I am pretty sure it can't, because a mathematical model is a sort of mechanism, and Roger Penrose is of the opinion that consciousness can't be a mechanism because of his Gödel's theorem argument. Regardless of whether that holds water, I don't see a mechanism - something that could in principle be built out of clockwork - can possibly be conscious! That puts a lot of constraints on physical consciousness.

I am also very dubious about the decoherence explanation of the wave function collapse. It seems like a cop-out to me - I mean you still have a wave function that becomes more and more complicated as one system interacts with another, but nothing actually performs the collapse - not consciousness - the effect is just statistical. I mean ordinary statistical mechanics is rather different because it averages over the classical behaviour of a molecules bouncing about in a box (at least in the simple case). Whereas QM follows a very different logic - and I feel it needs a micro-explanation as to what is going on!

David

I am also very dubious about the decoherence explanation of the wave function collapse. It seems like a cop-out to me - I mean you still have a wave function that becomes more and more complicated as one system interacts with another, but nothing actually performs the collapse - not consciousness - the effect is just statistical. I mean ordinary statistical mechanics is rather different because it averages over the classical behaviour of a molecules bouncing about in a box (at least in the simple case). Whereas QM follows a very different logic - and I feel it needs a micro-explanation as to what is going on!

David

I also think the lack of a possibility for a mathematical model for consciousness goes beyond Gödel's theorems. This is more about decidability like Turing's undecidability theorem that compliments Gödel's theorems, in that we cannot mathematically model our ability to see truth or to decide all things. But free will would be something entirely different. And what about intention? It's a problem because it appears to order matter, but how?

In one way, it shouldn't be that surprising if consciousness is fundamental that causality and mechanism are not found. Even within quantum theory causation is not really there, nor mechanism. It seems that causation and mechanism are emergent properties in the universe.