This paper argues, first, that the information problem poses a foundational challenge to mainstream semantics. It proposes, second, to address this problem by drawing on notions from Kit Fine’s essentialist framework. More specifically, it claims that the information problem can be avoided by strengthening standard truth theories, employing an operator expressing the notion of a relative constitutive semantic requirement. As a result, the paper proposes to construe semantic theories as theories of semantic requirements, and semantic knowledge as knowledge of such (...) requirements. (shrink)

A possible event always seems to be more probable than an impossible event. Although this constraint, usually alluded to as regularity , is prima facie very attractive, it cannot hold for standard probabilities. Moreover, in a recent paper Timothy Williamson has challenged even the idea that regularity can be integrated into a comparative conception of probability by showing that the standard comparative axioms conflict with certain cases if regularity is assumed. In this note, we suggest that there is a natural (...) weakening of the standard comparative axioms. It is shown that these axioms are consistent both with the regularity condition and with the essential feature of Williamson’s example. (shrink)

A cardinal characteristic can often be described as the smallest size of a family of sequences which has a given property. Instead of this traditional concern for a smallest realization of the given property, a basically new approach, taken in [4] and [5], asks for a realization whose members are sequences of labels that correspond to 1-way infinite paths in a labelled graph. We study this approach as such, establishing tools that are applicable to all these cardinal characteristics. As an (...) application, we demonstrate the power of the tools developed by presenting a short proof of the bounded graph conjecture [4]. (shrink)