Re: the error in Godels proof

"Rupert" <rupertmccallum@xxxxxxxxx> wrote >
|-|erc wrote:
Suppose a theorem prover exists that mimics all
of mathematics.

for every input to the TP, it outputs TRUE,
FALSE, or NONSENSE.

when it inputs Godel's statement, the output is
NONSENSE.


Well, tell us more about this theorem prover.

However you go about defining your theorem prover,
this contention of
yours will be a philosophical one. Mathematically,
it will leave
Goedel's proof untouched.


I could say the same about you, that Godels proof
achieves nothing, nothing
can be calculated or anything useful come about of
it, so it is also philosophical.

Godels proof is the belief that "this has no proof"
is true and the accompanying
ideas that this petty utterence will forever defeat a
total formal mathematics.

You have it the wrong way around, moving TOWARDS a
solution is mathematical.

Herc



Moving mathematics forward is exactly why Godel's
theorem is significant, and why your philosophy is not
significant to mathematics.

Mathematics is a language. Mathematics is not identical
to calculation, as you would have it. As a first order
description of some activity, a mathematical result
consistent with some set of assumptions cannot explain
itself. That explanation has to be bracketed by a
higher (meta) set of assumptions.

Mathematicians doing everyday work of calculating
results by standards of reducing problems to those
previously solved, whether with pencil and paper or
in your vision of automated theorem proving, do not
have to be worried about the antinomies with which
Godel (and Russell before) concerned himself. Researchers
breaking new ground in correlating theory with result,
however, have to know that they are not creating
contradictions in the process of proving theorems.
If mathematics is about anything, it is about truth,
and in the making of true statements, a theorem
offers its complete meaning, no part of which may
oppose the meaning of any other part. This, then,
briefly, is the usefulness of Godel's theorem --
the knowledge of the existence of a systematized means
to demarcate known results from new definitions. An
example of this phenomenon might be the rule which
disallows division by zero in arithmetic.

So now that we have identified the importance of Godel's
Theorem with your own standard of usefulness, what is
your argument left with? The output I read is: NONSENSE.

Tom
.

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