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From: Robert Kaufman on 16 Jul 2010 05:01
Hi!

I've been doing some reading lately where the
authors seem to say that when contradictions
arise in various disciplines of Mathematics and
Science we can ignore them, because they really don't
affect much of anything in their disciplines, and
even somehow have a stimulating effect in their
fields. Is this true, and If it's true, would someone please
explain to me what this all means. Also, how does this affect
reductio ad absurdum proofs?

Respectfully,

Robert Kaufman
From: hagman on 16 Jul 2010 09:56
On 16 Jul., 15:01, Robert Kaufman <Yearachm...(a)verizon.net> wrote:
> Hi!
>
> I've been doing some reading lately where the
> authors seem to say that when contradictions
> arise in various disciplines of Mathematics and
> Science we can ignore them, because they really don't
> affect much of anything in their disciplines, and
> even somehow have a stimulating effect in their
> fields. Is this true, and  If it's true, would someone please
> explain to me what this all means. Also, how does this affect
> reductio ad  absurdum proofs?
>
> Respectfully,
>
> Robert Kaufman

Can we ignore contradictions?
Yes and No.

In mathematics, a contradiction is deadly as it makes
every statement true, hence worthless.
In other sciences, e.g. physics, some observations may contradict a
theory
(e.g. the Michelson Morley experiment contradicted ether theory)
or two theories might contracdict each other
(wave theory of light and particle theory of light)
maybe only by small amounts notable only in certain extrme situations
(Newton vs. Einstein vs. Quantum theory).
But then this is a sign that the theory needs some refinement.
In "every day" physics we may ignore differences between Newton and GR
or quantum mechanics when explaining how colliding billard balls
bounce;
but then again we have no explanation as to why they do not simply
pass through each other anyway.
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