Arithmetic, set theory, reduction and explanation.
Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship...
| Publicado en: | Synthese Vol. 195; no. 11; pp. 5059 - 5090 |
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| Formato: | Artículo |
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Springer Nature
Nov2018
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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=133200396&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 133200396 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Nov2018 vid: 195 iid: 11 pid: 237 pub: Springer Nature artinfo: ui: 133200396 10.1007/s11229-017-1450-8 ppf: 5059 ppct: 31 formats: fmt: – @attributes: type: T – @attributes: type: P size: 609KB tig: atl: Arithmetic, set theory, reduction and explanation. aug: au: D’Alessandro, William affil: Department of Philosophy, University of Illinois-Chicago, 1423 University Hall (MC 267), 601 South Morgan Street, 60607-7109, Chicago, IL, USA su: Philosophy of science Philosophy of mathematics Philosophers Set theory Arithmetic sug: subj: Philosophy of science Philosophy of mathematics Philosophers Set theory Arithmetic keyword: Explanation Intertheoretic reduction ab: Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important and well-known case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense of this claim, I offer some evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate and successful foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2018. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2018 holdings: @attributes: islocal: N |
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