Pictorial Aspects of Mathematical Notation in Wittgenstein: Numbers and 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

Pictorial Aspects of Mathematical Notation in Wittgenstein: Numbers and 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 prototypesof certain activities. (1) The pictorial aspect of numerals is expressed in the key definition of a cardinal number: "A cardinal number is an internal property of a list". (PR, p. 140) Wittgenstein's concrete and finitistic approach takes numeral for concrete objects as opposed to Frege-Russell's approach based on abstract sets.

Název v anglickém jazyce

Pictorial Aspects of Mathematical Notation in Wittgenstein: Numbers and 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 prototypesof certain activities. (1) The pictorial aspect of numerals is expressed in the key definition of a cardinal number: "A cardinal number is an internal property of a list". (PR, p. 140) Wittgenstein's concrete and finitistic approach takes numeral for concrete objects as opposed to Frege-Russell's approach based on abstract sets.

Druh

O - Ostatní výsledky

CEP obor

AA - Filosofie a náboženství

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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