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

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

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

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

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

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

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

This article proposes revisions to the Laws of Cricket and to the criminal law of England. The Laws of Cricket should be revised so that an umpire may give a batsman out without having to specify precisely how he got out. The criminal law should be revised so that (e.g.) aiding and abetting a murderer is not subsumed under the crime of murder.

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

One can have no prior credence whatsoever (not even zero) in a temporally indexical claim. This fact saves the principle of conditionalization from potential counterexample and undermines the Elga and Arntzenius/Dorr arguments for the thirder position and Lewis' argument for the halfer position on the Sleeping Beauty Problem, thereby supporting the double-halfer position. -/- .

Dozens of articles have addressed the challenge that gambles having undefined expectation pose for decision theory. This paper makes two contributions. The first is incremental: we evolve Colyvan's ``Relative Expected Utility Theory'' into a more viable ``conservative extension of expected utility theory" by formulating and defending emendations to a version of this theory proposed by Colyvan and H\'ajek. The second is comparatively more surprising. We show that, so long as one assigns positive probability to the theory that there is a (...) uniform bound on the utility of possible gambles (and assuming a uniform bound on the amount of utility that can accrue in a fixed amount of time), standard principles of anthropic reasoning (as formulated by Brandon Carter) place lower and upper bounds on the expected values of gambles advertised as having no expectation--even assuming that with positive probability, all gambles advertised as having infinite expected utility are administered faithfully. Should one accept the uniform bound premises, this reasoning thus dissolves (or nearly dissolves, in some cases) several puzzles in infinite decision theory. (shrink)

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

(No abstract is available for this citation).

Thirders sometimes feel compelled to give the same answer – a credence of 1/3 – to the original and the duplicating Sleeping Beauty problem, which leads to some unwanted consequences. I will argue that they do not have to feel compelled to give the same answer, because the original and the duplicating version of the Sleeping Beauty problem are different types of decision problems. If one accepts that it is rationally permissible to give different answers to different types of decision (...) problems, both versions do not require the same solution. (shrink)

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.

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)

Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you've lost track of the time. I provide a principle of chance deference which handles these problem cases. This principle has a surprising consequence for Adam Elga's Sleeping Beauty Puzzle.

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 (...) 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 Sleeping Beauty. I present two such cases in this paper. (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)

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)

I argue that different views in the metaphysics of time make different observational predictions in both classical and relativistic cases. Because different views in the metaphysics of time differ over which facts are merely indexical facts, they make different observational predictions about certain self-locating propositions. I argue for this thesis by distinguishing the three main updating procedures that apply in cases of self-locating uncertainty, and I present a series of cases which cumulatively show that every one of these updating procedures (...) distinguishes eternalism and presentism in both classical and relativistic settings. (shrink)

The epistemology of self-locating belief concerns itself with how rational agents ought to respond to certain kinds of indexical information. I argue that those who endorse the thesis of Time-Slice Rationality ought to endorse a particular view about the epistemology of self-locating belief, according to which ‘essentially indexical’ information is never evidentially relevant to non-indexical matters. I close by offering some independent motivations for endorsing Time-Slice Rationality in the context of the epistemology of self-locating belief.

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 (...) draw some general conclusions about their impact on eternal beliefs. (shrink)

How should we respond to evidence when our evidence indicates that we are rationally impaired? I will defend a novel answer based on the analogy between self-doubt and memory loss. To believe that one is now impaired and previously was not is to believe that one’s epistemic position has deteriorated. Memory loss is also a form of epistemic deterioration. I argue that agents who suffer from epistemic deterioration should return to the priors they had at an earlier time. I develop (...) this argument regarding memory loss then extend it to cases of self-doubt. (shrink)

