Phenomenological Approach to Infinity and Continuum

Result code in 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>

Result on the web

<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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Result language

angličtina

Original language name

Phenomenological Approach to Infinity and Continuum

Original language description

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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

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

Article name in the collection

Philosophy of Logic and Mathematics

ISBN

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ISSN

1022-3398

e-ISSN

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Number of pages

3

Pages from-to

248-250

Publisher name

Austrian Ludwig Wittgenstein Society

Place of publication

Kirchberg am Wechsel

Event location

Kirchberg am Wechsel

Event date

Aug 5, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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