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.

>>7
If it determines that the analyzed TM will halt, it goes into an infinite loop.
Obviously you don't see the circular reasoning here. In a environment with finite resources, a TM may enter into an "infinite loop", however we can easily and accurately determine if such a loop has been entered into. Consider a finite set of states and state transitions (implied by finite resources). We can simply mark a state as visited upon execution, and if any state is visited more than once we have detected a loop and exit. The program must eventually return, or visit an already visited state. In such a case, the program will loop forever but we have successfully ascertained the result and can now do what we wish with it (whether that be, to ourselves loop infinitely or return doesn't matter.) In fact, the entire argument that humans can solve the halting problem is based on anecdotal evidence of us examining our own programs or some such, but any such program will have such a microscopic number of states that it is completely laughable to say is non-computable.