Philosophia Mathematica 20 (3):305-323 (2012)
|Abstract||The purpose of this article is show that second-order logic, as understood through standard semantics, is intimately bound up with set theory, or some other general theory of interpretations, structures, or whatever. Contra Quine, this does not disqualify second-order logic from its role in foundational studies. To wax Quinean, why should there be a sharp border separating mathematics from logic, especially the logic of mathematics?|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
B. Hale (forthcoming). Properties and the Interpretation of Second-Order Logic. Philosophia Mathematica.
Ignacio Jané (1993). A Critical Appraisal of Second-Order Logic. History and Philosophy of Logic 14 (1):67-86.
Jouko Vaananen (2001). Second-Order Logic and Foundations of Mathematics. Bulletin of Symbolic Logic 7 (4):504-520.
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.
Jouko Väänänen (2012). Second Order Logic or Set Theory? Bulletin of Symbolic Logic 18 (1):91-121.
Bart Jacobs (1989). The Inconsistency of Higher Order Extensions of Martin-Löf's Type Theory. Journal of Philosophical Logic 18 (4):399 - 422.
Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Kenny Easwaran (2010). Logic and Probability. Journal of the Indian Council of Philosophical Research 27 (2):229-253.
Yuri Gurevich & Saharon Shelah (1983). Interpreting Second-Order Logic in the Monadic Theory of Order. Journal of Symbolic Logic 48 (3):816-828.
Added to index2012-02-11
Total downloads52 ( #20,006 of 549,198 )
Recent downloads (6 months)3 ( #25,790 of 549,198 )
How can I increase my downloads?