Re: Identification of systems (was Re: terms)

Cliff Joslyn (joslyn@KONG.GSFC.NASA.GOV)
Wed, 13 Sep 1995 19:12:06 -0500


>In a message dated 95-09-12 00:37:50 EDT, you write:
>
>>SOME kind of relation between any two entities. Ultimately, just by being
>
>Cliff, this is the meaning of a set, not a system. And equating "set" with
>"system" leads to severe philosophical and practical confusions. Systems
>Theory (the study of interrelated things) is a subset of Set Theory (the
>study of groups of things), not the reverse.

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.

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