Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Pathological Self-Reference and the Halting Problem [was:The empty string as a code]
Posted:
Jun 2, 2012 4:36 PM
|
|
> > Yes. The notion of "provability" is mathematical. The notion
> > of "knowability" isn't.
>
> You're incorrect (at least) in the context of model-theoretical
> proof/provability. For instance, if you didn't _know_ the universe U
> of a model M is a singleton, you couldn't prove Axy[x=y] to be true
> or false.
Daryl doesn't know that this is a Godel Statement!
!(PROVE(this-formulas-godel-number))
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
He'll whine about it not being maths or being a crank or something.
Daryl can you make out any DIFFERENCE between these 2 formula?
ALL(T1) EXIST(T2)
T1|-!(PRV(GS-GN)) & T2|-PRV[ T1|-!(PRV(GS-GN)) ]
-> T1=/=T2
If a theory T1 has a statement GS !Prove(GS)
then it cannot be proven in that same theory.
A stronger version that G is in every theory.
A(T1)E(G)E(T2) T1=/=T2 & T1|-G & T2|-PRV( T1|-G )
Also Daryl, how do you remove RUSSELL'S SET from invoking in ZFC?
Herc
--
http://freewebs.com/namesort/matheology/THE-HAMMER.jpg
|
|
|
|
