Non-computability.

According to Roger Penrose, humans can perform non-computable feats, such as dealing with Gödel questions. He uses this as a foundation to claim that the human mind cannot be expressed in terms of classical processes, and as such must be party to the only other (known) game in town: Quantum Mechanics.

Now, I haven't had the patience to sit through all of his arguments yet, though I slowly make progress. My understanding is that a large part of his stance is that an algorithm cannot usefully deal with a Gödel question, or equivalently, with the halting problem, while a human can.

My objection to this is that such problems always demand a certain quality of response when asked of UTMs: failing to respond forever is not acceptable as correct, nor is providing any response other than one that yields a truth when taken in combination with the question. This much is fine, however, when it is time for the human to answer, he is permitted the liberty of rejecting the question on the grounds that it is inherently unanswerable.

Obviously I am interested in artificial intelligence, and also find his assertion to be simply a self-serving one with a contrived philosophical backdrop for foundation. If anyone knows of, or can think of, a more sophisticated argument than the one above (or expose my flaws in my assessment of it) I would like to hear it.

Apologies for bringing up a largely philosophical question, my only excuse is that I cannot trust any other board with the question.

If the proof of uncomputability (of the halting function) is still rigorous given a finite resources environment (and this appears to be so), but the proof of computability is itself just as rigorous, where is the problem?
What are you asking here? - it isn't quite clear to me.

I'm sure that someone has taken on the scenario with finite resources rigorously. Here (in this thread) we really have only the situation where it falls apart due to resource saturation. A universe where the analyst candidate has the privilege of having much more or infinite resources changes the argument here, but beyond that I'm not sure that case can be thought to be meaningful; if the universe of computation has finite states available then some process could be contrived to be so large as to defy analysis.

It seems, also, that a case can be contrived for a finite TM which cannot be analyzed even from the privileged position. Is this the paradoxical consequence? It sounds like it to me.