Comment by andrewla

I think philosophically this comes down to the Universal Church-Turing Thesis.

If you believe that there is computation being done by nature/physics that is strictly more powerful than what a Turing machine is capable of, then consciousness might be beyond the reach of a silicon computer.

I personally believe that the UCTT is very likely to be true, not least because we have not yet proposed an oracle that is physically feasible and yet is beyond the capabilities of a Turing Machine.

That said, in the space of feasibility there are open questions -- even if P != NP, a non-deterministic Turing machine can be simulated by a deterministic one, just potentially with an exponential increase in computation time or space.