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Summary The Sleeping Beauty Problem concerns a perfectly rational agent who is put to sleep for two days. Depending on the toss of a fair coin, she is awakened once (Heads) or twice (Tails). However, after each waking, she is put back to sleep with a drug that erases her memories of the waking. The question which constitutes the problem is this: "When she is first awakened, what degree of belief will she have that the outcome of the coin toss is Heads?" The problem has proven exceedingly difficult to solve and attracts attention both for its intrinsic interest and because of the many connections between the correct answer to the problem and a wide variety of other philosophical topics including: the status of chance-credence and frequency-credence principles, the evidential relevance of essentially indexical information, the acceptability of conditionalization principles, the proper understanding of Dutch Book arguments, the status of indifference principles, and the proper interpretation of quantum mechanics.
Key works The problem was first raised in the philosophical literature by Elga 2000, who defended the 1/3 answer. Lewis 2001 responded, defending the 1/2 answer.  Important early papers defending 1/3 include Arntzenius 2003, Dorr 2002, Horgan 2004, and Hitchcock 2004. Important early papers defending 1/2 include White 2006 and Meacham 2008. The literature has since exploded in size.
Introductions Elga 2000Titelbaum 2013
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  1. Frank Arntzenius (2003). Some Problems for Conditionalization and Reflection. Journal of Philosophy 100 (7):356-370.
  2. Frank Arntzenius (2002). Reflections on Sleeping Beauty. Analysis 62 (1):53–62.
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  3. Jean Baratgin & Bernard Walliser (2010). Sleeping Beauty and the Absent-Minded Driver. Theory and Decision 69 (3):489-496.
    The Sleeping Beauty problem is presented in a formalized framework which summarizes the underlying probability structure. The two rival solutions proposed by Elga (Analysis 60:143–147, 2000) and Lewis (Analysis 61:171–176, 2001) 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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  4. Paul Bartha, How to Put Self-Locating Information in its Place.
    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.
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  5. Nick Bostrom (2007). Sleeping Beauty and Self-Location: A Hybrid Model. Synthese 157 (1):59 - 78.
    The Sleeping Beauty problem is test stone for theories about self- locating belief, i.e. theories about how we should reason 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 (...)
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  6. L. Bovens & J. L. Ferreira (2010). Monty Hall Drives a Wedge Between Judy Benjamin and the Sleeping Beauty: A Reply to Bovens. Analysis 70 (3):473-481.
    Consider van Fraassen's ( 1981) Judy Benjamin (JB) problem. Judy is dropped in an area that is divided vertically in Blue (B) and Red (R) and horizontally in Headquarters (Q) and Second Company (S). These divisions define four quadrants, as in Figure 1 (roman script headings). Judy initially believes that there is an equal chance of being in each quadrant. She is then told by a fully reliable source that if she is in R, then there is a chance of (...)
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  7. Luc Bovens (2010). Judy Benjamin is a Sleeping Beauty. Analysis 70 (1):23-26.
    (No abstract is available for this citation).
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  8. Luc Bovens & Wlodek Rabinowicz (2010). The Puzzle of the Hats. Synthese 172 (1):57 - 78.
    The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and (...)
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  9. D. J. Bradley (2012). Four Problems About Self-Locating Belief. Philosophical Review 121 (2):149-177.
    This article defends the Doomsday Argument, the Halfer Position in Sleeping Beauty, the Fine-Tuning Argument, and the applicability of Bayesian confirmation theory to the Everett interpretation of quantum mechanics. It will argue that all four problems have the same structure, and it gives a unified treatment that uses simple models of the cases and no controversial assumptions about confirmation or self-locating evidence. The article will argue that the troublesome feature of all these cases is not self-location but selection effects.
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  10. Darren Bradley (forthcoming). Everettian Confirmation and Sleeping Beauty: Reply to Wilson. British Journal for the Philosophy of Science:axt042.
    In Bradley ([2011b]), I offered an analysis of Sleeping Beauty and the Everettian interpretation of quantum mechanics (EQM). I argued that one can avoid a kind of easy confirmation of EQM by paying attention to observation selection effects, that halfers are right about Sleeping Beauty, and that thirders cannot avoid easy confirmation for the truth of EQM. Wilson ([forthcoming]) agrees with my analysis of observation selection effects in EQM, but goes on to, first, defend Elga’s ([2000]) thirder argument on Sleeping (...)
