Carnap’s Criterion of Logicality

Abstract

Characterizing in a principled manner the distinction between logical and non-logical expressions has been a longstanding issue in the philosophy of logic. In The Logical Syntax of Language, Carnap proposes a syntactic solution to this problem, which aims at grounding the claim that logic and mathematics are analytic. Roughly speaking, his idea is that logic and mathematics correspond to the largest part of science for which it is possible to completely specify by ‘syntactic’ means which sentences are valid and which are not. Despite a renewed interest in the notion of analyticity, both inside and outside of Carnap scholarship, Carnap’s definition of logical expressions has not received all the attention that it deserves. I shall argue that it is well worth a second look. More precisely, my aim will be to defend Carnap’s idea against some technical problems that Carnap’s original definition faces and against wider Quinean attacks on syntax-based conventionalism.

This chapter originates from discussions held during a reading seminar on Carnap’s Logical Syntax of Language, which was organized at the IHPST by Pierre Wagner. I would like to thank the participants, and especially Serge Bozon, Philippe de Rouilhan, and Pierre Wagner for their helpful comments. A preliminary version was presented during a conference at the IHPST in 2005. I would like to thank the audience for its accurate remarks, and particularly Richard Creath, whose 1996 paper convinced me to take a fresh look at Carnap’s definition of logical expressions, and Steve Awodey, for some stimulating criticisms and for drawing my attention to Saunders Mac Lane’s review of Carnap’s book.