Re: SUO: Re: IFF Comments Requested
> >
>> Sixth. Let me back off from having FOM fun with y'all and get to the
>> main point. The purpose of ontologies is to represent facts about
>> worlds, not to play elegant games in the foundations of mathematics.
>> Matthew West wants to describe oil flowing along pipelines, that kind
>> of thing. Now, what connection, even of the most remote kind, can you
>> suggest there is going to be between ANY such activity of describing
>> the real world, and ANY of this mathematical gamesmanship of topos
>> theory? So far, I can't see any.
>
>I think you are wrong, here, Pat. No, we are not here to play
>mathematical games, but really do have pragmatic concerns just exactly
>like Matt does.
I'm sure you are: I didn't mean to criticize your motives, only your document.
>However, we do need to build a framework which enables
>us to cobble together different ontologies (theories) in a reasonable
>fashion and perhaps even a framework to enable us to "compose" theories,
>i.e., to be able to "place" theories in an overarching framework and
>then link or (God help us) even "project" those theories'
>"intersections". If we don't do this, who will? Personally, I think
>category theory will help.
Ah, now THAT does make sense. BUt this seems to be quite a different
theme than the one in the IFF document. What you are saying here is
that the category theory can provide a framework for a kind of
structural meta-theory of ontologies; for talking about structural
relationships between ontologies, as is done in the SpecWare system
also. That isn't what the IFF seems to be saying at all, though: it
is talking about categories being the *subject-matter* of ontologies.
For example, your picture of categories in the structural meta-theory
is quite compatible with the ontologies themselves being written in,
say, DAML and being about, say, states of viscosity of different
grades of crude oil.
>
>I intend to discuss your issues a bit further (and later), since I don't
>see any incongruity between the "logic" view and the "category theory"
>view. The category theory view is simply more general.
Well, if so, I'm tempted to ask, why is FOL offered as the basic
axiomatization of topos theory for foundational reasons in the IFF
document?
Pat
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