David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Etica E Politica 5 (1):1 (2003)
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Andrzej Mostowski (1952/1982). Sentences Undecidable in Formalized Arithmetic: An Exposition of the Theory of Kurt Gödel. Greenwood Press.
N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.
George Boolos (1995). Introductory Note to Kurt Gödel's ``Some Basic Theorems on the Foundations of Mathematics and Their Implications''. In Solomon Feferman (ed.), Kurt Gödel, Collected Works. Oxford University Press 290-304.
Mark Steiner (2001). Wittgenstein as His Own Worst Enemy: The Case of Gödel's Theorem. Philosophia Mathematica 9 (3):257-279.
Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.
Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
Added to index2009-01-28
Total downloads123 ( #17,953 of 1,725,873 )
Recent downloads (6 months)34 ( #32,012 of 1,725,873 )
How can I increase my downloads?