SUO: Re: IFF Comments Requested
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>
>JF = Jim Farrugia
>PH = Pat Hayes
>
>JF: Please submit your comments by October 18, 2001, replying
> to this subject line ("IFF Comments Requested"), so that
> we can easily gather all comments. (At some point later,
> we may suggest other subject lines to group together
> related comments.
>
>PH: OK, I have a few.
>
>PH: First, I fail to see the utility of the emphasis placed on
>category theory.
> This is not motivated anywhere, but it badly needs to be motivated if you
> expect anyone to take it seriously enough to even read the sources to
> find out what you are talking about.
>
>I think that the following is a fair statement:
>A modest amount of category theory, along with
>a modest amount of set theory, is indispensable
>to understanding what mathemtics is about and how
>mathematics is done today. This is important, not
>just for representing the ontology of mathematical
>objects, structures, and systems, but further, and
>more importantly for applications, because these
>objects, structures, and systems are used in
>modeling most other objects, processes, and
>situations of any complexity that anyone
>might happen to care about.
Well, maybe. I would still like to see a bit more detail, however.
This response really amounts to saying that Category Theory is a Good
Thing. In fact, however, I think that its influence has almost
entirely been in pure mathematics (where indeed it is part of the
general competence expected of a professional mathematician these
days) but hardly at all outside pure mathematics (and even within
large parts of mathematics, it really amounts to little more than a
style of terminological usage.) Most ontological modelling is not
mathematical modelling, and category theory plays virtually no
significant role in mathematical modelling in any case. Fractal
theory would be far more germane, for example.
Ontology is supposed to be concerned with what there is, and the best
theories we have about what there actually is are general relativity
and quantum theory. One could make out exactly this kind of case for
an approach to ontology based on those disciplines, and it would be
just as poor a case.
Pat Hayes
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