“The term system has a number of meanings. There are systems of numbers and of equations, systems of value and of thought, systems of law, solar systems, organic systems, management systems, command and control systems, electronic systems, even the Union Pacific Railroad system. The meanings of "system" are often confused. The most general, however, is: A system is a set of interacting units with relationships among them. The word "set" implies that the units have some common properties. These common properties are essential if the units are to interact or have relationships. The state of each unit is constrained by, conditioned by, or dependent on the state of other units. The units are coupled. Moreover, there is at least one measure of the sum of its units which is larger than the sum of that measure of its units.”

—  James Grier Miller

Source: Living systems, 1978, p. 16; As cited in: Sven Rasegård (2002) Man and Science: A Web of Systems and Social Conventions. p. 29

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James Grier Miller24
biologist 1916–2002

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Source: Systems Design of Education (1991), p. 31

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This observation immediately suggests a close parallel between the concept of a system and the development of the mathematical concept of a set. Given any specific aggregate of things; e. g., five oranges, three sticks, five fingers, there are some properties of the aggregate which depend on the specific nature of the things of which the aggregate is composed. There are others which are totally independent of this and depend only on the "set-ness" of the aggregate. The most prominent of these is what we can call the cardinality of the aggregate…
It should now be clear that system hood is related to thinghood in much the same way as set-ness is related to thinghood. Likewise, what we generally call system properties are related to systemhood in the same way as cardinality is related to set-ness. But systemhood is different from both set-ness and from thinghood; it is an independent category.”

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“The most general form of systems theory is a set of logical or mathematical statements about all conceptual systems. A subset of this concerns all concrete systems. A subsubset concerns the very special and very important living systems, i. e., general living systems theory.”

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