On Jan 26, 2009, at 9:55 AM, Schiffel, Jeffrey A wrote:
On Jan 23, 2009, at 2:25 PM, Schiffel, Jeffrey A 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.
??? 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.
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.