Infinity and the mind was: Infinite universe

From: Simon Gordon (
Date: Thu May 01 2003 - 19:14:48 MDT

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

> > All formal systems are expressable as finite
> > of symbols (by
> > definition), and thus trivially mappable to
> > integers. QED.
> Thanks Perry, thats all i need to know. Clearly i
> want my systems to be a little more generic than
> just formal systems

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
> theory has uncountable sets why cant the set of all
> primitive entities be uncountable?

> Or even infinite to
> the same extent as the set of all sets is infinite

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,
> > because it is the set
> > of all consistent mathematical systems.
> I consider formal systems to be a subset of the set
> consistent mathematical systems but you have equated

> them.

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" ;)">
See also the other sections of the everything thread.


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