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

**Date:** Sun Apr 27 2003 - 18:39:54 MDT

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--- Ben Goertzel <ben@goertzel.org> wrote: > > With

regards to informal systems, they are

*> conceivable
*

*> > so sure they exist. Formal systems are but a tiny
*

*> > infinitesimal subset of the set of all
*

*> mathematical
*

*> > systems, according to my intuition ;)
*

*> >
*

*> I don't understand how you're defining "mathematical
*

*> systems" ...
*

*>
*

system def= a coherent structure of interelating

elements.

"mathematical system" is as opposed to a physical

system, i.e. a system which exists as an independent

abstraction. Mathematical systems do not have to

conform to any formal rule structure, they just have

to "live" in the same abstract mathematical plain as

the other systems e.g. algebra, topology, systems of

set theory. You have to remember that there are a vast

many branches of mathematics that havent even been

conceived yet, clearly the SIAIs have got their work

cut out, we have only scratched the tip of the iceberg

mathematically. The sort of mathematics we have got at

the moment is presumably very basic and simple in

comparison, but its hard to imagine that ALL the

mathematical discoveries that SIs will ever make will

fall into the "formalizable" category. At some point

we are bound to hit some really weird stuff which

cannot even be axiomatized!

Simon.

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