Tolerance, Intuition, and Empiricism

Abstract

Although Carnap had defended a modified version of the Kantian conception of pure spatial intuition and geometry in his doctoral dissertation, Der Raum (1922), it seems that he had abandoned both pure intuition and the synthetic a priori while he was working on Der logische Aufbau der Welt in 1924–5, and this was certainly the case when he became a leading member of the Vienna Circle in the mid to late 1920s. In a well-known passage in his ‘Intellectual Autobiography’ (1963) Carnap describes how the characteristic Vienna Circle doctrine of the analytic character of all logical and mathematical truths, based on the Frege-Russell reduction of mathematics to logic and Wittgenstein’s conception of tautology, allowed them to make a major advance over earlier forms of empiricism: What was important in this conception from our point of view was the fact that it became possible for the first time to combine the basic tenet of empiricism with a satisfactory explanation of the nature of logic and mathematics. Previously, philosophers had only seen two alternative positions: either a non-empiricist conception, according to which knowledge in mathematics is based on pure intuition or pure reason, or the view held, e.g., by John Stuart Mill, that the theorems of logic and of mathematics are just as much of an empirical nature as knowledge about observed events, a view which, although it preserved empiricism, was certainly unsatisfactory. (1963a, p. 47)