Godels 2nd theorem ends in paradox

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

Godels 2nd theorem ends in paradox

Postby bas on January 25th, 2019, 8:06 pm 

Godels 2nd theorem ends in paradox


Godel's 2nd theorem is about

"If an axiomatic system can be proven to be consistent and complete from
within itself, then it is inconsistent.”

But we have a paradox

Gödel is using a mathematical system
his theorem says a system cant be proven consistent


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
Banned User
Posts: 18
Joined: 17 Jun 2010

Re: Godels 2nd theorem ends in paradox

Postby Lomax on January 25th, 2019, 8:58 pm 

bas, I know you aren't reading anybody's replies, but your argument falls for at least three reasons. Firstly, to say that "his logic" cannot prove its own consistency is not to say that it is inconsistent - the proof of it, if there is one, may come from outside. You cite the words "from within itself" and then omit them. Secondly, his incompleteness theorems only deal specifically with axiomatic systems capable of generating Peano arithmetic - there is no Peano arithmetic in the syllogism you present above. Thirdly, you make the further omission of the words "complete and". Even if your argument did not have the other gaping flaws, you would only have shown that his logic is either incomplete or inconsistent. And there is no shame in incompleteness. Scientists have been working with it since the dawn of [END OF SENTENCE MISSING]
User avatar
Forum Administrator
Posts: 3717
Joined: 01 Jul 2010
Location: Nuneaton, UK
TheVat liked this post

Re: Godels 2nd theorem ends in paradox

Postby hyksos on January 25th, 2019, 11:20 pm 

bas's use of periods is inconsistent or complete, but not both.
User avatar
Active Member
Posts: 1828
Joined: 28 Nov 2014
Lomax liked this post

Return to Mathematics

Who is online

Users browsing this forum: No registered users and 48 guests