Besides the usual business of solving paradoxes, there has been recent philosophical work on their essential nature. Lycan characterises a paradox as “an inconsistent set of propositions, each of which is very plausible.” Building on this definition, Paseau offers a numerical measure of paradoxicality of a set of principles: a function of the degrees to which a subject believes the principles considered individually (all typically high) and of the degree to which the subject believes the principles considered together (typically low).We argue (a) that Paseau’s measure fails to score certain paradoxes properly and (b) that this failure is not due to the particular measure but rather that any such function just of credences fails to adequately capture paradoxicality. Our analysis leads us to conclude that Lycan’s definition also fails to capture the notion of paradox.

Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the formof equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.

Contextualists and relativists about predicates of personal taste, epistemic modals, and so on (“CR-expressions”) agree that the interpretation of these expressions depends, in some sense, on context. Relativists claim that the sort of context-sensitivity exhibited by CR-expressions is importantly different from that exhibited by paradigm context-sensitive expressions. This bifurcation is often motivated by the claim that the two classes of expressions behave differently in patterns of agreement and disagreement. I provide cases illustrating that the same sorts of discourse phenomena that have been thought problematic for contextualists can arise with paradigm context-sensitive expressions.These cases motivate a more unified treatment of paradigm context-sensitive expressions and the expressions that have figured in recent contextualism/relativism debates.

I shall offer some very plausible assumptions for the measure of confirmation and show that they imply that E confirms H relative to background K to degree f (PK(E|H)/PK(E|~H)), where f is a strictly increasing function. An additional assumption about how measures of confirmation combine then makes f be proportional to a logarithm.

This article deals with supervaluationism and the failure of truth-functionality. It draws some distinctions that may contribute to a better understanding of this semantic framework.

William Roche and Elliott Sober argue that explanatoriness is evidentially irrelevant. This conclusion is surprising since it conflicts with a plausible assumption—the fact that a hypothesis best explains a given set of data is evidence that the hypothesis is true. We argue that Roche and Sober’s screening-off argument fails to account for a key aspect of evidential strength: the weight of a body of evidence. The weight of a body of evidence affects the resiliency of probabilities in the light of new evidence. Thus, Roche and Sober are mistaken. Explanatoriness is evidentially relevant.

Ned Block says ‘yes’ (2012, 2013). His position is based on the phenomenon of identity-crowding. According to Block, in cases of identity-crowding, something is consciously seen even though one cannot attend to it.1 In taking this view, Block is opposing a position I have taken in recent work (Tye 2009a, 2009b, 2010). He is also contributing to a vigorous recent debate in the philosophy of mind over the relation, if any, between consciousness and attention.Who is right? Not surprisingly, I think I am.

Michael Tye’s response to my “Grain” (Block 2012) and “Windows” (Block 2013) raises general metaphilosophical issues about the value of intuitions and judgments about one’s perceptions and the relations of those intuitions and judgments to empirical research, as well as specific philosophical issues about the relation between seeing, attention and de re thought. I will argue that Tye’s appeal to what is (§. 2) “intuitively obvious, once we reflect upon these cases” (“intuition”) is problematic. I will also argue that first person judgments can be problematic when used on their own as Tye does but can be valuable when integrated with empirical results.

Cardinality arguments against regular probability measures aim to show that no matter which ordered field H we select as the measures for probability, we can find some event space F of sufficiently large cardinality such that there can be no regular probability measure from F into H. In particular, taking H to be hyperreal numbers won’t help to guarantee that probability measures can always be regular. I argue that such cardinality arguments fail, since they rely on the wrong conception of the role of numbers as measures of probability. With the proper conception of their role we can see that for any event space F, of any cardinality, there are regular hyperreal-valued probability measures.