Earlier quoted context omitted.
Consciousness is at it's heart irrational. Using reason or science to explain it won't work.
Ironically, you are stating a hypothesis which is fully within the purview of reason and science. While it is in principal possible that the answer is undecidable with existing logical systems, there's certainly no existing proof that it is undecidable.
Proofs are founded on reason and logic, but reason and logic are themselves a product of consciousness. It would be a tautology.