Lauener Foundation for Analytical Philosophy
Friday 30 May 2008
3rd International Lauener Symposium on Analytical Philosophy
In Honour of Professor Ruth Barcan Marcus
Prof. Dr. Timothy Williamson
Barcan Formulas in Second-Order Modal Logic
On the natural extension of Kripke-style possible worlds semantics to second-order modal logic, the Barcan schema and its converse are valid for the second-order quantifiers even though they are invalid for the first-order quantifiers.
I will argue that this creates a metaphysical puzzle, which is no mere artifact of a particular style of formal semantics. Rather, natural comprehension principles for the second-order quantifiers cohere best with a metaphysical conception on which the Barcan schema and its converse hold for both first-order and second-order quantifiers.