RE: SUO: Set/Class Distinction
Dear Ian,
I'd like to add my strong support for all Chris says below.
Matthew West
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> -----Original Message-----
> From: Chris Menzel [mailto:cmenzel@philebus.tamu.edu]
> Sent: 18 September 2001 06:00
> To: standard-upper-ontology@ieee.org
> Subject: Re: SUO: Set/Class Distinction
>
>
>
> Ian wrote:
> > A while back John Sowa recommended that we eliminate the concept of
> > 'Class' in the SUMO, because it is not clearly
> differentiated from 'Set' and
> > because it does not seem to have any utility beyond the
> concept of 'Set'.
> > If no one objects, I'll go ahead and replace all of the
> occurrences of
> > 'Class' in the SUMO with 'Set'.
>
> Wow, that strikes me as a really seriously bad idea that runs into
> problems similar to the ones John noted in regard to "Class".
> The term
> "set" is deeply entrenched in mathematics, logic,
> linguistics, theoretical
> computer science, and philosophy. There are different set
> theories, of
> course, but, with the quirky exception of Quine's NF, which
> no one uses,
> in *all* of them sets differ markedly from SUMO classes in a number of
> critically important ways. Notably:
>
> 1. Sets are extensional. SUMO classes are not assumed to be.
>
> 2. SUMO classes have complements. Sets do not.
>
> 3. There is a universal SUMO class, i.e., a class (viz.,
> Entity) of which
> everything is an instance. There is (on pain of contradiction) no
> universal set.
>
> 4. In most set theories, sets are well-founded; in particular
> they cannot
> be self-membered. Some SUMO classes (notably, Entity) are
> instances of
> themselves.
>
> 5. SUMO appears to have a general comprehension principle --
> made possible
> through the KappaFn operator -- that yields the existence of
> a SUMO class
> corresponding to every statable condition of the language. There is no
> such principle for sets, again on pain of contradiction.*
>
> It therefore strikes me as rather perverse, to say the least,
> to ignore
> these profound differences and appropriate the term "Set" in
> the manner
> you propose.
>
> *The SUMO teeters on the brink of contradiction here, since
> it appears to
> allow the existence of the Russell class of all classes that are not
> instances of themselves: (KappaFn ?x (not (instance ?x ?x))).
> The only
> reason SUMO seems to avoid contradiction is that it does not have a
> general conversion principle for classes: it is not provable
> in general
> that x is in the class of A's if and only x is an A, i.e.,
> formally, one
> can't in general prove, for any given condition A of the language
> containing the variable ?x, (iff A (instance ?x (KappaFn A))). This
> principle is essential for deriving the Russell paradox, and
> its omission
> is intuitively unwarranted if you're gonna have KappaFn around. But
> KappaFn is nothing but trouble. You keep ignoring me, but I'll say it
> again: you ought to clobber it.
>
> -chris
>
> --
>
> /\ ASCII ribbon | Chris Menzel -- http://philebus.tamu.edu/~cmenzel
> \/ campaign | Philosophy Dept, Texas A&M University
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