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Brouwer’s Weak Counterexamples and the Creative Subject: A Critical Survey

Fletcher

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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.

Journal Article Type Article
Acceptance Date Feb 11, 2020
Publication Date May 9, 2020
Publicly Available Date Mar 28, 2024
Journal Journal of Philosophical Logic
Print ISSN 0022-3611
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 49
Pages 1111-1157
DOI https://doi.org/10.1007/s10992-020-09551-y
Keywords Brouwer, Intuitionistic analysis, Intuitionistic logic, Weak counterexamples,Creative subject, Choice sequences
Publisher URL https://link.springer.com/article/10.1007%2Fs10992-020-09551-y

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