Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Topic: Godels theorems end in paradox
Replies: 2   Last Post: Feb 3, 2013 7:47 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 891
Registered: 3/3/09
Godels theorems end in paradox
Posted: Feb 3, 2013 7:06 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Australias leading erotic poet colin leslie dean has shown Godels theorem ends in 2 paradoxes


Paradox 1\
Godels theorem proved that provability is not the same a truth
Ie truth of a maths statement is independent of its proof
provability-within-the-theory-T is not the same as truth
?Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250)
For each consistent formal theory T having the required small amount of number theory
? provability-within-the-theory-T is not the same as truth; the theory T is incomplete.

It is shown by colin leslie dean that Godels 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

for if the theorem is true
then truth does equate with proof- as he has given proof of a true
but his theorem says
truth does not equate with proof.
thus a paradox

2 paradox 2
Australias leading erotic poet colin leslie dean has shown Godels second theorem ends in paradox



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


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

godel is useing a a mathematical system
his theorem says a system cant be proven consistent
this must then apply to the system he used to create the theorem thus his theorem applies to itself

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2016. All Rights Reserved.