In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...) paradox, and that what it shows is that conditionalisation, often claimed to be integral to the Bayesian canon, has to be rejected as a general rule in a finitely additive environment. (shrink)

I show that centered propositions—also called de se propositions, and usually modeled as sets of centered worlds—pose a serious problem for various versions of Lewis's Principal Principle. The problem, put roughly, is that in scenarios like Elga's `Sleeping Beauty' case, those principles imply that rational agents ought to have obviously irrational credences. To solve the problem, I propose a centered version of the Principal Principle. My version allows centered propositions to be objectively chancy.

In two excellent recent papers, Jacob Ross has argued that the standard arguments for the ‘thirder’ answer to the Sleeping Beauty 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 Sleeping Beauty problems. In this note I develop a new argument for the thirder answer that doesn't generalise in this way.

The view that chances are relative frequencies of occurrence within actual, finite reference classes has long been written off. I argue that it ought to be reconsidered. Focusing on non-deterministic chance, I defend a version of finite frequentism in which reference classmates are required to have qualitatively identical pasts. While my analysis can evade or resist several standard objections, it has a counterintuitive consequence: non-trivial chances entail the existence of past light cones that are perfect intrinsic duplicates. In mitigation, I (...) argue that our scientific knowledge is consistent with the hypothesis that there are many such duplicates in the actual world. Moreover, my analysis has some striking advantages: it is simple, it is metaphysically undemanding, and it makes possible a satisfying explanation of the chance–credence connection. 1 Introduction2 Target3 Sketch and Skirmish4 Articulation5 Standard Worries5.1 Frequency tolerance5.2 Leibniz’s dictum5.3 Single case chance5.4 Missing values5.5 Explanation5.6 Counterfactual chances6 Chance and Credence6.1 An indefeasible indifference intuition6.2 Articulating the credence principle6.3 Appraising the credence principle7 Confirmation8 Laws9 Summing Up. (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)

This paper defends the claim that there is a deep tension between the principle of countable additivity and the one-third solution to the Sleeping Beauty problem. The claim that such a tension exists has recently been challenged by Brian Weatherson, who has attempted to provide a countable additivity-friendly argument for the one-third solution. This attempt is shown to be unsuccessful. And it is argued that the failure of this attempt sheds light on the status of the principle of indifference that (...) underlies the tension between countable additivity and the one-third solution. (shrink)

Conceptual limitations restrict our epistemic options. One cannot believe, disbelieve, or doubt what one cannot grasp. I show how, even granting an epistemic ought-implies-can principle, such restrictions might lead to epistemic dilemmas: situations where each of one’s options violates some epistemic requirement. An alternative reaction would be to take epistemic norms to be sensitive to one’s options in ways that ensure dilemmas never arise. I propose, on behalf of the dilemmist, that we treat puzzlement as a kind of epistemic residue, (...) roughly analogous with guilt, appropriate only when one has violated an epistemic requirement. Sometimes, in bumping up against the limits of one’s concepts, it is appropriate to be puzzled no matter what one believes. Puzzlement can thus play the same role in an epistemic dilemmist’s theory that guilt plays in the theories of many moral dilemmists. (shrink)

In a recent issue of Analysis I gave a critique of some arguments made by Di Nucci concerning the so-called Simple View – the view that an agent performs an action intentionally only if he intends so to act. In turn Di Nucci offers a reply that concentrates on two points. The first has to do with a group of examples, one having to do with waking a flatmate, and the others with routine actions such as shifting gears while driving. (...) I rejected these examples, arguing that it is not at all obvious that in them the Simple View is violated. Additionally, I pointed out that these are not cases of agents doing something they thought they could not do, and so have no direct bearing on the issues of practical rationality that motivate Bratman's treatment of the Simple View, which Di Nucci is concerned to defend . Di Nucci accepts this second point. He claims, however, that I failed to understand the dialectic of his argument. …. (shrink)

In this paper I show that Elga’s argument for a restricted principle of indifference for self-locating belief relies on the kind of mistaken reasoning that recommends the ‘staying’ strategy in the Monty Hall problem.

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)

This paper is about epistemic dilemmas, i.e., cases in which one is doomed to have a doxastic attitude that is rationally impermissible no matter what. My aim is to develop and defend a position according to which there can be genuine rational indeterminacy; that is, it can be indeterminate which principles of rationality one should satisfy and thus indeterminate which doxastic attitudes one is permitted or required to have. I am going to argue that this view can resolve epistemic dilemmas (...) in a systematic way while also enjoying some important advantages over its rivals. (shrink)

This paper is about an anti-expertise paradox that arises because of self-referential sentences like: = I do not believe that is true. The first aim is to motivate, develop, and defend a novel view of epistemic rationality according to which there can be genuine rational indeterminacy, i.e., it can be indeterminate which doxastic states an agent is rationally permitted or required to have. The second aim is to show how this view can provide a solution to this paradox while also (...) avoiding the problems that plague its rivals. (shrink)

One argument for the thirder position on the Sleeping Beauty problem 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)

This article argues that there can be epistemic dilemmas: situations in which one faces conflicting epistemic requirements with the result that whatever one does, one is doomed to do wrong from the epistemic point of view. Accepting this view, I argue, may enable us to solve several epistemological puzzles.

According to a popular account, rationality is a kind of coherence of an agent’s mental states and, more specifically, a matter of fulfilling norms of coherence. For example, in order to be rational, an agent is required to intend to do what they judge they ought to and can do. This norm has been called ‘Enkrasia’. Another norm requires that, ceteris paribus, an agent retain their intention over time. This has been called ‘Persistence of Intention’. This paper argues that thus (...) understood norms of rationality may at times conflict. More specifically, Enkrasia and Persistence of Intention may place demands on the agent that are impossible to fulfil. In these cases, the framework of requirements does not provide us with norms that make us rational. A rival account, according to which rationality is a kind of responsiveness to one’s available reasons, can overcome the problem. (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 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.

It is well known that de se (or ‘self-locating’) propositions complicate the standard picture of how we should respond to evidence. This has given rise to a substantial literature centered around puzzles like Sleeping Beauty, Dr. Evil, and Doomsday—and it has also sparked controversy over a style of argument that has recently been adopted by theoretical cosmologists. These discussions often dwell on intuitions about a single kind of case, but it’s worth seeking a rule that can unify our treatment of (...) all evidence, whether de dicto or de se. -/- This paper is about three candidates for such a rule, presented as replacements for the standard updating rule. Each rule stems from the idea that we should treat ourselves as a random sample, a heuristic that underlies many of the intuitions that have been pumped in treatments of the standard puzzles. But each rule also yields some strange results when applied across the board. This leaves us with some difficult options. We can seek another way to refine the random-sample heuristic, e.g. by restricting one of our rules. We can try to live with the strange results, perhaps granting that useful principles can fail at the margins. Or we can reject the random-sample heuristic as fatally flawed—which means rethinking its influence in even the simplest cases. (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)

Building on recent formal work by Aleks Knoks, we explore how the idea that certain epistemic norms may be indeterminate could be implemented in a default logic.

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

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

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