How mathematics confronts its paradoxes

Result code in 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>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

How mathematics confronts its paradoxes

Original language description

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.

Czech name

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Czech description

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Type

J_ost - Miscellaneous article in a specialist periodical

CEP classification

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OECD FORD branch

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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Dějiny věd a techniky (History of Science and Technology)

ISSN

0300-4414

e-ISSN

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Volume of the periodical

49

Issue of the periodical within the volume

4

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

16

Pages from-to

249-264

UT code for WoS article

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EID of the result in the Scopus database

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