I don't think we're in any disagreement: systems theory is a subset of set
theory; all systems are sets; not all sets are systems, right? In the
mathematical systems theory of MEsarovic and Klir, a system is any subset
of the crossproduct of a number of other sets. Note that it need not be a
PROPER subset. If indeed the system is EQUAL to the cross-product, then it
is still a system, but it is a DEGENERATE system, in that it has reached
the limit condition if its being equal to its universe of discourse.
This was, in fact, my point: by pushing, as Gaines did, the boundaries of
what we consider a system to the limit, we end up with the kinds of
degenerate, vacuous cases like that above: just sets!
Let's put it another way. Linguistically, a system is a set of entities
which have entered into a relation. If that relation is the null relation,
then it remains only a set, but is it still a system? To do anything
INTERESTING or USEFUL in systems theory, we have to qualify the kinds of
relations in SOME way.
O---------------------------------------------------------------------------->
| Cliff Joslyn, NRC Research Associate, Cybernetician at Large
| Mail Code 522.3, NASA Goddard Space Flight Center, Greenbelt, MD 20771 USA
| joslyn@kong.gsfc.nasa.gov http://groucho.gsfc.nasa.gov/joslyn 301-286-2598
V All the world is biscuit-shaped. . .