Alvin Plantinga’s evolutionary argument against naturalism (EAAN) claims that if both naturalism (N) and evolutionary theory (E) are true, then all our beliefs are unreliable (premiss 1). Consequently, given N&E, the belief in N&E is unreliable (premiss 2) and N&E is self-defeating (conclusion). The empirical verification argument against naturalism (EVAAN) is more cautious and improves EAAN by withstanding a rejoinder of the evolutionary naturalist to premiss 1. EVAAN claims that non-abstract beliefs that are not empirically verifiable are unreliable, given N&E (...) (premiss 1a). This anticipates the evolutionary naturalist’s claim that empirical verifications play a crucial role in peer assessments and sexual selection of intelligence, and that, therefore, N&E makes empirically verifiable beliefs often reliable (premiss-1 rejoinder). However, even then it can be argued that the belief in N&E is unreliable, given N&E (premiss 2), because N&E is neither abstract, nor empirically verifiable (premiss 1b). EVAAN distinguishes reliably verifiable intelligence from metaphysical intelligence and claims that, if N&E is true, humans are lacking metaphysical intelligence. This paper also contains an argument against EAAN, by supporting the premiss-1 rejoinder. (shrink)

Principles of expert deference say that you should align your credences with those of an expert. This expert could be your doctor, the objective chances, or your future self, after you've learnt something new. These kinds of principles face difficulties in cases in which you are uncertain of the truth-conditions of the thoughts in which you invest credence, as well as cases in which the thoughts have different truth-conditions for you and the expert. For instance, you shouldn't defer to your (...) doctor by aligning your credence in the de se thought 'I am sick' with the doctor's credence in that same de se thought. Here, I generalise principles of expert deference to handle these kinds of problem cases. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

When our measurement instruments sample from only a subspace of the domain that we are seeking to understand, or when they sample with uneven sampling density from the target domain, the resulting data will be affected by a selection effect. If we ignore such selection effects, our conclusions may suffer from selection biases. A classic example of selection bias is the election poll taken by the Literary Digest in 1936. On the basis of a large survey, the Digest predicted that (...) Alf Langdon, the Republican presidential candidate, would win by a large margin. But the actual election resulted in a landslide for the incumbent, Franklin D. Roosevelt. How could such a large sample yield such a wayward prediction? The Digest, it turned out, had harvested the addresses for its survey mainly from telephone books and motor vehicle registries. This introduced a strong selection effect. The poor of the depression era, a group that disproportionally supported Roosevelt, often did not have phones or cars. Observation selection effects are an especially subtle kind of selection effect that is introduced not by limitations in our measurement apparatuses but by the fact that all evidence is preconditioned on the existence of an observer to “have” the evidence and to build the instruments in the first place. Observation selection effects have only quite recently become the subject of systematic study. As well as being of philosophical interest, they are important in many scientific areas, including cosmology, parts of evolution theory, and the foundations of thermodynamics and quantum theory. There are also interesting applications to the search for extraterrestrial life and questions such as whether we might be living in a computer simulation created by an advanced civilization.. (shrink)

When reasoning about self-locating belief, one should reason as if one were a randomly selected bit of information. This principle can be considered to be an application of Bostrom's Strong Self-Sampling Assumption\cite{Bostrom} according to which one should reason as if one were a randomly selected element of some suitable reference class of observer-moments. The reference class is the class of all observer-moments. In order to randomly select an observer-moment from the reference class, one first randomly chooses a possible world $w$ (...) and then selects an observer-moment $z$ from world $w$. The probability that one selects $z$ given that one has chosen $w$ should be proportional to the amount of information that $z$ is capable of representing. There are both wagering arguments and relative frequency arguments that support our theory of anthropic reasoning. Our theory works best when the amount of information represented is finite. The infinite case is represented as a limit of a finite cases. We can learn from experience how best to represent the infinite case as a limit of finite cases and also learn from experience whether our theory or some other theory is the superior theory of anthropic reasoning. In order to test which theory is best, we use standard Bayesian methodology: We just need prior probabilities for the theories that are being tested and then we only have to use Bayes' rule. (shrink)

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.

