One point in Keith's response, IMO, requires a comment.
On Fri, 25 May 2001 10:33:00 -0500 kbmill@ksu.edu (Keith B Miller)
writes:
> I reply to specific questions below:
>
> The word "truth" is not in the document for a very good reason.
> Science
> cannot every demonstrate that something is "true" in the sense of a
> logical
> or mathematical proof. Some scientific theories are so well
> established
> and supported by such an overwhelming amount of evidence that they
> are no
> longer seriously questioned. An example is the vast size and age of
> the
> universe. But such theories cannot be demonstrated to be "true" in
> an
> absolute sense.
>
What Keith says of science also applies to mathematics and logic. Truth
and proof depend on the system. What is necessarily true in Aristotle's
syllogistic does not always hold in the PM system. Theorems in Euclidean
geometry contradict some of those in Lobachevskian and Riemannian
geometries. Goedel makes it clear that it is impossible to prove the
truth of the axioms within any formal system, which means that we are
left with a conditional: If one accepts [put the axiom system or other
basis here], then the following theorems are true within the system. We
need always to remember that human beings are finite in their
understanding.
Dave
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