Can Church’s thesis be viewed as a Carnapian explication?

Paula Quinon

Abstract

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.
Author Paula Quinon (FASS)
Paula Quinon,,
- Faculty of Administration and Social Science
Journal seriesSynthese, ISSN 0039-7857, e-ISSN 1573-0964, (N/A 200 pkt)
Issue year2019
Pages1-28
Publication size in sheets1.35
Keywords in EnglishExplications; Rudolf Carnap; The Church–Turing thesis; Church’s thesis; Computability; Axiomatic systems; Structuralism
ASJC Classification1211 Philosophy; 3300 General Social Sciences
DOIDOI:10.1007/s11229-019-02286-7
URL https://link.springer.com/article/10.1007%2Fs11229-019-02286-7
Languageen angielski
Score (nominal)200
Score sourcejournalList
ScoreMinisterial score = 200.0, 03-02-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.149; WoS Impact Factor: 2018 = 1.262 (2) - 2018=1.149 (5)
Citation count*
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?