X-Message-Number: 10226 Subject: Bob's Bazzar of the Bizarre From: "Perry E. Metzger" <> Date: 13 Aug 1998 11:43:22 -0400 > From: Peter Merel <> > > Robert Ettinger writes, > > >Because of press of business of more immediate concern, I don't yet have the > >technical refutation of Goedel in a form I am satisfied with [...] > > To say "Goedel is wrong" is to claim that Russell, who acknowledged > Goedel's results at great expense when they doomed his Principia, > was wrong. It's to say every computer scientist and mathematician > since Goedel, every one of whom has accepted the power of Goedel's > formulation, is mistaken. More importantly, to me, it is to say that *I* am somehow mistaken, because I personally understand Goedel's proof and cannot see any holes in it. Furthermore, the related result for Turing Machines is even more airtight -- it is such an intensely obvious result in retrospect (the genius was coming up with it in the first place) that I find the entire notion that Bob Ettinger has even a shred of a mistake to point out in it highly unlikely. At least Goedel had to do some significant work to do the Goedel numbering trick. Universal Turing Machines are, however, entirely obvious, so the idea of retrospective ones is easy to grasp once it is pointed out to you. As you can map the one proof into the other, a flaw in the one would be a flaw in the other. I find it hard to believe a flaw exists in either. We can go beyond this, of course. Goedel's undecidable question was a contrived construct, but there are now actual problems for which it is known that no answer exists, like the Continuum Hypothesis. I presume that Bob has a demonstration that the proof that the Continuum Hypothesis is undecidable is false, too, eh? Although it is in some theoretical sense possible that Ettinger has a disproof of Goedel's work, in practice I would say that the odds are that Bob has simply lost it and possesses nothing that one would refer to as an actual disproof. Perry Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=10226