Lampert, Timm (2017) Turing's Fallacies. [Preprint]
|
Text
turingfinal2.pdf Download (293kB) | Preview |
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.
Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
Social Networking: |
Item Type: | Preprint | ||||||
---|---|---|---|---|---|---|---|
Creators: |
|
||||||
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: | https://philsci-archive.pitt.edu/id/eprint/13398 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
View Item |