The Pragmatic Nature of Mathematical Inquiry

In 1926 Hermann Weyl’s Philosophy of Mathematics and Natural Science appeared in Oldenbourg’s Handbuch der Philosophie. At the time Hilbert’s formalist program to “eradicate via proof theory all the foundational questions of mathematics” was in full swing. As a pupil of Hilbert, Weyl was looking to the complete and ultimate success of Hilbert’s program, a confidence evident in Weyl’s treatment of the foundations of mathematics in the original version of Philosophy of Mathematics and Natural Science. But in an appendix to that same text appearing twenty years later, Weyl (1949, p. 219) admitted that this confidence was misplaced: