Fig. 13

Orthoexistence does not posses purpose but man, society, and hence universe can attain purposes, can develop wills. In its assembly, the material world appears without purpose, or with partial purposes, subsumes of a general selfcreation property.

2. The image, that we could say that we are compelled to construct about the totality of the existence, appears in general as a ring (Fig. 13). Some of its portions are not yet clearly defined. Important is the fact that this ring closure contains a link with "open" characteristics, with the property of an unstructurable continuum, a link that could be the instrument of closing and finalizing a cycle, a link that is open in order that it could be closed by creation. Hegel⁵ considers the existence of an essence of the world, in fact an Itself having essence and being diversifiable in "existent real" like "movement and developing formation". According to Hegel, the existence-in-itself, of spiritual nature, goes into its contrary, the existence in fact, and then, through the man, the cycle closes back into the spirit. He has thus a three-stage movement via contraries. Nevertheless this is an idealistic overturn of what it appears to us like something predominantly material. Owing to his overturned scheme Hegel could not accept the mathematical knowledge but for the existence-in-fact and hence said: "The evidence of this deficient knowledge, of which Mathematics is so proud and of which it beasts so much in front of Philosophy, lies only in the poverty of its purpose and in the deficient character of its material, and hence it is of a kind that Philosophy, should despise"⁶. Hegel is against Mathematics in the process of knowing the "essence",since according to him it is useless here. Within his idealisticscheme, Mathematics, Logics do not have important parts, in fact being eliminated just with respect to most profound things. For him, the conclusive proof that Mathematics cannot describe the world is the fact that it does not comprise the contradiction, and hence the dialectics.

Philosophical experiments show how contradictions appear at a certain limit of knowledge, by reflecting a certain object. Behind this limit a certain contradiction may disappear; but we shall find new contradictions, corresponding to new limits. How could then be the world constituted by monades, by a single principle ? Could not there be two principles as the basis for all contradictions ? Who has got the program for our universe? A spirit providing the contradiction of the material world and by this its dialectics ? We tried to answer this by the principles of energymatter (E) and informatter (I), providinga vision, so far only generally sketched, but giving a certainoverall logics together with a natural opening, expressionof the principle opening of all possible logics.
Energymatter represents a support matter, to remain in motionless state and total equilibrium, were not the second principle, informatter. By its properties and the information it carries, informatter opposes itself the equilibrium type found in depths and motionlessness. Its information provides the complex dynamics, lawful, of the material world. Informatter without information remains an active principle but determining a deep movement. In this state it could generate rudimentary existence based on orthoexistence support. Only systematic generation of information via conscious and their inprint in informatter can lead to really logical universe. Inprinting by adequate material devices of a new deep information can represent an act imposed by the material world.
Why should we be satisfied by Nature laws and hence by the deep information sustained by them ? How can we evaluate them, what comparison can we use? Our consciousness can judge in such a way since nothing is above it. It is of the order of the world essence when it actually manifests itself as such, both at individual and social levels.

In a previous work⁷ we observed that if we were to consider the spiritual states as real states and if we wished to treat them mathematically, we could address to the Sets Theory, the fundamental of modern Mathematics. The sets consider the world as distinct objects, the world is represented by discontinuum. The link with the continuum is done by confrontation with geometric, topological objects. The set of points can constitute a line, the connection between continuum and discontinuum being a difficult problem of Mathematics and for human intellect.But the spiritual states are continuous, whereas the machine states of the central nervous system are determined by the assembly of the physical states of all neurons contained in the nervous system, exactly like in an automaton. The correspondence between these two is not clarified yet and perhaps it is not important yet to know this, but only to see if we can apply some kind of mathematics to the spiritual states, some kind of specific topology. The present stage of mathematical development does not offer a Mathematics of the spiritual states, similar to that of space and time, with substance properties.

Regarding our problem we have the choice:either the spiritual life of man is not a mathematical object,or it is a new mathematical object; the future sciencehas to decide upon these two alternatives. If it were a new mathematicalobject, it is possible the relation between Logics, Mathematics,and automata.
Myself feel that the spiritual states ar not in their depth a mathematical object, although certain aspects of the spiritual life could be, to a certain degree, expressed mathematically. The problem of Mathematics and Logics is connected by the existence of certain structures. These structures can be mathematically described and this can be done to anything that is structured in the material world, hence in the deep zone too. Something that is not structured cannot be mathematically described, but we can apply to an unstructured substance some structurability and hence impose upon it some Logics and some Mathematics. Hence spirituality is not alien, in principle, to Logics and Mathematics, it is but only susceptible to Logics and Mathematics, without being dominated by them in any moment.

The Ring of the Existence 47