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

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)

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

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

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

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)

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

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)

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

What degrees of belief does Sleeping Beauty's evidence support? That depends.

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

Parodic earlier draft of "Sleeping Beauty: why violations of probability laws are `Deal' breakers".