Modal Structuralism with Theoretical Terms.
In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced...
| Publicado en: | Erkenntnis Vol. 88; no. 2; pp. 721 - 746 |
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| Autores principales: | , |
| Formato: | Artículo |
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Springer Nature
Feb2023
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=161692616&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 161692616 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01650106 5KZ jtl: Erkenntnis issn: 01650106 maglogo: N pubinfo: dt: Feb2023 vid: 88 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 161692616 10.1007/s10670-021-00378-w ppf: 721 ppct: 25 formats: fmt: – @attributes: type: T – @attributes: type: P size: 358KB tig: atl: Modal Structuralism with Theoretical Terms. aug: au: Andreas, Holger Schiemer, Georg affil: Department of Economic, Philosophy, and Political Science, University of British Columbia (Okanagan), Kelowna, Canada Department of Philosophy, University of Vienna, Vienna, Austria su: University of Oxford Oxford University Press Structuralism Philosophy of mathematics Semantics Poststructuralism Arithmetic Mathematics sug: subj: University of Oxford Oxford University Press Structuralism Philosophy of mathematics Semantics Poststructuralism Arithmetic Mathematics ab: In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all admissible interpretations of the Peano axioms. Moreover, we compare this application with the modal structuralism by Hellman (Mathematics without numbers: towards a modal-structural interpretation. Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Erkenntnis is a copyright of Springer, 2023. All Rights Reserved. item: Erkenntnis holder: Springer Nature dt: @attributes: year: 2023 holdings: @attributes: islocal: N |
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