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Title: The Implications of Gödel's Theorem
Authors: Lucas, John R.
Keywords: mechanismGödel, Kurt
Issue Date: 2003
Publisher: EUT Edizioni Università di Trieste
Source: J.R. Lucas, "The Implications of Gödel's Theorem", in: Etica & Politica / Ethics & Politics, V (2003) 1
Series/Report no.: Etica & Politica / Ethics & Politics
V (2003) 1
After a brief and informal explanation of the Gödel’s theorem as a version of the Epimenides’ paradox applied to Elementary Number Theory formulated in first-order logic, Lucas shows some of the most relevant consequences of this theorem, such as the impossibility to define truth in terms of provability and so the failure of Verificationist and Intuitionist arguments. He shows moreover how Gödel’s theorem proves that first-order arithmetic admits non-standard models, that Hilbert’s programme is untenable and that second-order logic is not mechanical. There are furthermore some more general consequences: the difference between being reasonable and following a rule and the possibility that one man’s insight differs from another’s without being wrong. Finally some consequences concerning moral and political philosophy can arise from Gödel’s theorem, because it suggests that – instead of some fundamental principle from which all else follows deductively – we can seek for different arguments in different situations.
Type: Article
ISSN: 1825-5167
Appears in Collections:Etica & Politica / Ethics & Politics (2003) V/1

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