In the most recent episode of SpaceTimeMind, philosophers Richard Brown and Pete Mandik discussed physicalism. More precisely, they discussed “local physicalism” or physicalism about the mind, the proposal that mentality is explicable in terms of entities which are governed by the most fundamental laws of the material world (i.e. the brain). Early on in the conversation (6:10), the two bracketed the question of the feasibility of physicalism as a global thesis—the theory that everything which exists supervenes on physical entities.
Brown names mathematical entities and moral facts as potential candidates for entities which exist outside of physics. However, he says we can do philosophy of mind without settling the ontology of math and meta-ethics, and implies that one can be a physicalist about the mind without being a physicalist about those two domains.
I disagree with the first point. I think a philosophy of mind must be embedded in a larger metaphysical picture, one which accounts for and situates the objects of perception and thought, and explains how they interact with mentality. Since mathematics and morality are clearly things humans think about, we thus have to account for how they get into our cognitive systems. If a physicalistic account of numbers or ethical facts can’t be given, then we are obliged to either explain how a physical system like the brain can access supernatural realms, quine immaterial entities, or abandon physicalism. Without doing one of these three things, we will have left our philosophy of mind incomplete. It would be just as if the Cartesian never addressed how the immaterial mind could interact with the mechanical body—an ontological gap would beg to be bridged.