McGee on open-ended schemas
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
A mathematical theory T is categorical if, and only if, any two models of T are isomorphic. If T is categorical, it can be shown to be semantically complete: for every sentence ϕ in the language of T, either ϕ follows semantically from T or ¬ϕ does. For this reason some authors maintain that categoricity theorems are philosophically significant: they support the realist thesis that mathematical statements have determinate truth-values. Second-order arithmetic (PA2) is a case in hand: it can be shown to be categorical and semantically complete. The status of second-order logic is a controversial issue, however. Worries about the purported set-theoretic nature and ontological commitments of second-order logic have been influential in the debate.
|Keywords||No keywords specified (fix it)|
No categories specified
(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
Jouko Väänänen (2012). Second Order Logic or Set Theory? Bulletin of Symbolic Logic 18 (1):91-121.
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Otávio Bueno (2010). A Defense of Second-Order Logic. Axiomathes 20 (2-3):365-383.
Olivier Lessmann (2003). Categoricity and U-Rank in Excellent Classes. Journal of Symbolic Logic 68 (4):1317-1336.
Gabriel Uzquiano (2002). Categoricity Theorems and Conceptions of Set. Journal of Philosophical Logic 31 (2):181-196.
Vilém Novák (1987). First-Order Fuzzy Logic. Studia Logica 46 (1):87 - 109.
Stephen Read (1997). Completeness and Categoricity: Frege, Gödel and Model Theory. History and Philosophy of Logic 18 (2):79-93.
Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg (2007). McGee on Open-Ended Schemas. In Helen Bohse & Sven Walter (eds.), Selected Contributions to GAP.6: Sixth International Conference of the German Society for Analytical Philosophy, Berlin, 11–14 September 2006. mentis.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #445,994 of 1,102,858 )
Recent downloads (6 months)0
How can I increase my downloads?