David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 41 (1):53-58 (2000)
This lecture, given at Beijing University in 1984, presents a remarkable (previously unpublished) proof of the Gödel Incompleteness Theorem due to Kripke. Today we know purely algebraic techniques that can be used to give direct proofs of the existence of nonstandard models in a style with which ordinary mathematicians feel perfectly comfortable--techniques that do not even require knowledge of the Completeness Theorem or even require that logic itself be axiomatized. Kripke used these techniques to establish incompleteness by means that could, in principle, have been understood by nineteenth-century mathematicians. The proof exhibits a statement of number theory--one which is not at all "self referring"--and constructs two models, in one of which it is true and in the other of which it is false, thereby establishing "undecidability" (independence)
|Keywords||models of arithmetic nonstandard models of arithmetic|
|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
Mark Steiner (2001). Wittgenstein as His Own Worst Enemy: The Case of Gödel's Theorem. Philosophia Mathematica 9 (3):257-279.
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.
Bernd I. Dahn (1979). Constructions of Classical Models by Means of Kripke Models (Survey). Studia Logica 38 (4):401 - 405.
Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
Yi-Zhuang Chen (2004). Edgar Morin's Paradigm of Complexity and Gödel's Incompleteness Theorem. World Futures 60 (5 & 6):421 – 431.
N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.
Neil Thompson (2012). Arithmetic Proof and Open Sentences. Philosophy Study 2 (1):43-50.
Stephen Cole Kleene (1967/2002). Mathematical Logic. Dover Publications.
Joram Hirshfeld (1988). Nonstandard Combinatorics. Studia Logica 47 (3):221 - 232.
Ernest Nagel (1958). Gödel's Proof. [New York]New York University Press.
Juliet Floyd (2001). Prose Versus Proof: Wittgenstein on Gödel, Tarski and Truth. Philosophia Mathematica 9 (3):280-307.
Herbert A. Simon & Stuart A. Eisenstadt (1998). Human and Machine Interpretation of Expressions in Formal Systems. Synthese 116 (3):439-461.
Chris Mortensen (1987). Inconsistent Nonstandard Arithmetic. Journal of Symbolic Logic 52 (2):512-518.
Added to index2010-08-24
Total downloads45 ( #52,424 of 1,696,540 )
Recent downloads (6 months)1 ( #343,026 of 1,696,540 )
How can I increase my downloads?