Re: SUO: Re: nature of organisation
----- Original Message -----
From: "Chris Menzel" <cmenzel@philebus.tamu.edu>
To: "John F. Sowa" <sowa@bestweb.net>
Cc: "IEEE Standard Upper Ontology List" <standard-upper-ontology@ieee.org>
Sent: Tuesday, August 28, 2001 8:54 AM
Subject: Re: SUO: Re: nature of organisation
> Actually it goes farther than that, John. The two don't disagree on sets
> at all, regardless of cardinality. VNBG and ZF differ only in that,
> roughly speaking, VNBG quantifies over a layer of classes -- so-called
> "proper classes" -- over and above all the sets, whereas ZF only
> quantifies over the sets. Unlike sets, proper classes cannot be members
> of other classes. (Let me note that in the last couple of posts I've sent
> out I might have used "class" carelessly to mean "proper class" here and
> there -- in VNBG, all sets are classes, but some classes, viz., the proper
> classes, are not sets.)
<snip>
> No, it becomes relevant when you get past cardinality entirely. Proper
> classes can in fact be defined in VNBG as collections that are "too big"
> to have a cardinality.
<snip>
> > To avoid such confusions, I recommend that we drop the word 'class'
> > from SUMO and adopt the following conventions:
> >
> > 1. The word 'set' without any other qualifiers means the mathematical
> > notion of set.
>
> Sounds good.
SUMO is in the object level. So, I believe this accords quite well with the
IFF (categorical) approach. At the object level (which remains over John's
categorical rug -- see the discussion of role types and visibility of IFF
terminology and axiomatizations [http://suo.ieee.org/email/msg05960.html])
ontologies only work with sets (small classes), small functions, small
relations etc. At the lower metalevel (the first level swept under John's
categorical rug) ontologies work mainly with classes (sets xor proper
classes), class functions, class relations, etc. At the upper metalevel (the
second and deepest level swept under John's categorical rug -- some people's
Paradisio is other people's Inferno ;^) ontologies also work with
conglomerates and conglomerate functions -- the really, really big (and
right) stuff.
Robert E. Kent
rekent@ontologos.org