I do not know if there will be one day a complete theory describing all possible logics, and especially allowing to systematically discover all the eventual unknown logics. The two choices I quoted would perhaps be even not sufficient. On the other hand we know several other logics, using different choices, and different of Aristotelian logic (Also sometimes called Cartesian, but it is better to avoid this name, which rather refers to the method. See chapter II-6). Let us have an overview.
Let us remind that this logic relates to 1) Objects perfectly separated from each other and 2) Which we can say without nuance or ambiguity if such or such of their property is true or false. (For example alive or dead) All the reasonings, concepts and methods which result from this are the mathematics. In electronics, it is the digital computing.
In the case of objects which only satisfy «more or less» a criterion, we obtain more or less true or false statements (what is expressed by a percentage, for instance a tank more or less full). In electronics, this is called analog computing.
As in the previous case, but this time the percentage don't express a measurement, but a probability to have the statement completely true or completely false. In electronics, this was sometimes called stochastic logic, and when I was a student I noted an attempt to build calculation integrated circuits using this principle. (The output of each gate was flowing random zeroes and ones, the signal being represented by the average. Ordinary AND OR gates allowed then to do additions, multiplications, etc).
A roughly true or false statement leads to this logic, which discoverer is the Iranian (note 1) Lofti Zadeh, and which flexibility was recognised as a noticed breakthrough in industry. (For example, in the automatic control of a subway: «It is rather time to slow down».) Fuzzy logic uses variable thresholds to determine at which moment a value can be regarded as true and to start an action. In spite of its name it does not have anything vague, and it often shows the most effective for flexible and adaptive drive of vehicles, of industrial processes...
We can represent these various logics with diagrams, which describe on a plane the places of the various possible states of a statement. Aristotelian logic has only two possible points. The places of gradated logics are distributed on a line segment connecting the two previous points.
Fuzzy and gradual logics are based on alternatives to the second choice, since the concept of truth or falseness is here progressive. They apply to objects where the criterion of membership (to keep with the Sets Theory language) varies gradually instead of having only two exclusive values. But in this case we can still get back to Aristotelian logic, as soon as we introduce into the later the concept of a rational number (or real number) which describes the gradation. As a matter of facts, fuzzy logic and gradual logic are emulated by completely Aristotelian microprocessors and computers. But we shall see later cases where gradated or fuzzy logic cannot be reduced to Aristotelian logic, when it deals with non-measurable objects.
Is there a logic which would be an alternative to the first choice, while being able to be reduced to Aristotelian logic? It would be quite useful and practical, in a number of fields where it is necessary to handle complex concepts or representations of concrete reality which we cannot easily place in categories. For example objects often have to be classified in categories, and this is usually done according to tree like structures. For example companies, associations, groups being of ecological interest... have each one a branch. But where would you place a company of ecological products? In the branch companies or the branch ecology? If a tree structure is considered, we should create two sub-branchings, which lead to considerable difficulties at the time of a search, since the good answers are not all together at the same place. But if we then admit that two branches may have a joint sub-branching, things work well again. Further reasoning does no more lead to a tree structure, but to a network structure, devoid of any centre or hierarchy, where the objects are connected by closing definitions in an X dimensions space. Is there computer data bases working thus? This case evokes a first choice where the objects are not clearly distinct the ones from the others. However it seems that we can still be brought back to Aristotelian logic by using a complex definition of the objects according to several set criteria or numerical criteria.
On the other hand in the examples which will follow it seems that it is necessary to give up any reference to Aristotelian logic or mathematics which results from it. What I try to bring new in the bargain is to still regard these new cases as fully valid logics, non-Aristotelian logics quite as valuable as the Aristotelian logic or the fuzzy logic, but which apply to objects with different properties (choice 1 or 2 at the beginning of this chapter, see choice 3, 4...): non-Aristotelian objects. But the methods which shall be described further still allow for making reasoning and predictions useable in practice, and this is why I claim that we can still name them logics.
