Quine on logical truth and consequence

Abstract

According to Quine, logic is first-order. For him, two underlying logic of all rational thought is a standard first-order logic without identity, without individual constants and without function constants, a logic which is two-valued, tenseless, extensional, non-modal, non-intuitionistic and one-sorted, a logic which is (in a sense) a proper sublogic of virtually every logic used as an underlying logic in tha literature of classical mathematics and science, a logic which merits being called conservative. His conception of the logical properties gives priority to logical truth. Roughly, Quine holds that in arder for a sentence to be logically trae it is necessary and sufficient for it to be true and to remain true under any uniform lexical substitution of its content-terms. Derivatively, in order for a sentence to be logically implied by a set of sentences F it is necessary and sufficient for there to be no single uniform lexical substitution of content-terms that makes every member of F true and false. Since, intuitively speaking, the relation of a sentence to its lexical subctitutions is a matter of grammar, logical truth and logical implication are thus a matter, a Quine omphasizec, of grammar and truth. My parpase ic to diccuss Quinas distintive view of logical truth and logical implication and to analyze the main features and philosophical import of his conception. This paper has five sections. The first fixes the terminology and stresses the fact that Quine takes logical truth to be prior to logical implication. Section two identifies three core features of the Quinean conception; his fixed-universe, fixed-content, non-modal conception is discussed in the light of Tarcki's distinctive contribution to these perennial issues. Section three analyses the grounds for Quine`s view and his claim that his account is co-extensional with the current model-theoretic conception. Two necessary conditions for this alleged adequacy are considered: (a) the first-order language must contain elementary arithmetic, (b) identity must be nonlogical. In section four the role that Quines "parsimonious' ontology plays in his conception is briefly discussed in historical perspective. Section five conludes with a brief historical survey of the main achievements of Bolzano, Russell, Tarski and Quine logical truth and consequence.