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2019/02/24

The key to modern history

Diablerie de foule


This book by Pierre-Yves Lenoble gives part of the key to modern history, based on very relevant quotations, five of which I repeat here. Allow me to complete this key as much as possible, i.e. with new references and links to background articles on each major point.

« Since the end of the last world war, a new form of war has emerged. Sometimes referred to as subversive war or revolutionary war, it differs essentially from the wars of the past in that victory is not expected only from the clash of two armies on a battlefield. This shock, which was once intended to destroy an enemy army in one or more battles, no longer occurs. War is now a set of actions of all kinds (political, social, economic, psychological, military, etc.) aimed at overthrowing the power established in one country and replacing it with another regime. To achieve this, the attacker tries to exploit the internal tensions of the attacked country, the political, ideological, social, religious, economic oppositions, likely to have a profound influence on the populations to conquer. »
(Roger Trinquier, La guerre moderne, Ed. La table ronde, 1961, Pp.15)


« Today, we no longer conquer the ground to have men, we conquer souls, we conquer the psyche. Once you have the psyche, you have the man. When you have the man, the terrain follows. The devil's greatest trick is to make it look like he doesn't exist. It is time to use the word "subversion". A formidable weapon because it tries not to show itself. [...] This formidable method is part of the infiltration of part of the media, part of those who teach souls, hearts and brains, I mean the clergy, the school, the University. In the past, in order to hold power, it was necessary to control the Church, and therefore souls; in the 19th century, it was education, and therefore brains. Today, it is the audiovisual sector that prevails, and the University. In the West, we no longer learn, as we do in the countries of the East, the love of the homeland, of work, but laxity, indiscipline, disrespect for ancient virtues, the search for artificial paradises. In a word, what I call "the reverse order". »
(Alexandre de Marenches, Dans le secret des princes, Ed. Stock, 1986, Pp. 376-377)


« The French Revolution was the first revolution of the bourgeois and middle class; of what was called the Third State in history.
The Paris Commune was to be the first revolution of the proletarian class, which remained relatively in the shadows until then. It was the first realization in history - still ephemeral and hastily suffocated - of the dictatorship of the proletariat, a hitherto unpublished form of subversion.
It was the first advent of the Fourth State, which was an improvement on everything that had preceded it. As such, it marked a date in the evolution of the processes used by the spirit of revolt. All the pontiffs of contemporary subversion, of the so-called socialist and communist phase, were unanimous in declaring it. The greatest in the lead, Marx and Lenin, ostentatiously repudiated any attachment to the bourgeois, republican and democratic revolutions of the 1789 and 1848 type. They saw it as a means, a route, not the goal. All of them proclaimed their direct filiation with the Paris Commune, even when they criticized its lack of technical preparation.
All of them, without exception, bow before it as if it were a kind of leader and devote many speeches, brochures and books to it. It was the first bell ringing of what the Bolshevik revolution was supposed to be. Marx, Lenin, Trotsky, Kautsky, Lawrof and many others deal with this subject and argue about it.
The great mistake is to assume that the Paris Commune was a spontaneous movement, and this error is repeated about all revolutions.
Every time, there are men, by the hundreds of thousands, naive enough to believe that something can be done on its own, and that it can come out of the void without having been done by someone. If we think about it, it is a philosophical absurdity and a challenge to common sense. Especially in an age that claims to be scientific and when we should know that even those processes that we once thought were automatic and regulated by abstract laws of nature, such as the decomposition of a corpse, disease, old age, so-called natural death, are determined by concrete and living agents, called bacilli, toxins, which work for this purpose. Without them there would be no decomposition, no fever, no decrepitude, no death, and if these agents are invisible to us, it does not mean that they are less real.
The same is true for society, which is humanity in space, and for history, which is humanity in time.
Bacilli, toxins, in human form, which the eye of generations does not discern, which the eye of historians ignores, or more often, pretends to ignore, - but whose existence is not a mystery to the bacteriologist of society and history -, cause fevers, decrepitude or decomposition, paralysis or convulsions, old age, damage and death.
Victims believe that the process is done by itself, under laws that are inevitable and inseparable from the nature of things, and that is why they do not react. Indeed, how can we react, without being foolish, against the inevitable and the nature of things?....
There was no more spontaneity in the 1871 Commune than there was in 1789, 1793, 1848, 1848, 1905 or 1917 and no more in the unrest in China, Hindu, Sudanese, Syrian, Turkish, Moroccan and Afghan. Nor are there any more in all the strikes of our time. It is nevertheless true that, just as in the animal organism, for bacilli and toxins to be able to effectively manifest their deadly action, it is necessary for this organism to be weakened and dilapidated by bad weather or overwork. Otherwise, this healthy organism, in the fullness of its strength, would have the means to defend itself and destroy the harmful action.
»
(Emmanuel Malynski and Léon de Poncins, La guerre occulte, 1940, Pp.19-20 ; this part is a summary by de Poncins of the book La mission du peuple de Dieu - 6ème partie - La grande conspiration mondiale, 1928)