Without any pretension to exhaust this vast subject, let us state here that the concept of communion obviously applies to objects which our usual conceptualisation regards as distinct, but which in reality are just different faces of the same thing. They no longer comply with the first choice. The most typical case is that of the Christian communion between God and the individual. (Let us remind that in a discussion on logic it is not the matter to state on the existence or non-existence of God, nor about the various theories of the Christian mystics. I simply discuss the logics behind one of these theories.) This theory seems to lead to a paradox: God is unique and indivisible, and at the same time He however exists in a very great number of individuals. What I say here is that this paradox does not come from reality, but comes from the fact that we project on it the idea, the a priori that God and the soul of each individual are inevitably separated and independent objects, which comply with the usual choice 1. Nothing proves that all the objects and aspects of reality are indeed independent and clearly separated from each other, and it is useless to throw a fit neither to hide them under the carpet if one day we find some which are not. And which «communicate mysteriously» without «material means» to exchange information. Quantum mechanics provides us with some beautiful examples, with the idea of non-locality, and it is a shame to have waited sixty years to start to speak about it. (We still have to wait a little more, up to the fourth part of this book, on physics)
The notion of non-duality is more delicate to apprehend. The most well known example is that of the non-duality between a particle and its wave in physics. Personally my first approach of the non-duality was with Hatha Yoga, where, to hold a posture, there are at the same time activity (some muscles work) and relaxation (immobility of the posture, systematic relaxation of all the muscles which are not used for holding it). Here again, this contradiction is only an appearance, which comes from the fact that our conceptual mind a priori assumes that activity and relaxation are contrary, and thus mutually exclude each other as two enemies who cannot hold the same place together. This is especially the case in the typically Western ideologies of competition, work, effectiveness... In fact if we simply accept that these two «opposites» can exist simultaneously, and even may collaborate, then the problem disappears, the headache also and the mind can get relaxed in turn. Many very significant notions result from this, essential to understand the Oriental contribution to world civilisation: non-violence, non-action (note 44), non-self... These notions, which completely violate the choice 1 by linking apparently different or incompatible objects, are not «difficult» neither «abstract» nor «highly esoteric», they are very easy to understand once we just accept them without trying any more «to understand how the opposites are not excluded each other». But if we attempt to forcibly make re-enter these ideas into Aristotelian statements, by inevitably excluding one of the two terms, then this leads to coarse misinterpretations. For example the non-action would be doing nothing, non-self would be the end of consciousness, emptiness (chapter V-10) nihilism...
Let us note that this vocabulary is often badly defined, and that some authors employ the word duality to express this concept of non-separation, contrary to what is made here. In particular in scientific literature, where we find «the duality wave-particle» (Subatomic particles sometimes behave as punctual objects, sometimes as waves, depending on the experiment). It is better to know this to avoid any misinterpretation. We followed the majority practice here, that the dictionary vaguely confirms, and which seems the most logical: in the non-duality wave-particle, there is only one real object, which appears as two different objects only to our imperfect understanding. The expression «non-...» in «non-action» (note 44), «non-self», or non-existent» (for Emptiness) is also rather confusing, as, if not warned, people easily misunderstand with a straight negation, which is indeed the standard use of this «non-...». So we have to wait for a more accurate word or expression in place of this «non-...». I should propose, for instance, a «non-dual action», or a «non-ego action», where the «non-» is clearly an Aristotelian negation.
