Anti-nominalism reconsidered

Many philosophers of mathematics are attracted by nominalism, the doctrine that there are no sets, numbers, functions or other mathematical objects. John Burgess and Gideon Rosen have put forward an intriguing argument against nominalism, based on the thought that philosophy cannot overrule internal mathematical and scientific standards of acceptability. I argue that Burgess and Rosen's argument fails because it relies on a mistaken view of what the standards of mathematics require. © 2007 The Author.