Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations (...) in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma. (shrink)

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)

Horgan and Mahtani (Erkenntnis 78: 333–351, 2013) present a new argument for the 1/3 answer to the Sleeping Beauty problem resting on a principle for updating probabilities which they call “generalized conditionalization.” They allege that this new argument is immune to two attacks which have been recently leveled at other arguments for thirdism. I argue that their new argument rests on a probability distribution which is (a) no more justified than an alternative distribution favoring a different answer to the problem, (...) and (b) ultimately unjustified. I go on to show that generalized conditionalization cannot be applied in the manner suggested, given the cogency of the aforementioned attacks on thirder arguments. Hence, the new argument fails to advance the case for the 1/3 answer. (shrink)

I argue that a popular view about self-locating evidence implies that there are cases in which agents have surprisingly strong evidence for their own reincarnation. The central case is an ‘Immortal Beauty' scenario, modelled after the well-known Sleeping Beauty puzzle. I argue that if the popular ‘thirder’ solution to the puzzle is correct, then Immortal Beauty should be confident that she's going to be reincarnated. The essay also examines another pro-reincarnation argument due to Michael Huemer (2021). I argue that his (...) argument fails, and that my argument establishes an alternative way in which mere existence can be evidence for reincarnation. I then examine whether my result generalizes. (shrink)

I raise skeptical doubts about the prospects of Bayesian formal epistemology for providing an adequate general normative model of epistemic rationality. The notion of credence, I argue, embodies a very dubious psychological myth, viz., that for virtually any proposition p that one can entertain and understand, one has some quantitatively precise, 0-to-1 ratio-scale, doxastic attitude toward p. The concept of credence faces further serious problems as well—different ones depending on whether credence 1 is construed as full belief (the limit case (...) of so-called partial belief) or instead is construed as absolute certainty. I argue that the notion of an “ideal Bayesian reasoner” cannot serve as a normative ideal that actual human agents should seek to emulate as closely as they can, because different such reasoners who all have the same evidence as oneself—no single one them being uniquely psychologically most similar to oneself—will differ from one another in their credences (e.g., because they commence from different prior credences). I argue that epistemic probability, properly understood, is quantitative degree of evidential support relative to one’s evidence, and that principled epistemic probabilities arise only under quite special evidential circumstances—which means that epistemic probability is ill suited to figure centrally within general norms of human epistemic rationality. (shrink)

In the 1970’s, a controversy arose about a probability problem posed by Irving Copi. One side argued that a common spontaneous intuition about the problem is correct; the other side argued that this intuition is mistaken. Here, I argue (1) that the naïve intuition yields the correct answer, but accidentally and for a wrong reason; (2) that a more reflective intuition yields a wrong answer, and hence, is also mistaken; and (3) that an even more reflective intuition yields the correct (...) answer for a correct reason. This warrants what I call optimistic fallibilism concerning intuitions about probability: although intuition is certainly prone to error in this domain, intuition has the capacity for self-correction. A naïve intuition that is mistaken can be replaced by a distinct, reflective intuition; and a reflective intuition that is mistaken can be replaced by another reflective intuition – with the process ultimately yielding a sound intuition. (shrink)

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

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

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

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.

To ascertain the rational credences for the epistemic agents in the famous cases of self-locating belief, one should model the processes by which those agents acquire their evidence. This approach, taken by Darren Bradley (Phil. Review 121, 149–177) and Joseph Halpern (Ergo 2, 195–206), is immensely reasonable. Nevertheless, the work of those authors makes it seem as if this approach must lead to such conclusions as the Doomsday argument being correct, and that Sleeping Beauty should be a halfer. I argue (...) that this is due to an implicit existential bias: it is assumed that the first step in those processes is the determination that the agent in question must necessarily exist. It is much more reasonable to model that determination as contingent and a result of other, earlier, steps in the process. This paper offers such alternative models. They imply an endorsement of what has mockingly been called “presumptuous” reasoning, and a massive shift of credences in favor of (1) the existence of a multiverse and (2) the Everettian interpretation of quantum mechanics. (shrink)