Date: Tue, 4 Sep 2001 21:56:34 +0100
From: Jan Straathof <janstr-AT-chan.nl>
Subject: RE: Heidegger's Philosophy of Time


dear Tudor, you wrote:

>All mathematic truths are tautologies, starting with 2x2=4 and ending
>who knows with what. Do you think that all arithmetic, algebra,
>analysis, geometry, trigonometry, etc., lead us not further than before
>we met them?

a tautology (e.g.: a=a; 2x2=2x2; 'it is raining or it is not raining')
is a proposition that, regardless of the truthvalue of its components,
is always true; it cannot be rejected because it needs no proof, it
cannot be proved, thus it adds nothing (new) to our understanding,
it possesses no (new) information; in fact, for a tautology to be true,
we have to do (or prove) nothing --- when i encounter a tautology
my first reaction is always: "so what?" ;-)

2x2=4, however, is not a tautology, it is an arithmetic operation;
you can ask yourself if 2x2=4 (or 2x2=5) is true or not, and to
prove the truth of 2x2=4 (or 2x2=5) you must demonstrate/show
a way to do so (e.g. via a geometrical construction)

"a=a" has no meaning, because we need no, nor can we provide
any, evidence to prove it; on the other hand "2x2=4" has meaning,
because we can obtain/provide evidence (operations, constructions,
actions etc.) to prove or reject its truth

yours,
jan







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