Emperor's New Mind - criticism - Journal of Omnifarious
Feb. 1st, 2005
02:37 pm - Emperor's New Mind - criticism
Gödel's Incompleteness Theorem implies that there are truth's that are out of the reach of an algorithmic intelligence
I consider this argument to be weak. Basically, he's stating that there are things that we know are true who's truth we cannot have arrived at by algorithmic means. That there is no known procedure at all, no matter how complex, by which we could've arrived at the conclusion that some particular assertion is true.
This is weak because people do not reason in a vacuum. We are bombarded with a torrent of sensory stimuli every moment of our lives. The axioms of math, those things in math that we hold to be self-evidently true, come from our observations of the world.
The idea, for example, of having some symbol represent the square root of -1 is an abstraction someone came up with to solve a particular problem. It was generalized by others and its implications were fleshed out, and it was discovered to be a good way to describe a number of phenomena in math, and even in the world.
But, this idea had no basis in formal mathematics. It wasn't arrived at by someone carrying out formal steps of a proof reasoning from the basic axioms of math to this new concept. It was created out of whole cloth and found to be extraordinarily useful.
I think he's mistaking math for reality here. To me, Gödel's Incompleteness Theorem is a warning that math can never completely describe reality.