This time we entered resolutely in a field where Aristotelian logic is no longer of any help. This is because we are now dealing with non-measurable objects: feelings, political tendencies, tastes, etc. We cannot give an Aristotelian formalism to the non-duality; we cannot explain it on the blackboard nor «to show it» at students sitting in a lecture theatre. We have to experience it within our minds, and for this reason these knowledges are not transmitted by speech, but by exercises, situations to live is, such as the Hatha Yoga (which is thus really an heuristics (note 2), and not a gymnastic) and many other similar disciplines available in various cultures. It is absolutely essential, to understand the non-Aristotelian logics given here, not to try «to analyse them» while trying to bring them back to Aristotelian dualities. It is also essential to acquire a minimum of experience of meditation (note 3) in suitable courses. I assume all along this book that the reader will have a minimum understanding in these fields, which form part of the stock of general knowledge of the up to date gentleman in this beginning of third millennium, and reject in advance as inept any criticism which would be based on an «analysis» without effort to acquire the necessary meditative capacities.
The Westerner or scientist reader will not miss to point at me calling for elements of a peculiar culture, for these new logics, when he considers Aristotelian logics as universal. It is that there is a matter of perspective: to the Easterner as well it is non-duality and Yin-Yang dialectics (to be seen just next) which appear as much universal, and Aristotelian logics a curious Western invention. Yes, this is as much symmetrical. Then, what to think? That reality behaves differently, depending if it is a Westerner or an Easterner who thinks at it? Definitively not, and I am obfuscated in advance at any attempt to interpret what I write according to this kind of cultural relativism. Simply, the varied cultures on our planet evolved while exploring different fields of the life experience. The utilitarianist West discovered Aristotelian logics, which rules physics and financials; the East preferred to discover non-dual logics which rather govern social life and inner life. There is no opposition of any kind between the two, but simply complementarity. As we saw with the first axiom of the Sets Theory in chapter I-2, a different first choice simply applies to different objects. Thus there is nothing astonishing to find different aspects of life obeying to different logics, we just have to accept this fact. What is important to understand now, is that all the logics that we study here allow in the same way to do reasonings on objects or facts, and to discover objects or facts which were unknown. This still matches the definition of logics seen in chapter I-1.
When we perform an Aristotelian reasoning, such as a calculus, we perform a series of elementary operations, AND, OR, THEN... while retaining the intermediate results into our memory. This is what is called reasoning. This is also the way a computer works, with its instructions and its memory registers. A computer can also use numbers to handle the gradated logics, and even the fuzzy logic. But when the objects on which we reason are non-measurable, for instance feelings, or political orientations, this is no longer possible. The legitimate question is then: where the non-Aristotelian results come from, if we cannot compute them?
It happens that the human brain is enjoying this faculty, from its very functioning, which is very different of that of a computer: it is based on neural networks And these networks are precisely able of integrating a great deal of data, while obtaining the reply into only one operation! A simple example is characters recognition, with artificial neurones: for instance each pixel of the image is connected to an artificial neurone. When we start, all the outputs are at zero. But the neurones interact the one with the other, and quickly the outputs diverge, until giving the ASCII code of the letter, into only one operation, very short. But the most incredible is that the neural network can be programmed to recognize several letters! It is this faculty which allows the brain to perform incredibly complex activities, such as walking, without us needing to calculate for this, and even not thinking at it. For instance riding a bicycle requires to solve differential equations of the third order... however we do this with an incredible ease, without even suspecting this complexity!
Then, to apprehend a non-duality requires no other mental faculties than for riding a bicycle. The best comparison is with instinctive shooting: the policemen trained to do this do not enjoy superior intellectual faculties, and no mysterious tantric powers. However, into emergency situations where we do not have time for reasoning or calculating, they are able to decide of the conduct to follow, and undertake an accurate enough action to be entrusted with deadly weapons, in full safety for the innocents standing just besides the target. The non-Aristotelian results we are studying now are produced in the same way. The state of mind which allows to obtain them is called meditation, and it is quite simply a state where we stop doing Aristotelian reasoning, which allows for our neuronal networks to spontaneously enter in function into their natural way.
So there is nothing magical, mysterious or «irrational» about non-Aristotelian logic, it is simple stuff, common, which only require to remove prejudices to be understood. But it is an happy thing that the human brain is natively possessing powerful non-Aristotelian reasoning capacities, because, as we shall see in the chapter I-4, these faculties are of paramount importance to understand and manage our societies and our lives.
