-The general definition by Bertalanffy (himself): "Ein System ist eine Menge (im mathematischen Sinn) von Elementen, zwischen denen Wechselbeziehungen bestehen". (This is what I heared more times during scientific congresses): ergo: it is (more or less) identical to a set.
-However, Bertalanffy's definition regards only the inner environment: there is (according to him): (a) no question about an empty set (which is a big problem in mathematics, as far as I know); (b) he (Bertalanffy) does not speak of the outer environment (Popper's world 1 and Herbert Simon's inner and outer environment).
-What could be your answer? Thanks, Marc
In my view, in a set, the elements can have separate existence whereas in a system all the members have simultaneous existence.
Yes. A system is defined by the relationships between elements. A set is simply a collection of elements. The collection (set) can be empty. However, it makes no sense to talk about an empty system, because there cannot be any relationship that would define a system.
Dear Jochen,
Thank you ueberhaupt for your answer.
However, the term collection is 'too nice' for the original German word Menge. This term could be better translated as heap, so chaos. But not in the sense of fractalizable chaos (because then you necessarily come to an 'ordered' element) , but more in the sense of Shakepearian people or Gustav Le Bon's mob (which are really 'un-ordered'). Marc.
In your terminology I would rather see set as a crowd of people, and a system then as a sozial organization (the system is the whole of the social/biological/economical...) described by the interactions or relationships between the people.
A set can have an inherent structure (ordering), but this is not meant by the interactions that make up a system. If I think about this, I find that system should be something dynamic. I haven't found an example where a static system could not be described as a set with a particular ordering structure.
If the interaction of the elements within a set change the structure of the set, the set itself is not the same as before, so there is no mathematical identity. Thus, a system can describe a spectrum of sets, and the transitions between these sets. The superset or algebra (the spectum of sets) is again associated with relationships between its elements (the sets), so this is still a system. It is the same system, because it is completely defined by the interactions between the original elements.
In my view, in a set, the elements can have separate existence whereas in a system all the members have simultaneous existence.
I do agree with Mr. Kattel . Just a complement, a set can even be empty or singleton, but such system does not make sense !
A set can be empty or singleton, whereas a system is not.
Otherwise, they are a same concept. It can be noted that, in science studies related to physics, chemistry, environment , etc., a system term is more common.
Thank you, Tareq, for the nice answer. Indeed, reading scientific literature the term system is more common.
A system or structure is a set with some relations in it, relations among elements in some well defined sense, while a set is just a collection of well defined objects. I include well definedness in my description, to avoid the pitfalls of paradoxes, since not all arbitrary collections constitute well defined sets.
A house and a house will all family members living in it and their relations , all the furnitures and materials that are in the house used by members of the house are examples of a set and a system respectively.
The collection of people in a country is a set which is denoted by the name of the country but the cultural, political, economic and all other assets of the people included is a social structure.
Thank you both, Dejenie and Thomas. Specially for Dejenie: a system is not identical to a structure. (Please read Wilden).
...and a system is (according to me, and consequently against Bertalanffy) not a set!
A system is a set which consists of more than one element and there are some obvious characterizations or relations among its elements. So it can be obtained a system from any set by defining a relation on this set. In regard to the nature of relation, there are no conditions imposed on it. In case of added some condition on a system, then we may obtain a group, ring, field,...etc.
Thank you, Tareq, for searching after the difference between system and set. If you follow my question, you know by now which direction I am going to follow. Anyhow, thanks! Marc.
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