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

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Abstract
This paper reveals two fallacies in Turing's undecidability proof of firstorder 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 nonexistence of a circlefree 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  

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Keywords:  ChurchTuring 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:  https://philsciarchive.pitt.edu/id/eprint/13398 
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