AAP 2026 CONFERENCE

Can a theorem of pure mathematics definitively refute a philosophical view? According to one popular argument, the answer is yes. The theorem in question comes from model theory, and the philosophical view is functionalism: one of the
most popular and well-studied views in the philosophy of mind. According to this argument, functionalism is logically inconsistent, and Beth’s definability theorem demonstrates this by showing that functionalism collapses into reductionism - exactly what functionalists purport to deny.

In this paper, we examine whether the argument really is as devastating as its proponents have claimed. Unfortunately for those hoping to refute functionalism in this way, we show that the argument fails for reasons both logical and philosophical. We conclude that at best, it simply fails to challenge any actually held functionalist views, and at worst, relies upon an equivocation concerning the relevant notion of definability in order to derive its conclusion.