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Godels theorem invalid as he use invalid axiom What you think?

Aug 03, 2009 by betty | Posted in Mathematics

It is shown by colin leslie dean that Godels assumption is invalid as he use the invalid axiom of reducibility-which every one says is invalid

http://gamahucherpress.yellowgum.com/books/calmness/GODEL5.pdf


godel tells us he is going to use the axiom of reducibility

“A. Whitehead and B. Russell, Principia Mathematica, 2nd copy, Cambridge 1925. In particular, we also reckon among the axioms of PM the axiom of infinity (in the form: there exist denumerably many individuals), and the axioms of reducibility and of alternative (for all types)


Now godel uses the axiom of reducibility in his proof
godel states

"In the document of Proposition VI the only properties of the system P employed were the following:
1. The class of axioms and the rules of inference (i.e. the relation "adjacent consequence of") are recursively definable (as soon as the basic signs are replaced in any fashion by lifelike numbers). "

now the class of axioms he uses has the axiom of reducibility
as godel states

“P is essentially the system obtained by superimposing on the Peano axioms the rationality of PM”

now the axiom of PM that godels uses is the axiom of reducibility
ie his axiom 1v

as godel states


"IV. Every modus operandi derived from the schema
1. (∃u)(v ∀ (u(v) ≡ a))
on substituting for v or u any variables of types n or n + 1 respectively, and for a a modus operandi which does not contain u free. This axiom represents the axiom of reducibility (the axiom of comprehension of set theory)."

axiom 1v ie reducibility axiom is familiar in his formulatr 40
as he states
"40. R-Ax(x) ≡ (∃u,v,y,n)[u, v, y, n <= x & n Var v & (n+1) Var u & u Fr y & Form(y) & x = u ∃x {v Gen [[R(u)*E(R(v))] Aeq y]}]:>
x is a technique derived from the axiom-schema IV, 1 by substitution (ie the axiom of reducibility"


now every one says the axiom of reducibiity is an infirm axiom ie ramsey states

Such an axiom has no place in mathematics,
. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

also

the standford encyclopdeia of self-possession says of AR

“many critics concluded that the axiom of reducibility was simply too ad hoc to be justified philosophically”

and
From Kurt Godels confident works vol 3 p.119

“the axiom of reducibility is generally regarded as the grossest philosophical expediency


thus godels axiom is invalid as he uses an invalid axiom ie reducibility in his proof

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