Date: Jun 2, 2012 4:36 PM
Author: INFINITY POWER
Subject: Re: Pathological Self-Reference and the Halting Problem [was:The empty string as a code]
> > 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

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