ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Manuscrito (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452019000400544 |
Resumo: | Abstract In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed. |
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ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMSPlatonic FormsObject of scientific knowledgeEkthesisEudoxusMathematicsAbstract In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed.UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência2019-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452019000400544Manuscrito v.42 n.4 2019reponame:Manuscrito (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMP10.1590/0100-6045.2019.v42n4.phinfo:eu-repo/semantics/openAccessHASPER,PIETER SJOERDeng2019-11-22T00:00:00Zoai:scielo:S0100-60452019000400544Revistahttp://www.scielo.br/scielo.php?script=sci_serial&pid=0100-6045&lng=pt&nrm=isoPUBhttps://old.scielo.br/oai/scielo-oai.phpmwrigley@cle.unicamp.br|| dascal@spinoza.tau.ac.il||publicacoes@cle.unicamp.br2317-630X0100-6045opendoar:2019-11-22T00:00Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP)false |
dc.title.none.fl_str_mv |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
title |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
spellingShingle |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS HASPER,PIETER SJOERD Platonic Forms Object of scientific knowledge Ekthesis Eudoxus Mathematics |
title_short |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
title_full |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
title_fullStr |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
title_full_unstemmed |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
title_sort |
ARISTOTLE’S ARGUMENT FROM UNIVERSAL MATHEMATICS AGAINST THE EXISTENCE OF PLATONIC FORMS |
author |
HASPER,PIETER SJOERD |
author_facet |
HASPER,PIETER SJOERD |
author_role |
author |
dc.contributor.author.fl_str_mv |
HASPER,PIETER SJOERD |
dc.subject.por.fl_str_mv |
Platonic Forms Object of scientific knowledge Ekthesis Eudoxus Mathematics |
topic |
Platonic Forms Object of scientific knowledge Ekthesis Eudoxus Mathematics |
description |
Abstract In Metaphysics M.2, 1077a9-14, Aristotle appears to argue against the existence of Platonic Forms on the basis of there being certain universal mathematical proofs which are about things that are ‘beyond’ the ordinary objects of mathematics and that cannot be identified with any of these. It is a very effective argument against Platonism, because it provides a counter-example to the core Platonic idea that there are Forms in order to serve as the object of scientific knowledge: the universal of which theorems of universal mathematics are proven in Greek mathematics is neither Quantity in general nor any of the specific quantities, but Quantity-of-type-x. This universal cannot be a Platonic Form, for it is dependent on the types of quantity over which the variable ranges. Since for both Plato and Aristotle the object of scientific knowledge is that F which explains why G holds, as shown in a ‘direct’ proof about an arbitrary F (they merely disagree about the ontological status of this arbitrary F, whether a Form or a particular used in so far as it is F), Plato cannot maintain that Forms must be there as objects of scientific knowledge - unless the mathematics is changed. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-12-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452019000400544 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0100-60452019000400544 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/0100-6045.2019.v42n4.ph |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência |
publisher.none.fl_str_mv |
UNICAMP - Universidade Estadual de Campinas, Centro de Lógica, Epistemologia e História da Ciência |
dc.source.none.fl_str_mv |
Manuscrito v.42 n.4 2019 reponame:Manuscrito (Online) instname:Universidade Estadual de Campinas (UNICAMP) instacron:UNICAMP |
instname_str |
Universidade Estadual de Campinas (UNICAMP) |
instacron_str |
UNICAMP |
institution |
UNICAMP |
reponame_str |
Manuscrito (Online) |
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Manuscrito (Online) |
repository.name.fl_str_mv |
Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP) |
repository.mail.fl_str_mv |
mwrigley@cle.unicamp.br|| dascal@spinoza.tau.ac.il||publicacoes@cle.unicamp.br |
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1748950065880236032 |