Ante rem structuralism and the semantics of instantial terms
Ante rem structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless, ante rem structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an e...
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| Veröffentlicht in: | Synthese (Dordrecht) 2022-10, Vol.200 (5), p.420, Article 420 |
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| creator | Gutiérrez, Sofía Meléndez |
| description | Ante rem
structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless,
ante rem
structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an exactly analogous problem. If it cannot be sorted out, then the postulation of
ante rem
structures is futile. In a recent paper, Stewart Shapiro argued that the problem may be solved by analysing some of the singular terms of mathematics not as genuinely referring expressions, but as instantial terms. In this paper, I discuss several competing accounts of the semantics of terms of this kind, and argue that they are all untenable for the
ante rem
structuralist. Shapiro, then, still owes us an account of the semantics of instantial terms that suits the
ante rem
structuralist project. Without it, the
ante rem
structuralist is still unable to determine the reference of the singular terms of mathematics. |
| doi_str_mv | 10.1007/s11229-022-03856-y |
| format | Article |
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structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless,
ante rem
structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an exactly analogous problem. If it cannot be sorted out, then the postulation of
ante rem
structures is futile. In a recent paper, Stewart Shapiro argued that the problem may be solved by analysing some of the singular terms of mathematics not as genuinely referring expressions, but as instantial terms. In this paper, I discuss several competing accounts of the semantics of terms of this kind, and argue that they are all untenable for the
ante rem
structuralist. Shapiro, then, still owes us an account of the semantics of instantial terms that suits the
ante rem
structuralist project. Without it, the
ante rem
structuralist is still unable to determine the reference of the singular terms of mathematics.</description><identifier>ISSN: 1573-0964</identifier><identifier>ISSN: 0039-7857</identifier><identifier>EISSN: 1573-0964</identifier><identifier>DOI: 10.1007/s11229-022-03856-y</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Education ; Epistemology ; Logic ; Mathematics ; Metaphysics ; Original Research ; Philosophy ; Philosophy of Language ; Philosophy of Science ; Semantics ; Structuralism</subject><ispartof>Synthese (Dordrecht), 2022-10, Vol.200 (5), p.420, Article 420</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-ef73464a6a7b55cb47d890aa4c6e99f350ae8b03325def7877088ee46e78067b3</cites><orcidid>0000-0003-1786-158X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11229-022-03856-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11229-022-03856-y$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Gutiérrez, Sofía Meléndez</creatorcontrib><title>Ante rem structuralism and the semantics of instantial terms</title><title>Synthese (Dordrecht)</title><addtitle>Synthese</addtitle><description>Ante rem
structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless,
ante rem
structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an exactly analogous problem. If it cannot be sorted out, then the postulation of
ante rem
structures is futile. In a recent paper, Stewart Shapiro argued that the problem may be solved by analysing some of the singular terms of mathematics not as genuinely referring expressions, but as instantial terms. In this paper, I discuss several competing accounts of the semantics of terms of this kind, and argue that they are all untenable for the
ante rem
structuralist. Shapiro, then, still owes us an account of the semantics of instantial terms that suits the
ante rem
structuralist project. Without it, the
ante rem
structuralist is still unable to determine the reference of the singular terms of mathematics.</description><subject>Education</subject><subject>Epistemology</subject><subject>Logic</subject><subject>Mathematics</subject><subject>Metaphysics</subject><subject>Original Research</subject><subject>Philosophy</subject><subject>Philosophy of Language</subject><subject>Philosophy of Science</subject><subject>Semantics</subject><subject>Structuralism</subject><issn>1573-0964</issn><issn>0039-7857</issn><issn>1573-0964</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AIMQZ</sourceid><sourceid>AVQMV</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>K50</sourceid><sourceid>M1D</sourceid><sourceid>M2O</sourceid><recordid>eNp9kE1LAzEQhoMoWKt_wFPAc3TysUkWvJSiVSh40XPIbmd1S3e3JtlD_72pK-jJ08zA874DDyHXHG45gLmLnAtRMhCCgbSFZocTMuOFkQxKrU7_7OfkIsYtAOdawYzcL_qENGBHYwpjncbgd23sqO83NH0gjdj5PrV1pEND2z6m4-V3NGHo4iU5a_wu4tXPnJO3x4fX5RNbv6yel4s1qyVXiWFjpNLKa2-qoqgrZTa2BO9VrbEsG1mAR1uBlKLYZNYaA9YiKo3GgjaVnJObqXcfhs8RY3LbYQx9fumEEUJDzthMiYmqwxBjwMbtQ9v5cHAc3NGSmyy5bMl9W3KHHJJTKGa4f8fwW_1P6gt7Nmp-</recordid><startdate>20221007</startdate><enddate>20221007</enddate><creator>Gutiérrez, Sofía Meléndez</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7XB</scope><scope>8FK</scope><scope>8G5</scope><scope>AABKS</scope><scope>ABSDQ</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AIMQZ</scope><scope>AVQMV</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GB0</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>K50</scope><scope>LIQON</scope><scope>M1D</scope><scope>M2O</scope><scope>MBDVC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0003-1786-158X</orcidid></search><sort><creationdate>20221007</creationdate><title>Ante rem structuralism and the semantics of instantial terms</title><author>Gutiérrez, Sofía Meléndez</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-ef73464a6a7b55cb47d890aa4c6e99f350ae8b03325def7877088ee46e78067b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Education</topic><topic>Epistemology</topic><topic>Logic</topic><topic>Mathematics</topic><topic>Metaphysics</topic><topic>Original Research</topic><topic>Philosophy</topic><topic>Philosophy of Language</topic><topic>Philosophy of Science</topic><topic>Semantics</topic><topic>Structuralism</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gutiérrez, Sofía Meléndez</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Philosophy Collection</collection><collection>Philosophy Database</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest One Literature</collection><collection>Arts Premium Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>DELNET Social Sciences & Humanities Collection</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Art, Design & Architecture Collection</collection><collection>ProQuest One Literature - 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structures were posited as the subject matter of mathematics in order to resolve a problem of referential indeterminacy within mathematical discourse. Nevertheless,
ante rem
structuralists are inevitably committed to the existence of indiscernible entities, and this commitment produces an exactly analogous problem. If it cannot be sorted out, then the postulation of
ante rem
structures is futile. In a recent paper, Stewart Shapiro argued that the problem may be solved by analysing some of the singular terms of mathematics not as genuinely referring expressions, but as instantial terms. In this paper, I discuss several competing accounts of the semantics of terms of this kind, and argue that they are all untenable for the
ante rem
structuralist. Shapiro, then, still owes us an account of the semantics of instantial terms that suits the
ante rem
structuralist project. Without it, the
ante rem
structuralist is still unable to determine the reference of the singular terms of mathematics.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11229-022-03856-y</doi><orcidid>https://orcid.org/0000-0003-1786-158X</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Education Epistemology Logic Mathematics Metaphysics Original Research Philosophy Philosophy of Language Philosophy of Science Semantics Structuralism |
| title | Ante rem structuralism and the semantics of instantial terms |
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