On the available partial respects in which an axiomatization for real valued arithmetic can recognize its consistency
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 71 (4):1189-1199 (2006)
Gödel’s Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show that axiomatizations for a computer’s floating point arithmetic can recognize their cut-free consistency in a stronger respect than is feasible under integer arithmetics. This paper will include both new generalizations of the Second Incompleteness Theorem and techniques for evading it
|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 (2001). Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles. Journal of Symbolic Logic 66 (2):536-596.
Dan E. Willard (2005). An Exploration of the Partial Respects in Which an Axiom System Recognizing Solely Addition as a Total Function Can Verify its Own Consistency. Journal of Symbolic Logic 70 (4):1171-1209.
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.
Leszek Aleksander Kołodziejczyk (2006). On the Herbrand Notion of Consistency for Finitely Axiomatizable Fragments of Bounded Arithmetic Theories. Journal of Symbolic Logic 71 (2):624 - 638.
Laureano Luna & Alex Blum (2008). Arithmetic and Logic Incompleteness: The Link. The Reasoner 2 (3):6.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
Albert Visser (2012). The Second Incompleteness Theorem and Bounded Interpretations. Studia Logica 100 (1-2):399-418.
Added to index2010-08-24
Total downloads3 ( #292,614 of 1,100,944 )
Recent downloads (6 months)1 ( #290,065 of 1,100,944 )
How can I increase my downloads?