How mathematics confronts its paradoxes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11410%2F16%3A10367605" target="_blank" >RIV/00216208:11410/16:10367605 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

How mathematics confronts its paradoxes

Popis výsledku v původním jazyce

Paradoxes in mathematics such as the casus irreducibilis (Cardano 1545), the paradoxes of the calculus (Berkeley 1734) or Russell&apos;s paradox (Russell 1903) show surprisingly many common features. It is possible to see these paradoxes as linguistic phenomena occurring at a specific stage in the development of the particular theory. It seems that even though each paradox taken in isolation is well understood, the paradoxes as a general phenomenon still lack sufficient historical analysis. The paper analyzes the historical development of the language of the particular mathematical theory (i.e. algebra, calculus, and predicate logic respectively) and argues that the paradoxes occur at a particular phase of the historical development of the language; it characterizes that stage as the stage when in the language we begin to construct representations of representations. It argues that the paradoxes exhibit the expressive boundaries of the language of mathematics as introduced in (Kvasz 2008). That is why these paradoxes exhibit several common features-they correspond to the same epistemological phenomenon, namely expressive boundaries of language.

Název v anglickém jazyce

How mathematics confronts its paradoxes

Popis výsledku anglicky

Paradoxes in mathematics such as the casus irreducibilis (Cardano 1545), the paradoxes of the calculus (Berkeley 1734) or Russell&apos;s paradox (Russell 1903) show surprisingly many common features. It is possible to see these paradoxes as linguistic phenomena occurring at a specific stage in the development of the particular theory. It seems that even though each paradox taken in isolation is well understood, the paradoxes as a general phenomenon still lack sufficient historical analysis. The paper analyzes the historical development of the language of the particular mathematical theory (i.e. algebra, calculus, and predicate logic respectively) and argues that the paradoxes occur at a particular phase of the historical development of the language; it characterizes that stage as the stage when in the language we begin to construct representations of representations. It argues that the paradoxes exhibit the expressive boundaries of the language of mathematics as introduced in (Kvasz 2008). That is why these paradoxes exhibit several common features-they correspond to the same epistemological phenomenon, namely expressive boundaries of language.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

50301 - Education, general; including training, pedagogy, didactics [and education systems]

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Dějiny věd a techniky (History of Science and Technology)

ISSN

0300-4414

e-ISSN

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Svazek periodika

49

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

16

Strana od-do

249-264

Kód UT WoS článku

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EID výsledku v databázi Scopus

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