However these non-Aristotelan logics can no longer be handled by our classical computers with a Von Neuman architecture.
But let us go now to the most important non-Aristotelian systems recognized today:
The numerous misunderstanding on this subject comes from the many fanciful definitions of the Yin and Yang, which are widespread even in the East. For instance I find in one of the best French dictionaries: «Yang. Cosmological force...» With my opinion and according to the most serious sources on the subject, it is necessary to really envision the Yin and Yang not as objects or «forces» which would exist somewhere in the world, but as terms of a logic, which can apply to very diverse objects (energies or others) and which play exactly the same role in the Yin-Yang dialectics, than the true and the false in Aristotelian logic (choice 2). However, unlike true and false, Yin and Yang do not exclude each other; they are always simultaneously present, but in a non-dual way, each one respectful of the other and collaborating with it. They are even not a compromise (as in a gradated logic) where they would deprive each other of their force; quite to the contrary each one is magnified and achieved by the presence of the other, completely contrary to the two terms of Aristotelian logic, which exclude each other.
This book is not the place for a complete course on Yin-Yang dialectics. It is necessary to meditate in appropriate courses to understand it (In this, anyway, it is very much like Aristotelian logics, which seems easy or obvious to us only because we learnt it at school). However the reader will be able to meditate the classical examples which follow, and gain a fair understanding, as long as he does not try to reduce it to Aristotelian reasoning or apply it to irrelevant stuff such as stock exchange.
a) The cold Yin and the hot Yang. Excess in a direction or in the other is dangerous, but an «ideal» and constant temperature would quickly become insipid. The body likes a fresh shower after sweating, or the sauna after shivers. But if these situations were prolonged they would quickly become very unpleasant, even deadly.
b) The Yang male and Yin female. This is a situation where typically confrontation is unavoidingly sterile, and the compromise tedious. The free dance, the abundant play of Yin and Yang therefore allows each one to be achieved, and offers a world of infinite possibilities in many fields. In Taoist China, «gender war» is a poetical metaphor for the sexual play. But be careful, because there are, even in the East, a deviation of Yin-Yang dialectics, where Yang is good and strong, and the Yin bad and weak. Sexists don't know how to justify themselves...
c) The Yang authority and the Yin freedom. In education, to remove one of these terms produces seriously unbalanced individuals. («Bourgeois» education without compassion neither freedom, creating fascist neurotics, «libertarian» education without authority neither reference, creating despaired individuals, unable to love others nor to do something with their lives) Any child needs a good willed authority to support him in his fight to become good, and a true essential freedom to achieve his goal in life. Typically, when these two forces dialogue, they mutually moderate their negative aspects, while reinforcing mutually their constructive results. In the case of a government, authority must be able to express without obstacles to guarantee public freedom; freedom must bring a possibility for social improvement without creating a chaos where this freedom is always the first to disappear.
d) On the other hand, a very common mistake is to confuse Yin and Yang with good and evil, which arises serious problems, mainly to offer a «metaphysical justification» to evil. The refutation of these deviations will be the main topic of chapter I-5.
e) If we consider for instance acid to be Yin and basic to be Yang, we obtain interesting holistic approaches about the biochemical functioning of the body, the sympathic-parasympathic interplay, of things like food or the chemistry of a compost. Such interpretations were launched in the 1970' by the macrobiotic Zen, and the most interesting was that the results were apparently matching with the scientific knowledge of these domains. The macrobiotic approach had however the huge advantage of being much simpler and pleasant to understand, for non-scientists. As far as I know, this exploration no longer takes place today, and it is a real pity for alternative medicines where there are so much arbitrarian and fancy theories ( Chapter II-8)
Yin-Yang dialectics cannot be reduced to a simple graduation between two extremes, like in a gradual logic, which would in turn be reduced to Aristotelian logic. Indeed there is no «dosage» of Yin and Yang, which remain always together fully present, one or the other being in front of the stage according to the situation. The Yin-Yang relationship is not measurable. The Yin-Yang dialectics rather expresses the quality of the relationship between these two terms: collaboration, non-conflict and even non-compromise. But when we know what does this mean, speaking of Yin-Yang dialectics is accurate enough to know what can happens, as much as with an Aristotelian reasoning. It can even be much simpler, in situations which would require a complex and imperfect set of Aristotelian rules to be understood.
