How to make (mathematical) assertions with directives.
It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical...
| Publicado en: | Synthese Vol. 202; no. 5; pp. 1 - 17 |
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| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Nov2023
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| Materias: | |
| 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=173034474&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 173034474 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Nov2023 vid: 202 iid: 5 pid: 237 pub: Springer Nature artinfo: ui: 173034474 10.1007/s11229-023-04360-7 ppf: 1 ppct: 16 formats: fmt: – @attributes: type: T – @attributes: type: P size: 324KB tig: atl: How to make (mathematical) assertions with directives. aug: au: Caponetto, Laura San Mauro, Luca Venturi, Giorgio affil: Newnham College, University of Cambridge, Cambridge, UK Dipartimento di Ricerca e Innovazione Umanistica, Università di Bari, Bari, Italy https://ror.org/03ad39j10 Dipartimento di Civiltà e Forme del Sapere, Universitá di Pisa, Pisa, Italy su: Success Collections sug: subj: Success Collections keyword: Assertions Directives Mathematical Language Proofs Speech Act Theory ab: It is prima facie uncontroversial that the justification of an assertion amounts to a collection of other (inferentially related) assertions. In this paper, we point at a class of assertions, i.e. mathematical assertions, that appear to systematically flout this principle. To justify a mathematical assertion (e.g. a theorem) is to provide a proof—and proofs are sequences of directives. The claim is backed up by linguistic data on the use of imperatives in proofs, and by a pragmatic analysis of theorems and their proofs. Proofs, we argue, are sequences of instructions whose performance inevitably gets one to truth. It follows that a felicitous theorem, i.e. a theorem that has been correctly proven, is a persuasive theorem. When it comes to mathematical assertions, there is no sharp distinction between illocutionary and perlocutionary success. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2023. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2023 holdings: @attributes: islocal: N |
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