From: Lee Corbin (lcorbin@tsoft.com)
Date: Thu May 30 2002 - 01:36:14 MDT
I appreciated Hal's "quining" of "If this sentence is true, then
God exists". I don't know why I find these so amusing---I just
wrote a post attributing cunning to The Sentence, namely, that
you mustn't let it trick you into assuming it has a truth value.
> If a statement is declared a theorem (as I understand it), it must be true,
> by fiat definition, *for those limited logical purposes*.
Well, at least that's the intent of the author, unless
used ironically.
> The three original words and the colon assert that the final
> two words are true. So what? One might also freely assert that:
>
> Theorem: God does not Exist.
>
> Theorem: dogs are cats.
>
> Lee's point, or so I assumed, was the simple and useful reminder that logic
> alone has no power over ontology. Hence, `logic, not grounded in reality[,]
> must be used with care'.
Yes, that was my point, and I guess that I have to agree with
you that "logic alone has no power over ontology", but it's a
hard call, and good arguments occur to me for both sides. To
take one side, and provide one example,
"All A's are B's, all B's are C's" definitely proves "All A's
are C's.", whatever the identities or values of A, B, and C,
as Louis pointed out. Yet the conclusion from
All young stars are made of many gaseous molecules.
All things made of many gaseous molecules obey the
laws of statistical dynamics".
somehow *does* limit the ontological possibilities! Quite
amazing, when you stop to think about it.
Lee
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