Geometric diagrams as an effective notation.
In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's 'Why a diagram is (sometimes) worth 10,000 words', between diagrammatic and sentential notations as...
| Publicado en: | Philosophical Investigations Vol. 47; no. 4; pp. 558 - 584 |
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| Formato: | Artículo |
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Wiley-Blackwell
Oct2024
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| 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=180110787&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 180110787 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01900536 BS4 jtl: Philosophical Investigations issn: 01900536 maglogo: Y pubinfo: dt: Oct2024 vid: 47 iid: 4 pid: 480 pub: Wiley-Blackwell artinfo: ui: 180110787 10.1111/phin.12440 ppf: 558 ppct: 26 formats: fmt: – @attributes: type: T – @attributes: type: C – @attributes: type: P size: 710KB tig: atl: Geometric diagrams as an effective notation. aug: au: Mumma, John affil: California State University, San Bernardino California, , USA su: Mathematical proofs Mathematical notation Mathematics Geometry Vocabulary sug: subj: Mathematical proofs Mathematical notation Mathematics Geometry Vocabulary ab: In what way does a mathematical proof depend on the notation used in its presentation? This paper examines this question by analysing the computational differences, in the sense of Larkin and Simon's 'Why a diagram is (sometimes) worth 10,000 words', between diagrammatic and sentential notations as a means for presenting geometric proofs. Wittgenstein takes up the question of mathematical notation and proof in Section III of Remarks on the Foundations of Mathematics. After discussing his observations on a proof's 'characteristic visual shape' in Section III with respect to arithmetical proofs, the paper shows how the notion of a characteristic visual shape illuminates the special effectiveness of diagrammatic notation in geometry. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Philosophical Investigations is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Philosophical Investigations holder: Wiley-Blackwell dt: @attributes: year: 2024 holdings: @attributes: islocal: N |
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