What you say in your last statement is true and helps to clarify a subtle point. I tend to shove all of that stuff (logic, set theory, problems of undecidabilit

What you say in your last statement is true and helps to clarify a subtle point. I tend to shove all of that stuff (logic, set theory, problems of undecidability, etc) into the nondescript box labeled "philosophy of mathematics." When I meant a field was "small," it was not meant to be pejorative. Philosophy of mathematics is a rich and productive field with many applications within its varied fields. The main problems I see are the ones described the article I linked, in that people attempt to apply the theorems to things like physics, politics, law, or postmodern philosophy. Of course Goedel's theorems do not totally exist in a bubble that only contains arcane mathematical incantations. For instance, Goedel's theorems imply (like the halting problem) that you cannot create a compiler that would be able to determine whether a program will not terminate and reject it, by considering what happens when you feed it a Goedel statement. However, this problem is something that I would also classify under "philosophy of mathematics." Also, I hope I did not provide any implication that my view (or any view, for that matter), is the final word on the subject. I'm not dead-set in my own beliefs on incompleteness and if you can provide a convincing argument of a rigorous, nonmathematical application of Goedels theorems, I'd be more than happy to change my mind. There is considerable discussion as to what exactly the incompleteness theorems imply, and there are many eminent minds on the many different sides of the argument. For instance, I believe Stephen Hawking is somebody who believes that physics cannot ultimately be formulated into a final number of finite principles. Do I believe this to be a rigorous application of Goedel's incompleteness theorems? No. Do I believe that this can be applied to fields outside a relatively restricted problem space? No. Does this mean I'm right? Of course not. As to your point about Strong AI, I don't want to open that can of worms in this thread. I'm not yet convinced that the human mind is equivalent to any finite state machine, so I'm afraid that we don't even agree upon its the basic premises. However, I would love to discuss it any time outside of the thread.