Re: SUO: Set/Class Distinction
Pierluigi wrote:
> It may be possible to look at Chris Menzel's points from another
> perspective, and suggest that, at least in those set theories that take
> classes more seriously (e.g. VNBG), classes are the more general concept.
>
> From this point of views, classes, rather than sets, may have a better
> claim to be in a s.u.o. Classes have the advantage of having an
> unrestricted comprehension principle, which seems to me a very intuitive
> feature.
But comprehension is *not* unrestricted in VNBG -- the variable in the
comprehending formula ranges only over SETS (and urelements, if you've got
them). Proper classes -- the classes that aren't sets -- cannot themselves
be members of classes, as you indicate later in your message. It is a
distinctive feature of SUMO that all classes are first class citizens
in this respect -- all classes can be members of other classes.
> Classes are extensional.
This is not assumed in the SUMO.
> As Chris noted, complements, unions and intersections exist.
But again, not TRUE complements. The complement of a class C in VNBG is
the class of all SETS not in C, not the class of *everything* (including
all classes) not in C.
Now, maybe SUMO should just clobber its theory of classes and adopt
VNBG-ish classes. But that's a different matter. The point for now is
only that the two notions of class are quite distinct.
-chris