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  11. Darren Bradley (2011). Confirmation in a Branching World: The Everett Interpretation and Sleeping Beauty. British Journal for the Philosophy of Science 62 (2):323-342.
    Sometimes we learn what the world is like, and sometimes we learn where in the world we are. Are there any interesting differences between the two kinds of cases? The main aim of this article is to argue that learning where we are in the world brings into view the same kind of observation selection effects that operate when sampling from a population. I will first explain what observation selection effects are ( Section 1 ) and how they are relevant (...)
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  12. Darren Bradley (2011). Self-Location is No Problem for Conditionalization. Synthese 182 (3):393-411.
    How do temporal and eternal beliefs interact? I argue that acquiring a temporal belief should have no effect on eternal beliefs for an important range of cases. Thus, I oppose the popular view that new norms of belief change must be introduced for cases where the only change is the passing of time. I defend this position from the purported counter-examples of the Prisoner and Sleeping Beauty. I distinguish two importantly different ways in which temporal beliefs can be acquired and (...)
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  13. Darren Bradley (2007). Bayesianism And Self-Locating Beliefs. Dissertation, Stanford University
    How should we update our beliefs when we learn new evidence? Bayesian confirmation theory provides a widely accepted and well understood answer – we should conditionalize. But this theory has a problem with self-locating beliefs, beliefs that tell you where you are in the world, as opposed to what the world is like. To see the problem, consider your current belief that it is January. You might be absolutely, 100%, sure that it is January. But you will soon believe it (...)
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  14. Darren Bradley (2003). Sleeping Beauty: A Note on Dorr's Argument for 1/3. Analysis 63 (279):266–268.
    Cian Dorr (2002) gives an argument for the 1/3 position in Sleeping Beauty. I argue this is based on a mistake about Sleeping Beauty's epistemic position.
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  15. Darren Bradley & Hannes Leitgeb (2006). When Betting Odds and Credences Come Apart: More Worries for Dutch Book Arguments. Analysis 66 (290):119–127.
    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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  16. Rachael Briggs (2010). Putting a Value on Beauty. in Tamar Szabo Gendler and John Hawthorne (Eds.), Oxford Studies in Epistemology, Volume 3. Oxford University Press:3-34.
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  17. Jessi Cisewski, Joseph B. Kadane, Mark J. Schervish, Teddy Seidenfeld & Rafael Stern, The Rest of Sleeping Beauty.
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  18. Dennis Dieks (2007). Reasoning About the Future: Doom and Beauty. [REVIEW] Synthese 156 (3):427 - 439.
    According to the Doomsday Argument we have to rethink the probabilities we assign to a soon or not so soon extinction of mankind when we realize that we are living now, rather early in the history of mankind. Sleeping Beauty finds herself in a similar predicament: on learning the date of her first awakening, she is asked to re-evaluate the probabilities of her two possible future scenarios. In connection with Doom, I argue that it is wrong to assume that our (...)
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  19. Cian Dorr, A Challenge for Halfers.
    Let me regale you with yet another variant of the story of Sleeping Beauty. In this one, the experiment takes place in a room with a skylight, so that Beauty can see what the weather is like outside as soon as she wakes up. The weather can be in any one of n different states on any given day. Beauty regards each of these states as equiprobable; moreover, she takes there to be no correlation between the weather on Monday and (...)
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  20. Cian Dorr (2002). Sleeping Beauty: In Defence of Elga. Analysis 62 (4):292–296.
    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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  21. Kai Draper (2013). The Evidential Relevance of Self-Locating Information. Philosophical Studies 166 (1):185-202.
    Philosophical interest in the role of self-locating information in the confirmation of hypotheses has intensified in virtue of the Sleeping Beauty problem. If the correct solution to that problem is 1/3, various attractive views on confirmation and probabilistic reasoning appear to be undermined; and some writers have used the problem as a basis for rejecting some of those views. My interest here is in two such views. One of them is the thesis that self-locating information cannot be evidentially relevant to (...)
