Back to Search
Start Over
Mathematics and the Mind.
- Source :
-
British Journal for the Philosophy of Science . Dec2004, Vol. 55 Issue 4, p731-737. 7p. - Publication Year :
- 2004
-
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 Godel 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 Güdel sentence. The pros and cons of the argument are considered in relation to the conception of mathematical truth. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATHEMATICS
*SOCIAL sciences
*NATURAL history
*PHILOSOPHY
*ARITHMETIC
*COMPUTERS
Subjects
Details
- Language :
- English
- ISSN :
- 00070882
- Volume :
- 55
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- British Journal for the Philosophy of Science
- Publication Type :
- Academic Journal
- Accession number :
- 15679227
- Full Text :
- https://doi.org/10.1093/bjps/55.4.731