Gödel’s 1st theorem is meaningless and invalid
http://gamahucherpress.yellowgum.com/bo ... GODEL5.pdf
1) Gödel’s 1st theorem is meaningless
a) “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,[1] but not provable in the theory (Kleene 1967, p. 250)
note
"... there is an arithmetical statement that is true..."
In other words there are true mathematical statements which cant be proven
But the fact is Godel cant tell us what makes a mathematical statement true thus his theorem is meaningless
Godels 1st theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem
http://gamahucherpress.yellowgum.com/bo ... GODEL5.pdf
2) Godels theorm is 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