The fundamental problem with Godels theorems- why the first and second theorems end in paradox
in [Math]
|
Prev: Way off topic: oil and politics (was: Hexagonal grid and itsthree directions)
Next: PRIME NUMBER CURVED NUMERATIONS-- HOPE RESEARCH ANNOUNCES NEW RESEARCH -- CLASSIC 3 AND 4 EQUALIZATION
From: byron on 29 May 2010 07:02 colin leslie dean points out The fundamental problem with Godels theorems are he creates an imprdeicative statement and the theorems apply to themselves ie are impredicative- thus leading to paradox ie this is godels impredicative statement used in his first theorem http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Meaning_of_the_first_incompleteness_theorem [quote]the corresponding Gödel sentence G asserts: G cannot be proved to be true within the theory T[/quote] as was pointed out many years ago if you use or create impredicative statements then what you will get is paradox and as dean has shown that is what happens with godels theorems philosophers such as russell mathematicians such as poincare have outlawed these statements from mathematics as they lead to paradox in maths and they lead to paradox in godels theorems why because if godels theorems are true then they apply to godels theorems as well if godels first theorem is true then it applies to it self [quote]it is shown by colin leslie dean that Godels first theorem ends in paradox it is said godel PROVED "there are mathematical true statements which cant be proven" in other words truth does not equate with proof. if that theorem is true then his theorem is false PROOF for if the theorem is true then truth does equate with proof- as he has given proof of a true statement but his theorem says truth does not equate with proof. thus a paradox[/quote] if godels second theorem is true then it applies to it self [quote] http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Proof_sketch_for_the_second_theorem The following rephrasing of the second theorem is even more unsettling to the foundations of mathematics: If an axiomatic system can be proven to be consistent and complete from within itself, then it is inconsistent. now this theorem ends in self-contradiction http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf But here is a contradiction Godel must prove that a system cannot be proven to be consistent based upon the premise that the logic he uses must be consistent . If the logic he uses is not consistent then he cannot make a proof that is consistent. So he must assume that his logic is consistent so he can make a proof of the impossibility of proving a system to be consistent. But if his proof is true then he has proved that the logic he uses to make the proof must be consistent, but his proof proves that this cannot be done[/quote] as was pointed out many years ago if you use or create impredicative statements then what you will get is paradox and as dean has shown that is what happens with godels theorems
From: Don Stockbauer on 29 May 2010 07:31 On May 29, 6:02 am, byron <spermato...(a)yahoo.com> wrote: > colin leslie dean points out The fundamental problem with Godels > theorems are he creates an imprdeicative statement and the theorems > apply to themselves ie are impredicative- thus leading to paradox > ie this is godels impredicative statement used in his first theoremhttp://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#M... > [quote]the corresponding Gödel sentence G asserts: G cannot be proved > to be true within the theory T[/quote] > > as was pointed out many years ago if you use or create impredicative > statements then what you will get is paradox > and as dean has shown > that is what happens with godels theorems > > philosophers such as russell > mathematicians such as poincare > have outlawed these statements from mathematics as they lead to > paradox in maths > > and they lead to paradox in godels theorems > why > because if godels theorems are true > then they apply to godels theorems as well > > if godels first theorem is true then it applies to it self > > [quote]it is shown by colin leslie dean that Godels first theorem ends > in paradox > > it is said godel PROVED > "there are mathematical true statements which cant be proven" > in other words > truth does not equate with proof. > > if that theorem is true > then his theorem is false > > PROOF > for if the theorem is true > then truth does equate with proof- as he has given proof of a true > statement > but his theorem says > truth does not equate with proof. > thus a paradox[/quote] > > if godels second theorem is true > then it applies to it self > [quote]http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#P... > > The following rephrasing of the second theorem is even more > unsettling to the foundations of mathematics: > > If an axiomatic system can be proven to be consistent and complete > from within itself, then it is inconsistent. > > now this theorem ends in self-contradiction > > http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf > > But here is a contradiction Godel must prove that a system cannot > be proven to be consistent based upon the premise that the logic he > uses must be consistent . If the logic he uses is not consistent then > he cannot make a proof that is consistent. So he must assume that his > logic is consistent so he can make a proof of the impossibility of > proving a system to be consistent. But if his proof is true then he > has proved that the logic he uses to make the proof must be > consistent, but his proof proves that this cannot be done[/quote] > > as was pointed out many years ago if you use or create impredicative > statements then what you will get is paradox > and as dean has shown > that is what happens with godels theorems Godel's theorems are like taking useful simple garden tools like rakes and hoes and arranging thousands of them into a sentence which when read from the air says "This sentence cannot be used to do gardening with."
From: Spotter on 29 May 2010 10:36
"byron" <spermatozon(a)yahoo.com> wrote in message news:0012f9bc-61f2-4f00-a980-77a582ecc566(a)h20g2000prn.googlegroups.com... colin leslie dean points out The fundamental problem with Godels Lern hau two writting proper, fukcwit |