jnana Posted May 7 Posted May 7 The Foundations of Mathematics end in meaningless jibbering nonsense A) Mathematics ends in contradiction-6 proofs http://gamahucherpress.yellowgum.com/wp-content/uploads/MATHEMATICS.pdf and https://www.scribd.com/document/40697621/Mathematics-Ends-in-Meaninglessness-ie-self-contradiction Proof 5 ZFC is inconsistent:thus ALL mathematics falls into meaninglessness https://brilliant.org/wiki/zfc/ ZFC. ZFC, or Zermelo-Fraenkel set theory, is an axiomatic system used to formally define set theory (and thus mathematics in general). but ZFC is inconsistent:thus ALL mathematics falls into meaninglessness proof it all began with Russells paradox and to get around the consequences of it Modern set theory just outlaws/blocks/bans this Russells paradox by the introduction of the ad hoc axiom the Axiom schema of specification ie axiom of separation which wiki says http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory "The restriction to z is necessary to avoid Russell's paradox and its variants. " http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory "Axiom schema of specification (also called the axiom schema of separation or of restricted comprehension): If z is a set, and \phi! is any property which may characterize the elements x of z, then there is a subset y of z containing those x in z which satisfy the property. The "restriction" to z is necessary to avoid Russell's paradox and its variant" now Russell's paradox is a famous example of an impredicative construction, namely the set of all sets which do not contain themselves the axiom of separation is used to outlaw/block/ban impredicative statements like Russells paradox but this axiom of separation is itself impredicative http://math.stanford.edu/~feferman/papers/predicativity.pdf "in ZF the fundamental source of impredicativity is the seperation axiom which asserts that for each well formed function p(x)of the language ZF the existence of the set x : x } a ^ p(x) for any set a Since the formular p may contain quantifiers ranging over the supposed "totality" of all the sets this is impredicativity according to the VCP this impredicativity is given teeth by the axiom of infinity" thus ZFC thus it outlaws/blocks/bans itself thus ZFC contradicts itself and 1)ZFC is inconsistent 2) that the paradoxes it was meant to avoid are now still valid and thus mathematics is inconsistent Now we have paradoxes like Russells paradox Banach-Tarskin paradox Burili-Forti paradox with the axiom of seperation banning itself ZFC is thus inconsistent and thus ALL mathematics is just rubbish meaningless jibbering nonsense B) Godels theorems end in meaninglessness 1) Godels 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-inva... 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 now godel constructs an impredicative statement G which AR was meant to ban The impredicative statement Godel constructs is http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems#F... “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 by doing so he invalidates his whole proof and his proof/logic is flawed 2) from http://pricegems.com/articles/Dean-Godel.html "Mr. Dean complains that Gödel "cannot tell us what makes a mathematical statement true", but Gödel's Incompleteness theorems make no attempt to do this" Godels 1st theorem “....., there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250) but Godel did not know what makes a maths statement true thus his theorem is meaningless checkmate https://en.wikipedia.org/wiki/Truth#Mathematics Gödel thought that the ability to perceive the truth of a mathematical or logical proposition is a matter of intuition, an ability he admitted could be ultimately beyond the scope of a formal theory of logic or mathematics[63][64] and perhaps best considered in the realm of human comprehension and communication, but commented: Ravitch, Harold (1998). "On Gödel's Philosophy of Mathematics".,Solomon, Martin (1998). "On Kurt Gödel's Philosophy of Mathematics" http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf and https://www.scribd.com/document/32970323/Godels-incompleteness-theorem-invalid-illegitimate
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