ABSTRACT
Quine claimed that the contribution that mathematics makes to our best science provides sufficient evidence for the platonic existence of mathematical entities like numbers and sets. This chapter considers Quine’s position as well as recent extensions of it that emphasize inference to the best explanation (IBE). I show how a version of IBE that is based on scientific practice must retain the view that explanation requires truth, but should drop the claim that explanatory considerations can fix the natures of novel entities. If this restricted version of IBE is adopted, then IBE arguments for mathematical platonism fail. This chapter goes on to consider the fictionalist position that explanation does not require truth. I claim that fictionalists face a challenge that has been pressed by Colyvan: indicate how a fictional claim bears on the fact being explained. Until a positive account of the explanatory power of fictional claims is provided, we should stick with our starting assumption that explanation requires truth.
