From: Lee Corbin (lcorbin@tsoft.com)
Date: Sat Jun 15 2002 - 12:30:50 MDT
Louis writes
> I wish I knew why you keep trying to say that logic somehow only works in a
> specific area (like mathematics) and somehow doesn't apply to the real
> world. Logic applies to ANY claim. It doesn't matter what the subject
> being discussed is.
Yes, I understand. The confusion arises over a difference between
the application of *formal logic* and everyday (or Aristotelian, as
you remind us) logic. I'll concede that when all the premises are
true, then the conclusions (or consequents) are true. The whole
point, however, is this: HOW DO YOU KNOW IF YOU'VE MADE AN ERROR?
Even *formal* proofs only provide an external machine-type check.
Complete certainty (outside mathematics and meaningless syllogisms)
is not possible. All actual knowledge is conjectural.
> > and even then, it's simply not practical for
> > obtaining absolute certainty.
>
> Again, I say NO. That's the whole POINT of logic. If you apply
> the rules of logic, then YES, you can achieve ABSOLUTE CERTAINTY.
We disagree, for the point I just made.
> On the other hand, the theory of relativity WAS written as a formal proof.
> Einstein started with a simple observation (that the speed of light was the
> same to all observers) and from that proved (using ONLY mathematics) that
> - time slows for swiftly moving objects
> - length contracts for swiftly moving objects
> - the space around matter and energy must be curved
> - time and space are interchangeable
> and even
> - the universe must be changing size !
>
> That was an amazing example of a proof. Scientists knew
> WITH CERTAINTY that it was correct, even though we couldn't
> measure some of the predictions until decades later.
Nonsense. Many eminent scientists refused to believe Einstein's
arguments for decades. The application of mathematical arguments
to physics is *not* a straightforward application of logic or
syllogisms. Einstein's "proofs" as you call them, were merely
mathematical derivations which (in principle) were fully capable
of containing conceptual flaws. (Many extremely intelligent and
knowledgeable scientists of the time *did* think that they contained
flaws. Would you accuse those eminent physicists as being illogical
or of making logical errors?)
> With your repeated claims that logic "isn't practical" and "you can prove 1
> = 2", your claim sounded more like "one must withhold judgment because you
> can't trust logic".
Sorry if I sounded that way to you; I meant only that we
cannot be certain of *our* own applications of logic, and
for several reasons:
One is that we cannot be certain of the premises involved
in any of the logical formulations (e.g. Modus Tollens, or
use of the Contra-Positive). Another is, if the number and
intricacy of the deductions is very great, we cannot be
certain that we haven't just blown it. Third, a step that
seems completely straight-forward and legitimate may
actually contain a subtle error.
Lee
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