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Topic: Pathological Self-Reference and the Halting Problem [was:The
empty string as a code]

Replies: 4   Last Post: Jun 2, 2012 5:20 PM

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 INFINITY POWER Posts: 117 Registered: 11/1/11
Re: Pathological Self-Reference and the Halting Problem [was:The empty string as a code]
Posted: Jun 2, 2012 4:36 PM
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> > 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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Date Subject Author
6/2/12 Graham Cooper
6/2/12 INFINITY POWER
6/2/12 Graham Cooper

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