« Manipulation of public opinion.
52 - In addition to this, there is what was already revealed in previous developments but is now being fully discovered: the uniform control of public opinion. And this by all means: by speech and writing, by the press and theatre, by cinema and radio, by art and even by science, by school and the trades, and again, by pressure, by means of works of assistance, on the poor. And from all this, this is the lamentable result: the modern mass man. The latter no longer has an opinion of his own, no longer has his own will; he is only a passive instrument in the hands of the leader. To take any initiative at all is practically impossible for him; and yet, without this spirit of initiative, it is impossible for man to give himself this personal culture which is an element of life for the human community.  »
(Humani Generis Unitas. Pope Pius XI - Ineditum, 1938, §52 ; in Georges Passelecq, Bernard Suchecky, L'Encyclique cachée de Pie XI, Ed. La Découverte, 1995, Pp. 242-243)

Some metaphysical explanations


Here as in M. Léon de Poncins, of whom we have already had the opportunity to speak, there are many very fair considerations in all that relates to the criticism of the modern world; the authors, who rightly denounce common errors such as the belief that revolutions are "spontaneous movements", are among those who believe that the modern deviation, whose stages they study more specifically during the 19th century, must necessarily respond to a well-defined and conscious "plan", at least among those who lead this "occult war" against everything that has a traditional, intellectual or social character. However, when it comes to seeking "responsibilities", we have many reservations to make; moreover, it is not so simple or easy, it must be recognized, since, by definition, what it is about does not even appear to be outside, and the apparent pseudo leaders are only more or less unconscious instruments. In any case, there is a tendency here to exaggerate considerably the role attributed to Jews, to the point of assuming that they alone ultimately lead the world, and without making certain necessary distinctions about them; how can we not realize, for example, that those who take an active part in certain events are only Jews entirely detached from their own tradition, and who, as always happens in such cases, have hardly kept that the defects of their race and the bad sides of its particular mentality? There are, however, some passages (notably pp. 105-110) that are quite close to some truths about "counter-initiation": it is quite true that these are not any "interests" of any kind, which can only be used to move common instruments, but a "faith" which constitutes "an unfathomable metapsychic mystery for the even high intelligence of the ordinary man"; and it is no less so than "there is a current of Satanism in history"... But this current is not only directed against Christianity (and it is perhaps this too narrow a way of looking at things that is the cause of many "optical errors"); it is also, in exactly the same way, against any tradition, be it Eastern or Western, and without except Judaism. 
(René Guénon, Etudes sur la Franc-Maçonnerie et le Compagnonnage, t. I, Compte-rendu juillet 1936).


Another point to remember is that Unknown Superiors, of whatever kind, and whatever the field in which they want to act, never seek to create "movements", following an expression that is very much in vogue today; they only create "states of mind", which is much more effective, but perhaps a little less within everyone's reach. It is indisputable, although some claim to be unable to understand it, that the mentality of individuals and communities can be changed by a systematized set of appropriate suggestions; basically, education itself is little more than that, and there is no "occultism" in it. Moreover, there can be no doubt that this faculty of suggestion can be exercised, at all degrees and in all fields, by men "in the flesh", when we see, for example, a whole crowd illusioned by a simple fakir, who is however only an initiate of the lowest order, and whose powers are quite comparable to those of a Gugomos or a Schroepfer. This power of suggestion is due, in short, only to the development of certain special faculties, when it applies only to the social domain and is exercised over "opinion", it is above all a matter of psychology: a determined "state of mind" requires favourable conditions to establish itself, and one must know, or take advantage of these conditions if they already exist, or provoke their realization oneself. Socialism responds to certain current conditions, and this is what makes it so likely to succeed; whether the conditions change for one reason or another, and socialism, which can never be anything more than a means of action for Unknown Superiors, will quickly transform itself into something else whose character we cannot even foresee. This is perhaps the most serious danger, especially if the Unknown Superiors know, as there is every reason to admit, how to modify this collective mentality called "opinion"; it is a work of this kind that took place during the 18th century and led to the Revolution, and when it broke out, the Unknown Superiors no longer needed to intervene, the action of their subordinate agents was fully sufficient. Before it is too late, it is necessary to prevent such events from recurring, and that is why, let us say with Mr. Copin-Albancelli, "it is very important to enlighten the people on the Masonic question and what is behind it".
(René Guénon, Réflexions à propos du « Pouvoir Occulte », 11 Juin 1914, La France antimaçonnique)


