Philosophia Mathematica 14 (2):229-254 (2006)

Abstract
In his 1951 Gibbs Lecture Gödel formulates the central implication of the incompleteness theorems as a disjunction: either the human mind infinitely surpasses the powers of any finite machine or there exist absolutely unsolvable diophantine problems (of a certain type). In his later writings in particular Gödel favors the view that the human mind does infinitely surpass the powers of any finite machine and there are no absolutely unsolvable diophantine problems. I consider how one might defend such a view in light of Gödel's remark that one can turn to ideas in Husserlian transcendental phenomenology to show that the human mind ‘contains an element totally different from a finite combinatorial mechanism’.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkj008
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 56,999
Through your library

References found in this work BETA

On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
What is Cantor's Continuum Problem?S. C. Kleene - 1948 - Journal of Symbolic Logic 13 (2):116-117.
Is Mathematics Syntax of Language?Kurt Gödel - 1953 - In K. Gödel Collected Works. Oxford University Press: Oxford. pp. 334--355.

View all 7 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Gödel and the Intuition of Concepts.Richard Tieszen - 2002 - Synthese 133 (3):363 - 391.
Gödel and 'the Objective Existence' of Mathematical Objects.Pierre Cassou-Noguès - 2005 - History and Philosophy of Logic 26 (3):211-228.
Mechanism and Godel's Theorem.William H. Hanson - 1971 - British Journal for the Philosophy of Science 22 (February):9-16.
Godel's Theorem and Mechanism.David Coder - 1969 - Philosophy 44 (September):234-7.

Analytics

Added to PP index
2010-08-17

Total views
54 ( #184,684 of 2,410,442 )

Recent downloads (6 months)
1 ( #540,320 of 2,410,442 )

How can I increase my downloads?

Downloads

My notes