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Weyl and the Problem of SpaceWeyl and Intuitionistic Infinitesimals

Weyl and the Problem of Space: Weyl and Intuitionistic Infinitesimals [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Weyl and the Problem of SpaceWeyl and Intuitionistic Infinitesimals

Part of the Studies in History and Philosophy of Science Book Series (volume 49)
Editors: Bernard, Julien; Lobo, Carlos
van Atten, Mark
Weyl and the Problem of Space — Oct 10, 2019
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References (37)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-11526-5
Pages
125 –159
DOI
10.1007/978-3-030-11527-2_5
Publisher site
See Chapter on Publisher Site

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.]

Published: Oct 10, 2019

Keywords: L.E.J. Brouwer; Constructivism; Infinitesimals; Intuitionism; Nonstandard analysis; Physics; G. Reeb; A. Robinson; R. Vesley; H. Weyl

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