"De Re Mathematical Necessities: An Aristotelian Explanation"
Abstract: I will argue three things: First, that there are de re mathematical necessities: Necessities within physical systems similar to physical necessities, but which carry an even stronger, mathematical modal strength. These de re mathematical necessities play a key role in mathematical explanations in the natural sciences. Second, I argue Platonist ontologies of mathematics which appeal to necessarily-existent abstract objects entirely fail to explain de re mathematical necessities. I argue a better explanation can be found in an Aristotelian ontology of mathematics, which bases the truth-conditions for mathematical propositions in structural universals.
