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Turing's Fallacies

Lampert, Timm (2017) Turing's Fallacies. [Preprint]

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Abstract

This paper reveals two fallacies in Turing's undecidability proof of first-order logic (FOL), namely, (i) an 'extensional fallacy': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a meaningful sentence is proven, and (ii) a 'fallacy of substitution': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a true sentence is proven. The first fallacy erroneously suggests that Turing's proof of the non-existence of a circle-free machine that decides whether an arbitrary machine is circular proves a significant proposition. The second fallacy suggests that FOL is undecidable.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Lampert, Timmlampertt@staff.hu-berlin.de
Keywords: Church-Turing Theorem; Cantor's Theorem; Diagonalization; Formalization; Alan Turing
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
General Issues > Philosophers of Science
Depositing User: Dr. Timm Lampert
Date Deposited: 08 Sep 2017 22:25
Last Modified: 08 Sep 2017 22:25
Item ID: 13398
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
General Issues > Philosophers of Science
Date: 6 September 2017
URI: http://philsci-archive.pitt.edu/id/eprint/13398

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