My Math Forum  

Go Back   My Math Forum > College Math Forum > Applied Math

Applied Math Applied Math Forum

Closed Thread
LinkBack Thread Tools Display Modes
January 22nd, 2019, 10:04 PM   #1
Banned Camp
Joined: Jun 2010

Posts: 17
Thanks: 0

Gödel's theorem is invalid his G statement is banned by axiom of the system he uses

Godels theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem

a flaw in theorem Godels sentence G is outlawed by the very axiom he uses to prove his theorem
ie the axiom of reducibiilty AR -thus his proof is invalid

russells axiom of reducibility was formed such that impredicative statements were banned

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 axiom of reducibility]"

now godel constructs an impredicative statement G which AR was meant
to ban

The impredicative statement Godel constructs is

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 in doing so he invalidates his whole proof

Last edited by bas; January 22nd, 2019 at 10:18 PM. Reason: add
bas is offline  
Closed Thread

  My Math Forum > College Math Forum > Applied Math

axiom, banned, gödel, gödels, godels, invalid, statement, system, theorem

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Axiom of Regularity is a Theorem zylo Topology 7 March 19th, 2018 09:14 AM
Theorem axiom of separation and yours implications in methaphisics lemgruber Math 1 January 12th, 2015 01:04 PM
The axiom of choice and the well ordering theorem RyanPowers Applied Math 1 September 26th, 2014 04:51 PM
Axiom or theorem? Theta Number Theory 6 June 14th, 2014 01:35 PM
Proof of Bolzano-Weierstrass theorem using Axiom of Complete kindlychung Real Analysis 0 September 26th, 2010 08:51 AM

Copyright © 2019 My Math Forum. All rights reserved.