accepted solution to the Sleeping Beauty problem is the one-third solution. Another widely held view is that an agent’s credences should be countably additive. In what follows, I will argue that these two views are incompatible, since the principles that underlie the one-third solution are inconsistent with the principle of Countable Additivity (hereafter, CA). I will then argue that this incompatibility is a serious problems for thirders, since it undermines one of (...) the central arguments for their position. (shrink)

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.

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.

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)

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)

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.

Analyses of the Sleeping Beauty Problem are polarised between those advocating the “1/2 view” (“halfers”) and those endorsing the “1/3 view” (“thirders”). The disagreement concerns the evidential relevance of self-locating information. Unlike halfers, thirders regard self-locating information as evidentially relevant in the Sleeping Beauty Problem. In the present study, we systematically manipulate the kind of information available in different formulations of the Sleeping Beauty Problem. Our findings indicate that patterns of judgment on different formulations (...) of the Sleeping Beauty Problem do not fit either the “1/2 view” or the “1/3 view.” Human reasoners tend to acknowledge self-locating evidence as relevant, but discount its weight significantly. Accordingly, self-locating information may trigger more cautious judgments of confirmation than familiar kinds of statistical evidence. We also discuss how these results can advance the debate by providing a more nuanced and empirically grounded account or explication of the evidential impact of self-locating information. (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)

I argue against the halfer response to the Sleeping Beauty case by presenting a new problem for halfers. When the original Sleeping Beauty case is generalized, it follows from the halfer’s key premise that Beauty must update her credence in a fair coin’s landing heads in such a way that it becomes arbitrarily close to certainty. This result is clearly absurd. I go on to argue that the halfer’s key premise must be rejected on pain (...) of absurdity, leaving the halfer response to the original Sleeping Beauty case unsupported. I consider two ways that halfers might avoid the absurdity without giving up their key premise. Neither way succeeds. My argument lends support to the thirder response, and, in particular, to the idea that agents may be rationally compelled to update their beliefs despite not having learned any new evidence. (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)

Hitchcock advances a diachronic Dutch Book argument (DDB) for a 1/3 answer to the Sleeping Beauty problem. Bradley and Leitgeb argue that Hitchcock’s DDB argument fails. We demonstrate the following: (a) Bradley and Leitgeb’s criticism of Hitchcock is unconvincing; (b) nonetheless, there are serious reasons to worry about the success of Hitchcock’s argument; (c) however, it is possible to construct a new DDB for 1/3 about which such worries cannot be raised.

The Sleeping Beauty problem is test stone for theories about self-locating belief, i.e. theories about how we should reasons when data or theories contain indexical information. Opinion on this problem is split between two camps, those who defend the "1/2 view" and those who advocate the "1/3 view". I argue that both these positions are mistaken. Instead, I propose a new "hybrid" model, which avoids the faults of the standard views while retaining their attractive properties. This model _appears_ (...) to violate Bayesian conditionalization, but I argue that this is not the case. By paying close attention to the details of conditionalization in contexts where indexical information is relevant, we discover that the hybrid model is in fact consistent with Bayesian kinematics. If the proposed model is correct, there are important lessons for the study of self-location, observation selection theory, and anthropic reasoning. (shrink)

In the Sleeping Beauty problem, Beauty is woken once if a coin lands heads or twice if the coin lands tails but promptly forgets each waking on returning to sleep. Philosophers have divided over whether her waking credence in heads should be a half or a third. Beauty has centered beliefs about her world and about her location in that world. When given new information about her location she should update her worldly beliefs before updating her (...) locative beliefs. When she conditionalizes in this way, her credence in heads is a half before and after being told it is Monday. In applications of Dutch Book arguments to the Sleeping Beauty problem, the probability of a particular outcome has often been confounded with consequences of that outcome. Heads and tails are equally likely but twice as much is at stake if the coin falls tails because Beauty is fated to make the same choice twice. As a consequence, the possibility of tails should be given twice the weight of the possibility of heads when deciding whether to bet on heads even though heads and tails are equally likely. (shrink)

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 problem has spawned a debate between “Thirders” and “Halfers” who draw conflicting conclusions about Sleeping Beauty’s credence that a coin lands Heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the Experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used (...) for self-locating beliefs or centered propositions. We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the Experiment. (shrink)

About a decade ago, Adam Elga introduced philosophers to an intriguing puzzle. In it, Sleeping Beauty, a perfectly rational agent, undergoes an experiment in which she becomes ignorant of what time it is. This situation is puzzling for two reasons: First, because there are two equally plausible views about how she will change her degree of belief given her situation and, second, because the traditional rules for updating degrees of belief don't seem to apply to this case. In (...) this dissertation, my goals are to settle the debate concerning this puzzle and to offer a new rule for updating some types of degrees of belief. Regarding the puzzle, I will defend a view called "the Lesser view," a view largely favorable to the Thirders' position in the traditional debate on the puzzle. Regarding the general rule for updating, I will present and defend a rule called "Shifted Jeffrey Conditionalization." My discussions of the above view and rule will complement each other: On the one hand, I defend the Lesser view by making use of Shifted Jeffrey Conditionalization. On the other hand, I test Shifted Jeffrey Conditionalization by applying it to various credal transitions in the Sleeping Beauty problem and revise that rule in accordance with the results of the test application. In the end, I will present and defend an updating rule called "General Shifted Jeffrey Conditionalization," which I suspect is the general rule for updating one's degrees of belief in so-called tensed propositions. (shrink)

