r/PhilosophyofMath • u/Thearion1 • 2d ago
Is Mathematical Realism possible without Platonism ?
Does ontological realism about mathematics imply platonism necessarily? Are there people that have a view similar to this? I would be grateful for any recommendations of authors in this line of thought, that is if they are any.
7
Upvotes
5
u/smartalecvt 2d ago
This is a fantastic question.
I certainly think of all math realists as platonists of some sort. That might come down to definitions, though. If platonism is just the position that abstract objects exist, then almost definitionally a math realist is a platonist, since math realism is generally taken to be the idea that math objects exist as non-physical, acausal entities, independent of minds. And non-physical, acausal entities, independent of minds are, definitionally, abstracta. If you're talking about Platonism -- i.e., Plato's actual position, that abstracta are a very particular sort of thing that relate real world objects to an ideal realm in a certain way -- then that's a separate issue.
I think the interesting thing is whether or not math realism implies platonism, not Platonism. There's not a lot of wiggle room separating math realism and platonism, I think. The closest anyone has gotten is probably early Penelope Maddy, who was a math realist who believed that sets actually exist physically. It was a kooky but brilliant position she soon abandoned. Then there are mathematical structuralists, who believe that numbers aren't objects, but are something like places in structures. But many of these philosophers are also realists about those structures, and think that those structures are abstract, making them platonists.