A Pictorial Aspect of Mathematical Notation in Wittgenstein: Proofs

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A Pictorial Aspect of Mathematical Notation in Wittgenstein: Proofs

Popis výsledku v původním jazyce

The core in Wittgenstein’s conception of mathematics can be summed up in the motto that “arithmetical rules are statements of internal relations.” (PPO: p. 390) I am going to focus on Wittgenstein’s insistence on a certain pictorial aspect of mathematical notation, which is, of course, his Tractarian heritage. Mathematical notation must always be capable to depicture a state of affairs. This is true of numbers, but also of mathematical proofs. Numbers and proofs are for Wittgenstein a sort of prototypes of certain activities. Mathematical propositions are statements of internal relations as well. A proof of a mathematical proposition aims to picture or rather lay down its internal relatedness to a system of other mathematical rules. We may say that “the completely analysed mathematical proposition is its own proof.” (PR: p. 192) Proof is so a picture of an experiment, even more “it can be thought of as a cinematographic picture” (RFM: p. 159).

Název v anglickém jazyce

A Pictorial Aspect of Mathematical Notation in Wittgenstein: Proofs

Popis výsledku anglicky

The core in Wittgenstein’s conception of mathematics can be summed up in the motto that “arithmetical rules are statements of internal relations.” (PPO: p. 390) I am going to focus on Wittgenstein’s insistence on a certain pictorial aspect of mathematical notation, which is, of course, his Tractarian heritage. Mathematical notation must always be capable to depicture a state of affairs. This is true of numbers, but also of mathematical proofs. Numbers and proofs are for Wittgenstein a sort of prototypes of certain activities. Mathematical propositions are statements of internal relations as well. A proof of a mathematical proposition aims to picture or rather lay down its internal relatedness to a system of other mathematical rules. We may say that “the completely analysed mathematical proposition is its own proof.” (PR: p. 192) Proof is so a picture of an experiment, even more “it can be thought of as a cinematographic picture” (RFM: p. 159).

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Philosophy of Logic and Mathematics

ISBN

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ISSN

1022-3398

e-ISSN

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Počet stran výsledku

3

Strana od-do

123-125

Název nakladatele

The Austrian Ludwig Wittgenstein Society

Místo vydání

Kirchberg am We chsel

Místo konání akce

Kirchberg am We chsel

Datum konání akce

5. 8. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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