Herc does not understand any induction schema
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From: George Greene on 26 Jun 2010 13:33 On Jun 25, 10:37 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > Notice that Cooper states that he is using a sort of induction > schema, This is breathtakingly IRrelevant. I never heard him say that (he spawns far too many of these for all of us to keep up with all of them), but IF he did, EVERYbody who saw it SHOULD have laughed in his face and told him what THE ACTUAL induction schema looks like, AND FORBADE him to use any other. > possibly of the form: > (phi(1) & An (phi(n) -> phi(n+1))) -> phi(omega) This doesn't even deserve TO BE CALLED an induction schema because it doesn't imply phi( all the rest of the n's ). It doesn't imply An[phi(n)], which is what induction MEANS. More to the point, to the extent that phi(.) IS EXPECTING A NATURAL NUMBER as an argument, AND omega IS NOT one, phi(omega) MAY NOT EVEN BE GRAMMATICAL. Finally, this alleged induction schema IS TRIVIALLY FALSIFIED just by constructing the list of finite prefixes OF ANY real. The WHOLE real, itself, IS NOT ON that list, yet this schema says it would be. SO THE SCHEMA*IS*JUST*FALSE*. The PROBLEM, though, is that that kind of argument WILL NOT impress Herc because Herc DOES NOT claim to be using our kind of axiomatic formal language IN THE FIRST PLACE!!! He REJECTS that paradigm! He is going to insist on continuing to talk in natural language, wherefore, I repeat, SIMPLIFY, SIMPLIFY, SIMPLIFY! When he says "permutation", THROW IT OUT. When he says "induction schema", THROW IT OUT. When he says "list of all computable reals", REFUSE to discuss computable anything AND JUST talk about infinitely long lists of finite things! THEN we MIGHT eventually have a chance. |