CHAPTER XXI

Tertium Organum, by P.D. Ouspensky, [1922], at sacred-texts.com

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EVERYTHING that has been said about mathematical magnitudes is true also with regard to logical concepts. Finite mathematical magnitudes and logical concepts are subject to the same laws.

We have now established that the laws discovered by us in a space of three dimensions, and operating in that space, are inapplicable, incorrect and untrue in a space of a greater number of dimensions.

And as this is true of mathematics, so is it true of logic.

As soon as we begin to consider infinite and variable magnitudes instead of those which are finite and constant, we perceive that the fundamental axioms of our mathematics cannot be applied to the former class.

And as soon as we begin to think in other terms than those of concepts, we must be prepared to encounter an enormous number of absurdities from the standpoint of existing logic.

These absurdities seem to us such, because we approach the world of many dimensions with the logic of the three-dimensional world.

It has been proven already that to an animal, i.e., to a two-dimensional being, thinking not by concepts, but by perceptions, our logical ideas must seem absurd.

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The logical relations in the world of many dimensions seem equally absurd to us. We have no reason whatsoever to hope that the relations of the world of causes can be logical from our point of view. On the contrary, it may be said that EVERYTHING LOGICAL is phenomenal. Nothing can be logical, from our standpoint, there. All that is there must seem to us a logical absurdity, nonsense. We must remember that it is impossible to penetrate there with our logic.

The relation of the general trend of the thought of humanity toward the "other world" has always been highly incorrect.

In "positivism" men have denied that other world altogether. This was because, not admitting the possibility of relations other than those formulated by Aristotle and Bacon, men denied the very existence of that which seemed absurd and impossible from the standpoint of those formula. Also, in spiritism they attempted to construct the noumenal world on the model of the phenomenal, that is, against reason, against nature, they wanted at all costs to prove that the other world is logical from our standpoint, that the same laws of causality operate just as in our world, and that the other world is nothing more than the extension of ours. The "other world" of spiritists or spiritualists in all existing descriptions of it is a naive and barbaric concept of the unknown.

Positive philosophy perceived the absurdity of all dualistic theses, but having no power to expand the field of its activity, limited by logic and "the infinite sphere," it could think of nothing better than to DENY.

Mystical philosophy alone felt the possibility of relations other than those of the phenomenal world. But it was arrested by hazy and unclear sensations, finding it impossible to define and classify them.

Nevertheless, science must come to mysticism, because in mysticism there is a new method—and then to the study of different forms of consciousness, i.e., of forms of receptivity different from our own. Science should throw off almost everything old and should start afresh with a new theory of knowledge.

Science cannot deny the fact that mathematics grows, expands, and escapes from the limits of the visible and measurable world. Entire departments of mathematics take into consideration quantitative relations which did not and do not exist in the real world of

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positivism, i.e., relations which have no correspondence to any realities in the visible, three-dimensional world.

But there cannot be any mathematical relations to which the relation of some realities would not correspond. Therefore mathematics transcends the limits of our world, and penetrates into a world unknown. This is the telescope, by the aid of which we begin to investigate the space of many dimensions with its worlds. Mathematics goes ahead of our thought, ahead of our power of imagination and perception. Even now it is engaged in calculating relations which we cannot imagine or comprehend.

It is impossible to deny all this, even from the strictly "positivistic," i.e., positive standpoint. Thus science, having admitted the possibility of the expansion of mathematics beyond the limits of the sensuously perceived world—that is beyond the limits of a world accessible (though theoretically) to the organs of sense and their mechanical aids—must thereby recognize the expansion of the real world far beyond the limits of any "infinite sphere" or of our logic, i.e., must recognize the reality of "the world of many dimensions."

The recognition of the reality of the world of many dimensions is the already accomplished transition to, and understanding of, the world of the wondrous. And this transition to the wondrous is impossible without the recognition of the reality of new logical relations which are absurd and impossible from the standpoint of our logic.

What are the laws of our logic?

They are the laws of our receptivity of the three-dimensional world, or the laws of our three-dimensional receptivity of the world.

