Fletcher, P ORCID: https://orcid.org/0000-0002-6183-0265 (2020) Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey. Journal of Philosophical Logic.

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Abstract

I survey Brouwer’s weak counterexamples to classical theorems, with a view to discovering (i) what useful mathematical work is done by weak counterexamples; (ii) whether they are rigorous mathematical proofs or just plausibility arguments; (iii) the role of Brouwer’s notion of the creative subject in them, and whether the creative subject is really necessary for them; (iv) what axioms for the creative subject are needed; (v) what relation there is between these arguments and Brouwer’s theory of choice sequences. I refute one of Brouwer’s claims with a weak counterexample of my own. I also examine Brouwer’s 1927 proof of the negative continuity theorem, which appears to be a weak counterexample reliant on both the creative subject and the concept of choice sequence; I argue that it provides a good justification for the weak continuity principle, but it is not a weak counterexample and it does not depend essentially on the creative subject.

Item Type: Article
Additional Information: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Uncontrolled Keywords: Brouwer Intuitionistic analysis Intuitionistic logic Weak counterexamples Creative subject Choice sequences
Subjects: Q Science > QC Physics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 27 May 2020 15:32
Last Modified: 27 May 2020 15:32
URI: https://eprints.keele.ac.uk/id/eprint/8044

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