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.

>>102
You could have applied a little grep.

Anyway, >>27 is trying to enumerate states. Infodynamics applies to this kind of procedure, and the jig is up once entropy is maximal and resource pressure forces an infinite loop or termination.

This is why >>92 doesn't want to run both TMs from the same tape: solving the problem in finite space is only possible by removing a class containing all of the principally insoluble cases (including the candidate TM itself!) Recast to the infinite case, this would have the effect of removing Turing Completeness, so it's easy to see that we're no longer talking about Turing Machines with limited resources, we're talking about something else.

At this point the problem is no longer interesting for any of the same reasons. The machines just aren't TC any longer, and the problem space isn't related to completeness in any form.