David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 40 (2):207-226 (1999)
An open formalism for arithmetic is presented based on first-order logic supplemented by a very strictly controlled constructive form of the omega-rule. This formalism (which contains Peano Arithmetic) is proved (nonconstructively, of course) to be complete. Besides this main formalism, two other complete open formalisms are presented, in which the only inference rule is modus ponens. Any closure of any theorem of the main formalism is a theorem of each of these other two. This fact is proved constructively for the stronger of them and nonconstructively for the weaker one. There is, though, an interesting counterpart: the consistency of the weaker formalism can be proved finitarily
|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
Dan E. Willard (2002). How to Extend the Semantic Tableaux and Cut-Free Versions of the Second Incompleteness Theorem Almost to Robinson's Arithmetic Q. Journal of Symbolic Logic 67 (1):465-496.
Juliette Kennedy (2009). Gödel's Modernism: On Set Theoretic Incompleteness, Revisited. In Sten Lindström, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.), Logicism, Intuitionism and Formalism: What has become of them? Springer.
Alexander Bochman (1998). Biconsequence Relations: A Four-Valued Formalism of Reasoning with Inconsistency and Incompleteness. Notre Dame Journal of Formal Logic 39 (1):47-73.
Carlo Cellucci (1993). From Closed to Open Systems. In J. Czermak (ed.), Philosophy of Mathematics, pp. 206-220. Hölder-Pichler-Tempsky.
Laureano Luna & Alex Blum (2008). Arithmetic and Logic Incompleteness: The Link. The Reasoner 2 (3):6.
Scott Hotton & Jeff Yoshimi (2011). Extending Dynamical Systems Theory to Model Embodied Cognition. Cognitive Science 35 (3):444-479.
Nick Zangwill (1999). Feasible Aesthetic Formalism. Noûs 33 (4):610-629.
Cristian S. Calude (2002). Incompleteness, Complexity, Randomness and Beyond. Minds and Machines 12 (4):503-517.
Nick Zangwill (2005). In Defence of Extreme Formalism About Inorganic Nature: Reply to Parsons. British Journal of Aesthetics 45 (2):185-191.
Glen Hoffmann (2007). The Semantic Theory of Truth: Field's Incompleteness Objection. Philosophia 35 (2):161-170.
Raymond M. Smullyan (1993). Recursion Theory for Metamathematics. Oxford University Press.
Added to index2010-08-24
Total downloads3 ( #333,273 of 1,410,004 )
Recent downloads (6 months)1 ( #176,758 of 1,410,004 )
How can I increase my downloads?