Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox
The hypothesis is that a line can be divided into an infinite number of parts. The question is whether extension is a property of these infinitely small parts of the line. If the infinitely small parts are extensional then they can be further divided. On the other hand, if they have no extension how...
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ftslacadscienart:oai:ojs.zrc-sazu.si:article/3565 2023-05-15T18:12:56+02:00 Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox Manj kot nekaj, a več kot nič: Zenon, infinitezimali in paradoks kontinuuma Dolenc, Sašo 2016-01-11 application/pdf https://ojs.zrc-sazu.si/filozofski-vestnik/article/view/3565/3260 https://ojs.zrc-sazu.si/filozofski-vestnik/article/view/3565 slv slv ZRC SAZU, Založba ZRC https://ojs.zrc-sazu.si/filozofski-vestnik/article/view/3565 Filozofski vestnik; Vol. 23 No. 3 (2002): Philosophy and Scientific Revolution, Aesthetics, Empire and Society of Control Filozofski vestnik; Letn. 23 Št. 3 (2002): Filozofija in znanstvena revolucija, Estetika, Imperij in družba nadzora 1581-1239 0353-4510 philosophy of science philosophy of nature continuum infinitesimals history of mathematics infinity Zeno’s aporias filozofija znanosti filozofija narave kontinuum infinitezimali zgodovina matematika neskončnost Zenonove aporije info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2016 ftslacadscienart 2022-08-11T20:09:21Z The hypothesis is that a line can be divided into an infinite number of parts. The question is whether extension is a property of these infinitely small parts of the line. If the infinitely small parts are extensional then they can be further divided. On the other hand, if they have no extension how can they compose the line? The sum of non-extensional units can not be extensional. None of the answers explains the problem which is thus further considered to be the continuum paradox. Although the infinitesimal calculus does not solve the continuum paradox, it finds a way to deal with it by introducing infinitesimals as infinitely small parts that are neither extensional nor non-extensional. Even if infinitesimals have no extension, they can compose a line. Če predpostavimo, da je črta neskončno deljiva, jo lahko razdelimo na neskončno majhne dele, za katere ni jasno ali so razsežni ali ne. Če imajo razsežnost, jih lahko še naprej delimo, torej še niso neskončno razdeljeni. Če pa nimajo razsežnosti, potem ni jasno, kako lahko iz njih sestavimo razsežno črto, saj vsota nerazsežnih enot ne more biti razsežna. Nobeden od obeh možnih odgovorov problema ne razreši, zato problem obravnavamo kot paradoks kontinuuma. Čeprav infinitezimalni račun paradoksa kontinuuma ne razreši, vpelje infinitezimale kot neskončno majhne dele, ki niso ne točke ne daljice. Iz infinitezimalov lahko sestavimo črto, čeprav sami nimajo razsežnosti. Article in Journal/Newspaper sami ZRC SAZU Publishing (Znanstvenoraziskovalni center - Slovenske akademije znanosti in umetnosti) |
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Open Polar |
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ZRC SAZU Publishing (Znanstvenoraziskovalni center - Slovenske akademije znanosti in umetnosti) |
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ftslacadscienart |
language |
Slovenian |
topic |
philosophy of science philosophy of nature continuum infinitesimals history of mathematics infinity Zeno’s aporias filozofija znanosti filozofija narave kontinuum infinitezimali zgodovina matematika neskončnost Zenonove aporije |
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philosophy of science philosophy of nature continuum infinitesimals history of mathematics infinity Zeno’s aporias filozofija znanosti filozofija narave kontinuum infinitezimali zgodovina matematika neskončnost Zenonove aporije Dolenc, Sašo Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox |
topic_facet |
philosophy of science philosophy of nature continuum infinitesimals history of mathematics infinity Zeno’s aporias filozofija znanosti filozofija narave kontinuum infinitezimali zgodovina matematika neskončnost Zenonove aporije |
description |
The hypothesis is that a line can be divided into an infinite number of parts. The question is whether extension is a property of these infinitely small parts of the line. If the infinitely small parts are extensional then they can be further divided. On the other hand, if they have no extension how can they compose the line? The sum of non-extensional units can not be extensional. None of the answers explains the problem which is thus further considered to be the continuum paradox. Although the infinitesimal calculus does not solve the continuum paradox, it finds a way to deal with it by introducing infinitesimals as infinitely small parts that are neither extensional nor non-extensional. Even if infinitesimals have no extension, they can compose a line. Če predpostavimo, da je črta neskončno deljiva, jo lahko razdelimo na neskončno majhne dele, za katere ni jasno ali so razsežni ali ne. Če imajo razsežnost, jih lahko še naprej delimo, torej še niso neskončno razdeljeni. Če pa nimajo razsežnosti, potem ni jasno, kako lahko iz njih sestavimo razsežno črto, saj vsota nerazsežnih enot ne more biti razsežna. Nobeden od obeh možnih odgovorov problema ne razreši, zato problem obravnavamo kot paradoks kontinuuma. Čeprav infinitezimalni račun paradoksa kontinuuma ne razreši, vpelje infinitezimale kot neskončno majhne dele, ki niso ne točke ne daljice. Iz infinitezimalov lahko sestavimo črto, čeprav sami nimajo razsežnosti. |
format |
Article in Journal/Newspaper |
author |
Dolenc, Sašo |
author_facet |
Dolenc, Sašo |
author_sort |
Dolenc, Sašo |
title |
Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox |
title_short |
Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox |
title_full |
Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox |
title_fullStr |
Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox |
title_full_unstemmed |
Less then Something, but More then Nothing - Zeno, Infinitesimals and the Continuum Paradox |
title_sort |
less then something, but more then nothing - zeno, infinitesimals and the continuum paradox |
publisher |
ZRC SAZU, Založba ZRC |
publishDate |
2016 |
url |
https://ojs.zrc-sazu.si/filozofski-vestnik/article/view/3565/3260 https://ojs.zrc-sazu.si/filozofski-vestnik/article/view/3565 |
genre |
sami |
genre_facet |
sami |
op_source |
Filozofski vestnik; Vol. 23 No. 3 (2002): Philosophy and Scientific Revolution, Aesthetics, Empire and Society of Control Filozofski vestnik; Letn. 23 Št. 3 (2002): Filozofija in znanstvena revolucija, Estetika, Imperij in družba nadzora 1581-1239 0353-4510 |
op_relation |
https://ojs.zrc-sazu.si/filozofski-vestnik/article/view/3565 |
_version_ |
1766185413395873792 |