RE: SUO: Logic and Ontology
Dear Chris,
Thank you. I was rather hoping for a response like this.
See some comments/questions below.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.r.west@is.shell.com
Internet: http://www.shell.com
> -----Original Message-----
> From: Chris Menzel [mailto:cmenzel@tamu.edu]
> Sent: 05 March 2002 19:26
> To: West, Matthew R SITI-ITPSIE
> Cc: Standard-Upper-Ontology (E-mail)
> Subject: Re: SUO: Logic and Ontology
>
>
> On Tue, Mar 05, 2002 at 04:10:08PM +0100, West, Matthew R
> SITI-ITPSIE wrote:
> > I was recently sent a copy of Axiomathes, and noticed a paper
> > with the above title.
> >
> > Cocchiarella, Nino B.; "Logic and Ontology", Axiomathes 12:
> 117-150, 2001
> >
> > The part of the paper that interested me was the different
> > interpretations that could be made of predication, depending on
> > whether your basic ontology is based on nominalism,
> conceptualism, or
> > realism (or some graduation between).
> >
> > One of these, attributed to Quine, sems to coincide with my own
> > interpretation of predication, and I repeat it here.
> >
> > "Quine's understanding of his ontology as platonistic and of sets
> > as universals is based on a rather involuted argument,
>
> To say the least.
>
> > the essentials of which are as follows:
> >
> > if we were to adopt platonism as a theory of universals as
> represented
> > by higher order logic in which predicate as well as individual
> > variables can be bound, then
> >
> > 1. predicate quantifiers can be given a referential ontological
> > interpretation only if predicates are (mis)construed as
> singular terms
> > (i.e. terms that can occupy the argument or subject positions of
> > predicates); and
>
> There is a false assumption here, namely, that because the
> predicates of
> natural language cannot be grammatical subjects, it is
> therefore somehow
> wrong to allow the predicates of a *logical* language to occur as
> logical subjects (i.e., to occur in subject position in atomic
> formulas). But this is a confusion. True enough, natural language
> predicates like "is a philosopher" cannot occupy the subject positions
> of natural language sentences; we can't say, e.g., "Is a
> philosopher is
> a property". Rather, you have to choose some nominalized counterpart,
> e.g., the gerund "being a philosopher" if you want to have a
> legitimate
> noun phrase. But it is a confusion to argue that it is therefore
> illegitimate in a *logical* language to allow predicates to occur in
> subject position, e.g., to allow both
>
> (1) (philosopher Quine)
>
> and
>
> (2) (property philosopher).
>
> But why? A nominalized predicate denotes exactly what the predicate
> itself expresses. "Being a philosopher" denotes exactly the
> property we
> attribute to Quine when we say "Quine is a philosopher". Why
> should we
> therefore not allow a single logical expression to play the roles of
> both natural language expressions? We can tell those roles
> apart simply
> by observing where the logical expression occurs:
> "philosopher" in (1),
> occurring as it does in predicate position, corresponds to the NL
> predicate "is a philosopher"; "philosopher" in (2), occurring
> as it does
> in subject position, corresponds in this instance to the
> gerundive form
> of the predicate, viz., "being a philosopher". Simple.
MW: Good. I agree.
>
> If you MUST have something corresponding to nominalization,
> introduce a
> term forming operator ^ that applies to predicates; then
> instead of (2)
> you can write
>
> (2') (property ^philosopher).
>
> But note that ^ plays NO semantic role whatsoever and hence is only
> superfluous syntactic sugar, and in fact a potential source of
> confusion that is best avoided.
MW: Not for me.
>
> > 2. assuming extensionality,
>
> If you want, though there are tons of troublesome counterexamples
> (discussed here at great length a long time back). I'll simply note,
> with no intention of defending it, that you can't do justice to modal
> intuitions on this assumption, unless you are willing to countenance
> merely possible objects.
MW: Which I am of course, and it fits well with a 4D perspective.
>
> > 3. predicates, as singular terms, can only denote sets, ...
>
> Assuming the preceding highly problematic assumption.
