From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Jun 14 2002 - 05:52:55 MDT
A friend recently pointed out to me that it's not such
a simple matter as one might think deciding when to
change your mind about an issue, especially if you've
thought a certain way about something for a long time.
It is always wise, she said, to recall the algebra "proof"
that 1 = 2. If you've any long acquaintance with algebra,
then of course you can spot the flaw in
Assume a = b
then a^2 = ab ;multiplying both sides by a
also a^2 - b^2 = ab - b^2 ;subtracting b^2
(a-b)*(a+b) = b(a-b) ;factoring
a + b = b ;dividing through by a-b
b + b = b ;since a=b
1 + 1 = 1 ;dividing through by b
2 = 1
There are many other faulty proofs in mathematics and
logic whose flaw isn't so apparent, yet it's hardly
intelligent to presume that an argument is air tight
just because you haven't yet found a flaw in it.
I don't know of any rigorous guidelines to suggest to
one that an apparently completely rational argument
may have a hole in it. But one is that if the conclusion
of an argument goes against long deeply held beliefs that
you have, then it's wise to reserve judgment for an
extended period.
I suppose that the proper course is to acknowledge the
seemingly conclusive nature of a new argument or rational
deduction, and to admit that one is not in possession of
any demonstration of the flaw in said argument, but to
maintain that the conclusion flies so strongly against
other beliefs, or appears to, that a suspension of
judgment is called for.
Of course, it's then your intellectual duty---that is,
if you are concerned about what is true in the end---
to quietly pursue a rectification of all your beliefs.
To do anything else, naturally, would be to simply bury
your head in the sand.
Lee
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