Webb focuses on Gödel sentences as a criterion of consciousness.
But consciousness should be construed in terms of the ability for self-critical thinking.
Self-critical thinking requires a concept of truth.
Because machines lack an adequate concept of truth, as Webb admits, they can't think critically in the way the humans can.
A machine's inability to recognise the truth of Gödel sentences is just a symptom of its inability to think self-critically.
John Lucas (1971).