das

stop playing the fool

note Nx refers to itself (n+1) N x ≡ R(3) * n N x and is circular Self-referring statements is a circular statement.

Ponicare Russell et al said self referencing statements ie impredicative definitions are invalid texts books on logic tell us self referencing ,statements (petitio principii) are invalid Godel uses at least 2 in his incompleteness theorem 1 The general result as to the existence of undecidable propositions reads: Proposition VI: To every ω-consistent recursive class c of formulae there correspond recursive class-signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg© (where v is the free variable of r). Godel gives a prof of this he uses in that proof forumlas 1-45 formula 16 is self referencing 16. 0 N x ≡ x (n+1) N x ≡ R(3) * n N x note N x appears on both sides of the formular formula 28 which is defined from formular 16 is self referencing 28. 0 St v,x ≡ ε n {n <= l(x) & v Fr n,x & not (∃p)[n <= l(x) & v Fr p,x]} (k+1) St v,x ≡ ε n {n ∃p)[n < p < k St v,x & v Fr p,x]} note St v,x appears on both sides of the formular thus his incompleteness theorem is derived from 2 invalid self referencing statements and according to colin leslie dean his theorem is thus invalid http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf GÖDEL’S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS GÖDEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS CASE STUDY IN THE MEANINGLESSNESS OF ALL VIEWS By COLIN LESLIE DEAN B.SC, B.A, B.LITT (HONS), M.A, B,LITT (HONS), M.A, M.A (PSYCHOANALYTIC STUDIES), MASTER OF PSYCHOANALYTIC STUDIES, GRAD CERT (LITERARY STUDIES) GAMAHUCHER PRESS WEST GEELONG, VICTORIA AUSTRALIA 2007

sorry godel states godel is useing circular statement and philosophy poncicare russell et al say they are invalid sorry impredicative statements are as godel ponicare and russel said they are said they are and they are invalid as godel says they are

godel uses impredicative statements which philosophers say are invalid thus as dean points out godels theorems are invalid it is no uses giving us the standard view as dean overthrows it

if you cant say ramsey is right or wrong you cant say dean is wrong when he uses ramsey to show godel s invalid

then why do you argue dean is wrong when he says godels theorems are invalid because he uses invalid axioms and statements based on the testimony of ramsey russell ponicare and philosophers

then are they right

why are you reluctant to say ramsey russell ponicare and philosophers are wrong

simple question is ramsey et al right in saying AR is invalid are ponicare russell etal right in saying impredicative statements are invalid they are either right or wrong -which is it-simple question

is ramsey right when he says axiom of reducibility has no place in mathematics are ponicare russell and philosophers right in saying impredicative statements are invalid

i asked for a simple yes or no-is that so hard are those mathematician right or wrong when they say ar IMPREDICATIVE STATEMENTS ARE INVLAID IS A YES OR NO SO HARD

simple yes or no ramsey say the axiom of reducibility is he right or wrong russell wittgenstien and others say the axiom id invalid are they right or wrong Poncicare Russell and philosophers say impredicative statements are invalid are they right or wrong

go read any book on philosophy and they all say circular statements ie petitio principi are invalid http://philosophy.lander.edu/logic/circular.html http://en.wikipedia.org/wiki/Begging_the_question even godel said they made mathematics false any first year phil students know this look on the net and you will see

sorry i know why he is invalid he tells us he uses impredicative statements and these are philosophically invalid -thus making his proof invalid

i dont have to all have to do is take godels word for it that he makes statements that refer to themselves you try finding these statements he says they are there -and they make his proof invalid philosophically

sorry Godel uses impredicative statements and philosophy says they are invalid and thus his proof is invalid even godel says they make maths false

sorry any proof which uses invalid statements is invalid if you use a contradictory statement to prove statements are contradictory your proof is invalid - even if statements are contradictory

Godel has arrived at this by using statements philosophy says are invalid thus philosophically his claims are philosophically invalid by using statements that refer to themselves in his proof his proof is philosophically invalid Poincare and Russell said such statements just lead to paradox or contradiction Poincare outlawed impredicative definitions But the problem of outlawing impredicative definitions was that a lot of useful mathematics would have to be abandoned “ruling out impredicative definitions would eliminate the contradiction from mathematics, but the cost was too great

The Australian philosopher Colin leslie Dean points Godels theorem is invald for 5 reasons: he uses the axiom of reducibility, he uses the axiom of choice, he miss uses the theory of types, he ends in 3 paradoxes and he uses vicious circle statements. Dean out that Godels uses impredicative statements in his incomplertenes theorem that makes it invalid GÖDEL’S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS GÖDEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS CASE STUDY IN THE MEANINGLESSNESS OF ALL VIEWS By COLIN LESLIE DEAN B.SC, B.A, B.LITT (HONS), M.A, B,LITT (HONS), M.A, M.A (PSYCHOANALYTIC STUDIES), MASTER OF PSYCHOANALYTIC STUDIES, GRAD CERT (LITERARY STUDIES) GAMAHUCHER PRESS WEST GEELONG, VICTORIA AUSTRALIA 2007 Quote from Godel “ The solution suggested by Whitehead and Russell, that a proposition cannot say something about itself , is to drastic... We saw that we can construct propositions which make statements about themselves,… ((K Godel , On undecidable propositions of formal mathematical systems in The undecidable , M, Davis, Raven Press, 1965, p.63 of this work Dvis notes, “it covers ground quite similar to that covered in Godels orgiinal 1931 paper on undecidability,” p.39.) What Godel understood by "propositions which make statements about themselves" is the sense Russell defined them to be 'Whatever involves all of a collection must not be one of the collection.'Put otherwise, if to define a collection of objects one must use the total collection itself, then the definition is meaningless. This explanation given by Russell in 1905 was accepted by Poincare' in 1906, who coined the term impredicative definition, (Kline's "Mathematics: The Loss of Certainty" Note Ponicare called these self referencing statements impredicative definitions texts books on logic tell us self referencing ,statements (petitio principii) are invalid Godels has argued that impredicative definitions destroy mathematics and make it false Gödel has offered a rather complex analysis of the vicious circle principle and its devastating effects on classical mathematics culminating in the conclusion that because it "destroys the derivation of mathematics from logic, effected by Dedekind and Frege, and a good deal of modern mathematics itself" he would "consider this rather as a proof that the vicious circle principle is false than that classical mathematics is false” AXIOM OF REDUCIBILITY (1) 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 ( 2) “As a corollary, the axiom of reducibility was banished as irrelevant to mathematics ... The axiom has been regarded as re-instating the semantic paradoxes” 2)“does this mean the paradoxes are reinstated. The answer seems to be yes and no” - ) 3) It has been repeatedly pointed out this Axiom obliterates the distinction according to levels and compromises the vicious-circle principle in the very specific form stated by Russell. But The philosopher and logician FrankRamsey (1903-1930) was the first to notice that the axiom of reducibility in effect collapses the hierarchy of levels, so that the hierarchy is entirely superfluous in presence of the axiom. 4) Russell abandoned this axiom and many believe it is illegitimate and must be not used in mathematics Ramsey says 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