So we still remain in a logical reasoning, just calling for different mind faculties, as seen above: synthetic in place of analytical, known as intuition. These faculties are developed by meditation, when Aristotelian logics uses its own faculties and school training. To say that one would be true and the other false, is just ethnocentrism, or «mindocentrism»: considering that some mind faculties would be «good» and others «insane», as with left-handed people or dyslexic people (who are often good artists). This will be re-examined in chapter I-8. We could even invent a new word to name those too much Aristotelian people, unable to get the non-dual logics: «dysintuitive» for instance. But be reassured, we do not stigmatise them, we can even compensate for this disability by proposing them adapted school cursus, and they often become good engineers. I would however have fun seeing those persons who made of their mathematics a social selection criterion, to find themselves disabled in their turn in a society which at last would rediscover intuition and human sensitivity, or which would make mandatory to play violin in order to earn a decent living.
«True» and «false» are represented on a vertical line, as they can stand for «good» and «bad». On the countrary, Yin and Yang are neutral relatively to good and evil, they ALWAYS have the same ethical value. So they are presented on the same level.
Note: The opposite color dot at the centre of each zone symbolizes the fact that the opposite quality is never absent, but latent, ready to actuate in its turn, contrary to what occurs in a gradual logic where the progressive domination of one of the terms inevitably results in the according elimination of the other.
Note: The tradition represents the Yang with the white and the Yin with the black (or sometimes the reverse). But the black and the white being also used for the good and the evil, I represented the Yang with red (hot color) and the Yin with blue (cold color).
It is often said that the Yin-Yang dialectics relates to the relationship between two contrary objects, but it would be righter to say that it relates to two opposite aspects of a same object: masculine or female are both genders, heat and cold are both temperatures... which take Yin or Yang aspect according to circumstances. This second formulation avoids the hypostasis (note 5) about the two objects having kind of conflicting ego (for instance men against women, police against freedom...). If there is only one object which assumes both aspects in turn, then there is less hold for this hypostasis and the quality of the relation can be better understood. (See in chapter I-5 cases which we called reciprocal situations, axis confusions, clan hypostasis). Moreover this formulation is more coherent with that we already used with the other logics, with only one object which property 2, instead of being true or false, is non-dual Yin and Yang.
Yes man, western philosophy also discovered non-Aristotelian logics! Even if this was «forgotten» since. Qabalah and many humanist philosophies developed in the 11th and 12th centuries, in Italy, Occitania, and especially in Spain which was still mostly under Arab dominion. It was a golden age for arts, tolerance and sciences. The inquisition which followed could not destroy everything, as these ideas remained in the hands of secret societies like the Free Masonry. They re-emerged at the epochs of Renaissance and French Revolution, and they are at the origin of many modern philosophies, and even of important institutions such as the justice court, which plan was made after the Qabalistic symbol of the Three Pillars that we are about to see.
The Yin-Yang dialectics shown above envision the possible unbalance between the two terms. When this happens, then one of the two terms of a dialectic may have an harmful effect, as it is no longer balanced by the other. This important notion is much more developed in the Hebraic Qabalah, which we shall briefly summarise here.
