Abstract

In earlier papers, I have sketched some aspects of a semantical theory of quantification, developed in terms of the concept of a model set. Furthermore, I have indicated a method of relating this semantical, or half-semantical, theory to the usual deductive methods. This method turned on considering proofs of logical truth as frustrated attempts to describe a counter-example to the sentence to be proved. In this paper, I propose to relate some of the observations that were made in the earlier papers to the doctrines which are generally known as picture theories of language. My main thesis is that these theories can be related rather closely to the logic of quantification by developing them in a suitable direction, and by using the concept of a model set as a mediating link.