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
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