Moreover, the most skilful and dangerous "subversion" is certainly the one that does not betray itself by overt singularities that anyone can easily see, but that distorts the meaning of symbols or overturns their value without changing anything in their external appearances. But perhaps the most diabolical trick of all is to attribute to orthodox symbolism itself, as it exists in truly traditional organizations, and more particularly in initiatory organizations, which are especially targeted in such cases, the reverse interpretation that is properly the result of "counter-initiation"; and this, as we have recently pointed out, does not deprive itself of using this means to cause confusion and ambiguity from which it has some benefit. This is, in essence, the whole secret of certain campaigns conducted, either against esotericism in general, or against this or that form of initiation in particular, with the unconscious help of people, most of whom would be very surprised, and even frightened, if they could realize what they are being used for; unfortunately, sometimes those who believe they are fighting the devil are simply transformed into his best servants, without any doubt whatsoever!
(René Guénon, Du double sens des symboles, Études Traditionnelles, juillet 1937)


« Complete disaster risk through renunciation of the spirit
67. Our modern society is therefore sick; and the new formulas of unity, the new types of unity, far from curing it, can only make it even sicker. For they decompose, with the thought and ideal of life, of themselves mechanically dissociating, the internal consistency of human social life; and similarly the natural factors of its constitution, like its natural foundation, the unity of the human personality. In the final analysis, they risk leading humanity towards a catastrophe, through their mechanical atomistic conception of the human race, through the radical renunciation of the Spirit, deep down to the Spirit of God.
In the same sense, is it still necessary, with regard to these forms of Extensive Totalitarianism Unity, a last proof. Thought, with its purely mechanical processes, was no longer able, because it was despiritualized, to perceive the various natural factors of the construction of society and their essential interdependence, as well as Unity within Plurality; it could no longer grow from the bottom up, to the true Unity and Totality of a complete system of the world, comprising an intensive Totality, that is, an authentic Unity in an authentic Plurality. What it kept, so to speak, of the Spirit, was only the intelligence, which precisely no longer deserved, as we have seen, this name, taken in its deepest sense, that is, in the sense of the Spirit, but on the other hand must have expected all the more that the struggle was engaged against it in recent years.»
(Humani Generis Unitas. Pope Pius XI - Ineditum, 1938, §67 ; in Georges Passelecq, Bernard Suchecky, L'Encyclique cachée de Pie XI, Ed. La Découverte, 1995, Pp. 249-250)


After the considerations we have outlined and the examples we have given so far, we will be able to better understand exactly what the stages of anti-traditional action that has truly "made" the modern world as such consist of in general; but, above all, it must be realized that any effective action necessarily involving agents cannot, any more than any other, be a kind of spontaneous and "fortuitous" production, and that, especially in the human sphere, it must necessarily involve the intervention of human agents. The fact that this action is consistent with the specific characteristics of the cyclical period in which it occurred explains why it was possible and successful, but it is not sufficient to explain how it was carried out and does not indicate the means that were used to achieve it. Moreover, to be convinced, it is enough to think a little about this: the spiritual influences themselves, in any traditional organization, always act through human beings, who are the authorized representatives of tradition, although tradition is truly "superhuman" in its essence; all the more so in a case where only psychological influences come into play, and even of the lowest order, that is to say, the very opposite of a power that is transcendent in relation to our world, not to mention that the character of "counterfeiting" that manifests itself everywhere in this field, and to which we will still have to return, requires even more rigorously that it be so. On the other hand, since initiation, in whatever form it may take, is what truly embodies the "spirit" of a tradition, and also what allows the effective realization of "superhuman" states, it is obvious that it is to it that what is at stake here must be opposed most directly (insofar as such opposition is conceivable), and which tends, on the contrary, by all means, to lead men towards the "infra-human"; so the term "counter-initiation" is the most appropriate term to designate what is linked, as a whole and to varying degrees (for, as in initiation again, there are necessarily degrees), the human agents through which anti-traditional action is carried out; and this is not a simple conventional denomination used to more conveniently speak of what really has no name, but an expression that corresponds as exactly as possible to very specific realities.