If we desire to escape from the three-dimensional world and go farther, we must first of all work out the fundamental logical principles which would permit us to observe the relations of things in a world of many dimensions—seeing in them a certain reasonableness, and not complete absurdity. If we enter there armed only with the principles of the logic of the three-dimensional world, these principles will drag us back, will not give us a chance to rise from the earth.

First of all we must throw off the chains of our logic. This is the first, the great, the chief liberation toward which humanity

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must strive. Man, throwing off the chains of "three-dimensional" logic, has already penetrated, in thought, into another world. And not only is this transition possible, but it is accomplished constantly. Although unhappily we are not entirely conscious of our rights in "another world," and often sacrifice these rights, regarding ourselves as limited to this earthly world, paths nevertheless exist. Poetry, mysticism, the idealistic philosophy of all ages and peoples, preserve the traces of such transitions. Following these traces, we ourselves can find the path. Ancient and modern thinkers have given us many keys with which we may open mysterious doors; many magical formulæ, before which these doors open of themselves. But we have not understood either the purpose of these keys or the meaning of the formulæ. We have also lost the understanding of magical ceremonies and rites of initiation into mysteries which had a single purpose: to help this transformation in the soul of man.

Therefore the doors remained closed, and we even denied that there was anything whatever behind them; or, suspecting the existence of another world, we regarded it as similar to ours, and separate from ours, and tried to penetrate there unconscious of the fact that the chief obstacle in our path was our own division of the world into this world and that.

The world is one, only the ways of knowing it are different; and with imperfect methods of knowledge it is impossible to penetrate into that which is accessible to perfect methods only.

All attempts to penetrate mentally into that higher, noumenal world, or world of causes, by means of the logic of the phenomenal world, if they did not fail altogether, or did not lead to castles in the air, gave only one result: in becoming conscious of a new order of things, a man lost the sense of the reality of the old order. The visible world began to seem to him fantastic and unreal, everything all about him was disappearing, was vanishing like smoke, leaving a dreadful feeling of illusion. In everything he felt the abyss of infinity, and everything was plunging into the abyss.

This sense of the infinite is the first and most terrible trial before initiation. Nothing exists! A little miserable soul feels itself suspended in an infinite void. Then even this void disappears! Nothing exists. There is only infinity, a constant and continuous division and dissolution of everything. The mystical literature of

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all peoples abounds in references to this sensation of darkness and emptiness.

Such was that mysterious deity of the ancient Egyptians, about which there exists a story in the Orpheus myth, in which it is de-scribed as a "Thrice-unknown darkness in contemplation of which all knowledge is resolved into ignorance." ¹

This means that man must have felt horror transcending all limits as he approached the world of causes with the knowledge of the world of phenomena only, his instrument of logic having proved useless, because all the new eluded him. In the new as yet he sensed chaos only, the old had disappeared, gone away and become unreal. Horror and regret for the loss of the old mingled with horror of the new—unknown and terrible by its infinitude.

At this stage man experiences the same thing that an animal, becoming a man, would feel. Having looked into a new world for an instant, it is attracted by the life left behind. The world which it saw only for an instant seems but a dream, a vision, the creation of imagination, but the familiar old world, too, is never thereafter the same, it is too narrow, in it there is not sufficient room. The awakening consciousness can no longer live the free life of the beast. Already it knows something different, it hears some voices, even though the body holds it. And the animal does not know where or how it can escape from the body or from itself.

A man on the threshold of a new world experiences literally the same thing. He has heard celestial harmonies, and the wearisome songs of earth touch him no longer, nor do they move him—or if they touch and move him it is because they remind him of celestial harmonies, of the inaccessible, of the unknown. He has experienced the sensation of an unusual EXPANSION of consciousness, when everything was clear to him for a moment, and he cannot reconcile himself to the sluggish earthly work of the brain.

These moments of the "sensation of infinity" are accompanied by unusual emotions.

In theosophical literature, and in books on occultism, it is often asserted that on entering into the "astral" world, man begins to see new colors, colors which are not in the solar spectrum. ² In

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this symbolism of the new colors of the "astral sphere" is conveyed the idea of those new emotions which man begins to feel along with the sensation of the expansion of consciousness—"of the sea pouring into the drop." This is the "strange bliss" of which mystics speak, the "heavenly light" which saints "see," the "new" sensations experienced by poets. Even conversational psychology identifies "ecstasy" with entirely unusual sensations, inaccessible and unknown to man in the life of every day.

