Prof. Hartry Field will be our Quinn speaker this year on Friday, December 3 at 3:00 in DeBartolo Hall, Room 126.
The talk is titled: Conventionalism about Mathematics and Logic
There are two somewhat separable components of standard platonism: the existence of mathematical objects, and a certain kind of mathematical objectivity. The talk will consider three views of mathematics that are “pluralist” in that they are opposed to at least the second component of platonism: (i) fictionalism (which rejects the first component as well); (ii) the multiverse view (aka plenitudinous platonism); and (iii) mathematical conventionalism. I will tentatively argue that mathematical conventionalism must collapse into one of the other two views. This is disappointing, since one might have wanted a pluralism that extends to all of logic, and only conventionalism seems to offer an initial prospect of doing so. (More limited pluralism about logic remains a possibility.) If there’s time I’ll discuss how to cut off at the pass an argument of Peter Koellner’s against any significant pluralism in mathematics, based on the need for an objective notion of consistency.