Abstract

The conception of intuition in mathematics is prominent in early twentieth-century work on foundations of mathematics. The conception of mathematical intuition is partly based on Hilbert’s ideas about the methods of proof theory, a conception of intuitive evidence closer to the finitary method of Hilbert. Hilbert claimed some kind of evidence for finitist mathematics. Hilbert claimed intuitive evidence for individual instances of induction where the predicates involved are of the right kind, in practice primitive recursive. The objects of such intuition are abstract objects. This is perhaps clearest in Hilbert’s conception of mathematics and logic, in Hilbert’s distinction between intuitive and formal mathematics