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--- Peter Bleackley <[log in to unmask]>
wrote:

<snip>

> In a self-consistent system, therefore, the
> statement must be true. It is
> therefore unprovable. Thus the existence of true but
> unprovable statements
> is a logical necessity.
>
> Pete

I've always prefered to think of Goedel this way; if
there is a reason why some statement is true then that
reason is an explanation for the truth of that
statement.  "X is true because ..." is essentially the
same as saying "the proof that X is true is ..."
Therefore, things that are true but unprovable are
true FOR NO REASON AT ALL!

Goedel's proof has also been extended to algorithms in
that there are algorithms which work but cannot be
proven to work.  Thus there is such a thing as an
algorithm that works for no reason at all.

People who's religious faith in the infallability of
science are profoundly uncomfortable with the notion
that something can be true for no reason, i.e.,
without cause.  That's why they react so violently to
stories of ESP or reincarnation, etc. etc.  They claim
that since there's no reason why they should be true
they cannot be true.  But their own Goedel has stabbed
them in the back!  Things CAN be true for no reason
and with no cause.  Goedel has proven it.

The only solution is to learn to be comfortable with
uncertainty. "Look and it can't be seen.  Listen and
it can't be heard. Reach, and it can't be grasped." -
Tao Te Ching (ch:14)

--gary