RE: SUO: RE: SUMO - predicate vs relation
Bill,
See my comments below.
-Ian
> -----Original Message-----
> From: Bill Andersen [mailto:andersen@ontologyworks.com]
> Sent: Thursday, December 20, 2001 3:59 PM
> To: Ian Niles; SUO
> Cc: Chris Menzel
> Subject: Re: SUO: RE: SUMO - predicate vs relation
>
>
> On 12/20/01 16:33, "Ian Niles" <iniles@teknowledge.com> wrote:
>
> >> So, is it the case that instances of Predicate denote functions (or
> >> relations) on entities that result in such propositions?
> >>
> > This way of putting it sounds okay to me.
> >
> >> First off, it's not clear that we're not talking about
> linguistic tokens
> >> here. Even if we're not, putting a whole theory of the
> structure of
> >> propositions into the SUMO is a pretty heavy metaphysical
> burden, don't you
> >> think?
> >>
> > Hmmm. I don't see that there's a heavy metaphysical burden
> here. There are
> > all sorts of ways of cashing out the notion of proposition
> - some benign, some
> > Platonic.
>
> And Adam is concerned that row variables will confuse users!
> I think that's
> the least of his worries!
>
> >> In addition, under the "proposition-forming operator"
> interpretation, a
> >> binary predicate would correspond to a function of two
> arguments, and would
> >> thus be a ternary, not a binary, relation. So now you have this:
> >>
> >> (subclass BinaryPredicate TernaryRelation)
> >>
> > Well, this sort of maneuver is possible in the case of any
> relation. For
> > example, if one claims that fatherhood is a relation
> between two entities, a
> > father and an offspring, someone can retort that there are
> actually three
> > items here, the two original entities plus the relation of
> fatherhood. Once
> > the three items are posited, someone is free to claim that
> there is actually a
> > quaternary relation here, one specifying that fatherhood is
> the connection
> > between the two original entities. Of course, this can go
> on ad infinitum,
> > since it's always possible to objectify relations or, in
> Pierican terms, to
> > transform secondness into thirdness.
>
> Yes, I'm well aware of the regress problem with
> exemplification. But that's
> not the point here.
>
> You said that Predicates are Functions. That means they're
> relations with
> arity one greater than the number of arguments they take.
> This is a basic
> principle of set theory, and shouldn't be fudged around.
Well, I think you were the one who claimed they were functions, and I merely
declined to disagree. If you insist on regarding predicates as functions,
you could just suppose that in this case the result is not explicitly
indicated (since it's the atomic formula that results from applying the
predicate to its arguments).
>
> There is no regress involved. You have a domain of
> propositions and some
> operators that build propositions out of entities (possibly
> propositions).
>
> > But really, I think all of this takes us far afield of my
> original, innocuous
> > intention, which was just to have a means of distinguishing
> operators that
> > result in sentences from those that result in terms.
> Surely, this isn't as
> > controversial or as confusing as you make it out to be...
>
> Well, now you've admitted to what I asked originally (and you
> denied)! If
> predicates are sentence forming operators, then they're
> certainly linguistic
> tokens, just like "and" and "maybe" in English!
>
> But that's different than talking about the propositions
> denoted by such
> sentences, don't you think??
Well, I know that philosophers have an almost religious reverence for the
use/mention distinction, but I guess I think it's overblown. In fact,
ordinary language philosophers like Wittgenstein would argue that the whole
notion of a language-independent proposition results from a misunderstanding
of the nature of language (and the perceived need to posit a shadow entity
that has all of the properties which one wants a sentence to have but which
in fact cannot reasonably be ascribed to real sentences). Be that as it
may, I guess I think that making too much of the object level/meta-level
distinction will undermine our core aim here, which is to create an
engineering artifact. It's true that this distinction is very important for
theoretical concerns, but I think we always have to bear in mind that we're
trying to create a product that can be used with facility by smart engineers
without a Ph. D. in math or philosophy.
>
> Further, you have:
>
> (subclass SententialOperator Predicate)
>
> which makes very explicit the point I'm making.
>
> My suggestion is that it would be a whole lot cleaner to toss
> this talk of
> "proposition-forming operators" out. One option would be to
> do something
> like this:
>
> (subclass Predicate Word)
>
> (=> (and (relation ?R) (= (name ?R) ?N))
> (Predicate ?N))
>
> Where "name" is a relation from Entity to Word. Of course
> none of this
> takes care of complex predicates (lambdas) and the complex
> relations they
> denote. Presumably here:
>
> (lambda (?x) (and (Cabbage ?x) (SpaceAlien ?x)))
>
> Is a relation, just like Cabbage and SpaceAlien - a relation
> that has a
> complex name:
>
> "(lambda (?x) (and (Cabbage ?x) (SpaceAlien ?x)))"
I see that this approach assuages theoretical concerns, but I'm unconvinced
that it has any real effect as far as practical knowledge engineering is
concerned. However, I am willing to be enlightened.
>
> All of this is venturing into the realm of a metalinguistic
> theory which I
> don't know all that much about. I'm sure though that others
> will comment on
> this.
>
> .bill
>
>
>
>
>