Re: Godels incompleteness theorm proven wrong

On Sep 22, 9:38 pm, "elsiemelsi" <cyprin...@xxxxxxxxxxxxxxx> wrote:
[...]
Gödel proved

~P(x,y) & Q)g,y)
in other words ~P(x,y) & Q)g,y) is a mathematical version of the liar
paradox. It is a statement X that says X is not provable. Therefore if X
is provable it is not provable a contradiction. If on the other hand X is
not provable then its situation is more complicated. If X says it is not
provable and it really is not provable then X is true but not provable
Rather than accept a self-contradiction mathematicians settle for the
second choice [...]

Actually, that's not true; the assumption of "consistency" of the
system (the inability to prove anything that is false) rules out the
possibility of self-contradiction.

Godel used Peanos axioms but these axioms are impredicative and thus
according to Russell Poincaré and others must be avoided as they lead to
paradox.
quote

http://en.wikipedia.org/wiki/Preintuitionism

"This sense of definition allowed Poincaré to argue with Bertrand Russell
over Giuseppe Peano's axiomatic theory of natural numbers.

Peano's fifth axiom states:

* Allow that; zero has a property P;
* And; if every natural number less than a number x has the property P
then x also has the property P.
* Therefore; every natural number has the property P.

This is the principle of complete induction, it establishes the property
of induction as necessary to the system. Since Peano's axiom is as
infinite as the natural numbers, it is difficult to prove that the
property of P does belong to any x and also x+1. What one can do is say
that, if after some number n of trails that show a property P conserved in
x and x+1, then we may infer that it will still hold to be true after n+1
trails. But this is itself induction. And hence the argument is a vicious
circle.

Have you actually worked with Peano's Axioms before, or even proven
anything using induction? I suspect not.

A huge portion of this post appears to be gobbledygook.

--- Christopher Heckman

[...]

.

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