Certain reflections of this interaction between what is structured and an unstructured zone can lead to reflections of the unstructureness. If things were such, then man's intro-openness would manifest itself through the beingness phenomenon, thus ensuring the connection with the unstructured informatter, but through an intermediate zone that we can consider as an exchange buffer (Fig. 33). Here man can structure on a temporary basis, or it can inscribe permanent structures made by himself or by his community. The same principle stands for animals too, though their power of influence inside the exchange buffer will not be due to a conscious will or creative power, but rather to a probabilistic factor. And other possibilities may also exist for the above mentioned principle to operate.



Fig. 33


2. So far we considered the system as a concept connected with a structured reality. Does this mean that we cannot put the equality sign between system and structured reality ? In day by day language we do not err too much by taking structured reality as system.
Considering the theory and practice of systemsone can state that:

A. The system is a model, based on a certain view point (view angle) of the structured reality.
A communication system composed of equipment for data acquisition, coding, transmission, reception, decoding, processing and displaying the information is not in fact a system but only a structured partial reality, according to a model established by us. We must point out that "partially structured" refers only to structuring with respect to communication systems. The communication system is a completely structured reality, extremely complex (consider for example the atoms of the networks making up the communication and data processing equipment). Even at the same material level a structured reality can be looked at from different points of view. This aspect is quite common in practical technical systems. Hence we must admit that there are structured realities that we can model systemically from various points of view, including the experimental one. And we should also admit that we can consider the very system that we use in reality, thus creating (at a certain level of existence) structures that reflect the system we had in mind.
Thus our mind hosts always models for the world around us, for our work organization, etc. A systematic model, either in our mind or stored away on a hardware device, must have an orderly feature, thus implying the use of a language, starting with the natural one and ending with a mathematical one. The linguistic model that uses a natural language of maximum rigorousness, can hardly be distinguished from a logico-mathematical model3. Then we augment our observation in the following way:
  1. The system is the model of a structured reality observed from a certain viewpoint, or created using a language, or

  2. The system is a logico-mathematical linguistic model of a structured reality, model depending on an individual or social observer, and on his point of view.
A number of new problems now arise. Who and what is the observer ? Is he not a system too (structured or systematically modelled reality) ? Viewing from a different point of view one can consider that the system, as a linguistic model, is also a type of information. Then one asks himself: Considering all the types of information available regarding the surrounding reality, which are the types that can be considered systems ?

Considering a wellknown work in systems theory4, one sees that a system can be described using set theory. The set is a mathematical object, but we can also see it as a structured reality. The set can be indeed understood as an object (the structured reality) but also as a system (model). For the set taken as an abstract concept we have in fact system = structuredreality. We point out that the idea of conceptual coincidence between system and set can be found in several mathematical works5. In the mathematical object called set we can create different structures: "to give a structure to a set means to organize it"6.

B. The system appears as a mathematical object and it is in the same time an information, both of the type of a set.
But the concept of set was created by the logical mechanisms of our mind. And since the set theory has encountered a number of logical paradoxes, it seem that it is vulnerable from the point of view of a perfect closure.
But what kind of structured reality is the abstract set ? What is it structured into ? Is it only a concept? But the concept is not in itself material, but only to the extent to which it is the restructuring of a physical structure. Since the set is a a mathematical object, can it then be viewed as a structured reality only as far as the concept is concerned ? Can we disregard any physical concept ? Obviously, within a materialistic concept such a thing is not possible. The mental detachment of the concept of set from the physical support (the neouronic network of our central nervous system), detachment that also includes the integrative activity of the brain, is fictitious, even if we admitted that the integrative activity of the brain also includes the mental field, i.e. the informatter. Concept without support cannot be. However this concept does structure somehow the hardware memory of a computer, or the biological memory of our brain. Hence we can consider the concept, abstracted from any kind of support, as an abstract reality or as a mathematical object.

W. V. Quine states7 that although "one can prove that the entire mathematics can be expressed using set theory" one cannot but notice that "the set theory is discredited by paradoxes" which can simultaneously prove the truth and the falsehood. According to Quine the set theory cannot be considered a foundation for mathematics, since it is only a dictionary of mathematical terms. Hence Quine looks for the mathematical truth outside logics, outside set theory, i.e. in the mathematical objects viewed as of any other natural science.

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