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  22. Kai Draper (2008). Sleeping Beauty's Evidence. American Philosophical Quarterly 44 (1):61 - 70.
    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 (...)
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  23. Kai Draper & Joel Pust (2008). Diachronic Dutch Books and Sleeping Beauty. Synthese 164 (2):281 - 287.
    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.
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  24. Adam Elga (2004). Defeating Dr. Evil with Self-Locating Belief. Philosophy and Phenomenological Research 69 (2):383–396.
    Dr. Evil learns that a duplicate of Dr. Evil has been created. Upon learning this, how seriously should he take the hypothesis that he himself is that duplicate? I answer: very seriously. I defend a principle of indifference for self-locating belief which entails that after Dr. Evil learns that a duplicate has been created, he ought to have exactly the same degree of belief that he is Dr. Evil as that he is the duplicate. More generally, the principle shows that (...)
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  25. Adam Elga (2000). Self-Locating Belief and the Sleeping Beauty Problem. Analysis 60 (2):143–147.
    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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  26. Ian Evans, Don Fallis, Peter Gross, Terry Horgan, Jenann Ismael, John Pollock, Paul D. Thorn, Jacob N. Caton, Adam Arico, Daniel Sanderman, Orlin Vakerelov, Nathan Ballantyne, Matthew S. Bedke, Brian Fiala & Martin Fricke (2007). An Objectivist Argument for Thirdism. Analysis 68.
    Bayesians take “definite” or “single-case” probabilities to be basic. Definite probabilities attach to closed formulas or propositions. We write them here using small caps: PROB(P) and PROB(P/Q). Most objective probability theories begin instead with “indefinite” or “general” probabilities (sometimes called “statistical probabilities”). Indefinite probabilities attach to open formulas or propositions. We write indefinite probabilities using lower case “prob” and free variables: prob(Bx/Ax). The indefinite probability of an A being a B is not about any particular A, but rather about the (...)
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  27. J. Finkelstein, Sleeping Beauty: Theme and Variations.
    Six variations on the Sleeping beauty theme are presented.
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  28. Paul Franceschi, Sleeping Beauty and the Problem of World Reduction.
    I describe in this paper a solution to the Sleeping Beauty problem. I begin with the consensual emerald case and discuss then Bostrom's Incubator gedanken. I address then the Sleeping Beauty problem. I argue that the root cause of the flaw in the argument for 1/3 is an erroneous assimilation with a repeated experiment. I show that the same type of analysis also applies to Elga's version of the argument for 1/3. Lastly, I show that the core of the Sleeping (...)
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  29. Paul Franceschi, An Ontological Solution to the Sleeping Beauty Problem.
    I describe in this paper an ontological solution to the Sleeping Beauty problem. I begin with describing the 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 Entanglement urn. I draw then the consequences of considering that some balls in the Entanglement urn have ontologically different properties form normal ones. The upshot is that I (...)
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  30. Paul Franceschi, Sleeping Beauty in Flatland.
    I present a solution to the Sleeping Beauty problem. I begin with the consensual emerald case and describe then a set of relevant urn analogies and situations. These latter experiments make it easier to diagnose the flaw in the thirder's line of reasoning. I discuss in detail the root cause of the flaw in the argument for 1/3 which is an erroneous assimilation with a repeated experiment. Lastly, I discuss an informative variant of the original Sleeping Beauty experiment that casts (...)
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  31. Berry Groisman (2008). The End of Sleeping Beauty's Nightmare. British Journal for the Philosophy of Science 59 (3):409-416.
    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, (...)
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  32. Berry Groisman, Na'ama Hallakoun & Lev Vaidman (2013). The Measure of Existence of a Quantum World and the Sleeping Beauty Problem. Analysis 73 (4):695-706.
    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.
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  33. Joseph Halpern (2004). Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous Systems. In Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology. Oxford University Press. 111-142.
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  34. Patrick Hawley (2013). Inertia, Optimism and Beauty. Noûs 47 (1):85-103.
    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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  35. Christopher Hitchcock (2004). Beauty and the Bets. Synthese 139 (3):405 - 420.
