On the Nature of Mathematical Knowledge
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Tipo de documento: | Capítulo de livro |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-90-481-9422-3_10 http://hdl.handle.net/11449/228906 |
Resumo: | An important point of contention in the philosophy of mathematics concerns the existence of mathematical objects. Platonists believe they exist independently; nominalists, that they are only linguistic constructs; formalists, that mathematics is not at all a science of objects. I believe the existence of mathematical objects is in fact immaterial for the understanding of the nature of mathematical knowledge. Mathematical truths are formal and only the formal properties of arbitrary domains of objects – whether they exist on their own or are only “intentional correlates” of their theories – matter to mathematics. This perspective has the advantage of making the applicability of mathematics in science less “unreasonable”, connecting it directly to the indifference of formal truth to material context. In this paper I intend to argue for an epistemologically relevant ontologically uncommitted formalist philosophy of mathematics (far from the “rules of the game” variety of formalism) that strips the ontological problem of its philosophical relevance and renders the applicability problem more treatable. |
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On the Nature of Mathematical KnowledgeCausal TheoryFormal PropertyMathematical KnowledgeMathematical ObjectMathematical PracticeAn important point of contention in the philosophy of mathematics concerns the existence of mathematical objects. Platonists believe they exist independently; nominalists, that they are only linguistic constructs; formalists, that mathematics is not at all a science of objects. I believe the existence of mathematical objects is in fact immaterial for the understanding of the nature of mathematical knowledge. Mathematical truths are formal and only the formal properties of arbitrary domains of objects – whether they exist on their own or are only “intentional correlates” of their theories – matter to mathematics. This perspective has the advantage of making the applicability of mathematics in science less “unreasonable”, connecting it directly to the indifference of formal truth to material context. In this paper I intend to argue for an epistemologically relevant ontologically uncommitted formalist philosophy of mathematics (far from the “rules of the game” variety of formalism) that strips the ontological problem of its philosophical relevance and renders the applicability problem more treatable.Department of Mathematics Unesp-Rio ClaroDepartment of Mathematics Unesp-Rio ClaroUniversidade Estadual Paulista (UNESP)da Silva, Jairo José [UNESP]2022-04-29T08:29:23Z2022-04-29T08:29:23Z2011-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart151-160http://dx.doi.org/10.1007/978-90-481-9422-3_10Boston Studies in the Philosophy and History of Science, v. 290, p. 151-160.2214-79420068-0346http://hdl.handle.net/11449/22890610.1007/978-90-481-9422-3_102-s2.0-85101981339Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengBoston Studies in the Philosophy and History of Scienceinfo:eu-repo/semantics/openAccess2022-04-29T08:29:23Zoai:repositorio.unesp.br:11449/228906Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462022-04-29T08:29:23Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
On the Nature of Mathematical Knowledge |
title |
On the Nature of Mathematical Knowledge |
spellingShingle |
On the Nature of Mathematical Knowledge da Silva, Jairo José [UNESP] Causal Theory Formal Property Mathematical Knowledge Mathematical Object Mathematical Practice |
title_short |
On the Nature of Mathematical Knowledge |
title_full |
On the Nature of Mathematical Knowledge |
title_fullStr |
On the Nature of Mathematical Knowledge |
title_full_unstemmed |
On the Nature of Mathematical Knowledge |
title_sort |
On the Nature of Mathematical Knowledge |
author |
da Silva, Jairo José [UNESP] |
author_facet |
da Silva, Jairo José [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
da Silva, Jairo José [UNESP] |
dc.subject.por.fl_str_mv |
Causal Theory Formal Property Mathematical Knowledge Mathematical Object Mathematical Practice |
topic |
Causal Theory Formal Property Mathematical Knowledge Mathematical Object Mathematical Practice |
description |
An important point of contention in the philosophy of mathematics concerns the existence of mathematical objects. Platonists believe they exist independently; nominalists, that they are only linguistic constructs; formalists, that mathematics is not at all a science of objects. I believe the existence of mathematical objects is in fact immaterial for the understanding of the nature of mathematical knowledge. Mathematical truths are formal and only the formal properties of arbitrary domains of objects – whether they exist on their own or are only “intentional correlates” of their theories – matter to mathematics. This perspective has the advantage of making the applicability of mathematics in science less “unreasonable”, connecting it directly to the indifference of formal truth to material context. In this paper I intend to argue for an epistemologically relevant ontologically uncommitted formalist philosophy of mathematics (far from the “rules of the game” variety of formalism) that strips the ontological problem of its philosophical relevance and renders the applicability problem more treatable. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-01-01 2022-04-29T08:29:23Z 2022-04-29T08:29:23Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/bookPart |
format |
bookPart |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-90-481-9422-3_10 Boston Studies in the Philosophy and History of Science, v. 290, p. 151-160. 2214-7942 0068-0346 http://hdl.handle.net/11449/228906 10.1007/978-90-481-9422-3_10 2-s2.0-85101981339 |
url |
http://dx.doi.org/10.1007/978-90-481-9422-3_10 http://hdl.handle.net/11449/228906 |
identifier_str_mv |
Boston Studies in the Philosophy and History of Science, v. 290, p. 151-160. 2214-7942 0068-0346 10.1007/978-90-481-9422-3_10 2-s2.0-85101981339 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Boston Studies in the Philosophy and History of Science |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
151-160 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1803649680189423616 |