Re: SUO: RE: SUMO - predicate vs relation
On 12/21/01 11:53, "Ian Niles" <iniles@teknowledge.com> wrote:
>>> 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.
Actually, you did - You called them "proposition-forming operators", and we
have:
Operator:
1(Math.) A function whose domain consists of a set of functions.
(from the new Penguin dictionary of science). All I did was do a little
inference.
> 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).
Well, fine.. But where is this in the documentation? Isn't it just simpler
to be precise and to admit that "predicate" is a linguistic notion, and thus
not a subclass of Relation. This is just wrong, and there are two ways to
make it right:
1) Accept that predicates are sentence/proposition/whatever-forming
operators. Then you have to introduce the notion of operator
explicitly, hook it up to function in the right way, and hook
function up to relation in the right way. Then you need either
an account of propositions or an account of syntax, whichever way
you choose to go.
2) Just say that they're words without any special powers of formation
of anything, relax, and have a beer!
This isn't simply a matter of theoretical vs practical concerns. In fact
most of my concerns until late have been practical. This is a matter of an
existing axiomatization that's confusing. If it's confusing to me I'm sure
it's confusing to others as well.
.bill