From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Jun 14 2002 - 20:19:50 MDT
Louis writes
> From: "Lee Corbin" <lcorbin@tsoft.com>
>
> > I don't know of any rigorous guidelines to suggest to
> > one that an apparently completely rational argument
> > may have a hole in it.
>
> I do. It's called logic. Specifically, "syllogisms".
>
> Follow these steps:
> 1 - Rewrite the claim in steps called syllogisms. ANY claim can be
> re-written in proper syllogism form.
> 2 - Each syllogism will be one of 256 forms. Only 15 are valid. If any
> other forms besides these 15 are used, then the proof is invalid and should
> be rejected.
> 3 - Syllogisms only conclude that the conclusion is true if the first two
> propositions are true. If any proposition is false, then the proof proves
> nothing, and should be rejected.
> 4. - If you didn't reject the proof in steps 2 or 3, then it is a valid
> proof, that proves a conclusion is true.
>
> These steps have been used for 23 centuries to check proofs.
The problem is that at best, this is a rigorous procedure only
in mathematics, and even then, it's simply not practical for
obtaining absolute certainty.
Euclid lived 23 centuries ago, and was an extremely sharp cookie,
as you know. Nobody understood mathematical proof better than
he until the 18th century or so. But did you know that there is
an error in Proposition 1 of Book 1? (Zeno and Proclus believed
that it was flawed, though theirs was the minority position.)
Only David Hilbert (as you probably know) placed Euclidean Geometry
on a footing where we are convinced that were it all reduced to
symbolic logic, Euclid's basic proofs would go through.
But the difficulties in mathematics pale in comparison to the
difficulties in science. There cannot be a logically or
mathematically rigorous means to prove Darwin's theory of
evolution, for example. Anything more complicated than very
simple algebra and geometry is never demonstrated with
complete formality (it would simply be impractical in terms
of effort).
The point of my post was simply that one is entitled to withhold
judgment for a while when presented with evidence or argument
that while appearing very persuasive, goes against deeply held
beliefs. For a while, that is.
Lee
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