Hale's argument from transitive counting.
A core commitment of Bob Hale and Crispin Wright's neologicism is their invocation of Frege's Constraint—roughly, the requirement that the core empirical applications for a class of numbers be "built directly into" their formal characterization. According to these neologicists, if legitimate, Frege'...
| Publicado en: | Synthese Vol. 198; no. 3; pp. 1905 - 1934 |
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| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Mar2021
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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=149449428&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 149449428 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Mar2021 vid: 198 iid: 3 pid: 237 pub: Springer Nature artinfo: ui: 149449428 10.1007/s11229-019-02178-w ppf: 1905 ppct: 29 formats: fmt: @attributes: type: P size: 712KB tig: atl: Hale's argument from transitive counting. aug: au: Snyder, Eric Samuels, Richard Shaprio, Stewart affil: Smith College, Northampton, USA Ohio State, Columbus, USA su: Argument Counting Numerals Axioms Structuralism Kernel (Mathematics) Multiply transitive groups sug: subj: Argument Counting Numerals Axioms Structuralism Kernel (Mathematics) Multiply transitive groups keyword: Frege's Constraint Hume's Principle Neologicism ab: A core commitment of Bob Hale and Crispin Wright's neologicism is their invocation of Frege's Constraint—roughly, the requirement that the core empirical applications for a class of numbers be "built directly into" their formal characterization. According to these neologicists, if legitimate, Frege's Constraint adjudicates in favor of their preferred foundation—Hume's Principle—and against alternatives, such as the Dedekind–Peano axioms. In this paper, we consider a recent argument for legitimating Frege's Constraint due to Hale, according to which the primary empirical application of the naturals is transitive counting, or answering 'how many'-questions using numerals. We make two claims regarding Hale's argument. First, it fails to legitimate Frege's Constraint in virtue of resting on unsupported and highly contentious assumptions. Secondly, even if sound, Hale's argument would vindicate a version of Frege's Constraint which fails to adjudicate in favor of Hume's Principle over alternative characterizations of the naturals. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2021. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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