Is it possible to believe that mathematical objects enjoy some kind of mind-independent existence while holding physicalism?
And if they are mind-dependent, should one embrace constructivism necessarily?
It seems problematic to reject classical mathematics on the ground of physicalism, since physicalism itself require classical mathematics. Of course it's possible to build up analysis from the constructivist point of view, but scientists usually use classical math. So how to reconcile these claims?
EDIT: Here's the problem
If physicalism is true, mathematical objects to exist should be physical
Mathematical objects are either something implemented in the humand mind (constructivism) or some kind of things that exist in a non physical realm.
Therefore, if physicalism is true, mathematical objects exists only in the human mind (anti-realist stance, constructivism)
Physical statements make use of classical mathematics (which is non constructivist)
Therefore, if physicalism is true, mathematical objects exist not only in the human mind