Abstract

There is a long history of philosophical intuition that the human mind must be more than physical or mechanical. I argue that this intuition arises from the perfect “transparency” of physical and mechanical states, in the sense that such states have no obscure or occult elements, but are fully intelligible in mathematical terms. In the paper, I derive a contradiction from the claim that such a physical system has genuine intentionality, comparable with an intelligent human. The contradiction arises from the fact that, according to physicalism, the physical properties of a brain state determine the narrow propositional content of any conscious thought occurring in that state. This fact allows a physical property of brain states to be defined using Cantor’s diagonal construction, and then a contradiction results if a physical system is assumed to form thoughts involving that property.