Quantification in Dynamic Semantics

Abstract

In dynamic semantics three styles of quantification have been proposed that can be seen to involve two different ways of interpreting free and quantified variables:

- Variables as denoting single partial objects;

- Variables as ranging over a number of alternative total objects.

I will show that the first view leads to problems of underspecification and the second to problems of overspecification. I will propose a new style of dynamic quantification in which variables are interpreted in a way which avoids these problems:

- Variables as ranging over a number of alternative definite objects (concepts).

By relativizing quantification to ways of conceptualizing the domain, we avoid the cardinality problems which arise if quantification is over concepts rather than objects.