Infinity and continuum in the alternative set theory.

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00360959" target="_blank" >RIV/68407700:21240/22:00360959 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s13194-021-00429-7" target="_blank" >https://doi.org/10.1007/s13194-021-00429-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13194-021-00429-7" target="_blank" >10.1007/s13194-021-00429-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Infinity and continuum in the alternative set theory.

Popis výsledku v původním jazyce

Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor’s set theory. Vopěnka criticised Cantor’s approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopˇenka grasps the phenomena of vagueness. Infinite sets are defined as sets containing proper semisets, i.e. vague parts of sets limited by the horizon. The new interpretation extends the field of applicability of mathematics and simultaneously indicates its limits. Compared to strict finitism and other attempts at a reduction of the infinite to the finite Vopˇenka’s theory reverses the process: he models the finite in the infinite.

Název v anglickém jazyce

Infinity and continuum in the alternative set theory.

Popis výsledku anglicky

Alternative set theory was created by the Czech mathematician Petr Vopěnka in 1979 as an alternative to Cantor’s set theory. Vopěnka criticised Cantor’s approach for its loss of correspondence with the real world. Alternative set theory can be partially axiomatised and regarded as a nonstandard theory of natural numbers. However, its intention is much wider. It attempts to retain a correspondence between mathematical notions and phenomena of the natural world. Through infinity, Vopˇenka grasps the phenomena of vagueness. Infinite sets are defined as sets containing proper semisets, i.e. vague parts of sets limited by the horizon. The new interpretation extends the field of applicability of mathematics and simultaneously indicates its limits. Compared to strict finitism and other attempts at a reduction of the infinite to the finite Vopˇenka’s theory reverses the process: he models the finite in the infinite.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

European Journal for Philosophy of Scinece

ISSN

1879-4912

e-ISSN

1879-4920

Svazek periodika

12

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

—

Kód UT WoS článku

000733737100002

EID výsledku v databázi Scopus

2-s2.0-85121731608