Next SectionAn attempt to resolve the controversy regarding the solution of the SleepingBeautyProblem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum SleepingBeautyProblem. 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. (shrink)
In his 2007 paper “Quantum SleepingBeauty”, 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 “sleepingbeauty” 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 sleepingbeauty (...) class='Hi'>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)
The SleepingBeautyProblem 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)
In “Generalized Conditionalization and the SleepingBeautyProblem,” 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)
We present a new argument for the claim that in the SleepingBeautyproblem, 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)
Currently, it appears that the most widely accepted solution to the SleepingBeautyproblem 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)
I describe in this paper an ontological solution to the SleepingBeautyproblem. I begin with describing the Entanglement urn experiment. I restate first the SleepingBeautyproblem from a wider perspective than the usual opposition between halfers and thirders. I also argue that the SleepingBeauty 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 endorse the halfer conclusion on the probability of Heads once beauty is awaken and the thirder conclusion on conditional probabilities, and that original conclusions ensue on the probability of waking on Monday. (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.
I describe in this paper a solution to the SleepingBeautyproblem. I begin with the consensual emerald case and discuss then Bostrom's Incubator gedanken. I address then the SleepingBeautyproblem. 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 SleepingBeautyproblem is related to the problem of world reduction. (shrink)
I argue against the halfer response to the SleepingBeauty case by presenting a new problem for halfers. When the original SleepingBeauty 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 SleepingBeauty 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)
I maintain, in defending “thirdism,” that SleepingBeauty 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)
With the notable exception of David Lewis, most of those writing on the SleepingBeautyproblem 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.
Adam Elga takes the SleepingBeauty 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 SleepingBeauty, 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)
Terence Horgan defends the thirder position on the SleepingBeautyproblem, 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)
The SleepingBeautyproblem 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 SleepingBeauty 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.
The SleepingBeautyProblem is a challenging puzzle in probabilistic reasoning, which has attracted enormous attention and still fosters ongoing debate. The problem goes as follows: Suppose that some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin. After each waking, they will put you back to sleep with a drug (...) that makes you forget that waking. When you are first awakened, to what degree should you believe that the outcome of the coin toss is Heads? Theoretically, the two candidate answers are 1/2 and 1/3, the proponents of which are known as halfers and thirders, respectively. The present study examines for the first time the descriptive adequacy of both halfers’ and thirders’ analyses. Our results show that naïve reasoning does not simply fit either. Instead, they suggest that any psychologically adequate analysis of the SleepingBeautyProblem should take account that the impact on probabilistic reasoning of information about one’s spatio-temporal location in the world is systematically discounted. (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 we address in this article. We 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 paper. (shrink)
Hitchcock advances a diachronic Dutch Book argument (DDB) for a 1/3 answer to the SleepingBeautyproblem. 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 traditional solutions to the SleepingBeautyproblem 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)
In the SleepingBeautyproblem, 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 SleepingBeautyproblem, 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)
About a decade ago, Adam Elga introduced philosophers to an intriguing puzzle. In it, SleepingBeauty, 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 SleepingBeautyproblem 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)
In two excellent recent papers, Jacob Ross has argued that the standard arguments for the ‘thirder’ answer to the SleepingBeauty 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 SleepingBeauty problems. In this note I develop a new argument for the thirder answer that doesn't generalise in this way.
In the context of the SleepingBeautyproblem, 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 SleepingBeautyproblem 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)
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 (...) to learning where we are in the world ( Section 2 ). I will show how measurements in the Many Worlds Interpretation of quantum mechanics can be understood as learning where you are in the world via some observation selection effect ( Section 3 ). I will apply a similar argument to the SleepingBeautyProblem ( Section 4 ) and explain what I take the significance of the analogy to be ( Section 5 ). Finally, I will defend the Restricted Principle of Indifference on which some of my arguments depend ( Section 6 ). (shrink)
The SleepingBeautyproblem 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)
Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the SleepingBeautyproblem.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 SleepingBeautyproblem 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)
One argument for the thirder position on the SleepingBeautyproblem 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)
The SleepingBeautyproblem—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 SleepingBeauty 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 SleepingBeauty 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)
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 SleepingBeauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about SleepingBeauty. 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 SleepingBeauty. These considerations suggest that objective chance is playing an important and under-appreciated role in SleepingBeauty. 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 SleepingBeauty Cases11 Conclusion. (shrink)
