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In a recent article, Joel Pust argued that direct inference based on reference properties of differing arity are incommensurable, and so direct inference cannot be used to resolve the Sleeping Beauty problem. After discussing the defects of Pust's argument, I offer reasons for thinking that direct inferences based on reference properties of differing arity are commensurable, and that we should prefer direct inferences based on logically stronger reference properties, regardless of arity. |
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The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...) |
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The traditional solutions to the Sleeping Beauty problem say that Beauty should have either a sharp 1/3 or sharp 1/2 credence that the coin flip was heads when she wakes. But Beauty’s evidence is incomplete so that it doesn’t warrant a precise credence, I claim. Instead, Beauty ought to have a properly imprecise credence when she wakes. In particular, her representor ought to assign \(R(H\!eads)=[0,1/2]\) . I show, perhaps surprisingly, that this solution can account for the many of the intuitions (...) |
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“Double-halfers” think that throughout the Sleeping Beauty Scenario, Beauty ought to maintain a credence of 1/2 in the proposition that the fair coin toss governing the experimental protocol comes up heads. Titelbaum (2012) introduces a novel variation on the standard scenario, one involving an additional coin toss, and claims that the double-halfer is committed to the absurd and embarrassing result that Beauty’s credence in an indexical proposition concerning the outcome of a future fair coin toss is not 1/2. I argue (...) |
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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 (...) |
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Next SectionAn attempt to resolve the controversy regarding the solution of the Sleeping Beauty Problem in the framework of the Many-Worlds Interpretation led to a new controversy regarding the Quantum Sleeping Beauty Problem. We apply the concept of a measure of existence of a world and reach the solution known as ‘thirder’ solution which differs from Peter Lewis’s ‘halfer’ assertion. We argue that this method provides a simple and powerful tool for analysing rational decision theory problems. |
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Although many philosophers think backwards causation possible, puzzles arise when we consider worlds containing both backwards causal chains and agents capable of intervening in, and initiating, such chains. In these worlds, agents have the power to bilk, that is, the power to prevent an event from occurring which, had it occurred, would have been the cause of an earlier event. I argue, appealing to Max Black’s example and one other, that this power is absurd and hence that there are no (...) |
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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 (...) |
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Writing collectively as the Oscar Seminar in 2008, John Pollock and several colleagues advance an objectivist argument for a 1/3 solution to the Sleeping Beauty problem. In 2011, Joel Pust raises a serious objection to their argument to which Paul D. Thorn, a member of the Oscar Seminar, offers a subtle reply. I argue that the Oscar Seminar s argument for 1/3 is unsound. I do not, however, defend Pust’s objection. Rather I develop a new objection, one that is not (...) |
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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 (...) |
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