This paper proposes a new explanation for the paradoxes related to anthropic reasoning. Solutions to the Sleeping Beauty Problem and the Doomsday argument are discussed in detail. The main argument can be summarized as follows: -/- Our thoughts, reasonings and narratives inherently comes from a certain perspective. With each perspective there is a center, or using the term broadly, a self. The natural first-person perspective is most primitive. However we can also think and express from others’ perspectives with a theory (...) of mind. A perspective’s center could be unrelated to the topic of discussion so its de se thoughts need not to be considered, e.g. the perspective of an outside observer. Let’s call these the third-person perspective. First-person reasoning allows primitive self identification as I am inherently unique as the center of the perspective. Whereas from third-person perspective I am not fundamentally special comparing to others so a reference class of observers including me can be defined. It is my contention that reasonings from different perspectives should not mix. Otherwise it could lead to paradoxes even independent of anthropic reasoning. The paradoxes surrounding anthropic reasoning are caused by the aforementioned perspective mix. Regarding the sleeping beauty problem the correct answer should be double halving. Lewisian halving and thirding uses unique reasonings from both first and third-person perspectives. Indexical probabilities such as “the probability that this is the first awakening” or “the probability of me being one of the first 100 billion human beings” also mixes first- and third-person reasonings. Therefore invalid. Readers against perspectivism may disagree with point 1 and suggest we could reason in objective terms without the limit of perspectives. My argument is compatible with this belief. Objective reasoning would be analytically identical to the third-person perspective. My argument would become that objective reasoning and perspective reasonings should not mix. In the following I would continue to use “third-person perspective” but readers can switch that to “objective reasoning” if they wish so. (shrink)

Reasoning that takes into account self-locating evidence in apparently plausible ways sometimes yields the startling conclusion that rational credences are such as if agents had bizarre causal powers. The present paper introduces a novel version of the Sleeping Beauty problem—Choosing Beauty—for which the response to the problem advocated by David Lewis unappealingly yields this conclusion. Furthermore, it suggests as a general desideratum for approaches to problems of self-locating belief that they should not recommend credences that are as if anyone had (...) anomalous causal powers. Adopting this desideratum, as the paper shows, yields uniformly plausible verdicts on the most-discussed problems of self-locating belief. (shrink)

Michael Huemer argues, on statistical grounds, that ``existence is evidence for immortality". On reasoning derived from the anthropic principle, however, mere existence cannot be evidence against any non-indexical, ``eternal'' hypothesis that predicts observers. This note attempts to advertise the much-flouted anthropic principle's virtues and workings in a new way, namely by calling attention to the fact that it is the primary intension of one's indexically-described evidence that best characterizes one's epistemic position.

Technical criticism of Jacob Ross's "Sleeping Beauty, Countable Additivity and Rational Dilemmas" and Double Halfing.

The Sleeping Beauty Problem is a polarizing thought experiment involving a fair coin toss, memory erasure and temporal uncertainty. Despite its simplicity there is no agreed upon solution. In this work I put forward a set of arguments that support the so-called Halfer or 1/2 solution to the problem, while undermining the competing Thirder or 1/3 solution. In analyzing Elga’s original argument for the 1/3 solution, I bring to light a subtle but clear contradiction in his reasoning using temporal logic. (...) Temporal reasoning also helps to neutralize the main criticisms against the 1/2 solution. Surprisingly, for some questions of probability or credence, it appears we need to distinguish between an event that has yet to occur, and the same event after it has already occurred. Knowledge that an event has been decided can be a type of admissible evidence when updating credences. (shrink)

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. In this context, considering a (...) Monday-waking (drawing a red ball) leads to two different situations that are assigned each a different probability. This leads to a two-sided account of the Sleeping Beauty problem. On the one hand, the first situation is handled by the argument for 1/3. On the other hand, the second situation corresponds to a reasoning that echoes the argument for 1/2 but that leads however, to different conclusions. (shrink)

Unremarkable earlier draft of "Sleeping Beauty: A Critical Survey".

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 (...) 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)

Six variations on the Sleeping beauty theme are presented.

A perfectly rational Sleeping Beauty is put to sleep on Sunday night, and intermittently awoken either on Monday only (if a fair coin shows Heads) or on both Monday and Tuesday (if the fair coin shows Tails). According to experimental conditions, she neither remembers previous awakenings nor knows about passage of time, but she is aware of experimental conditions. Her credence for the coin having come up Heads is at the center of a scientific (mostly philosophical) controversy: halfers insist it (...) should be 1/2, while thirders claim it should be 1/3. Winkler (2017) reviewed the literature, in terminology accessible to statisticians. This paper presents a comprehensive treatment of the probability side of the problem, from the perspective of a frequentist applied statistician. Perceived contradictions are resolved (in line with Groisman 2008) or traced back to violation of model assumptions. Modeling was at the heart of the confusion and is also at the heart of the solution. (shrink)