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

Giambattista Formica
Pontifical Urbaniana University
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.
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DOI 10.1162/POSC_a_00019
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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.

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