Brouwer's Weak Counterexamples and the Creative Subject: A Critical Survey.
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 i...
| Publicado en: | Journal of Philosophical Logic Vol. 49; no. 6; pp. 1111 - 1158 |
|---|---|
| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Springer Nature
2020
|
| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=147157553&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 147157553 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00223611 JPH jtl: Journal of Philosophical Logic issn: 00223611 maglogo: N pubinfo: dt: 2020 vid: 49 iid: 6 pid: 237 pub: Springer Nature artinfo: ui: 147157553 10.1007/s10992-020-09551-y ppf: 1111 ppct: 47 formats: fmt: @attributes: type: P size: 960KB tig: atl: Brouwer's Weak Counterexamples and the Creative Subject: A Critical Survey. aug: au: Fletcher, Peter affil: School of Computing and Mathematics, Keele University, ST5 2BG, Keele, UK su: Mathematical proofs Plausibility (Logic) Axioms Evidence Continuity Argument sug: subj: Mathematical proofs Plausibility (Logic) Axioms Evidence Continuity Argument keyword: Brouwer Choice sequences Creative subject Intuitionistic analysis Intuitionistic logic Weak counterexamples ab: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Journal of Philosophical Logic is a copyright of Springer, 2020. All Rights Reserved. item: Journal of Philosophical Logic holder: Springer Nature dt: @attributes: year: 2020 holdings: @attributes: islocal: N |
|---|