From: Yash (yashk2000@yahoo.com)
Date: Fri Jan 18 2002 - 19:13:53 MST
Exactly!
To say "I have no belief" is such a blatant example of self-deception or
delusion or trying to mislead others.
Gödel's Theorem says just that! You have to resort to statements of an
external system if you want to prove all assertions of one system! I was
glad Joe used this in his text.
The Maths super-structure is built upon axioms for which we have no proof
although we know them to be true by intuition!
This is relatively faith-like to me.
So there's no point in persecuting somebody because of his faith.
There's only the continual search for truth and the continuous improvement
of the process of thinking and our belief system!
Not heresy, Blunderov, but truth as it is currently generally held to be.
I recommend John L. Casti's "Paradigm Lost", first Chapter, Hofstadter's
"Gödel, Escher, Bach" and David Deutsch's "The Fabric of Reality", Chapters
1, 2, 3, 4, 6, 7, 10:
1: The Theory of Everything
2: Shadows
3: Problem-solving
4: Criteria for Reality
6: Universality and the Limits of Computation
10: The Nature of Mathematics
Extract from Chapter 10:
pp234-235:
"...Hilbert hoped that...every true mathematical statement would in
principle be provable under the rules, and that no false statement would
be....Hilbert published a list of problems that he hoped mathematicians
might be able to solve during the course of the twentieth century. The tenth
problem was to find a set of rules of inference with the above properties,
and, by their own standards, to prove them consistent.
Hilbert was to be definitely disappointed. Thirty-one years later, Kurt
Gödel revolutionized proof theory with a root-and-branch refutation from
which the mathematical and philosophical worlds are still reeling: he proved
that Hilbert's tenth problem is insoluble. Gödel proved first that any set
of rules of inference that is capable of correctly validating even the
proofs of ordinary arithmetic could never validate a proof of its own
consistency. Therefore there is no hope of finding the provably consistent
set of rules that Hilbert envisaged. Second, Gödel proved that if a set of
rules of inference in some (sufficiently rich) branch of mathematics is
consistent (whether provably so or not), then within that branch of
mathematics there must exist valid methods of proof that those rules fail to
designate as valid. This is called Gödel's incompleteness theorem. To prove
his theorems, Gödel used a remarkable extension of the Cantor 'diagonal
argument'....He began by considering any consistent set of rules of
inference. Then he showed how to construct a proposition which could neither
be proved nor disproved under those rules. Then he proved that that
proposition would be true...
Thanks to Gödel, we know that there will never be a fixed method of
determining whether a mathematical proposition is true, any more than there
is a fixed way of determining whether a scientific theory is true. Nor will
there ever be a way of generating new mathematical knowledge. Therefore
progress in mathematics will always depend on the exercise of creativity. It
will always be possible, and necessary, for mathematicians to invent new
types of proof. They will validate them by new arguments and by new modes of
explanation depending on their ever improving understanding of the abstract
entities involved Gödel's own theorems were a case in point: to prove them.
he had to invent a new method of proof. I said the method was based on the
'diagonal argument', but Gödel extended that argumetn in a new way. Nothing
had ever been proved in this way before; no rules of inference laid down by
someone who had never seen Gödel's method could possibly have been prescient
enough to designate it as valid. Yet it is self-evidently vlid. Where did
this self-evidentness come from? It came from as Gödel's understanding of
the nature of proof. Gödel's proofs are as compelling as any in mathematics,
but only if one first understands the explanation that accompanies them.
...look at this proposition:
David Deutsch cannot consistently judge this statement to be true.
I am trying as hard as I can, but I cannot consistently judge it to be true.
For if I did, I would be judging that I cannot judge it to be true, and
would be contradicting myself. But you can see that it is true, can't you?
This shows it is at least possible for a proposition to be unfathomable to
one person yet self-evidently true to everyone else."
"
Krishnamurti seems to be saying not to expect truth in [existing] paths like
religions and sects. I don't think he meant that Truth is unnattainable or
that some intuitively true statements were untenable.
Just my interpretation.
Regards,
Yash.
-----Original Message-----
From: owner-virus@lucifer.com [mailto:owner-virus@lucifer.com]On Behalf
Of Blunderov
Mermaid quoted
"I maintain that Truth is a pathless land, and you cannot approach it by any
path whatsoever, by any religion, by any sect. That is my point of view, and
I adhere to that absolutely and unconditionally."Krishnamurti
Without in anyway wishing to introduce yet another red-herring, I have to
say-
But surely he contradicts his own self here? He makes a pretty emphatic
implied statement that truth cannot be attained and yet he holds this
statement to be true. Haven't we seen this before?
The main point being:
Every religion has to, in the final analysis, hold an item of faith.
Even the viriians. The viriians hold (I think) the item of faith that the
scientific method of thought is the best way forward for humanity.
The scientific system of thought cannot prove itself to be true. It would of
neccessity be self referencing.You have to subscribe.
Or does Blunderov speak heresy here?
Regards
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