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.
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??
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)))"
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