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Adam Elga argues that in certain cases when an agent cannot tell which of many subjectively indistinguishable experiences she is currently having, she should assign equal credence to being in each. This chapter derives instances of that indifference principle from the Certainty-Loss Framework (CLF) proposed and defended in this book, then defends those instances against criticisms from Brian Weatherson. Next, the chapter applies CLF to cases involving personal fission or cloning. Finally, the chapter uses CLF to examine how agents should assign degrees of belief to the outcomes of various quantum experiments if the Everett interpretation of quantum mechanics is true. If the Everettian interpretation can make sense of nonextreme degrees of belief about quantum outcomes to begin with, then CLF provides plausible results about how those degrees of belief should update over time.

This chapter explains how to apply the Certainty-Loss Framework (CLF) to stories involving self-locating belief and context-sensitivity. This formal modeling framework and its distinctive updating rules (Generalized Conditionalization and the Proper Expansion Principle) were defined and defended in previous chapters. Here the framework is used to model rational requirements in a number of stories, most importantly Adam Elga’s highly controversial Sleeping Beauty Problem. After analyzing solutions to that problem offered by Elga and by David Lewis, the chapter shows two different ways of constructing CLF models that refute Lewis’s solution (without invoking indifference principles or even Lewis’s Principal Principle). Objections to the CLF models are considered and rebutted.

This chapter develops and defends a new account of essentially indexical, de se, or self-locating belief with the aim of using it in later chapters to clarify the analogy between self-locating information and phenomenal information. The account is a modified version of David Lewis's analysis of self-locating information in terms of centered possible worlds, which are abstract objects consisting of a possible world plus a designated person and time in the world. It is argued that the modified analysis is better able than Lewis's to account for the way knowledge and belief change over time, and for one person's knowledge and belief about the knowledge and belief of others. The analysis is applied to two famous examples from the literature on essentially self-locating belief — David Lewis's case of the two omniscient gods, and Adam Elga's Sleeping Beauty puzzle. The chapter concludes with an appendix that sketches some of the formal details.

It has often been noticed that conciliatory views of disagreement are “self-undermining” in a certain way: advocates of such views cannot consistently maintain them when other philosophers disagree. This leads to apparent problems of instability and even inconsistency. Does self-undermining, then, show conciliationism to be untenable? If so, the untenability would extend not only to almost all views of disagreement, but to a wide range of other views supporting what one might call epistemic modesty: roughly, the idea that getting evidence that one has made an epistemic error in arriving at one's opinion may require adjusting that opinion. In this paper David Christensen argues that the phenomenon of self-undermining does not disclose any defect in views mandating epistemic modesty. Instead, it highlights an uncomfortable but natural consequence of reflecting on one's own possible epistemic imperfections, a sort of reflection that tends to cause epistemic ideals to conflict.