MATHEMATICAL TRUTH WITHOUT REFERENCE.
According to a canonical argument for mathematical platonism, if we are to have a uniform semantics which covers both mathematical and non-mathematical language, then we must understand singular terms in mathematics as referring to objects and understand quantifiers as ranging over a domain of such...
| Published in: | Problems / Problemos pp. 70 - 78 |
|---|---|
| Main Author: | |
| Format: | Article |
| Published: |
Vilnius University
2014 Supplement
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=100424171&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 100424171 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 13921126 3D4C jtl: Problems / Problemos issn: 13921126 maglogo: N pubinfo: dt: 2014 Supplement pid: 16037 pub: Vilnius University artinfo: ui: 100424171 ppf: 70 ppct: 8 formats: fmt: @attributes: type: P size: 1.5MB tig: atl: MATHEMATICAL TRUTH WITHOUT REFERENCE. aug: au: McCullough-Benner, Colin affil: University of Connecticut Department of Philosophy, 344 Mansfield Road, Unit 1054, University of Connecticut, Storrs, CT 06269-1054, USA su: Mathematical analysis Ontology Semantics Platonists Precept (Canon law) Compositionality (Linguistics) sug: subj: Mathematical analysis Ontology Semantics Platonists Precept (Canon law) Compositionality (Linguistics) keyword: anti-realism antirealizmas compositionality kompozicionalumas matematika Mathematics nereferentinė semantika non-referential semantics ontological commitment ontologinis įsipareigojimas platonism platonizmas antirealizmas kompozicionalumas matematika nereferentinė semantika ontologinis įsipareigojimas platonizmas ab: According to a canonical argument for mathematical platonism, if we are to have a uniform semantics which covers both mathematical and non-mathematical language, then we must understand singular terms in mathematics as referring to objects and understand quantifiers as ranging over a domain of such objects, and so treating mathematics as literally true commits us to the existence of (mind-independent, abstract) mathematical objects. In this paper, I argue that insofar as we can provide a uniform semantics for the better part of ordinary, non-mathematical language, we can provide a uniform semantics covering both mathematical and non-mathematical language without thereby committing ourselves to the existence of mathematical objects. Pagal kanoninį argumentą, remiantį matematinį platonizmą, vieninga semantika, apimanti matematinę ir nematematinę kalbą, įmanoma tik jei matematikos singuliarinius terminus laikysime nurodančiais objektus, o kvantorius -- apimančiais tokių objektų sritį, todėl jei matematikos teiginius laikome teisingais tiesiogine prasme, tai įpareigoja mus pripažinti (nuo mąstymo nepriklausomų, abstrakčių) matematinių objektų egzistavimą. Šiame straipsnyje siekiama įrodyti, kad jei mes galime sukurti vieningą semantiką reikšmingai daliai kasdienės nematematinės kalbos, tai galime sukurti vieningą semantiką apimančią matematinę ir nematematinę kalbą, neįsipareigodami matematinių objektų egzistavimui. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Problems / Problemos is the property of Vilnius University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Problems / Problemos holder: Vilnius University dt: @attributes: year: 2014 holdings: @attributes: islocal: N |
|---|