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Topic: a logical flaw in godels proof - thus proof meaninglessness
Replies: 6   Last Post: Jan 8, 2014 9:09 PM

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David C. Ullrich

Posts: 2,752
Registered: 12/13/04
Re: a logical flaw in godels proof - thus proof meaninglessness
Posted: Jun 7, 2013 12:15 PM
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On Fri, 7 Jun 2013 01:55:56 -0700 (PDT), spermatozon@yahoo.com wrote:

>australias leading erotic poet colin leslie dean points out
>a logical flaw in godels proof which makes his proof meaninglessness
>an axiom in the system godel uses ie axiom of reducibility AR bans his G statement
>
>http://www.scribd.com/doc/32970323/Godels-incompleteness-theorem-invalid-illegitimate
>
>IT SHOULD BE NOTED
>Godel sentence G is outlawed by the very axiom he uses to prove his theorem ie the axiom of reducibiility -thus his proof is invalid-and thus
>godel commits a flaw by useing it to prove his theorem
>
>http://www.enotes.com/topic/Axiom_of_reducibility
>
>
>russells axiom of reducibility was formed such that impredicative
>statements where banned
>
>http://www.scribd.com/doc/32970323/Godels-incompleteness-theorem-invalid-illegitimate
>
>
>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 [b]the logic of PM[/b]” ie AR
>
>now godel constructs an impredicative statement G which AR was meant
>to ban
>
>The impredicative statement Godel constructs is
>http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
>
>
>“the corresponding Gödel sentence G asserts: “G cannot be proved to be
>true within the theory T””


No, G does not _assert_ anything. It's just a well formed formula.

>
>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 by doing so he invalidates his whole proof and his proof/logic is
>flawed
>
>
>we have a dilemma
>
>DILEMMA
>1)
>if godel is useing AR then he cannot use G as it is outlawed
>thus his proof collapses
>2) if godel is not useing AR then he is lying when he tells us he is
>and thus his theorem cannot be about PM and related systems





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