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Gradational accuracy and nonclassical semantics
Review of Symbolic Logic 5 (4):513537 (2012)
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It is well known that the convex hull of the classical truth value functions contains all and only the probability functions. Work by Paris and Williams has shown that this also holds for various kinds of nonclassical logics too. This note summarises the formal details of this topic and extends the results slightly. 

Many accounts of structural rationality give a special role to logic. This paper reviews the problem case of cleareyed logical uncertainty. An account of rational norms on belief that does not give a special role to logic is developed: doxastic probabilism. 

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how phenomenal consciousness and gradational possibleworlds models in Bayesian perceptual psychology relate to epistemic modal space. The book demonstrates, then, how epistemic modality relates to the computational theory of mind; metaphysical modality; deontic modality; logical modality; the types of mathematical modality; to the (...) 

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracydominance result for stochastic theories in the C*algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracydominance if and only if they are given by a state on that algebra. When your estimates avoid accuracydominance, I say that they are sufficiently coherent. (...) 

This essay explores the thesis that for vague predicates, uncertainty over whether a borderline instance x of red/large/tall/good is to be understood as practical uncertainty over whether to treat x as red/large/tall/good. Expressivist and quasirealist treatments of vague predicates due to John MacFarlane and Daniel Elstein provide the stalkinghorse. It examines the notion of treating/counting a thing as F , and links a central question about our attitudes to vague predications to normative evaluation of plans to treat a thing as (...) 

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) 



The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency principle. These are used to explain the rationality of revisions to an agent’s degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them—especially reductions in confidence assignments to propositions antecedently regarded as certain—including certaintyreductions to instances of the law of excluded (...) 

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracydomination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracydomination deﬁnes a (...) 

Beliefs come in different strengths. An agent's credence in a proposition is a measure of the strength of her belief in that proposition. Various norms for credences have been proposed. Traditionally, philosophers have tried to argue for these norms by showing that any agent who violates them will be lead by her credences to make bad decisions. In this article, we survey a new strategy for justifying these norms. The strategy begins by identifying an epistemic utility function and a decisiontheoretic (...) 