# GÃ¶del's theorem is invalid his G statement is banned by axiom of the system he uses

Status
Not open for further replies.

#### bas

Godels theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem

a flaw in theorem Godels sentence G is outlawed by the very axiom he uses to prove his theorem
ie the axiom of reducibiilty AR -thus his proof is invalid

http://www.enotes.com/topic/Axiom_of_reducibility

russells axiom of reducibility was formed such that impredicative statements were banned

but godels uses this AR axiom in his incompleteness proof ie axiom 1v
and formular 40

and as godel states he is useing the logic of PM ie AR
"P is essentially the system obtained by superimposing on the Peano axioms the logic of PM [ie AR axiom of reducibility]"

now godel constructs an impredicative statement G which AR was meant
to ban

The impredicative statement Godel constructs is
http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems#F...

the corresponding GÃ¶del sentence G asserts: G cannot be proved to be true within the theory T

now godels use of AR bans godels G statement

thus godel cannot then go on to give a proof by useing a statement his own axiom bans
but in doing so he invalidates his whole proof

Last edited:
Status
Not open for further replies.