David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 14 (1):67-86 (1993)
Because of its capacity to characterize mathematical concepts and structures?a capacity which first-order languages clearly lack?second-order languages recommend themselves as a convenient framework for much of mathematics, including set theory. This paper is about the credentials of second-order logic:the reasons for it to be considered logic, its relations with set theory, and especially the efficacy with which it performs its role of the underlying logic of set theory
|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
George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
John Corcoran (1973). Gaps Between Logical Theory and Mathematical Practice. In Mario Augusto Bunge (ed.), The Methodological Unity of Science. Boston,Reidel. 23--50.
Harvey M. Friedman (1971). Higher Set Theory and Mathematical Practice. Annals of Mathematical Logic 2 (3):325-357.
Citations of this work BETA
Timothy Williamson (2013). Logic, Metalogic and Neutrality. Erkenntnis:1-21.
Stewart Shapiro (2005). Sets and Abstracts – Discussion. [REVIEW] Philosophical Studies 122 (3):315 - 332.
Similar books and articles
Richard Kaye (2007). The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications. Cambridge University Press.
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Otávio Bueno (2010). A Defense of Second-Order Logic. Axiomathes 20 (2-3):365-383.
Kenny Easwaran (2010). Logic and Probability. Journal of the Indian Council of Philosophical Research 27 (2):229-253.
Jaakko Hintikka (2009). A Proof of Nominalism: An Exercise in Successful Reduction in Logic. In A. Hieke & H. Leitgeb (eds.), Reduction - Abstraction - Analysis. Ontos.
Jouko Väänänen (2012). Second Order Logic or Set Theory? Bulletin of Symbolic Logic 18 (1):91-121.
Gregory H. Moore (1980). Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory. History and Philosophy of Logic 1 (1-2):95-137.
S. Shapiro (2012). Higher-Order Logic or Set Theory: A False Dilemma. Philosophia Mathematica 20 (3):305-323.
Jouko Vaananen (2001). Second-Order Logic and Foundations of Mathematics. Bulletin of Symbolic Logic 7 (4):504-520.
Added to index2010-08-10
Total downloads43 ( #42,446 of 1,101,875 )
Recent downloads (6 months)4 ( #91,837 of 1,101,875 )
How can I increase my downloads?