[FOM] Weyl and intuitionistic infinitesimals

[Mark van Atten]

A preprint of this paper is now available at
https://arxiv.org/abs/1803.05014

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.

Best wishes,
Mark.