Gödel’s 1st theorem is invalid

#1
Gödel’s 1st theorem is invalid

Godels 1st theorem is invalid

Godels 1st theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem


Godels theorem invalid

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

Axiom of reduciblity

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

G statement impredicative

the corresponding Gödel 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
 
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