It is quite remarkable that, in the whole of what properly constitutes modern civilization, whatever the point of view from which it is viewed, we must always observe that everything appears to be increasingly artificial, distorted and falsified; many of those who criticize this civilization today are struck by it, even when they do not know how to go further and have no idea of what is actually behind all this. It seems to us, however, that it would suffice a little logic to say to ourselves that, if everything has thus become artificial, the very mentality to which this state of affairs corresponds must not be less so than the rest, that it too must be "manufactured" and not spontaneous; and, as soon as we have made this simple reflection, we could no longer fail to see the concordant clues in this sense multiplying from all sides and almost indefinitely; but it must be assumed that it is unfortunately very difficult to escape so completely from the "suggestions" to which the modern world as such owes its very existence and duration, because those who declare themselves most resolutely "anti-modern" generally see none of this, and that is why their efforts are so often spent in total loss and almost devoid of any real scope.

Anti-traditional action had to aim both at changing the general mentality and at destroying all the traditional institutions in the West, since it was there that it was exercised first and foremost and directly, until it could then seek to extend to the whole world through the means of the Westerners thus prepared to become its instruments. Moreover, since the mentality had changed, the institutions, which therefore no longer corresponded to it, had to be easily destroyed; it is therefore the work of deviating from the mentality that appears here to be truly fundamental, as what everything else depends on in some way, and, consequently, it is on this that we must insist more particularly. This work, of course, could not be done all at once, although perhaps the most surprising thing is the speed with which Westerners were led to forget everything that had been linked to the existence of a traditional civilization in their country; If we consider the total misunderstanding of the Middle Ages in all respects in the 17th and 18th centuries, it should be easy to understand that such a complete and sudden change could not have been achieved in a natural and spontaneous way. In any case, it was first of all necessary to reduce the individual to himself, and this was above all, as we have explained, the work of rationalism, which denies the possession and use of any faculty of transcendent order; it goes without saying, moreover, that rationalism began to act even before receiving this name with its more specifically philosophical form, as we have seen in the case of Protestantism; and, moreover, the "humanism" of the Renaissance was itself nothing more than the direct precursor of rationalism itself, since what says "humanism" means the claim to reduce everything to purely human elements, therefore (at least in fact, if not again by virtue of an expressly formulated theory) exclusion from all that is supra-individual in nature.


It was then necessary to turn the individual's attention entirely towards external and sensitive things, in order to lock him up, so to speak, not only in the human sphere, but, by an even narrower limitation, in the corporeal world alone; this is the starting point of all modern science, which, constantly directed in this direction, had to make this limitation more and more effective. The constitution of scientific theories, or philosophical-scientific theories if you will, had to proceed gradually; and (here again, we only have to briefly recall what we have already explained) the mechanism directly paved the way for materialism, which was to mark, in a way that could not be remedied, the reduction of the mental horizon to the corporeal domain, now considered the only "reality", and moreover stripped itself of all that could not be regarded as simply "material"; naturally, the elaboration of the very notion of "matter" by physicists had to play an important role here. We had therefore properly entered into the "reign of quantity"; profane science, still mechanistic since Descartes, and becoming more especially materialist from the second half of the 18th century, had to, in its successive theories become increasingly exclusively quantitative, at the same time as materialism, creeping into the general mentality, managed to determine this attitude, independent of any theoretical affirmation, but all the more widespread and finally passed into the state of a kind of "instinct", which we called "practical materialism", and this very attitude had to be further reinforced by the industrial applications of quantitative science, which had the effect of attaching men more and more completely to "material" achievements alone. Man "mechanized" all things, and finally he came to "mechanize" himself, gradually falling into the state of false digital "units" lost in the uniformity and indistinction of the "mass", that is, ultimately in pure multiplicity; this is certainly the most complete triumph that one can imagine of quantity over quality.

However, at the same time as this work of "materialization" and "quantification" was continuing, which, moreover, is not yet complete and can never even be completed, since the total reduction to pure quantity is impossible in the manifestation, another work, apparently only contrary in appearance, had already begun, and this, let us recall, as soon as materialism itself appeared. This second part of the anti-traditional action was to aim, no longer at "solidification", but at dissolution; but, far from counteracting the first trend, that characterized by quantitative reduction, it was to help it when the maximum of possible "solidification" had been reached, and that this trend, having exceeded its first goal by wanting to go so far as to reduce the continuous to discontinuous, had itself become a trend towards dissolution. It was therefore at that time that this second work, which had initially been carried out, as a preparation, only in a more or less hidden way and in any case in restricted environments, had to appear in the day and in turn take on an increasingly general scope, at the same time as quantitative science itself became less strictly materialistic, in the strict sense of the word, and even ended up ceasing to rely on the notion of "matter", made more and more inconsistent and "evasive" by the very consequence of its theoretical developments. This is the state we are in now: materialism is no longer just surviving itself, and it can probably survive more or less long, especially as "practical materialism"; but, in any case, it has now ceased to play the main role in anti-traditional action. 

