> >
> > Jeffrey Schiffel originally
wrote:
> > >
>
> >
> >... A system is
smaller than the world. A system of systems
> >
> > is still very small compared to the world. They each have a
> >
> > known number of interacting parts. But the nature of the
> >
> > interactions is perhaps limits how ontologies in the usual
> >
> > sense can be used. The limitation is that ontologies are based
> >
> > in discrete mathematics.
> >
>
> >
> Pat Hayes replied
> >
>
> >
> ??? No they aren't. Where
did you get this odd notion from?
> >
> PatH
>
>
> > By
which I mean such as set theory, algebra, combinatorics, logic,
etc.
>
>
> > --
Jeff
>
> OK. But
set theory is not particularly discrete. Sets are the basis for all
mathematics,
>
including continuous mathematics. Similarly, logic is not particularly
concerned with
>
discrete structures: one can use logics to describe the continuum. (There is
a
>
technical issue in that purely first-order logic cannot completely
characterize the
>
finite/infinite distinction and hence cannot fully describe continuity; but
then pure
> FOL
cannot fully characterize finitude, either.)
> On the
other hand, ontologies don't seem to have any obvious
connection
> with combinatorics or algebra.
>
>
PatH
OK, not
“algebra,” but “algebras.” I
have in mind, for example, functions and similar transformational mappings,
topological spaces, and similar structures that are sometimes brought up in
discussions of ontological
structures.