Fictionalism, Mathematical Facts and Logical/Modal Facts

ISBN: 978-3-88405-511-3

Abstract

In this paper, Balaguer does two things.  First, he develops an anti-platonistic theory of what mathematical facts--or, more precisely, the proto-mathematical facts behind our mathematical theories--ultimately consist in.  On the view he develops, these proto-mathematical facts decompose into (a) logical/modal facts and (b) physical-empirical facts.  (Just about all of the mathematically interesting facts boil down to certain kinds of logical/modal facts, but B. argues that there are also some empirical facts about heads--in particular, about our mathematical intentions--that are relevant to determining which mathematical sentences are correct.)  Second, B develops a non-spooky theory of logical/modal facts, i.e., a theory that’s consistent with the rejection of both abstract objects and non-actual possible worlds.

About the Author

Mark Balaguer is professor of philosophy at California State University, Los Angeles.  He is the author of *Platonism and Anti-Platonism in Mathematics* (Oxford University Press, 1998), *Free Will as an Open Scientific Problem* (MIT Press, 2010), and numerous articles in the areas of metaphysics, philosophy of mathematics, philosophy of language, and metaethics.