Conceptual Contingency and Abstract Existence

I discuss the issue of whether the existence or non-existence of mathematical entities is a contingent matter. I focus on the debate between Hartry Field and Bob Hale and Crispin Wright, and I argue that a good reason for accepting that mathematical entities contingently exist or contingently fail to exist has been overlooked by all participants in this debate. © The Editors of The Philosophical Quarterly, 2000.