Re: SUO: Re: nature of organisation
> On the question of which Set Theory is being used, I confess
> that I *was* totally snookered by my naive conclusion that
> it was Zermelo-Frankel. One logician I spoke to a while back
> told me that the most commonly used Set theory was ZF, and in the
> absence of any disclaimer (plus some other clues) my suspicion
> was that SUMO also used it. Your contradictory assertion -- that
> "the most prominent theory" was VNBG -- was enlightening.
Quick point. Actually, I was a bit unclear there. Your logician pal was
correct that ZF is the most common set theory. What I meant was that VNBG
is the most prominent theory that includes both sets and classes. ZF only
quantifies over sets. In fact, though, VNBG is a conservative extension
of ZF (meaning, roughly, it doesn't tell you any more about SETS than ZF
does), and there's even a way of simulating class talk in ZF that, for all
practical and intuitive purposes, makes the two theories identical. What
misled you was not this fact about set theory, but rather, once again, the
quirky terminology of the Frame Ontology that it inherited from old KIF
that led you to think that all classes are sets. That comes out true in
the Frame Ontology only because it uses "set" to mean what "class" means
in VNBG, and "class" to mean what "class of 1-tuples" means in VNBG.
More later.
-chris