Perspectives on Science 18 (4):480-499 (2010)

Authors
Giambattista Formica
Pontifical Urbaniana University
Abstract
In spite of the many efforts made to clarify von Neumann’s methodology of science, one crucial point seems to have been disregarded in recent literature: his closeness to Hilbert’s spirit. In this paper I shall claim that the scientific methodology adopted by von Neumann in his later foundational reflections originates in the attempt to revaluate Hilbert’s axiomatics in the light of Gödel’s incompleteness theorems. Indeed, axiomatics continues to be pursued by the Hungarian mathematician in the spirit of Hilbert’s school. I shall argue this point by examining four basic ideas embraced by von Neumann in his foundational considerations: a) the conservative attitude to assume in mathematics; b) the role that mathematics and the axiomatic approach have to play in all that is science; c) the notion of success as an alternative methodological criterion to follow in scientific research; d) the empirical and, at the same time, abstract nature of mathematical thought. Once these four basic ideas have been accepted, Hilbert’s spirit in von Neumann’s methodology of science will become clear.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1162/POSC_a_00019
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
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

Some Facts About Kurt Gödel.Hao Wang - 1981 - Journal of Symbolic Logic 46 (3):653-659.
Discussion on the Foundation of Mathematics.John W. Dawson - 1984 - History and Philosophy of Logic 5 (1):111-129.

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

John von Neumann, Scientific Method and Empirical Economics.Salim Rashid - 1994 - Journal of Economic Methodology 1 (2):279-294.
That Von Neumann Did Not Believe in a Physical Collapse.Lon Becker - 2004 - British Journal for the Philosophy of Science 55 (1):121-135.
The Von Neumann Entropy: A Reply to Shenker.Leah Henderson - 2003 - British Journal for the Philosophy of Science 54 (2):291-296.
Von Neumann, Gödel and Complexity Theory.Alasdair Urquhart - 2010 - Bulletin of Symbolic Logic 16 (4):516-530.
Von Neumann's Argument for the Projection Postulate.Joseph D. Sneed - 1966 - Philosophy of Science 33 (1/2):22-39.
Reviews. [REVIEW]Yorick Wilks - 1982 - British Journal for the Philosophy of Science 33 (3):191-195.
The Birth of Quantum Logic.Miklós Rédei - 2007 - History and Philosophy of Logic 28 (2):107-122.

Analytics

Added to PP index
2010-10-03

Total views
241 ( #45,205 of 2,498,992 )

Recent downloads (6 months)
58 ( #13,950 of 2,498,992 )

How can I increase my downloads?

Downloads

My notes