Path: utzoo!utgpu!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!bloom-beacon!mit-eddie!uw-beaver!cornell!rochester!pt.cs.cmu.edu!andrew.cmu.edu!ap1i+ From: ap1i+@andrew.cmu.edu (Andrew C. Plotkin) Newsgroups: comp.ai Subject: Re: Artificial Intelligence and Intelligence Message-ID: Date: 16 Nov 88 01:49:01 GMT References: <490@soleil.UUCP> Organization: Carnegie Mellon Lines: 27 In-Reply-To: <490@soleil.UUCP> / Human beings KNOW the "halting problem for Turing machines", my point is / that machines can NOT know the "halting problem for Turing machines". / Please describe how you would give this knowledge to a computer. / All uncomputability problems come from dealing with infinity. / Like naive set theory, naive Artificial Intelligence does not deal with / paradoxes and the concept of "infinity". / Finite machines cannot understand "infinity". Finite machines can understand both infinity and the halting problem the same way they can understand any other theorem in a formal system. Give it the definitions and axioms, and let it crank out theorems. "The halting problem is Turing-insoluble" is a theorem that's not hard to prove. Program to do this sort of thing have been written. Hell, that's how humans did it. "Infinity" is a single concept; you don't need an infinite amount of information to comprehend it or use it. You only need the axioms and definitions that mention it. / For the concept of "infinity" to have any meaning at all you MUST have the / computational strength of reality. In mathematics, the concept of "infinity" has no meaning at all. In "real life," it is useful in describing certain aspects of the universe, but no more useful than the concept "two". A program which can handle one can handle the other. --Z