Proofs and mistakes: Their syntactics, semantics, and pragmatics
Identifieur interne : 000C06 ( Istex/Curation ); précédent : 000C05; suivant : 000C07Proofs and mistakes: Their syntactics, semantics, and pragmatics
Auteurs : Solomon Marcus [Roumanie]Source :
- Semiotica [ 0037-1998 ] ; 2012-02.
Descripteurs français
- Wicri :
- topic : Langage de programmation.
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:
DOI: 10.1515/sem-2012-0010
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ISTEX:3AD9DA50003F80A6C709B8AF9715698367E82B77Le document en format XML
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<term>Computer programs</term>
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<term>Finite sets</term>
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<term>Formal system</term>
<term>Global understanding</term>
<term>Incompleteness theorem</term>
<term>Infinite hierarchy</term>
<term>Infinite sequence</term>
<term>Integer</term>
<term>Logical positivism</term>
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<term>Mathematical notions</term>
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<term>Nicolas bourbaki</term>
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<term>Syntactic component</term>
<term>Syntactic dimension</term>
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<term>True statements</term>
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<term>Cardinal number</term>
<term>Cognitive</term>
<term>Cognitive models</term>
<term>Color theorem</term>
<term>Computer programs</term>
<term>Computer science</term>
<term>Correctness</term>
<term>Demonstrative text</term>
<term>Demonstrative texts</term>
<term>Everyday life</term>
<term>Finite sets</term>
<term>First half</term>
<term>Formal system</term>
<term>Global understanding</term>
<term>Incompleteness theorem</term>
<term>Infinite hierarchy</term>
<term>Infinite sequence</term>
<term>Integer</term>
<term>Logical positivism</term>
<term>Mathematical analysis</term>
<term>Mathematical community</term>
<term>Mathematical language</term>
<term>Mathematical notions</term>
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<term>Mistake</term>
<term>Modeling process</term>
<term>Natural languages</term>
<term>Nicolas bourbaki</term>
<term>Nineteenth century</term>
<term>Other hand</term>
<term>Particular case</term>
<term>Polygonal lines</term>
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<term>Positive integers</term>
<term>Possible interpretations</term>
<term>Possible opposites</term>
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<term>Pragmatic aspect</term>
<term>Pragmatic dimension</term>
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<term>Programming language</term>
<term>Quantum object</term>
<term>Real function</term>
<term>Real numbers</term>
<term>Respective theorem</term>
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<term>Scientific community</term>
<term>Scientific theory</term>
<term>Second half</term>
<term>Semantic</term>
<term>Semantic dimension</term>
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<term>Semantic mistakes</term>
<term>Semantics</term>
<term>Semiotic dimensions</term>
<term>Sharp distinction</term>
<term>Such mistakes</term>
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<term>Syntactic component</term>
<term>Syntactic dimension</term>
<term>Syntactic mistakes</term>
<term>Syntactics</term>
<term>True statements</term>
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<front><div type="abstract" xml:lang="en">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.</div>
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