Quine's double standard: undermining the indispensability argument via the indeterminacy of reference
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Principia (Florianópolis. Online) |
Texto Completo: | https://periodicos.ufsc.br/index.php/principia/article/view/14734 |
Resumo: | Quine has famously put forward the indispensability argument to force belief in the existence of mathematical objects (such as classes) due to their indispensability to our best theories of the world (Quine 1960). Quine has also advocated the indeterminacy of reference argument, according to which reference is dramatically indeterminate: given a language, there’s no unique reference relation for that language (see Quine 1969a). In this paper, I argue that these two arguments are in conflict with each other. Whereas the indispensability argument supports realism about mathematics, the indeterminacy of reference argument, when applied to mathematics, provides a powerful strategy in support of mathematical anti-realism. I conclude the paper by indicating why the indeterminacy of reference phenomenon shouldbe preferred over the considerations regarding indispensability. In the end, even the Quinean shouldn’t be a realist (platonist) about mathematics. |
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Quine's double standard: undermining the indispensability argument via the indeterminacy of referenceQuine has famously put forward the indispensability argument to force belief in the existence of mathematical objects (such as classes) due to their indispensability to our best theories of the world (Quine 1960). Quine has also advocated the indeterminacy of reference argument, according to which reference is dramatically indeterminate: given a language, there’s no unique reference relation for that language (see Quine 1969a). In this paper, I argue that these two arguments are in conflict with each other. Whereas the indispensability argument supports realism about mathematics, the indeterminacy of reference argument, when applied to mathematics, provides a powerful strategy in support of mathematical anti-realism. I conclude the paper by indicating why the indeterminacy of reference phenomenon shouldbe preferred over the considerations regarding indispensability. In the end, even the Quinean shouldn’t be a realist (platonist) about mathematics.Federal University of Santa Catarina – UFSC2003-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufsc.br/index.php/principia/article/view/1473410.5007/%xPrincipia: an international journal of epistemology; Vol. 7 No. 1-2 (2003); 17-39Principia: an international journal of epistemology; Vol. 7 Núm. 1-2 (2003); 17-39Principia: an international journal of epistemology; v. 7 n. 1-2 (2003); 17-391808-17111414-4247reponame:Principia (Florianópolis. Online)instname:Universidade Federal de Santa Catarina (UFSC)instacron:UFSCporhttps://periodicos.ufsc.br/index.php/principia/article/view/14734/13475Copyright (c) 2021 Otávio Buenohttp://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessBueno, Otávio2016-01-02T12:16:55Zoai:periodicos.ufsc.br:article/14734Revistahttps://periodicos.ufsc.br/index.php/principiaPUBhttps://periodicos.ufsc.br/index.php/principia/oaiprincipia@contato.ufsc.br||principia@contato.ufsc.br1808-17111414-4247opendoar:2016-01-02T12:16:55Principia (Florianópolis. Online) - Universidade Federal de Santa Catarina (UFSC)false |
dc.title.none.fl_str_mv |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
title |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
spellingShingle |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference Bueno, Otávio |
title_short |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
title_full |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
title_fullStr |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
title_full_unstemmed |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
title_sort |
Quine's double standard: undermining the indispensability argument via the indeterminacy of reference |
author |
Bueno, Otávio |
author_facet |
Bueno, Otávio |
author_role |
author |
dc.contributor.author.fl_str_mv |
Bueno, Otávio |
description |
Quine has famously put forward the indispensability argument to force belief in the existence of mathematical objects (such as classes) due to their indispensability to our best theories of the world (Quine 1960). Quine has also advocated the indeterminacy of reference argument, according to which reference is dramatically indeterminate: given a language, there’s no unique reference relation for that language (see Quine 1969a). In this paper, I argue that these two arguments are in conflict with each other. Whereas the indispensability argument supports realism about mathematics, the indeterminacy of reference argument, when applied to mathematics, provides a powerful strategy in support of mathematical anti-realism. I conclude the paper by indicating why the indeterminacy of reference phenomenon shouldbe preferred over the considerations regarding indispensability. In the end, even the Quinean shouldn’t be a realist (platonist) about mathematics. |
publishDate |
2003 |
dc.date.none.fl_str_mv |
2003-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ufsc.br/index.php/principia/article/view/14734 10.5007/%x |
url |
https://periodicos.ufsc.br/index.php/principia/article/view/14734 |
identifier_str_mv |
10.5007/%x |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.ufsc.br/index.php/principia/article/view/14734/13475 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2021 Otávio Bueno http://creativecommons.org/licenses/by-nc-nd/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2021 Otávio Bueno http://creativecommons.org/licenses/by-nc-nd/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Federal University of Santa Catarina – UFSC |
publisher.none.fl_str_mv |
Federal University of Santa Catarina – UFSC |
dc.source.none.fl_str_mv |
Principia: an international journal of epistemology; Vol. 7 No. 1-2 (2003); 17-39 Principia: an international journal of epistemology; Vol. 7 Núm. 1-2 (2003); 17-39 Principia: an international journal of epistemology; v. 7 n. 1-2 (2003); 17-39 1808-1711 1414-4247 reponame:Principia (Florianópolis. Online) instname:Universidade Federal de Santa Catarina (UFSC) instacron:UFSC |
instname_str |
Universidade Federal de Santa Catarina (UFSC) |
instacron_str |
UFSC |
institution |
UFSC |
reponame_str |
Principia (Florianópolis. Online) |
collection |
Principia (Florianópolis. Online) |
repository.name.fl_str_mv |
Principia (Florianópolis. Online) - Universidade Federal de Santa Catarina (UFSC) |
repository.mail.fl_str_mv |
principia@contato.ufsc.br||principia@contato.ufsc.br |
_version_ |
1789435110157713408 |