A note on applicability of the incompleteness theorem to human mind
type: Item
instance of: scholarly article
title: A note on applicability of the incompleteness theorem to human mind
zbMATH Open document ID: 0923.03013
DOI: 10.1016/S0168-0072(98)00044-X
author: Pavel Pudlák
published in: Annals of Pure and Applied Logic
publication date: 1999-06-24T00:00:00Z
review text: The author reviews Lucas' argument on an application of incompleteness theorems to show that machines can never think (of course, there are numerous counterarguments, too) and Penrose's neoclassical extension of Lucas' thesis (with its numerous countercounter arguments). Recall that many logicians hold that Gödel's theorems are not relevant to the question of the realization of intelligent machines, anymore than mathematics is relevant to the physical world! He states that in mathematics, people make ``a lot of mistakes'', but these are correctable, in principle. The author's basic approach is to present relations between reflection principles (in the sense of G. Kreisel and A. Levy) and consistency.
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 68T01
zbMATH DE Number: 1308100
zbMATH Keywords: artificial intelligence
zbMATH Keywords: ordinal logics
zbMATH Keywords: transfinite recursion
zbMATH Keywords: incompleteness theorems
zbMATH Keywords: reflection principles
zbMATH Keywords: consistency
reviewed by: Albert A. Mullin
MaRDI profile type: Publication
cites work: Transfinite recursive progressions of axiomatic theories
cites work: Q4893132
cites work: Q5611757
cites work: Q4792066
cites work: Q5513756
cites work: Reflection Principles and their Use for Establishing the Complexity of Axiomatic Systems
cites work: Q4211927
full work available at URL: s0168-0072(98)00044-x
OpenAlex ID: W2080448143
description: scientific article; zbMATH DE number 1308100