The intersection of intuitionism (Brouwer) and phenomenology (Husserl)

Abstract

There are important and interesting conceptual links between Brouwer’s intuitionism and Husserl’s transcendental phenomenology. This is true independently of whether or not there had ever been a historical intersection of the two approaches to mathematics and logic. But of course there was a historical intersection. It occurred primarily in the nineteen twenties and early thirties, in the middle of the foundational debate between Brouwer’s intuitionism and Hilbert’s formalism. During this period there is a fascinating development and exchange of ideas on intuitionism, phenomenology, and formalism in the work of Hermann Weyl, Oskar Becker, Felix Kaufmann, and Arend Heyting, which is set against the background of the ideas of L.E.J. Brouwer, Edmund Husserl and David Hilbert¹.

See, e.g., (Becker 1923), 1927, (Heyting 1931), (Kaufmann 1930), (Weyl 1918, 1921, 1925, 1926, 1928). See also the recent archival and scholarly research in, e.g., (Mancosu and Ryckman 2002), (van Atten 2005), and (van Dalen 1984). Philosophical and technical work in this tradition can be found, e.g., in (Martin-Löf 1984, 1987), (Sundholm 1983), (Tieszen 1989, 1992, 1994, 2000a,b), (van Atten et al. 2002), (van Atten 2004a, 2007). By the way, Brouwer and Husserl did actually meet once, in April 1928, in Amsterdam. We do not know what they talked about but their correspondence with other people indicates that they were evidently both pleased with the meeting.