Abstract

The present paper provides a reconstruction of Weyl’s and Gödel’s interpretations of intuitionism, embedding the discussion in the context of the Grundlagenstreit and the origins of constructive logic. The two interpretations exhibit a striking affinity and deviate substantially from the mainstream view, usually referred to as the Brouwer-Heyting-Kolmogorov explanation of constructive proofs. Gödel’s objections to intuitionism are fairly well-known, but the connection with Weyl appears to have received little attention from commentators. The crux of the matter is the concept and role of ideal elements in mathematics. The paper explains how different interpretations of intuitionism deal with this problem.