Comment by jbotz
Yes... the materialist says that consciousness is a manifestation of the material brain. But if the brain is a kind of computer the best formalism for it we have so far is the turing machine, which we know from cellular automata to be able to exist in a purely mathematical space, so materialism can't be correct.
The only way out from this paradox that can preserve materialism is to say that consciousness requires some feature of material reality that goes beyond turing completeness, perhaps quantum phenomena. shrug. Maybe so, but so far there is no evidence, and in the meantime AI is getting closer and closer to something like consciousness on plain old turing machine computers, no quantum computers required.
Why not both (or neither)? Perhaps the material brain can be conscious and differential equations too.