Godels theorems end meaninglessness and are invalid logically-proven by colin leslie dean
Godel -The dean proof 3
Godels 1st theorem is logically flawed:
His G statement is banned by the axiom of reducibility in the system Godel uses to prove his theorem ie Principia Mathematica
Godel uses his G statement to prove his 1 st theorem
“the corresponding Gödel sentence G asserts: “G cannot be proved to be true within the theory T””
BUT that statement is impredicative
BUT Godels axiom 1v is the axiom of reducibility
"IV. Every formula 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 formula which does not contain u free. This axiom represents the axiom of reducibility (the axiom of comprehension 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)"
http://www.enotes.com/topic/Axiom_of_reducibility
Russells axiom of reducibility was formed such that impredicative statements where banned.
thus
Godels G statement is banned
thus
Godel commits a logical flaw to prove his theorem-thus his theorem is invalid
Gödel used the axiom of reducibility (AR) in his proof, which is axiom IV in his system
1 The axiom of reducibility was intended to ban impredicative statements.
Gödel's G statement is impredicative, as it refers to itself indirectly.
Dean argues that since AR bans impredicative statements, it should also ban Gödel's G statement conclusion . If the G statement is banned by an axiom of the system Gödel uses, then his proof would not be logically valid
4) Deans proof-4 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
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"
thus his theorem is meaningless
5) Deans proof-5
Godels paper is called
On formally undecidable propositions of Principia. Mathematica and related systems
Godel used the axiom of reducibility in his proof But Russel dropped that axiom from the edition of PM Godel said he is useing thus his proof is invalid
Quote
http://www.mrob.com/pub/math/goedel.htm
“A. Whitehead and B. Russell, Principia Mathematica, 2nd edition, 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 choice (for all types)” (( K Godel , On formally undecidable propositions of principia mathematica and related systems in The undecidable , M, Davis, Raven Press, 1965, p.5)
but quote page
http://www.helsinki.fi/filosofia/gts/ramsay.pdf.
“Russell gave up the Axiom of Reducibility in the second edition of Principia (1925)”
This claim raises questions about the validity of his proof because that axiom was dropped in the second edition of PM
Implications of Dropping the Axiom: Gödel's proof relies on an axiom that was not included in the system he claims to be analyzing, it raises questions about the validity of his proof as it pertains specifically to that system. This discrepancy shows Gödel's application of PM does not fully align with its formal structure as presented in its later editions
free read
Scientific Reality is Only the Reality of a Monkey (homo-sapiens)
