you say
If you were to disprove logic as a means of showing that there may be better ways of thinking, I would congradulate you; unfortunately, you do not seek to improve the system, or create a more functional system, you simply seek to destroy. You are the cognitive virus

i shall leave it up to humanity to build upon the rubble
but remember destruction is a means to recreate
yin tang
from chaos comes order

but as an aside
mystic have been building upon this meaninglessness for a more spiritual outlook
i think you are to much of a scientific materialist to see it aint destruction at all

and what's theorem VI?
Theorem VI: For every w-consistent primitive recursive class of formulae there is a primitive recursive class-sign r such that neither forall(v,r) nor not(forall(v,r)) belongs to Conseq(K) (where v is the free variable of r).

which is not what you claim in your "paradox":
"hence in every formal system which satisfies assumptions 1 and 2 [ which uses system PM] and is w - consistent there exist undecidable propositions�

do you just make stuff up as you go along, hoping no-one will notice that you're talking out of your arse?

Spare us your adolescent philosophizing. Listen nightrover/Dean, there is no rubble you idiot. Godel's Incompleteness theorems have been proved through many, many different means. If you actually understood the theorems, and had an intuitive understanding of incompleteness in axiomatic systems, you would know that it's a natural consequence and involves no paradox. If you have a problem understanding Godel's theorems, you can rest assured the problem lies with you.