Why There Can Be Numbers

Carrie Jenkins

In a recent paper, David Builes defends the following argument against mathematical Platonism: 

"1. Necessarily, there are no bare particulars. 

2. Necessarily, if there are abstract mathematical objects, then there are bare particulars. 

3. Therefore, necessarily, there are no abstract mathematical objects."

There are many ways to resist this argument, some of which I will briefly summarize before focusing on one particular problem with it. Premise 2 depends on the assumption that any intrinsic property an abstract mathematical object might instantiate is "merely negative" or otherwise non-"sparse", such that bearing such a property does not suffice to make a particular non-bare. For many such properties, this is a problematically question-begging assumption. However, I conclude by explaining how Builes's argument, and this particular problem with it, shine light on some underexplored questions in the metaphysics of mathematics.

link: https://us06web.zoom.us/j/87649813438