Is this the Shortest disproof in history

Godel's incompleteness proof runs to over 60 pages. Colin leslie has proved him wrong in less that 150 words.
Is this the shortest disproof in history


Godel specifies that he uses Zermelo axiom system- so deans critique stands

quote
http://www.mrob.com/pub/math/goedel.html


"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

[191]a system made by adding a recursively definable ω-consistent class of axioms. As can be easily confirmed, the systems which satisfy assumptions 1 and 2 include the Zermelo-Fraenkel and the v. Neumann axiom systems of set theory,47"


Godel used Peanos axioms but these axioms are impredicative and thus acording to Russel Poincaré and others must be avoided as they lead to paradox. Godel himself accepts impredicative definition and notes that if we accept the criticism of them then most classical mathematics must be false-

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.

From this Poincaré argues that if we fail to establish the consistency of Peano's axioms for natural numbers without falling into circularity, then the principle of complete induction is improvable by general logic.


quote

http://www.friesian.com/goedel/chap-1.htm

recent research [9] has shown that more can be squeezed out of these restrictions than had been expected:

all mathematically interesting statements about the natural numbers, as well as many analytic statements, which have been obtained by impredicative methods can already be obtained by predicative ones.[10]

We do not wish to quibble over the meaning of "mathematically interesting." However, "it is shown that the arithmetical statement expressing the consistency of predicative analysis is provable by impredicative means." Thus it can be proved conclusively that restricting mathematics to predicative methods does in fact eliminate a substantial portion of classical mathematics.[11]

Gödel has offered a rather complex analysis of the vicious circle principle and its devastating effects on classical mathematics culminating in the conclusion that because it "destroys the derivation of mathematics from logic, effected by Dedekind and Frege, and a good deal of modern mathematics itself" he would "consider this rather as a proof that the vicious circle principle is false than that classical mathematics is false."[12]