Phenomenological Approach to Infinity and Continuum

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F18%3A00328906" target="_blank" >RIV/68407700:21240/18:00328906 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.alws.at/abstract_2018.pdf" target="_blank" >https://www.alws.at/abstract_2018.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Phenomenological Approach to Infinity and Continuum

Popis výsledku v původním jazyce

Since the 1960s, when Robinson non-standard analysis was established, several other non-standard models of natural and real numbers have been created. The not widely known theory of the Czech mathematician Petr Vopěnka, Alternative Set Theory, AST, was also developed. It is an alternative to Cantor Set Theory, which Vopěnka criticized for numerous reasons. Cantor’s justification for accepting the actual infinity was theological; in modern axiomatic systems it is expressed by the axiom of infinity. Infinite hierarchy of infinite cardinal and ordinal numbers finds minimal interpretation in the real world. The existence of independent theorems leads to dividing set theory into several branches, from which none can be considered the sole truth. Vopěnka’s AST relies on phenomenology and endeavours to interpret basic terms of infinite mathematics in the real world. It uses the infinite for the mathematization of indistinctness. Apart from classic sets and classes, here so-called semisets are introduced. AST can be partially formalized as the non-standard model. Similarly, as with other non-standard theories, it does not bring breakthrough mathematical results that have been impossible to describe in a standard manner. What is substantial is its philosophical interpretation, which attempts to retain correspondence with the real world. It offers the solution of certain old philosophical problems: Zeno's paradoxes, sorites, Leibniz’s conception of continuum, Pascal’s double infinity.

Název v anglickém jazyce

Phenomenological Approach to Infinity and Continuum

Popis výsledku anglicky

Since the 1960s, when Robinson non-standard analysis was established, several other non-standard models of natural and real numbers have been created. The not widely known theory of the Czech mathematician Petr Vopěnka, Alternative Set Theory, AST, was also developed. It is an alternative to Cantor Set Theory, which Vopěnka criticized for numerous reasons. Cantor’s justification for accepting the actual infinity was theological; in modern axiomatic systems it is expressed by the axiom of infinity. Infinite hierarchy of infinite cardinal and ordinal numbers finds minimal interpretation in the real world. The existence of independent theorems leads to dividing set theory into several branches, from which none can be considered the sole truth. Vopěnka’s AST relies on phenomenology and endeavours to interpret basic terms of infinite mathematics in the real world. It uses the infinite for the mathematization of indistinctness. Apart from classic sets and classes, here so-called semisets are introduced. AST can be partially formalized as the non-standard model. Similarly, as with other non-standard theories, it does not bring breakthrough mathematical results that have been impossible to describe in a standard manner. What is substantial is its philosophical interpretation, which attempts to retain correspondence with the real world. It offers the solution of certain old philosophical problems: Zeno's paradoxes, sorites, Leibniz’s conception of continuum, Pascal’s double infinity.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10101 - Pure mathematics

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

248-250

Název nakladatele

Austrian Ludwig Wittgenstein Society

Místo vydání

Kirchberg am Wechsel

Místo konání akce

Kirchberg am Wechsel

Datum konání akce

5. 8. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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