**From:** Simon Gordon (*sim_dizzy@yahoo.com*)

**Date:** Thu May 01 2003 - 19:14:48 MDT

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Sorry to bring up the same thread but i do believe

that metamathematics, particularly Godels theorems (if

you are to take Penrose's suggestions with any

seriousness), do have at least some level of relevance

to AGI. I also see SIs themselves being particularly

occupied with the intricacies of metamathematics (what

else is there for them to do with all that excessive

intelligence!!)

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*> > All formal systems are expressable as finite
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strings

*> > of symbols (by
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*> > definition), and thus trivially mappable to
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*> > integers. QED.
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*>
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*> Thanks Perry, thats all i need to know. Clearly i
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*> want my systems to be a little more generic than
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*> just formal systems
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Well, sadly the Church-Turing Thesis has yet to be

disproven, so I'm afraid that for now your wants may

remain unfulfilled.

*> because of set-theory-envy, if set
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*> theory has uncountable sets why cant the set of all
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*> primitive entities be uncountable?
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*> Or even infinite to
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*> the same extent as the set of all sets is infinite
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What is the "set of all sets"? Many kinds of set

theory can't express such a thing. Again, you keep

throwing out ideas about sets as though they somehow

had a life outside a particular flavor of set

theory. They don't, any more than the integers have a

life outside of theories like Peano's axioms.

*> > It is literally the set of all formal systems,
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*> > because it is the set
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*> > of all consistent mathematical systems.
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*>
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*> I consider formal systems to be a subset of the set
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of

*> consistent mathematical systems but you have equated
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*> them.
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What other sort of mathematics is there outside of

formal systems?

-------------------------------------------------------

It seems the above discussion has already occured

albeit in a much more fleshed out form on the

everything-list last year between Hal Finney, Russel

Standish and others. From a subjective point of view

these rantings are more than just interesting because

these knowledgeable people have clearly read from the

same source material as i have, namely : Rudy Rucker's

excellent book "Infinity and the Mind". BTW Perry

where i said "set of all sets" clearly i meant "class

of all sets" ;)

everything-list@eskimo.com/msg03883.html">http://www.mail-archive.com/everything-list@eskimo.com/msg03883.html

See also the other sections of the everything thread.

Simon.

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