>
> > 4. [which] must then also be the universals that are the
> values of the
> > predicate variables in predicate positions; and therefore
> >
> > 5. predication must be the same as membership, in which case
> >
> > 6. we might as well replace predicate variables by individual
> > variables (thereby accepting nominalism's exclusion of
> bound predicate
> > variables) and take sets as values of the individual variables,
> > arriving thereby at
> >
> > 7. a first order theory of membership (set theory) which
>
> Yes, you could perhaps do that, but now I *do* think you lose
> something
> important, as all predication on this approach is reduced to a single
> exemplification (or, if you will, membership) predicate. Seems to me
> that this *does* miss something important about meaning that
> is revealed
> in natural language. When we say "Quine is a philosopher", we mean
> simply that Quine is a philosopher; we are predicating that property
> directly of Quine. We do *not* mean that Quine and being a philosopher
> stand in the exemplification (or, if you will, membership) relation,
> which, if I'm understanding correctly, is what we would have to be
> expressing on the Quinean view. Of course, it is *true* that
> Quine and
> being a philospoher stand in the exemplification (membership) relation
> if, and only if, Quine is a philosopher; my claim is only that that is
> not what we *mean* when we say "Quine is a philosopher"; it is rather
> what we mean when we say "Quine exemplifies being a philosopher" and
> hence refer to the exemplification relation explicitly. Hence, the
> reduction to a single exemplification (or membership)
> relation seems to
> miss an important fact about meaning.
MW: Well I don't think in terms of exemplification (which I assume has
nominalist associations) but straight membership. When I say "Quine is a
philosopher" I mean "Quine is a member of the class philosopher". I don't
see this as being the same as exemplifies - which for me would imply some
sense of being stereotypical, rather than just a matter of happenstance
which membership is.
>
> > 8. is platonist because it has abstract entities as values
> of its one
> > type of variable.
> >
> > Thus beginning with higher order logic with bound predicate
> variables
> > as a version of platonism, we arrive at the nominalist position to
> > recognise only quantification with respect to individual
> variables (or
> > the subject positions of predicates) but with individual variables
> > that can have abstract sets as their values, which are therefore
> > really universals (i.e. entities that have a predicable nature)"
>
> A good rendition of the argument, I think; but serious problems with
> steps 1 and 2, as noted.
>
> > Well I'm sure there are some bits of that that have gone
> over my head,
> > but the bottom line is that predication = membership is a possible
> > interpretation of predication,
>
> Yes, though, as noted, this follows from highly dubious premises.
>
> > The bottom line here as far as I can see is that without stating a
> > particular meaning for predication, KIF is ambiguous.
>
> No more than any formal language that requires interpretation.
>
> > Or perhaps I should say that when you use KIF, you need to state the
> > meaning of predication you are using.
>
> Well, yes; it's called semantics. KIF has a well-defined
> semantics. In
> KIF 3.0, predication was in fact taken to be membership. On
> the latest
> semantics (for the above reasons, among others) it is not,
> though it is
> *consistent* with the semantics to understand predication as
> membership;
> that is, there are formal models of KIF in which properties are sets,
> and hence in which predication is membership. But this is not an
> assumption of the semantics itself.
MW: Good. So predication does mean membership, but by a different route.
I also assume that strict extensionality is not implied.
>
> > It strikes me that using different interpretations of
> predication adds
> > to the difficulties of integrating ontologies with different
> > ontologies of logic.
>
> Well, then don't use different interpretations. Not sure what your
> point is here.
MW: Well I had missed that there was a well-defined semantics in KIF.
When I last read KIF 3, I probably wouldn't have understood its
significance. Since there is one, this means that using any other
interpretation is non-conformant use of the language, (or at least
this should be part of the conformance requirements).
MW: Further, I can live with these semantics, because my use, which
would include strict extensionality, is a subset of those that don't
have strict extensionality. Right?
>
> Regards,
>
> -chris
>
> --
>
> /\ ASCII ribbon | Chris Menzel -- http://philebus.tamu.edu/~cmenzel
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