On the semantics of mathematical statements
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Manuscrito (Online) |
Texto Completo: | https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643350 |
Resumo: | Husserl developed – independently of Frege – a semantics of sense and reference. There are, however, some important differences, specially with respect to the references of statements. According to Husserl, an assertive sentence refers to a state of affairs, which was its basis what he called a situation of affairs. Situations of affairs could also be considered as an alternative referent for statements on their own right, although for Husserl they were simply a sort of referential basis. Both Husserlian states of affairs and situations of affairs are extensional. Tarskian semantics can be rendered as a sort of state of affairs semantics. However, to assess adequately the existence of dual theorems in mathematics and, more generally, seemingly unrelated interderivable statements like the Axiom of Choice and its many equivalents, states of affairs (and truth-values) are not enough. We need a sort of refinement of the notion of a situation of affairs, namely what we have called elsewhere an abstract situation of affairs. We are going to introduce abstract situations of affairs as equivalence classes of states of affairs denoted by closed sentences of a given language which are true in the same models. We first sketch the procedure for a first-order many-sorted language and then for a second-order manysorted language. |
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On the semantics of mathematical statementsSemânticaSenso e referênciaHusserlHusserl developed – independently of Frege – a semantics of sense and reference. There are, however, some important differences, specially with respect to the references of statements. According to Husserl, an assertive sentence refers to a state of affairs, which was its basis what he called a situation of affairs. Situations of affairs could also be considered as an alternative referent for statements on their own right, although for Husserl they were simply a sort of referential basis. Both Husserlian states of affairs and situations of affairs are extensional. Tarskian semantics can be rendered as a sort of state of affairs semantics. However, to assess adequately the existence of dual theorems in mathematics and, more generally, seemingly unrelated interderivable statements like the Axiom of Choice and its many equivalents, states of affairs (and truth-values) are not enough. We need a sort of refinement of the notion of a situation of affairs, namely what we have called elsewhere an abstract situation of affairs. We are going to introduce abstract situations of affairs as equivalence classes of states of affairs denoted by closed sentences of a given language which are true in the same models. We first sketch the procedure for a first-order many-sorted language and then for a second-order manysorted language. Universidade Estadual de Campinas2007-12-31info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTextoapplication/pdfhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643350Manuscrito: Revista Internacional de Filosofia; v. 30 n. 2 (2007): Jul./Dez.; 317-340Manuscrito: International Journal of Philosophy; Vol. 30 No. 2 (2007): Jul./Dez.; 317-340Manuscrito: Revista Internacional de Filosofía; Vol. 30 Núm. 2 (2007): Jul./Dez.; 317-3402317-630Xreponame:Manuscrito (Online)instname:Universidade Estadual de Campinas (UNICAMP)instacron:UNICAMPporhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643350/10841Porto Rico; ContemporâneoCopyright (c) 2007 Manuscrito: Revista Internacional de Filosofiahttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessHaddock, Guillermo E. Rosado2022-05-26T14:59:27Zoai:ojs.periodicos.sbu.unicamp.br:article/8643350Revistahttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscritoPUBhttps://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/oaimwrigley@cle.unicamp.br|| dascal@spinoza.tau.ac.il||publicacoes@cle.unicamp.br2317-630X0100-6045opendoar:2022-05-26T14:59:27Manuscrito (Online) - Universidade Estadual de Campinas (UNICAMP)false |
dc.title.none.fl_str_mv |
On the semantics of mathematical statements |
title |
On the semantics of mathematical statements |
spellingShingle |
On the semantics of mathematical statements Haddock, Guillermo E. Rosado Semântica Senso e referência Husserl |
title_short |
On the semantics of mathematical statements |
title_full |
On the semantics of mathematical statements |
title_fullStr |
On the semantics of mathematical statements |
title_full_unstemmed |
On the semantics of mathematical statements |
title_sort |
On the semantics of mathematical statements |
author |
Haddock, Guillermo E. Rosado |
author_facet |
Haddock, Guillermo E. Rosado |
author_role |
author |
dc.contributor.author.fl_str_mv |
Haddock, Guillermo E. Rosado |
dc.subject.por.fl_str_mv |
Semântica Senso e referência Husserl |
topic |
Semântica Senso e referência Husserl |
description |
Husserl developed – independently of Frege – a semantics of sense and reference. There are, however, some important differences, specially with respect to the references of statements. According to Husserl, an assertive sentence refers to a state of affairs, which was its basis what he called a situation of affairs. Situations of affairs could also be considered as an alternative referent for statements on their own right, although for Husserl they were simply a sort of referential basis. Both Husserlian states of affairs and situations of affairs are extensional. Tarskian semantics can be rendered as a sort of state of affairs semantics. However, to assess adequately the existence of dual theorems in mathematics and, more generally, seemingly unrelated interderivable statements like the Axiom of Choice and its many equivalents, states of affairs (and truth-values) are not enough. We need a sort of refinement of the notion of a situation of affairs, namely what we have called elsewhere an abstract situation of affairs. We are going to introduce abstract situations of affairs as equivalence classes of states of affairs denoted by closed sentences of a given language which are true in the same models. We first sketch the procedure for a first-order many-sorted language and then for a second-order manysorted language. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-12-31 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Texto |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643350 |
url |
https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643350 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8643350/10841 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2007 Manuscrito: Revista Internacional de Filosofia https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2007 Manuscrito: Revista Internacional de Filosofia https://creativecommons.org/licenses/by/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.coverage.none.fl_str_mv |
Porto Rico; Contemporâneo |
dc.publisher.none.fl_str_mv |
Universidade Estadual de Campinas |
publisher.none.fl_str_mv |
Universidade Estadual de Campinas |
dc.source.none.fl_str_mv |
Manuscrito: Revista Internacional de Filosofia; v. 30 n. 2 (2007): Jul./Dez.; 317-340 Manuscrito: International Journal of Philosophy; Vol. 30 No. 2 (2007): Jul./Dez.; 317-340 Manuscrito: Revista Internacional de Filosofía; Vol. 30 Núm. 2 (2007): Jul./Dez.; 317-340 2317-630X 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) |
collection |
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 |
_version_ |
1800216565725003776 |