Why Post Did [Not] Have Turing’s Thesis

Sieg, Wilfried; Szabó, Máté; McLaughlin, Dawn

doi:10.1007/978-3-319-41842-1_7

Cited by 2 publications

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“…For a more detailed discussion of Gandy's constraints and his underlying physical assumptions, seeSieg and Byrnes (1999).7 That said, it should not be thought that Sieg equates Turing's and Post's takes on computability. See, in this respect,Sieg et al (2016).8 For a full presentation of the technical details of Sieg's axioms, seeSieg (2002a).…”

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confidence: 99%

Explication as a Three-Step Procedure: the case of the Church-Turing Thesis

Benedetto

2021

Euro Jnl Phil Sci

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In recent years two different axiomatic characterizations of the intuitive concept of effective calculability have been proposed, one by Sieg and the other by Dershowitz and Gurevich. Analyzing them from the perspective of Carnapian explication, I argue that these two characterizations explicate the intuitive notion of effective calculability in two different ways. I will trace back these two ways to Turing’s and Kolmogorov’s informal analyses of the intuitive notion of calculability and to their respective outputs: the notion of computorability and the notion of algorithmability. I will then argue that, in order to adequately capture the conceptual differences between these two notions, the classical two-step picture of explication is not enough. I will present a more fine-grained three-step version of Carnapian explication, showing how with its help the difference between these two notions can be better understood and explained.

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confidence: 99%