the australian philosopher colin leslie dean points out that Godel use

peano axioms which is impredicative-thus his theorem is invalid

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
godel constructs his system P from which he proves his incompleteness

theorem

quote

Godel's first Incompleteness Proof at MROB at MROB
Quote:In the proof of Proposition VI the **only properties of the system P **

employed were the following:

1. The class of axioms and the rules of inference (i.e. the relation

"immediate consequence of") are recursively definable (as soon as the

basic signs are replaced in any fashion by natural numbers).

2. Every recursive relation is definable in the system P (in the sense of

Proposition V).

Hence in every formal system that satisfies assumptions 1 and 2 and is

ω-consistent, undecidable propositions exist of the form (x) F(x), where

F is a recursively defined property of natural numbers, and so too in

every extension of such

axiom 3 of system P reads

Quote:3. x2(0).x1 ∀ (x2(x1) ⊃ x2(fx1)) ⊃ x1 ∀ (x2(x1))

** The principle of mathematical induction**: If something is true for x=0, and

if you can show that whenever it is true for y it is also true for y+1,

then it is true for all whole numbers x.

now poincare and others have pointed out

**the principle of induction is **

impredicative thus invalid -texts books on logic also say impredicative

statements are invalid

quote

Preintuitionism - Wikipedia, the free encyclopedia
peanos 5 th axiom

Quote: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.

thus godels theorem is invalid

it does not matter that alot of maths is impredicative just because maths

ueses them does not make them valid- or any proof made useing them