Abstract

This dissertation is a discussion and defense of the view that model theory generally--and first-order model theory specifically--provides an adequate analysis of the notion of logical consequence presupposed by informal mathematical practice. The major theme is that the completeness theorem provides a rationale for choosing first-order model-theoretic consequence as the correct analysis of logical consequence. ;The discussion falls roughly into two parts. First, I consider the model-theoretic conception of logical consequence in general. Chapter I provides a general introduction to the philosophical problem of analyzing logical consequence and describes the model-theoretic notion of logical consequence. In Chapter II, I look at the intuitions that led to the model-theoretic conception. I pay special attention to Tarski's contributions in the 1930's. In Chapter II, I look at Etchemendy's objections to model-theoretic conceptions of consequence, in general, and to Tarski's ideas, in particular. ;The second part of the dissertation is concerned with the completeness theorem for first-order logic and its consequences. In Chapter IV, the completeness theorem itself is examined. I consider whether a notion of completeness, as a property of a logic, can be formulated without assuming the notions of a formal system of deduction or a model-theoretic semantics. In Chapter V, I present an account of the methodological importance of completeness. First-order model-theoretic consequence is compared with standard second-order logical consequence which is incomplete. This discussion is presented in the form of a critique of Shapiro . Chapter VI further examines some of the implications of incompleteness for standard second-order consequence