Weyl and intuitionistic infinitesimals

Abstract

As Weyl was interested in infinitesimal analysis and for some years embraced Brouwer's intuitionism, which he continued to see as an ideal even after he had convinced himself that it is a practical necessity for science to go beyond intuitionistic mathematics, this note presents some remarks on infinitesimals from a Brouwerian perspective. After an introduction and a look at Robinson's and Nelson's approaches to classical nonstandard analysis, three desiderata for an intuitionistic construction of infinitesimals are extracted from Brouwer's writings. These cannot be met, but in explicitly Brouwerian settings what might in different ways be called approximations to infinitesimals have been developed by early Brouwer, Vesley, and Reeb. I conclude that perhaps Reeb's approach, with its Brouwerian motivation for accepting Nelson's classical formalism, would have suited Weyl best.