Paradox 1\ Godels theorem proved that provability is not the same a truth Ie truth of a maths statement is independent of its proof or provability-within-the-theory-T is not the same as truth http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Meaning_of_the_first_incompleteness_theorem ?Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory (Kleene 1967, p. 250) For each consistent formal theory T having the required small amount of number theory ? provability-within-the-theory-T is not the same as truth; the theory T is incomplete.
It is shown by colin leslie dean that Godels theorem ends in paradox
it is said godel PROVED "there are mathematical true statements which cant be proven" in other words truth does not equate with proof.
if that theorem is true then his theorem is false
PROOF for if the theorem is true then truth does equate with proof- as he has given proof of a true statement but his theorem says truth does not equate with proof. thus a paradox
2 paradox 2 Australias leading erotic poet colin leslie dean has shown Godels second theorem ends in paradox
But here is a contradiction Godel must prove that a system cannot be proven to be consistent based upon the premise that the logic he uses must be consistent . If the logic he uses is not consistent then he cannot make a proof that is consistent. So he must assume that his logic is consistent so he can make a proof of the impossibility of proving a system to be consistent. But if his proof is true then he has proved that the logic he uses to make the proof must be consistent, but his proof proves that this cannot be done
godel is useing a a mathematical system his theorem says a system cant be proven consistent this must then apply to the system he used to create the theorem thus his theorem applies to itself