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.

>>20
You are misunderstanding my objections and perhaps my stance also.
I stated humans don't really solve the halting problem because their halting analysis is a very generalized heuristic case testing approach. I never said this could tackle the busy beaver, and often it has difficulty with fibs.
It looks more like you are cementing my point? Why the hostility in this case.

even fucking fibs can be proven to terminate only by inventing and verifying a hypothesis about certain invariants in the data it operates on, not by "checking states for loops".
Wrong, see >>16

In regards to >>26
your procedure still falls apart completely when the candidate is asked to analyze itself, as previously illustrated
This is something of a silly argument and I don't think it changes the result of the initial question.
In a strict sense, yes there is a contradiction or paradox when run on itself but this actually would occur in a human too if they were made to black box the program they were analysis and simply "run it to get the result."

Humans don't necessarily encounter a paradox because we aren't forced to follow to the same constraints imposed on a machine. We may inspect the inner workings of the program as we like and at any time "terminate" its execution.
This is actually rather unfair and if humans followed stricter definitions of the problem we would be forced to infinitely evaulate the program in our head to determine if it loops.
If you think this kind of thing is allowed, then as argued, we can run our halting detector on a seperate "thread" (or rather, read in the "source code" for the TM under test and simply analyze it step by step, we don't need to run it in it's own execution context) or similar and simply examine only as many states as we need to determine if the program halts or not. At which point, we could leave it running and simply return from our own "thread", loop infinitely, or whatever else you might want to do.
Any behavior a human exhibits can be emulated by a machine, we are simply holding machines to a higher standard in a brazen attempt to glorify ourselves as something more than rule based DFA.

>>18,26
but it [heuristic approach] doesn't solve the halting problem
That's exactly my point. It's what humans do (or at least it's what I do), and it's not comprehensive.

The entire finite resources example was meant to be a quick and tidy demonstration that humans can't solve the halting problem (or at least we can't verifiably demonstrate that they can in this uinverse) and the argument should have stopped there. The fact people have tried to dispute this is somewhat dissapointing.
I agree, however, for the purposes of this discussion it's probably not necessary, and people can have a more in depth conversation that eventually reaches the exact same conclusion if they like.