International Encyclopedia of Systems and Cybernetics

D. Mc NEIL describes as follows the minimal axiomatics of any would be general theory:

"1. There is a constitutive core of concepts which interrelate mutually with one another at the center of the theory, more in the manner of a volutionary loop than of a closed capsule or an aggregate cluster.

"2. There is a mutually productive, even a generative, connection between the central concepts and the peripheral ones where theory is reduced to practice.

"3. The core of the theory is the minimum algorithmic compression from which phenomena described by the theory can be reproduced.

"4. The core of concepts is irreducible in the sense that, although equivalent concepts may be substituted, no central concept can be removed without altering the scope and productivity of the theory or even render it meaningless.

"5. Two or more of the core concepts are complementary in some sense to another.

"6. The central concepts are well-defined, and their connotations harmonize insofar as possible with similar concepts of ordinary enlightened discourse.

"7. The central concepts are expressed at a uniform level of discourse, and different levels of discourse are clearly distinguished and used consistently;

"8. The more general theory relates to less general theories and to special cases through a correspondence principle which acts as a confirmation and a guarantor of the consistency of the more particular theories and of their applications.

"9. Whether explicitly or by implication, the theory describes dynamical fluxes having contours which trace relatively closed loops as well as relatively open links.

"10. Whether in the assumptions or in the expression of the formulation, there are invariants which provide standards for measures.

"11. The theories describe phenomena in the frame of reference of a conceptual space, thus implicitly relating the observer with the phenomena observed" (1993a, p.8).

To establish this list, Mc NEIL inspired himself from MAXWELL's electromagnetic theory and TURING's theory of universal computation (TURING machine).

Point 1 specifies a basic dynamic viewpoint. Point 3 acknowledges G. CHAITIN's work on the subject. Point 4 is obviously related to GÖDEL's incompleteness theorem. Point 6 aims at avoiding useless jargon. Point 7 takes RUSSELL and WHITEHEAD's theory of logical types in account. Point 8 is related to homomorphies and isomorphies. Point 9 is of 1st order cybernetics origin and Point 11 takes care of von FOERSTER's 2nd order cybernetics (of "observing systems").

This array of concepts is a kind of abstract generalization of the dynamic toroidal model that Mc NEIL also proposes. Applied to the concept of a General Theory of Systems it gets it out of the purely structural and static trap.