After having closed the corporeal world as completely as possible, it was necessary, while not allowing the restoration of any communication with the higher domains, to reopen it from below, in order to bring in the dissolving and destructive forces of the lower subtle domain; it is therefore the "unleashing" of these forces, one could say, and their implementation to complete the deviation of our world and effectively lead it towards the final dissolution, which constitute this second part or this second phase of which we have just spoken. Indeed, it can be said that there are two distinct phases, although they were partly simultaneous, because, in the overall "plan" of the modern deviation, they follow one another logically and have only successively their full effect; moreover, as soon as materialism was constituted, the first was in a way virtually complete and only had to take place through the development of what was involved in the same materialism; and it was precisely at that moment that the preparation of the second one began, of which only the first effects have yet to be seen, but which are already apparent enough to make it possible to predict what will follow, and so that we can say, without any exaggeration, that it is this second aspect of anti-traditional action which, from now on, really comes to the fore in the designs of what we first collectively referred to as the "adversary" and that we can, with greater precision, call the "counter-initiation". 
(René Guénon, Le Règne de la quantité et les signes du temps, 1945, chap. XXVIII : Les étapes de l’action antitraditionnelle, Pp.187-191)

If you hadn't yet understood...


« We can imagine that each individual accepts, voluntarily or unknowingly, a chip in him, which would contain a whole lot of information about him that would allow him to pay for everything, to know everything... But to be free from a certain number of constraints. [...] The real luxury of tomorrow will be to be isolable, to be able to isolate oneself, and true freedom will not be to be connected to others, but to have the right not to be connected. »
(Jacques Attali, interview to TV channel Public Sénat, 2008)

« Man, like the object, will be a nomad, without address or stable family, carrying on him, in him, everything that will make his social value. (...) When man becomes a prosthesis of himself, he will produce himself as a commodity. Life will be the object of artifice, creating value and profitability. »
(Jacques Attali, Lignes d'horizon, Fayard, 1990, Pp. 50 et 179)



« One could say that, among the instruments or means of any kind used for this purpose, "pseudo-initiation", by its very nature, must logically occupy the first place; it is only a cog, of course, but a cog that can command many others, on which these others come into contact in a way and from which they receive their impetus. [...] It immediately follows from this that the action thus exercised, instead of being truly "organic", can only have a purely "mechanical" character, which fully justifies the comparison of the mechanisms we have just used; And is not this character also, as we have already seen, the one that is found everywhere, and in the most striking way, in the present world, where the machine is invading everything more and more, where the human being himself is reduced, in all his activity, to resembling as much as possible an automaton, because all spirituality has been taken from him? But it is here that the inferiority of artificial productions explodes, even if a "satanic" skill has presided over their elaboration; one can well manufacture machines, but not living beings, because, once again, it is the spirit itself that is and will always be lacking. »
(René Guénon, Le Règne de la quantité et les signes du temps, 1945, Pp.177)

« When a people loses control of their own affairs, is reduced to slavery and becomes an instrument in the hands of others, apathy overwhelms them. He gradually lost all hope. [...] The defeated weaken and become unable to defend themselves. They are victims of anyone who wants to dominate them and the prey of big appetites. [...] See also the animals of prey, which do not breed in captivity. Thus, the tribal group that has lost control of its own affairs continues to weaken and eventually disappears. »
(Ibn Khaldoun, Al-Muqaddima [Introduction à l'histoire universelle], 1377 ; II, 23)

____________________
This article is a translation of the original article published in French.


2019/02/23

Tetravalent logic (Part 1)



Aristotle said: "Being is everything he knows", so that where there is real knowledge - not its appearance or shadow - knowledge and being are one and the same thing.
(R. Guénon, Mélanges, Chap. VI « Connais-toi toi même », 1976, Pp. 56)


All modern knowledge is based on logic. With a few rare exceptions - technical apparatus using fuzzy logic or states of quantum physics - all natural and human sciences (including Western philosophy since at least Plato) are based on classical logic, establishing the veracity or falsity of a proposal.

However, classical logic has limitations that have been known since its inception. These situations, which can be expressed in a few simple sentences, are negligently classified among the paradoxes.

The consequences of refusing to deal with these paradoxical situations are most critical, since this gap forces us to blindly focus on our understanding of the world and ourselves.