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used (...) for self-locating beliefs or centered propositions. We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment. (shrink)

One argument for the thirder position on the Sleeping Beauty problem rests on direct inference from objective probabilities. In this paper, I consider a particularly clear version of this argument by John Pollock and his colleagues (The Oscar Seminar 2008). I argue that such a direct inference is defeated by the fact that Beauty has an equally good reason to conclude on the basis of direct inference that the probability of heads is 1/2. Hence, neither thirders nor (...) halfers can find direct support in an appeal to objective probabilities. (shrink)

Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to (...) make it easier to see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful. (shrink)

Elga's presentation of The Sleeping Beauty Problem is often misread, with analyses that impute extra premises and derive false answers to the problem as Elga presented it. Here it is shown that hewing to the text requires that the Sleeping Beauty's degree of belief in a coin flip upon her first awakening is 1/2.

Since Elga published his “Self-locating belief and the Sleeping Beauty problem,” there has been an intense debate about which credence between 1/2 and 1/3 Beauty should assign to (H) the coin’s landing heads, when she is awakened on Monday. The Halfers claim that she ought to assign 1/2 to H at that moment. The Thirders argue that she ought to assign 1/3 to H then. Meanwhile, Pettigrew defended a new chance-credence coordination principle, called the “Evidential Temporal Principle” (...) (ETP), in a recent edition of his book. In this paper, I provide a novel argument against the Halfer view and a partial defense of the Thirder view, respectively based on ETP. In addition, I generalize ETP to what I call the “Evidential Centered Principle,” which links one’s credences in centered propositions with their objective chances. (shrink)

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 same information, but also at decision points where she has different but “symmetric” information. (shrink)

A new philosophical analysis is provided of the notorious Sleeping Beauty Problem. It is argued that the correct solution is one-third, but not in the way previous philosophers have typically meant this. A modified version of the Problem demonstrates that neither self-locating information nor amnesia is relevant to the core Problem, which is simply to evaluate the conditional chance of heads given an undated Monday-or-Tuesday awakening. Previous commentators have failed to appreciate the significance of the information that (...) class='Hi'>Beauty gains upon waking, and which is relevant to the conditional chance of heads: de re acquaintance with the awakening itself and the non-locating knowledge that it is an experimental awakening. David Lewis and company are committed to several unjustifiable and unacceptable probability assessments. Previous commentators have in effect confused the information that Beauty undergoes this particular experimental awakening for the information that she undergoes some experimental awakening or other. Lewis in particular thereby illegitimately tips the scales both in favor of heads and in favor of Monday. The Sleeping Beauty Problem is equivalent to a ball-in-urn word problem in elementary probability theory. (shrink)

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 argue that van Fraassen's Judy Benjamin Problem and Elga's Sleeping Beauty Problem have the same structure.

Concerning the notorious Sleeping Beauty problem, philosophers have debated whether 1/2 or 1/3 is rational as Beauty’s credence in the coin’s landing heads. According to Kierland and Monton, the answer depends on whether her goal is to minimize average or total inaccuracy because, while the expected average inaccuracy of Halfing is smaller than that of Thirding, the expected total inaccuracy of Thirding is lower than that of Halfing. In this paper, I argue that Halfing is average accuracy (...) dominated but Thirding is not; and that each of the standard forms of Halfing and Thirding regards a different credence assignment as better than itself in terms of total accuracy. Therefore, Halfing is irrational, and Thirding is likely to be rational, for the goal of minimizing average inaccuracy; but both Halfing and Thirding, at least in their standard forms, are irrational for the goal of minimizing total inaccuracy. (shrink)

The probability puzzle known as "Sleeping Beauty" raises interesting and difficult ques tions about the nature of evidence. It appears that the puzzle itself has already been solved, for there is a near consensus in the relevant philosophical literature that 1/3 is the correct answer.' Be that as it may, no new argument for that result is offered here. Instead, an at tempt is made to clarify the nature of certain problems that an answer of 1/3 raises for (...) theories of evidential reasoning. Various approaches to solving the most important of these problems are then considered and rejected. (shrink)

In two excellent recent papers, Jacob Ross has argued that the standard arguments for the ‘thirder’ answer to the Sleeping Beauty puzzle lead to violations of countable additivity. The problem is that most arguments for that answer generalise in awkward ways when he looks at the whole class of what he calls Sleeping Beauty problems. In this note I develop a new argument for the thirder answer that doesn't generalise in this way.

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)

It is argued that Lewis's approach to Elga's Sleeping Beaty problem is untenable and, therefore, the universality of the betting approach to probability has not been breached.

Writing collectively as the Oscar Seminar in 2008, John Pollock and several colleagues advance an objectivist argument for a 1/3 solution to the Sleeping Beauty problem. In 2011, Joel Pust raises a serious objection to their argument to which Paul D. Thorn, a member of the Oscar Seminar, offers a subtle reply. I argue that the Oscar Seminar s argument for 1/3 is unsound. I do not, however, defend Pust’s objection. Rather I develop a new objection, one that (...) is not threatened by the considerations to which Thorn appeals in his reply to Pust. (shrink)