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)

I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. Introduction What is probability? 2.1 Objective probability and the Principal Principle 2.2 Three ways of (...) satisfying the functional definition 2.3 Cautious functionalism 2.4 Is the functional definition complete? The Everett interpretation and subjective uncertainty 3.1 Interpreting quantum mechanics 3.2 The need for subjective uncertainty 3.3 Saunders' argument for subjective uncertainty 3.4 Objections to Saunders' argument 3.5 Subjective uncertainty again: arguments from interpretative charity 3.6 Quantum weights and the functional definition of probability Rejecting subjective uncertainty 4.1 The fission program 4.2 Against the fission program Justifying the axioms of decision theory 5.1 The primitive status of the decision-theoretic axioms 5.2 Holistic scepticism 5.3 The role of an explanation of decision theory Conclusion. (shrink)

In his 2007 paper “Quantum Sleeping Beauty”, 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 “sleeping beauty” 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 sleeping beauty 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)

Peter J. Lewis argued that the Everettian interpretation of quantum mechanics implies the unpopular halfer position in the Sleeping Beauty debate. We retorted that it is perfectly coherent to be an Everettian and an ordinary thirder. In a recent reply to our paper Lewis further clarifies the basis for his thinking. We think this brings out nicely where he goes wrong: he underestimates the importance of metaphysical considerations in determining rational credences.

Since the publication of Elga's seminal paper in 2000, the Sleeping Beauty paradox has been the source of much discussion, particularly in this journal. Over the past few decades the Everettian interpretation of quantum mechanics 1 has also been much debated. There is an interesting connection between the way these two topics raise issues about subjective probability assignments.This connection is often alluded to, but as far as we know Peter J. Lewis's ‘Quantum Sleeping Beauty’ is the first attempt to examine (...) it explicitly. Lewis claims that the two debates are not independent: to be specific, he argues that accepting the Everettian interpretation of quantum mechanics requires you to be a ‘halfer’ about Sleeping Beauty, in opposition to the more widely accepted ‘thirder’ solution.This paper will argue that Lewis is wrong. Everettians do not have to be halfers. It is perfectly cogent to be both an Everettian and a thirder. (shrink)

The Sleeping Beauty paradox in epistemology and the many-worlds interpretation of quantum mechanics both raise problems concerning subjective probability assignments. Furthermore, there are striking parallels between the two cases; in both cases personal experience has a branching structure, and in both cases the agent loses herself among the branches. However, the treatment of probability is very different in the two cases, for no good reason that I can see. Suppose, then, that we adopt the same treatment of probability in each (...) case. Then the dominant ‘thirder’ solution to the Sleeping Beauty paradox becomes incompatible with the tenability of the many-worlds interpretation. (shrink)

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (...) (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance. (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.

According to the Doomsday Argument we have to rethink the probabilities we assign to a soon or not so soon extinction of mankind when we realize that we are living now, rather early in the history of mankind. Sleeping Beauty finds herself in a similar predicament: on learning the date of her first awakening, she is asked to re-evaluate the probabilities of her two possible future scenarios. In connection with Doom, I argue that it is wrong to assume that our (...) ordinary probability judgements do not already reflect our place in history: we justify the predictive use we make of the probabilities yielded by science by our knowledge of the fact that we live now, a certain time before the possible occurrence of the events the probabilities refer to. Our degrees of belief should change drastically when we forget the date—importantly, this follows without invoking the “Self Indication Assumption”. Subsequent conditionalization on information about which year it is cancels this probability shift again. The Doomsday Argument is about such probability shifts, but tells us nothing about the concrete values of the probabilities —for these, experience provides the only basis. Essentially the same analysis applies to the Sleeping Beauty problem. I argue that Sleeping Beauty “thirders” should be committed to thinking that the Doomsday Argument is ineffective; whereas “halfers” should agree that doom is imminent—but they are wrong. (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 Sleeping Beauty Problem ( 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)