Since no one can ignore the fact that the modern world is going through an ultimate crisis, any contribution to broadening the scope of possibilities is welcome, and indeed, we might even say, necessary. This is the purpose of this article.

We will begin with a brief history of logic, going back before the appearance of classical logic, where we will see in passing that logic is born of metaphysics. This will lead us to an interposed dialogue between Heraclitus, Aristotle, Granger and Guénon.

We will then propose a formalization of a tetravalent logic with its truth tables, after having explained its necessity (part 2). We will end by applying the framework of this logic to the semantics of some attributes of the manifested and the unmanifested, where we will find each time the conceptions of Tradition (part 3).

It all starts with a negation

If we take a proposal P and its logical negation not(P) we can place ourselves in one of the following three cases:
  •     case 1: P is true or not(P) is true, exclusively;
  •     case 2: P and not(P) are both true, simultaneously;
  •     case 3: neither P nor not(P) are true, simultaneously.
Heraclitus of Ephesus (~541 - ~480 BC), descendant of the King of Athens and from a priestly family, proclaimed the unity and indivisibility of opposites, that is, the consideration of case 2, as evidenced by its Fragments:

    "All things are born according to the opposition... Change is an upward-descending road and the order of the world occurs according to this road..."

    "All things are mutually contrary. "

    "The god is day-night, winter-summer, war-peace, satiety-hunger. It changes like when you mix perfumes together; then you name it after their smell. "

    "What is cut in the opposite direction is assembled; from what is different is born the most beautiful harmony; everything becomes by discord. "

    "It is the disease that makes health pleasant and good, hunger satiety, fatigue and rest. "

    "What is contrary is useful; what struggles forms the most beautiful harmony; everything is done by discord. "

    "Join what is complete and what is not, what agrees and disagrees, what is in harmony and disagrees; of all things one and one, all things. "

    "They don't understand how what struggles with oneself can fit. The harmony of the world is in opposite tensions, as for the lyre and the bow. "

    "There is a hidden harmony, better than the apparent and where the god has mixed and deeply hidden differences and diversities. "

    "Death of fire, birth for air; death of air, birth for water. "

    "The same thing that lives and that which is dead, that which is awake and that which sleeps, that which is young and that which is old; for the change of one gives the other, and vice versa. "

The principle of non-contradiction rejects case 2: one cannot think P and non(P) true at the same time.

The principle of non-contradiction is an axiom, i.e. it is taken as a first truth that helps to demonstrate other theorems, but itself cannot be deduced or demonstrated. This is a relatively recent invention. It was popularized by Plato (428 - 348 BC) in La République (IV, 436b) and especially by Aristotle (~384 - ~322 BC): "It is impossible that the same attribute belongs and does not belong at the same time and in the same relationship to the same thing" (Metaphysics, Gamma Book, chapter 3, 1005 b 19-20).

The excluded middle was introduced by Aristotle as a consequence of the principle of non-contradiction.

The excluded middle (often wrongly described as a principle, because it is only a law) maintains that either a proposal is true or its negation is true. We cannot think the third hypothetical case, which is therefore rejected. [1]

It is essential to note that since ancient times the knowledge of truth and falsehood has been an experience of thought. The construction of logic derives from the knowledge of being, that is, of metaphysics.  (See in this regard G.G. Granger, Sciences et Réalité, Chap. De l’être au réel : le réel, concept moderne)

The combination of the principle of non-contradiction and the principle of the excluded middle have contributed to the foundation of the so-called classical formal mathematical logic.

In addition to its non-modal syllogistics, Aristotle developed a modal syllogistics in Book I of its Premiers Analytiques (ch. 8-22).

The first formal system of modal logic was developed by Avicenna, who proposed a theory of temporal modal syllogistics. Modal logic as a subject of study owes much to the writings of the Scholastics, in particular Guillaume of Ockham and  Jean Duns Scot, mainly for the analysis of assertions on the essence and the accident.

The "polyvalent logics" question the excluded middle since Lukasiewicz in 1910, which returns to the ancient question of "futurs contingents": if a proposal concerning the future could already be characterized in the present as true or false, we should admit that the course of events is determined in advance. Versatile logic challenges the principle of the excluded middle. They recognize values other than the true and the false, they admit modalities such as the possible, or, below that, the impossible (which is a reinforced false), and beyond the necessary (higher degree of the true).

Modal algebras developed since the 20th century provide models for the propositional calculation of modal logic in the same way that Boolean algebras are models for classical logic. [2]

There is now a whole spectra of intermediate logics, ranging from intuitionist to classical logic, depending in particular on the number of modalities (or truth values) and axioms chosen to constitute the logical system.

