David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method . It renders the proof of the so–called fixed point theorem transparent. We also point out various historical details and make some observations on circularity and some comparisons with natural language. The sketch does not include the messy details of the arithmetization of the language, but the motive for arithmetization and what it should accomplish are made obvious. We suggest this as a way to teach the incompleteness results to students that have had a basic course in logic, which is more efficient than the standard textbooks. For the sake of self–containment Cantor’s original diagonalization is included. A broader and more technical perspective on diagonalization is given in [Gaifman 2005]. Motivated partly by didactic considerations, the present paper presents things somewhat differently. It also includes various points concerning natural language and circularity that appear only here
|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
Yi-Zhuang Chen (2004). Edgar Morin's Paradigm of Complexity and Gödel's Incompleteness Theorem. World Futures 60 (5 & 6):421 – 431.
John Bell (2008). Incompleteness in a General Setting (Vol 13, Pg 21, 2007). Bulletin of Symbolic Logic 14 (1):21 - 30.
Haim Gaifman (2006). Naming and Diagonalization, From Cantor to Gödel to Kleene. Logic Journal of the Igpl 14 (5):709-728.
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.
Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.
H. Gaifman (2000). What Godel's Incompleteness Result Does and Does Not Show. Journal of Philosophy 97 (8):462-471.
Samuel R. Buss (1994). On Gödel's Theorems on Lengths of Proofs I: Number of Lines and Speedup for Arithmetics. Journal of Symbolic Logic 59 (3):737-756.
Added to index2009-01-28
Total downloads44 ( #46,803 of 1,692,449 )
Recent downloads (6 months)3 ( #78,120 of 1,692,449 )
How can I increase my downloads?