But if you call it "states of one's brain", then anyone would (rightfully) just ask what "states of one's brain" means. Calling it "states of one's brain" seems to me to be the same as fake causality, no? The people I am discussing this with are not the type to happily accept some abstracted, black-boxy level of quantum physics where we can treat a mind as we treat the wing of an airplane.

My original question was more to the point of: is the description of brain states in terms of quantum mechanics a sufficient rebuttal to positive ontological assertions about cognitive objects? If someone argues that "mathematical objects actually exist", do we merely have to begrudgingly dismiss this as "unsupported by any evidence" or can we go further and actually make a case that cognitive objects are just fuzzy clusters in some space of arrangements-of-particle-configurations-in-brains?