Semantics, unrestricted quantification and set theory

Dan Marshall (Lingnan University)

Dan Marshall (Lingnan) will present "Semantics, unrestricted quantification and set theory" at 11 in G10 Old Quad. 

Abstract: According to what might be called the Fregean, or Montagovian, approach to semantics, the semantic properties of sentences are to be determined by assigning semantic values to all (or nearly all) of the words that make up those sentences. Although extremely influential and pervasive, this approach faces serious problems in accounting for unrestricted quantification and other devices of absolute generality. The problem is that, in order to account for unrestricted quantification and absolute generality, the approach seems to require semantic values that involve a set of all sets. According to standard set theory, however, there are no such sets, and hence no such semantic values. In this paper, I discuss a number of ways of trying to resolve this problem and argue that none of them are successful. I conclude by suggesting that this approach to semantics should be rejected and briefly sketch an alternative approach that can account for unrestricted quantification and absolute generality.