Neologicism, Frege's Constraint, and the Frege‐Heck Condition.
One of the more distinctive features of Bob Hale and Crispin Wright's neologicism about arithmetic 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. In particular, t...
| Publicado en: | Nous (0029-4624) Vol. 54; no. 1; pp. 54 - 78 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Wiley-Blackwell
Mar2020
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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=141784780&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 141784780 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00294624 D97 jtl: Nous (0029-4624) issn: 00294624 maglogo: Y pubinfo: dt: Mar2020 vid: 54 iid: 1 pid: 480 pub: Wiley-Blackwell artinfo: ui: 141784780 10.1111/nous.12249 ppf: 54 ppct: 24 formats: fmt: – @attributes: type: T – @attributes: type: P size: 198KB tig: atl: Neologicism, Frege's Constraint, and the Frege‐Heck Condition. aug: au: Snyder, Eric Samuels, Richard Shapiro, Stewart affil: Ohio State University (Philosophy) su: Foundations of arithmetic Arithmetic Axioms Numerals Counting Mental arithmetic sug: subj: Foundations of arithmetic Arithmetic Axioms Numerals Counting Mental arithmetic ab: One of the more distinctive features of Bob Hale and Crispin Wright's neologicism about arithmetic 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. In particular, they maintain that, if adopted, Frege's Constraint adjudicates in favor of their preferred foundation – Hume's Principle – and against alternatives, such as the Dedekind‐Peano axioms. In what follows we establish two main claims. First, we show that, if sound, Hale and Wright's arguments for Frege's Constraint at most establish a version on which the relevant application of the naturals is transitive counting – roughly, the counting procedure by which numerals are used to answer "how many"‐questions. Second, we show that this version of Frege's Constraint fails to adjudicate in favor of Hume's Principle. If this is the version of Frege's Constraint that a foundation for arithmetic must respect, then Hume's Principle no more – and no less – meets the requirement than the Dedekind‐Peano axioms do. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Nous (0029-4624) is the property of Wiley-Blackwell 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: Nous (0029-4624) holder: Wiley-Blackwell dt: @attributes: year: 2020 holdings: @attributes: islocal: N |
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