Which system is the most relevant to use to rebuild our knowledge, after binary logic?

Do sciences really make us discover the reality of things? Do they build the world from scratch in their laboratories, and then force us to believe it?

G.G. Granger, a professor at the Collège de France, argued that scientific reality was only a way of accessing a certain type of object:

    "Validation is first exercised by self-control of the application of operating rules, which are themselves formal objects of a logic. But what fundamentally distinguishes this self-control is precisely that it ultimately concerns not isolated elements of the logical-mathematical formal object, but the whole system. It is then characterized by the prefix "meta": it is no longer simply a question of reasoning at the level of logic or mathematics, but at a higher meta-mathematical level. A formal system is then tested in its total structure, in terms of its non-contradiction, completeness and fertility. The first criterion normally expected of its reality is certainly the establishment of its non-contradiction. But it has been understood since Tarski and Gödel during the century that has just ended that the establishment by meta-mathematical means of the independence of certain parts of the system, the truth of certain proposals at the same time as the impossibility of demonstrating them in the system, and even the impossibility of demonstrating at its own mathematical level the non-contradiction of the system, were also in a new sense the attributes of its reality...[.] We see therefore that in all cases scientific reality is necessarily dependent on a use of the conceptual imagination. " (Science et Réalité, Ed. Odile Jacob, 2001, Chap. 8 "Systèmes et réalité", Pp. 241-242)

We have stressed that the construction of logic derives from the knowledge of being, that is, from metaphysics. It is therefore mandatory to look at what Tradition has to offer in this regard. We use a capital letter T to indicate that we go back further than Aristotle and Plato. We started with Heraclitus, we continue in the footsteps of René Guénon, starting by explaining the importance of the ternaries.

After 2 there are 3, which give birth to 4

"What we have just said already determines the meaning of the Triad, at the same time as it shows the need to make a clear distinction between ternaries of different genres;[...]

One of these two genres is the one where the ternary is constituted by a first principle (at least in a relative sense) from which two opposite terms derive, or rather complementary terms, because, even where the opposition is in appearances and has its raison d'être at a certain level or in a certain domain, complementarism always responds to a deeper point of view, and therefore no longer truly in conformity with the real nature of what it is about; such a ternary can be represented by a triangle whose vertex is placed at the top (fig. 1).


The other genus is the one where the ternary is formed, as we said earlier, by two complementary terms and by their product or resultant, and it is to this genus that the Far Eastern Triad belongs; unlike the previous one, this ternary can be represented by a triangle whose base is on the contrary placed at the top (fig. 2).


If we compare these two triangles, the second one appears to be a reflection of the first, which indicates that, between the corresponding ternaries, there is an analogy in the true meaning of this word, i. e. to be applied in the opposite direction; and, indeed, if we start from the consideration of the two complementary terms, between which there is necessarily symmetry, we see that the ternary is completed in the first case by their principle, and in the second, on the contrary, by their resultant, so that the two complementary terms are respectively after and before the term which, being of a different order, is almost isolated from them. This is further clarified in both figures by the direction of the arrows, going, in the first, from the upper vertex to the bottom, and, in the second, from the bottom to the lower vertex;[...]; and it is obvious that, in any case, it is the consideration of this third term that gives the ternary as such its full meaning.

Now, what must be clearly understood before going any further is that there could only be "dualism" in any doctrine if two opposed or complementary terms (and then they would rather be conceived as opposed) were first posed and considered as ultimate and irreducible, without any derivation from a common principle, which obviously excludes the consideration of any ternary of the first kind; one could therefore only find in such a doctrine ternaries of the second kind[...]

The consideration of two ternaries like the ones we have just mentioned, having in common the two complementary principles of each other, leads us to some other important remarks: the two inverted triangles which represent them respectively can be considered as having the same base, and, if we figure them united by this common base, we see first that the set of the two ternaries forms a quaternary, since, two terms being the same in both, there are in all only four distinct terms, and then only the last term of this quaternary, located on the vertical line resulting from the first term and symmetrically to it with respect to the base, appears as a reflection of this first term, the reflection plane being represented by the base itself, i. e. being only the median plane where the two complementary terms resulting from the first term are located and producing the last one (fig. 3).


We have just seen that the two extreme terms of the quaternary, which are at the same time respectively the first term of the first ternary and the last of the second, are both, by their nature, intermediaries in a way between the other two, although for the opposite reason: in both cases, they unite and reconcile in themselves the elements of complementarism, but one as a principle, and the other as a result. »
(The Great Triad, 1946, Chap. II - Different kinds of ternaries)

René Guénon developed in more detail the meaning of the quaternary in Le Symbolisme de la croix (1931), which is entirely consistent with the above passage.