    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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  36. Terry Horgan (2008). Synchronic Bayesian Updating and the Sleeping Beauty Problem: Reply to Pust. Synthese 160 (2):155 - 159.
    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 (...)
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  37. Terry Horgan (2007). Synchronic Bayesian Updating and the Generalized Sleeping Beauty Problem. Analysis 67 (293):50–59.
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  38. Terry Horgan (2004). Sleeping Beauty Awakened: New Odds at the Dawn of the New Day. Analysis 64 (1):10–21.
    1. The story of Sleeping Beauty is set forth as follows by Dorr (2002): Sleeping Beauty is a paradigm of rationality. On Sunday she learns for certain that she is to be the subject of an experiment. The experimenters will wake her up on Monday morning, and tell her some time later that it is Monday. When she goes back to sleep, they will toss a fair coin. If the outcome of the toss is Heads, they will do nothing. If (...)
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  39. Terry Horgan & Anna Mahtani (2013). Generalized Conditionalization and the Sleeping Beauty Problem. Erkenntnis 78 (2):333-351.
    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 (...)
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  40. C. S. Jenkins (2005). Sleeping Beauty: A Wake-Up Call. Philosophia Mathematica 13 (2):194-201.
    This note concerns a puzzle about probability which has recently caught the attention of a number of philosophers. According to the current philosophical consensus, the solution to the puzzle reveals that one can acquire new information, sufficient to change one's credences in certain events, just by having a certain experience, even though one knew all along that one would have an experience which felt exactly like this. I argue that the philosophical consensus is mistaken.
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  41. Karl Karlander & Levi Spectre (2010). Sleeping Beauty Meets Monday. Synthese 174 (3):397 - 412.
    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 (...)
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  42. Brian Kierland & Bradley Monton (2005). Minimizing Inaccuracy for Self-Locating Beliefs. Philosophy and Phenomenological Research 70 (2):384-395.
    One's inaccuracy for a proposition is defined as the squared difference between the truth value (1 or 0) of the proposition and the credence (or subjective probability, or degree of belief) assigned to the proposition. One should have the epistemic goal of minimizing the expected inaccuracies of one's credences. We show that the method of minimizing expected inaccuracy can be used to solve certain probability problems involving information loss and self-locating beliefs (where a self-locating belief of a temporal part of (...)
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  43. Namjoong Kim (2009). Sleeping Beauty and Shifted Jeffrey Conditionalization. Synthese 168 (2):295 - 312.
    In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule.
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  44. Namjoong Kim, Sleeping Beauty and De Nunc Updating.
    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, (...)
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  45. Hannes Leitgeb (2010). Sleeping Beauty and Eternal Recurrence. Analysis 70 (2):203-205.
    (No abstract is available for this citation).
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  46. David Lewis (2001). Sleeping Beauty: Reply to Elga. Analysis 61 (3):171–76.
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  47. Peter J. Lewis, Credence for Whom?
    There is an important sense in which an agent’s credences are universal: while they reflect an agent’s own judgments, those judgments apply equally to everyone’s bets. This point, while uncontentious, has been overlooked; people automatically assume that credences concern an agent’s own bets, perhaps just because of the name “subjective” that is typically applied to this account of belief. This oversight has had unfortunate consequences for recent epistemology, in particular concerning the Sleeping Beauty case and its myriad variants.
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  48. Peter J. Lewis (2010). Credence and Self-Location. Synthese 175 (3):369-382.
    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, (...)
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  49. Peter J. Lewis (2009). Reply to Papineau and Durà-Vilà. Analysis 69 (1):86-89.
    I argued that anyone who adopts the Everettian approach to the foundations of quantum mechanics must also accept the (unpopular) ‘halfer’ solution to the Sleeping Beauty puzzle. Papineau and Durà-Vilà have responded with an argument that it is perfectly cogent both to be an Everettian and to accept the (popular) ‘thirder’ solution to Sleeping Beauty. Here I attempt to rebut their argument, and to clarify my original position.
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  50. Peter J. Lewis (2007). Quantum Sleeping Beauty. Analysis 67 (293):59-65.
    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 (...)
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