top study-index prior next ------------------------------------------------------------------------ ABC DIALECTIC DICHOTOMIES 1 ------------------------------------------------------------------------ Foundation rule guarantees the logical consistency of rigorous propositions. We have seen in the previous section that it alows to eliminate basic logical contradictions, and to convert them to similar, but rigorous and logically consistent propositions. Does it mean that we are back in the "Cantorian paradise" of unconditionally rigorous and consistent deductive systems? In order to answer this question let us examine closer the UH and, in particular its element, the situation, the dipole consisting of two poles: subject and object. Let us suppose that I examine a piece of sugar. It is entirely determined by its attributes: shape, position, texture, colour, taste. Each attribute is reducible to my subjective sensations. I let it disolve. It is no more a distinct, discrete piece, but a fluid. However it still exists as the piece-origine of the liquid component. It exists as a term of relation and as an image. It may be cristallized out of the liquid. It exists as potentiality of a new piece. Whatever form its existence may take, it is reducible to subjective sensations, images, relations, potentialities. When concentrated upon, object vanishes and transforms itself into subject. ABC DIALECTIC DICHOTOMIES 2 Now, let us suppose that I examine introspectively my own subjectivity. I experience tactile sensations of hard and cold. My awareness attributes them on one hand to the 'hard and cold stone' and, on the other hand, to 'my finger' touching the stone. At the first glance a conforme mapping of the dichotomy subject / object. We are tempted to consider on the one hand the object 'stone' objectively 'hard' and 'cold' and, on the other hand, the finger, part of subject's structure, experiencing subjective sensations 'hard' and 'cold'. However, after closer examination 'finger' ceases to be subjective and becomes part of a particular object 'my body'. Indeed, 'subject', the conscious mind, the seat of awareness, although strongly related to the body, should not be confused with it. In order to illustrate their distinction let us imagine the finger being separated from the hand. It does not give any more the impression of being 'a part of me', it becomes an object like any other one. The conscious mind becomes aware of a discomfort, of a restriction in its possibilities of action, but it is in no way diminished, it did not loose a part of itself. Let now imagine an adroit operation succeeding in reattaching the finger to the hand. Again, it gives the impression of belonging to 'me'. Nevertheless, the finger did not undergo any essential modification during the procedure of separation and reattachement. As such it certainly did not regret the separation, nor was rejoiced to see the reunification. Integrated, or not, it clearly stays an object, perhaps an exceptionally important object, but an object all the same. Let us resume: the sensations 'hard' and 'cold' provoke the awareness of 'finger touching stone'. The sensations as such vanish: there is no 'empty' sensation 'hard' existing on its own independently of some part of my body touching someting hard. Shortly: when concentrated upon, sensation vanishes and transforms itself into object's attribute. Now, what about other subjective phenomena, such as images and emotions? They can exist only upon the background of awareness. I am aware of an image, of an emotion. In other terms image, or emotion are objects of awareness and the subject is the awareness itself. But there is no empty awareness, awareness of nothing is no awareness at all. So, finally what we have said about sensations holds for other subjective phenomena and we may generalize: subject when concentrated upon, vanishes and transforms itself into object. But I never entirely, exclusively concentrate upon any pole. The elementary phenomenon that I can experience is the situation, i.e. the dipole comprising simultaneously both poles. I may be identified with my entire situation, not with one of it's poles, no more with subject, than with object. If we may take the liberty of using a very vague analogy, I experience my situation as if I were looking at a picture representing myself-subject in a context-object. ABC DIALECTIC DICHOTOMIES 3 To resume: 1.Subject is not object. 2.Subject is confused, i.e. identical with object. 3.Being identical with object, subject is not identical with itself. 2. and 3. mean respectively: identity of oppositions and non-identity with itself. Logic applied at this level would conclude that human situation is a series of contradictions, a paradox. By extention it would decree that whole UH, that the human reality is paradoxical and, consequently, does not exist. It would not be the first time that a deductive, aprioristic theory desagrees with reality and nature. Who is right in such cases, the theory, or the nature? Hegel, informed that astronomical observations contradict his aprioristic model, that nature disagrees with his views answered: "So much the worse for the nature". Should we likewise say "So much the worse for human reality"? We would have to, if, disregarding the foundation rule, we considered logic as the founding discipline of cognition. Indeed in a hypothetical universe UL founded upon logic there is no place for human reality, nor, indeed for the human being at all. In conclusions we shall revue some typical theories and ideologies claiming to be founded in UL and we shall see that they invariably lead to sterile, stubborn dogmatism in science (eg. Theory of Ether) and to unhuman, cruel discrimination in social practice (Inquisition, Nazism, Gulag, etc.). In itself it is not a sufficient prove of UL being improper. There is no a priori reason why a most repulsive and disturbing universe should not reflect human reality. So we can only feel glad to find out that UH, while properly founding the contempotary state of cognition, happens to be open to flexibility and sincerity both intellectual and, more gene- rally, human. We have seen that the rules of foundation and of instances allow to eliminate logical antinomies and to secure the consistency