by Jan Sarnovsky
Head of Department of Cybernetics and AI
Director of Institute of Computer Technology
The system is complex if there are possible many various modes of description. Complexity, from Latin word complexus means “twisted together”; complex system consists of parts which are connected. This is the paradox of complexity: the sub-systems (parts) are distinct and, at the same time, connected.
The problem of complexity is, especially from the philosophical point of view, the subproblem known in philosophy as relation of whole and its parts. The problem of relation of whole and parts are analyzed in philosophy in detail. The notion of whole and part are discussed in the antique philosophical works. This notion was well-known already for Heraclitus. Plato very clearly writes about the priority of whole. The deep ideas about relation of whole and parts speak out Kant and especially Hegel. The relation of whole and parts Hegel understand as the unity of contradictions. The whole cannot exist without parts and parts cannot exist without whole, which forms its essence. In Hegel we can find also the instruction (or algorithm) how to overcome the contradiction between whole and parts. But the best way is to cite:
But further, although the whole is equal to the parts it is not equal to them as parts; the whole is reflected unity, but the parts constitute the determinate moment or the otherness of the unity and are the diverse manifold. The whole is not equal to them as this self-subsistent diversity, but to them together. But this their ‘together’ is nothing else but their unity, the whole as such. The whole is, therefore, in the parts only equal to itself, and the equality of the whole and the parts expresses only the tautology that the whole as whole is equal not to the parts but to the whole.
Conversely, the parts are equal to the whole; but because they are in themselves the moment of otherness, they are not equal to it as the unity, but in such a manner that one of the manifold determinations of the whole attaches to the part, or that they are equal to the whole as a manifold; that is to say, they are equal to it as a divided whole, that is, to the parts. Here we have the same tautology, that the parts as parts are equal, not to the whole as such, but in it to themselves, the parts.
In this way, the whole and the parts fall indifferently apart; each of these sides relates itself only to itself. But as thus held apart they destroy themselves. The whole which is indifferent to the parts is the abstract identity which is not internally differentiated; this is a whole only as internally differentiated, and moreover in such a manner that these manifold determinations are reflected into themselves and have immediate self-subsistence. And the identity of reflection has shown through its movement that it has this reflection into its other for its truth. Similarly the parts, as indifferent to the unity of the whole, are only the unrelated manifold, that which is within itself other, which as such is the other of itself and only sublates itself. This self-relation of each of the two sides is their self-subsistence; but this their self-subsistence which each has for itself is rather their self-negation. Accordingly each side has its self-subsistence not within itself but in the other., this other, which constitutes the subsistence, is its presupposed immediate which is supposed to be the first, and its beginning; but this first of each side is itself not a first, but has its beginning only in the other.
The truth of the relation consists therefore in the mediation; its essence is the negative unity in which both the reflected and the simply affirmative [seiende] immediacy are sublated. The relation is the contradiction which withdraws into its ground, into the unity which, as returning, is reflected unity; but since this latter has equally posited itself as sublated it is negatively related to itself, sublates itself and makes itself into a simply affirmative [seiende] immediacy. But this its negative relation, in so far as it is a first and an immediate, is mediated only through its other and is equally posited. This other, the simply affirmative immediacy, is equally only as sublated; its self-subsistence is a first, but only in order to vanish, and it has an existence that is posited and mediated.
In this determination the relation is no longer that of whole and parts; the immediacy which belonged to its sides has passed over into positedness and mediation; each is posited, in so far as it is immediate, as self-sublating and passing over into the other, and in so far as it is itself negative relation, as at the same time being conditioned by the other as its positive; just as its immediate transition, too, is equally a mediated transition, being a sublating that is posited by the other. Thus the relation of whole and parts has passed over into the relation of force and its expression.
Force is the negative unity into which the contradiction of whole and parts has resolved itself; the truth of that first relation.
The whole and parts is the thoughtless relation which ordinary thinking first happens to think of; or objectively it is a dead, mechanical aggregate having, it is true, form determinations through which the manifoldness of its self-subsistent matter is connected in a unity; but this unity is external to the matter. But the relation of force is the higher return-into-self in which the unity of the whole which constituted the relation of the self-subsistent otherness ceases to be external and indifferent to this manifoldness.
In the essential relation as now determined, the immediate and the reflected self-subsistence are posited as sublated or as moments; in the preceding relation they were independent, self-subsistent sides or extremes. In this there is contained first, that the reflected unity and its immediate determinate being, in so far as both are first and immediate, sublate themselves within themselves and pass over into their other; the former, force, passes over into its expression, and what is expressed is a vanishing something which withdraws into force as into its ground; it is, only as borne and posited by force. Secondly, this transition is not only a becoming and vanishing, but is a negative relation-to-self; or, that which alters its determination is at the same time reflected into itself and preserves itself; the movement of force is not so much a transition [übergehen] as a movement in which it transposes itself [sich selbst über setzt] and in this alteration posited by itself remains what it is. Thirdly, this reflected, self-related unity is itself sublated and a moment; it is mediated by its other and has it for condition; its negative self-relation, which is a first and begins the movement of its transition out of itself, has equally a presupposition by which it is solicited, and an other from which it begins.
This explanation maybe, perhaps, rather complicated, but if the force we will consider as the control, we can say, that the antinomy of whole and part of complex system are overcome and solved by control of this system. The control may be already a part of complex system as its organic sub-system, or can be implemented from the outside. So, the control may be this mystical element which is the bridge between whole and its parts.
The description and control of complex systems is connected with other Hegel’s method, the process from the abstract to the concrete. This method is very close to well known engineering method — system approach. The notion “concrete” can be the analog of complex. In this method, which is again discovered in cybernetics, are the element of historical motion. It corresponds with evolutional feature of complex systems.
To create new complex systems theory, from the philosophical viewpoint, is possible, by my opinion, only using the principles and methods of Hegel’s dialectic philosophy.