Article ID: CBB000740617

Gödel and “The objective existence” of Mathematical Objects (2005)

unapi

This paper is a discussion of Go del's arguments for a Platonistic conception of mathematical objects. I review the arguments that Go del offers in different papers, and compare them to unpublished material (from Go del's Nachlass). My claim is that Go del's later arguments simply intend to establish that mathematical knowledge cannot be accounted for by a reflexive analysis of our mental acts. In other words, there is at the basis of mathematics some data whose constitution cannot be explained by introspective analysis. This does not mean that mathematics is independent of the human mind, but only that it is independent of our `conscious acts and decisions', to use Godel's own words. Mathematical objects may then have been created by the human mind, but if so, the process of creation cannot be completely analysed and re-enacted. Such a thesis is weaker than some of the statements that Go del made about his conceptual realism. However, there is evidence that Godel seriously considered this weak thesis, or a position depending only on this weak thesis. He also criticized Husserl's Phenomenology from this point of view.

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Authors & Contributors
Heijenoort, Jean van
Tieszen, Richard L.
Gödel, Kurt
Dawson, John W., Jr.
Feferman, Solomon
Grattan-Guinness, Ivor
Journals
History and Philosophy of Logic
Synthese
Theoria (0495-4548)
Studies in History and Philosophy of Science
Perspectives on Science
Almagest
Publishers
Oxford University Press
Cambridge University Press
Princeton University Press
Harvard University Press
Gangemi Editore
W. W. Norton & Co.
Concepts
Mathematics
Philosophy of mathematics
Logic
Incompleteness theorems
Philosophy
Philosophy of science
People
Gödel, Kurt
Hilbert, David
Turing, Alan Mathison
Cantor, Georg Ferdinand Ludwig
Russell, Bertrand Arthur William
Frege, Gottlob
Time Periods
20th century
20th century, early
19th century
Ancient
Places
Middle and Near East
Mesopotamia
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