Learn More
) In Logic across the University: Foundations and Application–Proceedings of the Tsinghua Logic Conference, Beijing, ed. J. van Benthem and F. Liu, 47–54. Volume 47: Studies in Logic. London: College Publications. Levi, Isaac. 1967. Gambling with Truth: An Essay on Induction and the Aims of Science. Cambridge, MA: MIT Press.<lb>———. 1980. The Enterprise of(More)
This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method Bp, which specifies an initial belief state Bp(⊤), that is revised to the new(More)
We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over(More)
What is the relationship between degrees of belief and (all-or-nothing) beliefs? Can the latter be expressed as a function of the former, without running into paradoxes? We reassess this “belief-binarization” problem from the perspective of judgmentaggregation theory. Although some similarities between belief binarization and judgment aggregation have been(More)
In this paper, we compare and contrast two methods for revising qualitative (viz., “full”) beliefs. The first method is a naïve Bayesian one, which operates via conditionalization and the minimization of expected inaccuracy. The second method is the AGM approach to belief revision. Our aim here is to provide the most straightforward explanation of the ways(More)
“Luminosity” with respect to knowledge means that whenever one has knowledge, one is in a position to know that one has knowledge. Timothy Williamson has a well-known, sorites-like argument, based on the safety requirement for knowledge, for the surprising conclusion that we do not know what we know in ordinary perceptual circumstances (2000). Safety is the(More)
We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over(More)