What is wrong with this paradox

ladyjane · February 11, 2008, 8:26am

There is a paradox in Godels incompleteness theorem
Undecidability in a formal system is dependent on the system PM but the system PM has undecidability

Godel tells us that among those very wide range of formal systems that have undecidability are to be included those systems which arise from PM by the addition finitely many axioms
As he states
â€œIt is reasonable therefore to make the conjecture that these axioms and rules of inference are also sufficent to decide all mathematical questions which can be formally expressed in the given systems. In what follows it will be shown that this is not the case but rather that in both systems cited [PM and ZF] there exist relatively simple problems of ordinary whole numbers which cannot be decided on the basis of the axioms. [NOTE IT IS CLEAR] This situation does not depend upon the special nature of the constructed systems [PM and ZF] but rather holds for a very wide class of formal systems among which are included in particular all those which arise from the given systems [PM and ZF] by addition of finitely many axiomsâ€
In other words PM is included in those systems which have undecidablity

Thus we have the paradox that while PM is used to find if a formal system is undecidable it is undecidable itself
i.e.
hence in every formal system which satisfies assumptions 1 and 2 [ from P which uses system PM] and is w - consistent there exist undecidable propositions
In other words the very system which is used to find undecidability is included in the set of undecidable systems
PM is part of the very set it is used to create
GÃ¶del’s proof shows for some class of formal systems, they can not be both complete and consistent

if a system is consistent it will be incomplete
If PM is consistent it is incomplete i.e it has statements which cannot be proven true or false
thus

PM is used to prove that a system has statements which cannot be proven true or false
but
PM can only prove this if all its statement can be proven to be true
but
PM has statements which cannot be proven true or false
thus
it cant prove anything
but it is used to prove if systems are undecidadble

thus a paradox

PM being undecidable cant be used to create the set of undecidable systems of which it belongs-if it belongs to the set it cant prove anything and if it dont belong to the set it is not undecidable

Anthem · February 11, 2008, 12:50pm

Another repetitive post. This is the second time I’ve reported you. Keep going; we’re all rooting for a ban.

ladyjane · February 11, 2008, 1:06pm

geee you give the words anal retentive a new meaning

Anthem · February 11, 2008, 1:25pm

More like annoyed. you flood the natural science section with things that aren’t scientific, and moreover, they’re repetitive.

ladyjane · February 11, 2008, 1:33pm

so why is your post “on colin leslie dean” scientific

Anthem · February 11, 2008, 1:41pm

It’s alerting the scientific world to false scientific claims. The natural science section is also your most active (only active?) section, so it’s appropriate.

ladyjane · February 11, 2008, 1:45pm

so tell us wats wrong with the paradox

Anthem · February 11, 2008, 1:46pm

^^ No. That would be indulging you. you’re not worth it.

ladyjane · February 11, 2008, 1:51pm

well then you cant say dean does not know the maths then
unless you look at the paradox how can you say dean does not know the issues

Anthem · February 11, 2008, 1:52pm

you don’t even understand convergence, which is several levels below where the big boys are playing.

Come back after you’ve completed basic calculus.

ladyjane · February 11, 2008, 1:56pm

all i ask is just tell us the number root 2 converges to
if you cant
then
it dont exist

Anthem · February 11, 2008, 1:59pm

you’re wrong. I’ve tried explaining it to you, but you’re not smart enough to grasp the concept. And it’s really not even that hard.

ladyjane · February 11, 2008, 2:02pm

so tell us the number root 2 converges to

Anthem · February 11, 2008, 2:04pm

I’m not answering that question again. See one of my other three or four answers on that subject.