The Significance of Weyl’s Das Kontinuum

Abstract

In his 1918 monograph Das Kontinuum, Hermann Weyl initiated a program for the arithmetical foundations of mathematics. In the years following, this was overshadowed by the foundational schemes of Hilbert’s finitary consistency program and Brouwer’s intuitionistic redevelopment of mathematics. In fact, not long after his own venture, Weyl became a convert to Brouwerian intuitionism and criticized his old teacher’s program. Over the years, though, he became more and more pessimistic about the practical possibilities of reworking mathematics along intuitionistic lines, and pointed to the value of his own early foundational efforts. Weyl’s work in Das Kontinuum has come to be recognized for its importance as the opening chapter in the actual development of predicative mathematics, whose extent has been plumbed both mathematically and logically since the 1960s.

This is the second of my three lectures for the conference, Proof Theory: History and Philosophical Significance, held at the University of Roskilde, Denmark Oct. 31–Nov. 1, 1997. See the first footnote to the first lecture, “Highlights in proof theory” for my acknowledgments.