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

**Date:** Sun Apr 27 2003 - 11:02:53 MDT

**Next message:**geodesicallyincomplete@warpmail.net: "Re: Infinite universe"**Previous message:**Ben Goertzel: "RE: Infinite universe"**In reply to:**Perry E. Metzger: "Re: Infinite universe"**Next in thread:**Perry E. Metzger: "Re: Infinite universe"**Reply:**Perry E. Metzger: "Re: Infinite universe"**Reply:**Samantha Atkins: "Re: Infinite universe"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

--- "Perry E. Metzger" <perry@piermont.com> wrote: >

*> All formal systems are expressable as finite strings
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*> of symbols (by
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*> definition), and thus trivially mappable to
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*> integers. QED.
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Thanks Perry, thats all i need to know. Clearly i want

my systems to be a little more generic than just

formal systems 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

*> 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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I consider formal systems to be a subset of the set of

consistent mathematical systems but you have equated

them.

*> Of course, if you're going to bring things down to
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*> the level of "set"
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*> you start getting into a much deeper problem. "Sets"
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*> don't
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*> interact.
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Exactly. Sets dont interact, thats why they make such

good self-contained entities and can be thought of as

"universes".

*> And if you were willing to accept that we aren't in
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*> a universe and
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*> move on to "sets" as your fundamental universes,
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*> what sort of set
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*> theory are you going to adopt as "fundamental"?
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*> After all, in some set
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*> theories, you get the axiom of choice, in some you
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*> don't. In some, the
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*> continuum hypothesis is an axiom, in some it isn't.
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*> The list goes on
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*> and on.
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Axioms are not something i worry about too much: they

are decided by the anthropic principle. But in the

broader context there are "all possible set theories"

and so its just a matter of selecting which one we are

in.

*> Sets, you see, aren't as primitive as formal systems
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*> at all, even
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*> though they are much less powerful, just as integers
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*> aren't as
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*> primitive as formal systems although they are much
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*> less powerful.
*

I dont get this. If sets are a subset of the set of

all formal systems why are there more sets than there

are formal systems. Surely the most primitive entities

are also the most numerous.

Simon.

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