> > > > 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.