Rudolf Carnap on Logical Syntax



Carnap's work on "Logical Syntax" is the product of the years from 1931-1934. It could not have been done earlier and would not have been done later. To understand the work it is therefore desirable to have some appreciation of the context in which Carnap was working, the factors which influenced him, and the developments which caused him so rapidly to move on beyond the perspective presented by this work.
The Programme
Carnap accepted quote Russell's view of philosophy as logic quote. In the discussions of the Vienna Circle he had observed that many of the problems discussed were at bottom problems about the language of science and he believed that these problems could best be addressed by what he called "Logical Syntax". The use of this term is influenced not only by his view that the study of language, using modern logical methods, was the way to resolve philosophical problems, but also that this study need only address syntax.
The Methods
Carnap has begun with the new logical methods presented first by Frege and then more extensively in Principia Mathematica. The next most conspicuous source appears to be Hilbert's programme of metamathematics, both in its conception and in more detailed techniques which Carnap learned through Gödel and Tarski, who could be said to be logicians working in the context of Hilbert's programme. The impact of Hilbert's programme seems pervasive. Hilbert had proposed that problems in the foundations of mathematics should be resolved by a program of metamathematical work made possibly by considering mathematics as conducted in formal languages which could themselves be the subject of mathematical studies. Carnap generalises this metalinguistic view of foundational problems from its application by Hilbert in mathematics to broader philosophical purposes. The domain of the meaningful is split into analytic and synthetic judgements. The former are logical truths, the latter belong to science (in a very general sense) rather than philosophy, but the metatheory remains a part of philosophy as the logical study of the syntax of language.
The two features of Hilbert's programme which are most prominent in Carnap's work on Logical Syntax are firstly the metalinguistic aspect, but also the confidence in the sufficiency of syntax. It is this latter feature which was most precarious in the period when Carnap was working on Logical Syntax. Göel had perhaps first lent it greater credibility by his proof of the completeness of first order logic, but quickly delivered a terminal blow with his proof of the incompleteness of arithmetic.

Of these it is Gödel's contribution which is easier to spot in Carnap's work on logical syntax. The methods used by Gödel in his


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