Quine called a logician who views a second-order quantifier as ranging over predicates "confused". I am a "confused logician", and in this talk I will explore the philosophical plausibility and implication of such an interpretation of second-order quantifiers.
Quine's rejection came from his thoroughgoing nominal understanding of quantifiers. Nowadays, we are liberated from the Quinean constraint, thanks to Boolos and others. Boolos took a second-order quantifier as ranging over plurals, Rayo and Yablo took it as ranging over the ways objects are related, and there must be some other theories. However, there still seems to be a strong reluctance among philosophers to take a second-order quantifier as ranging over predicates as such. There are some understandable reasons for the reluctance, but they are not compelling. Actually, as I will argue, the predicative interpretation of second-order quantification is not as "confused" as it has been thought and has a number of advantages over its rivals.
I would classify my talk as mainly on the philosophy of logic, but it is also related to the philosophy of mathematics, the debate on absolute generality, the philosophy of language, and possibly the debate on universals in metaphysics. I will be exploring ideas rather than presenting a settled view, and comments or objections from any area of philosophy may be helpful and will be appreciated!
See the seminar webpage http://users.ox.ac.uk/~philmath/pomseminar.html for title and abstract of the last talk in the seminar this term, by Volker Halbach on 17 June.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Volker Halbach