Synthese 198 (Suppl 5):1047-1074 (2019)

Authors
Paula Quinon
Lund University
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.
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DOI 10.1007/s11229-019-02286-7
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.

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Citations of this work BETA

Implicit and Explicit Examples of the Phenomenon of Deviant Encodings.Paula Quinon - 2020 - Studies in Logic, Grammar and Rhetoric 63 (1):53-67.
Explication as a Three-Step Procedure: The Case of the Church-Turing Thesis.Matteo De Benedetto - 2021 - European Journal for Philosophy of Science 11 (1):1-28.

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