Carnap’s Syntax Programme and the Philosophy of Mathematics

Abstract

In the period leading up to The Logical Syntax of Language, from about 1928 onwards, logic and the foundations of mathematics were a principal focus of Carnap’s thinking. On the more technical side, he published the Abriss der Logistik in 1929, and started the ill-fated project called Untersuchungen zur allgemeinen Axiomatik in 1928.¹ 1930 saw the publication of a report on this project (1930d), and, on the more discursive side, of ‘Die alte und die neue Logik’ (1930a) and ‘Die Mathematik als Zweig der Logik’ (1930b), as well as the delivery of his address ‘Die logizistische Grundlegung der Mathematik’ (1931a) in September at Königsberg. Those years also saw conversations between Carnap and Gödel, including discussion of the incompleteness theorem as early as August 1930, and between Carnap and Tarski. All this activity is the background of the ‘sleepless night’ in January 1931 during which a fevered Carnap conceived of the central idea of Logical Syntax, as he reported in his ‘Intellectual Autobiography’ (1963a, p. 55).