of all rigorous propositions. Nevertheless, the problem seems to be displaced rather than solved: logic becomes consistent due to being rigorously founded in UH. The latter, however, appears in turn to be paradoxical and on top of that to a degree surpassing by far that of the unfounded logic. Indeed, the very element of UH, the situation appears to be a circle of paradoxes and, consequently, all propositions founded in UH appear without exception to be paradoxical. To crown the misfortune these paradoxes appear at the pre-logical level, lacking methods and tools to cope with them. Actually, not only methods are lacking, but even a pertinent terminology. Indeed, strictly speaking, we should not even use the logical term 'paradox' at the pre-logical level. ABC DIALECTIC DICHOTOMIES 4 At the first glance the choice of UH as founding universe seems to make the problems worse. However, are we free to chose the universe? Certainly not, if we want to be sincere. The universe is imposed upon us by the reality, as expression of the state of the art of science and, more generally of knowledge. Sincerity requires therefore to consider the founding universe as generalization of the current scientific universe extended over the entire domain of human reality. Now, the contemporary science reduced on the one hand its universe to phenomena and, on the other hand, determined its element- the observation as the dipole: observer / observed. Generalized over the entire domaine of human reality, scientific "observation" becomes human "situation" with its poles subject / object. Our choice of UH as founding universe is therefore by no means arbitrary. It is determined and justified by the state of the art of the contemporary science. It seems, consequently, that, rather than to cry over the lost Cantorian Paradise, we have to consider the problem as it is and not as we might have liked it to be. In a well known joke a drunkard is looking desperately for something under a unique street-lamp lighting a spot of a completely dark street. To a policeman offering assistance he explains that he had lost his key. 'Where?' asks the policeman. 'Over there' the drunkard points to a place a few hundred meters away. 'So why are you looking for it here?'. 'No light over there.' says the drunkard. We do not have much choice: whether we like it or not, we have to abandon the spot lighted by logic and try to situate and, possibly, solve our problem there where it finds itself: in the darkness of the pre-logical founding domain where even the pertinent terminology is lacking, let alone established methods, tools and theories. We shall therefore start with the terminology and look for appropriate terms to describe the apparently paradoxical structure of phenomenal dipoles in general and of the situation in particular. DICHOTOMY: synonym of 'phenomenal dipole', more suitable for natural sciences, than for epistemology. TERM (of a dichotomy): synonym of 'pole' (of a dipole). DIALECTIC: domaine dealing with dichotomies. A dichotomy is always 'dialectic'. Unlike the contradictory terms of a logical antinomy, the terms of a dialectic dichotomy are COMPLEMENTARY. While antinomy appears to logic as contradiction of opposite terms, DICHOTOMY appears to DIALECTIC as SYNTHESIS of COMPLEMENTARY TERMS. ABC DIALECTIC DICHOTOMIES 5 Dichotomy-situation is what appears directly to the awareness. However, we cannot call it 'object' of awareness, as 'object' designates allready one of its terms. 'Content' does not seem advisable because of its suggestion of 'containing' or 'enclosing' misleading with respect to awareness. We propose therefore the word PURPORT to designate that of what I am aware, i.e. the present situation. The purport of awareness is complete situation with its both poles, one appearing as founded, the other as founding. We may say that the situation and, indeed, any dichotomy appears as CENTERED on the founded pole and that the awareness CONCENTRATES itself upon the founded pole. The founded pole is the CENTER of the dichotomy. A situation may be, for instance, centered in the object. Then the object is the center of the situation and the awareness concentrates itself upon the object of the situation. The word "center" refers to a single pole. Sometimes we shall refer to both poles as to an oriented couple. In such cases the ORIENTATION of a dichotomy will always imply the direction from the center (the founded pole) towards its counterpart (the founding pole). Dialectic synthesis is a dynamic, oscilatory phenomenon: each pole becomes in turn the center of the situation, fades away and gives way to its counterpart. We shall refer to this phenomenon as to the PRINCIPLE OF ALTERNATIVE ORIENTATION. While logic approaches its problems with help of deductive axiomatic systems such as logical calculus, set theory and mathematics, dialectic uses MODELS of human reality. It is the principal objective of the present study to examin the domain of modeling, to investigate the consequences of properly founding knowledge in epistemological models. At this point the reader may feel taken aback and discouraged in face of the apparent immensity of our task. He may get the impression that we propose to restructure and reformulate the entire domain of science and to redo from the scratch all deductive sciences. Let us reassure him by anticipation. Once having abandonned the comfortable spot lighted by logic and plunged into the outer obscurity, we shall meet an astonishing amount of allies looking for the same key with help of their own personal torches often more brilliant than the street-lamp of logic. To mention just a few of them: Plato, Democrit, Heraklit, Descartes, Kant, Galileo, Newton, Boole, Riemann, Einstein, Planck, Hegel, Heidegger, Sartre, Haken with his Synergetic and Thom with his Morphogenetic. To our greatest relief we shall find ourselves dispensed from the obligation of conceiving theoretical, abstract models. We shall find the fundamental epistemological model ready and functioning in the nature: it is the human brain. It functions in the dialectic mode: all epistemological phenomena are structured as dichotomies, which may be grouped in 4 types: SYNERGY, TOPOLOGY, SCOPE and ENTITY. We shall discuss them in the following sections.