Semantics and logic: the meaning of logical terms

Salvatore Florio, Stewart Shapiro, and Eric Snyder

It is widely (but not universally) held that logical consequence is determined (at least in part) by the meanings of the logical terminology. One might think that this is an empirical claim that can be tested by the usual methods of linguistic semantics. Yet most philosophers who hold views about logic like this do not engage in empirical research to test the main thesis. Sometimes the thesis is just stated, without argument, and sometimes it is argued for on a priori grounds. Moreover, many linguistic studies of words like “or”, the conditional, and the quantifiers run directly contrary to the thesis in question.

From the other direction, much of the work in linguistic semantics uses logical symbols. For example, it is typical for a semanticist to write a biconditional, in a formal language, whose left hand side has a symbol for the meaning of an expression in natural language and whose right hand side is a formula consisting of lambda-terms and other symbols from standard logic works: quantifiers ∀, ∃, and connectives ¬, →, ∧, ∨, ↔. This enterprise thus seems to presuppose that readers already understand the formal logical symbols, and the semanticist uses this understanding to shed light on the meanings of expressions in natural language. This occurs even if the natural language expressions are natural language terms corresponding to the logical ones: “or”, “not”, “forall”, and the like.

The purpose of this talk is to explore the relation between logic and the practice of empirical semantics, hoping to shed light, in some way, on both enterprises.