Abstract

The general issue addressed in this dissertation is: what do the models of formal model-theoretic semantics represent? In chapter 2, I argue that those of first-order classical logic represent meaning assignments in possible worlds. This motivates an inquiry into what the interpretations of first-order quantified model logic represent, and in Chapter 3 I argue that they represent meaning assignments in possible universes of possible worlds. A possible universe is unpacked as one way model reality might be. The problem arises here as to how we are to understand the distinction between the actual and the possible as it relates to modal reality. ;Along with the development of the main arguments in Chapters 2 and 3, the dissertation assesses the status of semantic accounts or logical properties and relations. Specifically, what does the model-theoretic account of a logically possible situation add to the syntactic account ? ;Proofs of invalidity in terms of the models of formal semantics do not establish that it is possible for the premises to be true and the conclusion false, since a formal model is merely given by a consistent set of sentences. Unless there is some way to generate a non-formal model from a formal one, such proofs do not really go beyond syntactic notions. The dissertation ends by concluding that there is no way to generate a non-formal model from a formal one without relying on logical intuitions that are syntactical. ;Hence efforts to construct a semantic basis for model logic independent of syntactic commitments are misguided. However, in classical logic the independence of the semantic account from the syntactic one is grounded on the intuition that it is metaphysically possible for there to be a denumerably infinite totality of objects