BourbakiV1, Istex, Corpus, bibRecord, 000C06

Proofs and mistakes: Their syntactics, semantics, and pragmatics

Identifieur interne : 000C06 ( Istex/Corpus ); précédent : 000C05; suivant : 000C07

Proofs and mistakes: Their syntactics, semantics, and pragmatics

Auteurs : Solomon Marcus

Source :

Semiotica [ 0037-1998 ] ; 2012-02.

RBID : ISTEX:3AD9DA50003F80A6C709B8AF9715698367E82B77

English descriptors

KwdEn :
- Abductive approach, Cardinal number, Cognitive, Cognitive models, Color theorem, Computer programs, Computer science, Correctness, Demonstrative text, Demonstrative texts, Everyday life, Finite sets, First half, Formal system, Global understanding, Incompleteness theorem, Infinite hierarchy, Infinite sequence, Integer, Logical positivism, Mathematical analysis, Mathematical community, Mathematical language, Mathematical notions, Mathematician, Mistake, Modeling process, Natural languages, Nicolas bourbaki, Nineteenth century, Other hand, Particular case, Polygonal lines, Positive integer, Positive integers, Possible interpretations, Possible opposites, Pragmatic, Pragmatic aspect, Pragmatic dimension, Pragmatic mistakes, Pragmatics, Programming language, Quantum object, Real function, Real numbers, Respective theorem, Rigor, Scientific community, Scientific theory, Second half, Semantic, Semantic dimension, Semantic mistake, Semantic mistakes, Semantics, Semiotic dimensions, Sharp distinction, Such mistakes, Syntactic, Syntactic component, Syntactic dimension, Syntactic mistakes, Syntactics, True statements, Twentieth century, Variant.
Teeft :
- Abductive approach, Cardinal number, Cognitive, Cognitive models, Color theorem, Computer programs, Computer science, Correctness, Demonstrative text, Demonstrative texts, Everyday life, Finite sets, First half, Formal system, Global understanding, Incompleteness theorem, Infinite hierarchy, Infinite sequence, Integer, Logical positivism, Mathematical analysis, Mathematical community, Mathematical language, Mathematical notions, Mathematician, Mistake, Modeling process, Natural languages, Nicolas bourbaki, Nineteenth century, Other hand, Particular case, Polygonal lines, Positive integer, Positive integers, Possible interpretations, Possible opposites, Pragmatic, Pragmatic aspect, Pragmatic dimension, Pragmatic mistakes, Pragmatics, Programming language, Quantum object, Real function, Real numbers, Respective theorem, Rigor, Scientific community, Scientific theory, Second half, Semantic, Semantic dimension, Semantic mistake, Semantic mistakes, Semantics, Semiotic dimensions, Sharp distinction, Such mistakes, Syntactic, Syntactic component, Syntactic dimension, Syntactic mistakes, Syntactics, True statements, Twentieth century, Variant.

Abstract

We point out the syntactic, semantic, and pragmatic levels of proofs and of mistakes in mathematics and the increasing difficulties in checking the correctness of a proof. We analyze the role of mistakes in mathematical creativity and we point out the frequency of mistakes (malign or benign) in works opening new ways in science. Significant examples are provided.

Url:

https://api.istex.fr/document/3AD9DA50003F80A6C709B8AF9715698367E82B77/fulltext/pdf

DOI: 10.1515/sem-2012-0010

Links to Exploration step

ISTEX:3AD9DA50003F80A6C709B8AF9715698367E82B77

Le document en format XML

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<p>We point out the syntactic, semantic, and pragmatic levels of proofs and of mistakes in mathematics and the increasing difficulties in checking the correctness of a proof. We analyze the role of mistakes in mathematical creativity and we point out the frequency of mistakes (malign or benign) in works opening new ways in science. Significant examples are provided.</p>

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Proofs and mistakes: Their syntactics, semantics, and pragmatics

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