## GENERAL SYSTEMS THEORY: Mathematical aspects
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A. RAPOPORT sees G.S.T.: "as an effort to fuse the mechanistic and the organismic approaches so as to utilize the advantages of each. A system is not merely a totality of units (particles, individuals), each governed by laws of causality operating upon it, but rather a totality of relations among such of these units. The emphasis is on organized complexity, i.e., on the circumstance that the addition of a new entity introduces not only the relation of this entity to all others but also modifies the relations among all the other entities" (1966, p.5),

As a result, as stated in the same paper by RAPOPORT, the mathematics of the Simple linear causal relations is not anymore useful, and may even become quite misleading, Fortunately, during the last 30 years a number of new (or renewed) mathematical formalisms did emerge:

- expanded graph theory

- catastrophe theory

- fuzzy sets

- fractals

- deterministic chaos

… all of which offer new insights into dynamic behavior in networks of interdependent elements.

M. MESAROVIC gives the following syntactic definition of a general system: "A general system is defined by:

1. A set of implicitly defined formal objects

2. A set of elementary transformations T

3. A set of rules P for forming the sequences of T

4. A set of statements indicating initial forms of the formal objects for use in generating new forms of the objects" (1964, p.7).

This definition seems too deterministic in view of more recent developments.

### Categories

- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented

### Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

* Bertalanffy Center for the Study of Systems Science (2020).* Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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