The SleepingBeauty puzzle provides a nice illustration of the approach to self-locating belief defended by Robert Stalnaker in Our Knowledge of the Internal World (Stalnaker, 2008), as well as a test of the utility of that method. The setup of the SleepingBeauty puzzle is by now fairly familiar. On Sunday SleepingBeauty is told the rules of the game, and a (known to be) fair coin is ﬂipped. On Monday, Sleeping (...) class='Hi'>Beauty is woken, and then put back to sleep. If, and only if, the coin landed tails, she is woken again on Tuesday after having her memory of the Monday awakening erased.1 On Wednesday she is woken again and the game ends. There are a few questions we can ask about Beauty’s attitudes as the game progresses. We’d like to know what her credence that the coin landed heads should be (a) Before she goes to sleep Sunday; (b) When she wakes on Monday; (c) When she wakes on Tuesday; and (d) When she wakes on Wednesday? Standard treatments of the SleepingBeauty puzzle ignore (d), run together (b) and (c) into one (somewhat ill-formed) question, and then divide theorists into ‘halfers’ or ‘thirders’ depending on how they answer it. Following Stalnaker, I’m going to focus on (b) here, though I’ll have a little to say about (c) and (d) as well. I’ll be following orthodoxy in taking 1 2 to be the clear answer to (a), and in taking the correct answers to (b) and (c) to be independent of how the coin lands, though I’ll brieﬂy question that assumption at the end. An answer to these four questions should respect two different kinds of constraints. The answer for day n should make sense ‘statically’. It should be a sensible answer to the question of what Beauty should do given what information she then has. And the answer should make sense ‘dynamically’. It should be a sensible answer to the question of how Beauty should have updated her credences from some earlier day, given rational credences on the earlier day. As has been fairly clear since the discussion of the problem in Elga (2000), SleepingBeauty is puzzling because static and dynamic considerations appear to push in different directions.. (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 SleepingBeautyProblem 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 SleepingBeauty 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 SleepingBeautyProblem are in fact beliefs in two different propositions, i.e., there is no need to explain the change of belief. The SleepingBeautyProblem 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 SleepingBeautyproblem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about SleepingBeauty's credence that a coin lands heads. Our analysis is based on a probability model for what SleepingBeauty 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 SleepingBeauty computes for gambles that she might be offered during the experiment. (shrink)
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 SleepingBeautyproblem, 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 SleepingBeauty 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)
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 SleepingBeauty. I assess Bradley’s arguments and conclude that while he is right about confirmation in Everettian quantum mechanics, he is wrong about SleepingBeauty. 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 SleepingBeauty. These considerations suggest that objective chance is playing an important and under-appreciated role in SleepingBeauty. (shrink)
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 SleepingBeauty (...)problem, leading to the conclusion that the thirders are correct while identifying the main error in the halfers’ argument. (shrink)
Writing collectively as the Oscar Seminar in 2008, John Pollock and several colleagues advance an objectivist argument for a 1/3 solution to the SleepingBeautyproblem. 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)
The SleepingBeautyproblem has spawned a debate between “Thirders” and “Halfers” who draw conflicting conclusions about SleepingBeauty’s credence that a coin lands Heads. Our analysis is based on a probability model for what SleepingBeauty 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 SleepingBeauty computes for gambles that she might be offered during the Experiment. (shrink)
We present a game show that we claim can serve as a proxy for the notorious SleepingBeautyProblem. This problem has divided commentators into two camps, 'halfers' and 'thirders'. In our game show, the potential awakenings of SleepingBeauty, during which she will be asked about the outcome of the coin toss that determined earlier how many times she is awakened and asked, are replaced by potential contestants, deciding whether to choose heads or (...) tails in a bet they will get to place if chosen as contestants on the outcome of the coin toss that determined earlier how many of them are chosen as contestants. This game show bears out the basic intuition of the thirders. Our goal in this paper, however, is not to settle the dispute between halfers and thirders but to draw attention to our game-show proxy itself, which realizes a version of the SleepingBeautyProblem without the ambiguities plaguing the original. In this spirit, we design similar game-show proxies for variations on the SleepingBeautyProblem with stochastic experiments other than a coin toss. We do the same for a variation in which SleepingBeauty must decide upon being awakened whether or not to switch doors in the famous Monty Hall Problem and have the number of awakenings during which she gets to make that decision depend on the door she picked before she was put to sleep. (shrink)
I present a solution to the SleepingBeautyproblem. 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 light on the diagnosis of the fallacy in the argument for 1/3. (shrink)
Recent results confirm that long‐term expression of therapeutic transgenes can be achieved by using a transposon‐based system in primary stem cells and in vivo. Transposable elements are natural DNA transfer vehicles that are capable of efficient genomic insertion. The latest generation, SleepingBeauty transposon‐based hyperactive vector (SB100X), is able to address the basic problem of non‐viral approaches – that is, low efficiency of stable gene transfer. The combination of transposon‐based non‐viral gene transfer with the latest improvements of (...) non‐viral delivery techniques could provide a long‐term therapeutic effect without compromising biosafety. The new challenges of pre‐clinical research will focus on further refinement of the technology in large animal models and improving the safety profile of SB vectors by target‐selected transgene integration into genomic “safe harbors.” The first clinical application of the SB system will help to validate the safety of this approach. (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 SleepingBeautyProblem, showing that when (...) class='Hi'>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)
“Double-halfers” think that throughout the SleepingBeautyProblem, 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.
Philosophical interest in the role of self-locating information in the confirmation of hypotheses has intensified in virtue of the SleepingBeautyproblem. 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 a non-self-locating hypothesis. The other, a basic tenet of Bayesian confirmation theory, is the thesis that an ideally rational agent updates her credence in a non-self-locating hypothesis in response to new information only by conditionalization. I argue that we can disprove these two theses by way of cases that are much less puzzling than SleepingBeauty. I present two such cases in this paper. (shrink)
How should we update de dicto beliefs in the face of de se evidence? The SleepingBeautyproblem divides philosophers into two camps, halfers and thirders. But there is some disagreement among halfers about how their position should generalize to other examples. A full generalization is not always given; one notable exception is the Halfer Rule, under which the agent updates her uncentered beliefs based on only the uncentered part of her evidence. In this brief article, I (...) provide a simple example for which the Halfer Rule prescribes credences that, I argue, cannot be reasonably held by anyone. In particular, these credences constitute an egregious violation of the Reflection Principle. I then discuss the consequences for halfing in general. (shrink)