Mathematics is meant to be a rigorous deductive discipline based upon(adsbygoogle = window.adsbygoogle || []).push({});

sound principles

but

colin leslie dean showing that godels theorem - what godel did- is invalid

as it is based on invalid axioms

throws maths into crisis

because it now turns out that maths is not based upon sound principles

and ad hoc principles can be used if they apparently give the right

result

take the axiom of reducibility used by godel

it is ad hoc and unjustifiable as the The Stanford Dictionary of

Philosophy

The Stanford Dictionary of Philosophy states that ",

many critics

concluded that the axiom of reducibility was simply too ad hoc to be

justified philosophically."

with this admission and the fact that godel used an ad hoc principle

the foundations of maths have been destroyed for any one can now use any

ad hoc principle to prove anything

take Fermats last theorem

any one can now create an ad hoc principle which will prove the theorem

colin leslie dean has thrown mathematics into crisis by shattering its

logical foundations

and by showing that truth can be arrived at by any ad hoc avenue

thus showing the myth of mathematics as a rigorous deductive discipline

based upon sound principles

to reiterate Godel does use the axiom of reducibility in his proof of HIS

incompleteness theorem

it is is his axiom 1v

and he uses it in his formular 40

Godel uses the axiom of reducibility axiom 1V of his system is the axiom

of reducibility “As Godel says “this axiom represents the axiom of

reducibility (comprehension axiom of set theory)” (K Godel , On formally

undecidable propositions of principia mathematica and related systems in

The undecidable , M, Davis, Raven Press, 1965,p.12-13)

.

Godel uses axiom 1V the axiom of reducibility in his formula 40 where he

states “x is a formula arising from the axiom schema 1V.1 ((K Godel , On

formally undecidable propositions of principia mathematica and related

systems in The undecidable , M, Davis, Raven Press, 1965,p.21

“ [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 formula derived from the axiom-schema IV, 1 by substitution “

ramsey says of the axiom

The Stanford Dictionary of Philosophy states that Such an axiom has no place in mathematics, and anything which cannot be

proved without using it cannot be regarded as proved at all.

This axiom there is no reason to suppose true; and if it were true, this

would be a happy accident and not a logical necessity, for it is not a

tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

", many critics

concluded that the axiom of reducibility was simply too ad hoc to be

justified philosophically."

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# Crisis in mathematics

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