Can Church's thesis be viewed as a Carnapian explication?
Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerni...
| Publicado en: | Synthese Vol. 198; pp. 1047 - 1075 |
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| Formato: | Artículo |
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Springer Nature
Mar2021 Supplement 5
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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=149550158&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 149550158 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Mar2021 Supplement 5 vid: 198 pid: 237 pub: Springer Nature artinfo: ui: 149550158 10.1007/s11229-019-02286-7 ppf: 1047 ppct: 28 formats: fmt: @attributes: type: P size: 503KB tig: atl: Can Church's thesis be viewed as a Carnapian explication? aug: au: Quinon, Paula affil: International Center for Formal Ontology, Warsaw University of Technology, Warsaw, Poland su: Carnap, Rudolf, 1891-1970 Recursion theory Mathematical logic Mathematical forms sug: subj: Carnap, Rudolf, 1891-1970 Recursion theory Mathematical logic Mathematical forms keyword: Axiomatic systems Church's thesis Computability Explications Rudolf Carnap Structuralism The Church–Turing thesis ab: Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church's and Turing's theses as explications. This move opens up the possibility that both accounts could be adequate, albeit in their own different ways. In this paper, I focus on the question of whether Church's thesis can be seen as an explication in the precise Carnapian sense. Most importantly, I address an additional constraint that Carnap puts on the explicative power of axiomatic systems—an axiomatisation explicates when it is clear which mathematical entities form the theory's intended model—and that implicitly applies to axiomatisations of recursion theory used in Church's account of computability. To overcome this difficulty, I propose two possible clarifications of the pre-systematic concept of "computability" that can both be captured in recursion theory, and I show how both clarifications avoid an objection arising from Carnap's constraint. 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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