David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 79 (2):163 - 230 (2005)
In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|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
Felix Mühlhölzer (2010). Mathematical Intuition and Natural Numbers: A Critical Discussion. [REVIEW] Erkenntnis 73 (2):265–292.
Simon Friederich (2010). Structuralism and Meta-Mathematics. Erkenntnis 73 (1):67 - 81.
Walter Dean & Hidenori Kurokawa (2014). The Paradox of the Knower Revisited. Annals of Pure and Applied Logic 165 (1):199-224.
Albert Visser (2014). Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories. Mathematical Logic Quarterly 60 (1-2):92-117.
Similar books and articles
Calvin C. Elgot & Michael O. Rabin (1966). Decidability and Undecidability of Extensions of Second (First) Order Theory of (Generalized) Successor. Journal of Symbolic Logic 31 (2):169-181.
Solomon Feferman (2008). My Route to Arithmetization. Theoria 63 (3):168-181.
Miklós Erdélyi-Szabó (2000). Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis. Journal of Symbolic Logic 65 (3):1014-1030.
Karen Crawley, Limited Ink : Interpreting and Misinterpreting GÜdel's Incompleteness Theorem in Legal Theory.
Alfred B. Manaster (1975). Completeness, Compactness, and Undecidability: An Introduction to Mathematical Logic. Prentice-Hall.
Paul C. Rosenbloom (1950/2005). The Elements of Mathematical Logic. New York]Dover Publications.
Alfred Tarski (1968/2010). Undecidable Theories. Amsterdam, North-Holland Pub. Co..
Added to index2009-01-28
Total downloads46 ( #51,565 of 1,696,592 )
Recent downloads (6 months)4 ( #144,179 of 1,696,592 )
How can I increase my downloads?