The Logic and Metaphysics Workshop will meet on December 9th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Mark Colyvan (Sydney).
Title: Logic in Fiction
Abstract: This paper will address the question of whether the logic of a fiction can be specified as part of the fiction. For example, can one tell a fictional story in which it is part of the story that the logic in question is, say, K3? It seems unproblematic that we can do this. After all, we can tell a story about a world with a different geometry from ours, different physical laws, and even different numbers of dimensions (e.g. the two-dimensional world of Flatland). While allowing fictions to specify their own logics seems a natural extension of such science fiction, there are problems looming. Fictions are, by their very nature, incomplete. Specifying that the logic in question is classical is to embrace, amongst other things, classical principles such as excluded middle. But if the fictional world is incomplete, in what sense can it be part of the story that excluded middle holds? We would, in effect, be specifying that the incomplete situation described in the fiction is complete. Imposing excluded middle where it doesn’t belong leads to contradiction. These are especially pressing issues for (particular kinds of) fictionalism about mathematics.