The square of Aristotle

In classical modal logic, four modalities are identified for evaluating a proposal:
  •     necessary (if and only if the proposal is not possibly false; "what cannot but be true");
  •    contingent (if and only if the proposal is not necessarily false and not necessarily true; "what may be false");
  •     possible (if and only if the proposal is not necessarily false; "what may be true");
  •     impossible (if and only if the proposition is not possibly true; "what cannot but be false").


« Another way of showing the relationships between the four modalities is to arrange them in a square configuration, which goes back at least to Aristotle. The square of the modalities is isomorphic to the logical square of the terms and to that of the form A (universal affirmative), E (universal negative), I (particular affirmative) and O (particular negative) proposals of Aristotelian logic (fig. 4).

Fig. 4
There are, in each of these squares, four fundamental types of relationships between their respective four terms: contradiction or negation (on the diagonals) contradiction or incompatibility (on the upper horizontal side) subordinacy or non-exclusive disjunction (on the lower side) subordination or implication (on the vertical sides). » (Lucien Scubla, L’aporie de Diodore Cronos et les paradoxes de la temporalité. Jean-Pierre Dupuy et la philosophie, 2007)

These 4 modalities are linked, only one is needed to define the other three. The interpretation in intuitive logic is as follows:
  •     impossible ≡ necessary that does not... not...;
  •     possible ≡ no impossible ≡ no need that does not... not
  •     contingent ≡ not necessary ≡ possible that not... not;
In this interpretation, the possible and the impossible derive from the necessary (or its negation). The quota also results from the necessary, but also from the possible (and therefore from the impossible). The modal square is thus only a reduced deformation of the primordial diamond as described by Guénon, which is constructed on equilateral triangles instead of isosceles rectangular triangles (Fig. 5). This reduction, an example of a progressive loss of meaning, is a special case whose generality has been perfectly explained by Guénon (cf. La crise du monde moderne, Le règne de la quantité et les signes des temps). [3]

Fig. 5

Let us note how much the conceptualization described by Guénon agrees with and extends G. G. Granger's conclusion :
« The reality of science objects would therefore, according to our analyses, mean a certain relationship between a virtual aspect and a current aspect of the representation of the experience. This would be the meaning of a unity of science, a unity that it would not be useful to simply designate as a "concordance" of the two aspects. It is therefore legitimate to use the plural to refer to scientific realities, insofar as, as we have tried to show, the thinking of science, in each of its fields, determines specific criteria for its achievement of reality. » (Sciences et réalité, Conclusion, Pp. 243)

This essay is extended by the formal propositional calculation in tetravalent logic, detailed in the second part. 

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This article is a translation of the original article published in French.

[1] In classical binary logic, the excluded third theorem is derived from the principle of non-contradiction by introducing the relationship of equality or equivalence, the Boolean negation operator, by accepting the additional axioms:
  •     identity principle: P = P
  •     elimination of double negation: not(not(P)) = P
then by establishing the values of the truth tables of the operators NOT, AND and OR and by first demonstrating the equality not(A and B) = not(A) or not(B).

The principle of non-contradiction is the proposal "P and not (P) = FALSE".
implies the proposition: "not(P and not (P)) = TRUE"
implies the proposition:" not(P) or not (no (P)) = TRUE"
implies the proposition: "not(P) or P = TRUE"
implies that "P is TRUE" or "not(P) is TRUE"
so the proposal of the excluded middle is verified.


[2] Lewis founded modern modal logic in his 1910 Harvard thesis and in a series of articles published between 1912 and 1932, when his book Symbolic Logic, written in collaboration with Langford, was published.

The logicians Brouwer and
Heyting in 1930 criticized, in the name of "intuitionist logic", a certain type of reasoning held according to the principle of the excluded middle applied to finite sets. They believe that one has no logical right to infer the truth of a proposal from the falsity of its negation. Heyting does not say that the excluded middle principle is always wrong, but it limits its scope.

The mathematical structure of modal logic, i. e. Boolean algebras augmented by unary operations (often called modal algebras), began to emerge with McKinsey who showed in 1941 that Lewis' S2 and S4 systems were decidable.

[3] Why a representation in the form of a diamond and not a tetrahedron? The latter would place the Contingency and the areas of the Possible and the Impossible on the same level. It would "shorten" the distance between the Contingency and Necessity. There is no way to justify these assertions. On the contrary, we will see in the last part how useful it is to keep the diamond model.