dxm@lanl.ARPA (04/18/85)
My last posting got munged horribly, sorry about that. Here it is as it should be ( I hope ). >An inconsistency in a particular episode that has always bothered me goes >back to "I, Mudd", the one with Norman and the 300,000 Androids. >One of the gems of logic that the gang uses to overwhelm the Androids is: > Kirk: "Everything Harry Mudd tells you is a lie." > Mudd: "Norman, I am lying now." >This blows Norman away! It seems to me that the flaw in the logic is what >if Kirk is lying? > >--Evan Marcus >...{decvax|ucbvax}!vax135!petsd!pedsgd!pedsga!evan Actually, no flaws here. Kirk's statement is pretty much irrelevant. Norman will still blow a fuse, because Mudd's statement is a paradox all by it's lonesome. Try it; if Mudd is really lying, then his statement is false, so he is not lying ( ouch !). If he is telling the truth, then he is doing what he says he is; lying ( also ouch ). This is also called a "strange loop" by Douglas Hofstatder, who wrote a *very* good book called _Godel, Escher, Bach: An Eternal Golden Braid_ that discusses such things in depth. It is very readable, and utterly fascinating ( couldn't resist a plug here, I love this book ). Anyway, it turns out that you need a meta-language to handle paradoxes; that is, a language that refers to the language in which the paradox exists. Of course, paradoxes in the meta- language are resolved with meta-meta-languages, etc. If Norman is crashed this easily, one wonders how he survived 3,745,386 years... Doug Miller dxm@lanl ....!ihnp4!lanl!dxm US Mail Los Alamos National Laboratory, P.O.B 1663 MS J960, Los Alamos, NM 87545