The Qabalah evolved in the 11st century. It considers the Sephirotic Tree, which is a diagram formed by ten Sephirot (Singular Sephirah, plural Sephirot), which are places where are located various qualities, also called Virtues (in the meaning of power). Sephirot are distributed with various heights on three Pillars: the Rigour Pillar on the left, Balance Pillar in the middle, and Leniency Pillar on the right. The meaning of the Three Pillars is clearly a Yin-Yang dialectics, seemingly found independently of Eastern traditions. Some Sephirot are on the Pillar of Balance, others go per Yin-Yang pairs on the extreme Pillars. Lowest Sephirah relates to material and terrestrial realities, when while going up we go towards the spiritual, until the ultimate divine reality at the top Sephirah. The Sephirotic Tree is also called the Glyph (diagram) or Life Tree (Otz Chiim in Hebrew, Sok Ching in Tibetan, the coincidence is rather beautiful).
The ten Sephirot form a digest of the Hebrew esotericism. The Glyph is intended to express in a visual and immediate way their relations and thus to allow the cabalistic system to effectively function in our mind. The evolution of a person, of a civilization or the universe is done according to an ascending trajectory in the Glyph, from Sephirah to Sephirah, which can be straight on following the central Pillar, or in various zigzags from one extreme to another. Many situations of psychological or spiritual life are described in terms of relations or reciprocal influences between Sephirot, or paths in the Glyph. There are correspondences between the Sephirot, the paths, the Hebraic alphabet, the functions of the body and the mind, the planets, the chakras, the colors, etc... which would lead us far beyond the scope of this small summary. The book from which I studied the Qabalah is the one of Dion Fortune: «Mystical Qabalah». Similar Glyphs also existed since immemorial times among ancient Semitic peoples, and today among saharian peoples like the Targuis. Some years ago the Glyph re-emerged among the Berbers in Algeria.
Each level in the Tree has a metaphysical meaning, rather than logical, in relation with the Hebraic conceptions. But in a given level, we immediately notice that the relation between a pair of Sephirot is a Yin-Yang dialectics, with the Three Pillars (The one in the middle standing for the harmonisation of the Yin and the Yang, indispensable for the correct operation of the dialectics). What is new here, it that there is also a reversed tree, like the shade of the first, of black malefic Sephirot called Qliphoth. A Qliphah appears when the force of a Sephirah is not balanced by its opposite counterpart. If this imbalance appears transitorily during an evolution, the damage is not large; but if it settles, then the evil becomes strong, active and organised. This can be understood by considering again the three examples a, b, and c already used for explaining Yin-Yang dialectics:
a) The Yang hot not balanced with the Yin cold burns, desiccates and kills. Yin cold not compensated by Yang hot weakens, freezes and kills.
b) The male who does not recognize the value of the female is only an old male chauvinist pig. He cannot be happy, and develops a society and ideologies based on brutality, domination, or unhearty intellectualization... The female who does not recognize the masculine does the same thing, with other appearances, but as much unpleasant. In the total absence of relation, it is the very survival which is threatened.
c) Authority without any protective and compassionate purpose very usually leads to the unpleasant dictatorships and the very ugly Orwell's Big Brother, whereas freedom without discipline nor respect gives wimp democracies, the dreadful failures of the hippie communities, and Huxley' «Brave new world», very «free» and full of «fun», but the book ends exactly the same way that the Big Brother's one...
Often Hebrew words have an abstracted or spiritual meaning, and a daily life meaning; thus the Hebrew esoteric books, especially the Old Testament of the Christian Bible, are filled with jokes and puns, that of course no translation retained, which makes screamingly funny the sight of starchy prelates pontificating about them, sober as judges. Thus the concrete meaning of Qliphah is: prostitute. This very well expresses the idea of a native force intended to be beneficial, but which, expressing itself apart of its adequate frame, becomes perverse and source of suffering.
So the Qabalah explicitly processes the unbalances, that the eastern Yin Yang dialectics only regrets.
What we can do now is to left asides the metaphysical considerations contained in the Cabalistic Tree, to only consider its logical aspect.
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