In Eeva Martikainen (ed.), Human Approaches to the Universe. Luther-Agricola-Society (2005)

Alfred Driessen
University of Twente
In this contribution an attempt is made to analyze an important mathematical discovery, the theorem of Gödel, and to explore the possible impact on the consistency of metaphysical systems. It is shown that mathematics is a pointer to a reality that is not exclusively subjected to physical laws. As the Gödel theorem deals with pure mathematics, the philosopher as such can not decide on the rightness of this theorem. What he, instead can do, is evaluating the general acceptance of this mathematical finding and reflect on the consistency between consequences of the mathematical theorem with consequences of his metaphysical view. The findings of three mathematicians are involved in the argumentation: first Gödel himself, then the further elaboration by Turing and finally the consequences for the human mind as worked out by Penrose. As a result one is encouraged to distinguish two different types of intellectual activity in mathematics, which both can be carried out by humans. The astonishing thing is not the distinction between a formalized, logic approach on the one side and intuition, mathematical insight and meaning on the other. Philosophically challenging, however, is the claim that principally only one of these intellectual activities can be carried out by objects exclusively bound to the laws of physical reality.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Buy the book Find it on
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

On the Philosophical Relevance of Gödel's Incompleteness Theorems.Panu Raatikainen - 2005 - Revue Internationale de Philosophie 59 (4):513-534.
The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
From Closed to Open Systems.Carlo Cellucci - 1993 - In J. Czermak (ed.), Philosophy of Mathematics, pp. 206-220. Hölder-Pichler-Tempsky.
Metamathematics, Machines and Gödel's Proof.N. Shankar - 1994 - Cambridge University Press.
Gödel and 'the Objective Existence' of Mathematical Objects.Pierre Cassou-Noguès - 2005 - History and Philosophy of Logic 26 (3):211-228.


Added to PP index

Total views
1,835 ( #1,958 of 2,439,308 )

Recent downloads (6 months)
103 ( #5,947 of 2,439,308 )

How can I increase my downloads?


My notes