David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
It is often said that GödelÂ´s famous theorem of 1931 is equal to the Cretian Liar, who says that everything that he says is a lie. But GödelÂ´s result is only similar to this sophism and not equivalent to it. When mathematicians deal with GödelÂ´s theorem, then it is often the case that they become poetical or even emotional: some of them show a high esteem of it and others despise it. Wittgenstein sees the famous Liar as a useless language game which doesnÂ´t excite anybody. GödelÂ´s first incompleteness theorem shows us that in mathematics there are puzzles which have no solution at all and therefore in mathematics one should be very careful when one chooses a puzzle on which one wants to work. GödelÂ´s second imcompleteness theorem deals with hidden contradictions â€“ Wittgenstein shows a paradigmatic solution: he simply shrugs his shoulders on this problem and many mathematicians do so today as well. Wittgenstein says than GödelÂ´s results should not be treated as mathematical theorems, but as elements of the humanistic sciences. Wittgenstein sees them as something which should be worked on in a creative manner.
|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
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
FangWen Yuan (2008). Query the Triple Loophole of the Proof of Gödel Incompleteness Theorem. Proceedings of the Xxii World Congress of Philosophy 41:77-94.
Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Peter Smith (2013). An Introduction to Gödel's Theorems. Cambridge University Press.
Mark Steiner (2001). Wittgenstein as His Own Worst Enemy: The Case of Gödel's Theorem. Philosophia Mathematica 9 (3):257-279.
Charles Sayward (2001). On Some Much Maligned Remarks of Wittgenstein on Gödel. Philosophical Investigations 24 (3):262–270.
Raymond M. Smullyan (1993). Recursion Theory for Metamathematics. Oxford University Press.
Juliet Floyd (2001). Prose Versus Proof: Wittgenstein on Gödel, Tarski and Truth. Philosophia Mathematica 9 (3):280-307.
Added to index2010-11-17
Total downloads11 ( #308,441 of 1,902,168 )
Recent downloads (6 months)2 ( #346,051 of 1,902,168 )
How can I increase my downloads?