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
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Pathological SelfReference and the Halting Problem [was:The empty string as a code]
Replies:
4
Last Post:
Jun 2, 2012 5:20 PM




Re: Pathological SelfReference 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 modeltheoretical > 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(thisformulasgodelnumber))
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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(GSGN)) & T2PRV[ T1!(PRV(GSGN)) ] > 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 & T1G & T2PRV( T1G )
Also Daryl, how do you remove RUSSELL'S SET from invoking in ZFC?
Herc  http://freewebs.com/namesort/matheology/THEHAMMER.jpg



