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ScottL comments on Systems Theory Terms - Less Wrong
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I don’t think this: “All possible subgroups of elements also have the first two properties” is the same as “All possible subgroups of elements can themselves be considered systems and so must have the first two properties”, which it looks like you are reading it as. This means that rule 2: “Each element is affected by at least one other element in the system” says that the subgroup of elements you have selected can be affected by an element that is in the system, but not in the subgroup of elements you have selected.
For example, imagine that the corners in this square represented four elements and the lines the relations between them.
As per my understanding of the rules, this is a system. The first two rules are obviously true. If you look at the third one with the elements on the left side of the square, then the two selected elements don’t have any relations to each other, but they do have relations to other elements in the system. So, I believe that this passes the rule.
Ackoff talks a little more about it here.
Oh! So the subgroups are being considered as elements rather than as systems, and condition 3 is actually saying that every set of elements (other than the whole system, I assume) is affected by something outside itself? (Equivalently, however you partition the elements into two partitions there are influences flowing both ways across the boundary.)
You're right: that's a much more sensible definition, and I retract my claim that Ackoff's definition shows bad thinking. I maintain, however, that it shows bad writing -- though perhaps in context it's less ambiguous.
That last quotation, though. At first glance it nicely demonstrates that he has "your" reading in mind rather than "mine"; good for him. But look more closely at the last sentence. "No subset of elements is unrelated to any other subset". In particular, take two singleton subsets; his condition implies once again that every element is "related to" every other. So maybe I have to accuse him of fuzzy thinking again after all :-).