Mathematics and the mind

Abstract
Granted that truth is valuable we must recognize that certifiable truth is hard to come by, for example in the natural and social sciences. This paper examines the case of mathematics. As a result of the work of Gödel and Tarski we know that truth does not equate with proof. This has been used by Lucas and Penrose to argue that human minds can do things which digital computers can't, viz to know the truth of unprovable arithmetical statements. The argument is given a simple formulation in the context of sorites (Robinson) arithmetic, avoiding the complexities of formulating the Gödel sentence. The pros and cons of the argument are considered in relation to the conception of mathematical truth.
Keywords Arithmetic  Logic  Mathematics  Mind  Truth
Categories (categorize this paper)
DOI 10.1093/bjps/55.4.731
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,848
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Truth and Provability: A Comment on Redhead.Panu Raatikainen - 2005 - British Journal for the Philosophy of Science 56 (3):611-613.

Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
38 ( #148,278 of 2,210,516 )

Recent downloads (6 months)
8 ( #51,709 of 2,210,516 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature