Abstract

The Quine-Putnam indispensability argument runs as follows: We have reason to believe in Fs if Fs are indispensable to our best available science. Mathematical entities are indispensable to our best available science. Therefore, we have reason to believe in mathematical entities.According to the standard understanding, in order to refute the argument the nominalist has to show that mathematical entities are dispensable by providing an at least as good theory of the same phenomena that is not ontologically committed to mathematical entities. Most philosophers who write in this area, including John Burgess, Mark Colyvan, Hartry Field, Penelope Maddy, and Gideon Rosen, accept the standard understanding. Many nominalists who accept the standard understanding propose nominalistic paraphrases or alternatives, claiming that these are either equally good or better than our current scientific theories. Platonists deny that they are either equally good or better.