In Defense of Benacerraf’s Multiple-Reductions Argument†

Abstract

I discuss Steinhart's argument against Benacerraf's famous multiple reductions argument to the effect that numbers cannot be sets. Steinhart offers a mathematical argument according to which there is only one series of sets to which the natural numbers can be reduced (namely, the finite von Neumann ordinals), and thus attacks Benacerraf's assumption that there are multiple reductions of numbers to sets. I will argue that Steinhart's argument is problematic and should not be accepted.