This sensation of light and of unlimited joy is experienced at the moment of the expansion of consciousness (the unfoldment of the mystical lotus of the Hindu yogi), at the moment of the sensation of infinity, and it yields also the sensation of darkness and of unlimited horror.

What does this mean?

Now shall we reconcile the sensation of light with the sensation of darkness, the sensation of joy with that of horror? Can these exist simultaneously? Do they occur simultaneously?

They do so occur, and must be exactly thus. Mystical literature gives us examples of it. The simultaneous sensations of light and darkness, joy and horror, symbolize as it were the strange duality and contradiction of human life. It may happen to a man of dual nature, who following one side of his nature has been led far into "spirit," and on the other side is deeply immersed in "matter," i.e., in illusion, in unreality—to one who believes too much in the reality of the unreal.

Generally speaking the sensation of light, of life, of consciousness penetrating all, of happiness, gives a new world. But the same world to the unprepared mind will give the sensation of infinite darkness and horror. In this case the sensation of horror will arise from the loss of everything real, from the disappearance of this world.

In order not to experience the horror of the new world, it is necessary to know it beforehand, either emotionally—by faith or love—or intellectually, by reason.

And in order not to experience horror from the loss of the old world, it is necessary to have renounced it voluntarily either through faith or reason.

One must renounce all the beautiful, bright world in which we are living; one must admit that it is ghostly, phantasmal, unreal,

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deceitful, illusory, mayavic. One must reconcile oneself to this unreality, not be afraid of it, but rejoice at it. One must give up everything. One must become POOR IN SPIRIT, i.e., make oneself poor by the effort of one's spirit.

This most profound philosophical truth is expressed in the beautiful evangelical symbol:

These words become clear in the sense of a renouncement of the material world only. "Poor in spirit" does not mean poor materially, in the worldly meaning of the word, and still less does it signify poverty of spirit. Spiritual poverty is the renouncement of matter; such "poverty" is his when a man has no earth under his feet, no sky above his head.

This is the poverty of the man who is entirely alone, because father, mother, other men, even the nearest here on earth he begins to regard differently, not as he regarded them before; and renounces them because he discerns the true substances that he is striving toward; just as, renouncing the phenomenal illusions of the world, he approaches the truly real.

The moment of transition—that terrible moment of the loss of the old and the unfoldment of the new—has been represented in innumerable allegories in ancient literature. To make this transition easy was the purpose of the mysteries. In India, in Egypt, in Greece, special preparatory rituals existed, sometimes merely symbolical, sometimes real, which actually brought a soul to the very portals of the new world, and opened these portals at the moment of initiation. But no outward rituals and ceremonies could take the place of self-initiation. The great work must have been going on inside the soul and mind of man.

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But how can logic help a man to pass to the consciousness of a new and higher world?

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We have seen that MATHEMATICS has already found the path into that higher order of things. Penetrating there, it first of all renounces its fundamental axioms of identity and difference.

In the world of infinite and fluent magnitudes, a magnitude may be not equal to itself; a part may be equal to the whole; and of two equal magnitudes one may be infinitely greater than the other.

All this sounds like an absurdity from the standpoint of the mathematics of finite and constant numbers. But the mathematics of finite and constant numbers is itself the calculation of relations between non-existent magnitudes, i.e., an absurdity. And therefore only that which from the standpoint of this mathematics seems an absurdity, can be the truth.

Logic now goes along the same path. It must renounce itself, come to perceive the necessity for its own annihilation—then out of it a new and higher logic can arise.

In his Critique of Pare Reason Kant proved the possibility of transcendental logic.

Before Bacon and earlier than Aristotle, in the ancient Hindu scriptures, the formulæ of this higher logic were given, opening the doors of mystery. But the meaning of these formula was rapidly lost. They were preserved in ancient books, but remained there as some strange mummeries of extinguished thought, the words without real content.

New thinkers again discovered these principles, and expressed them in new words, but again they remained incomprehensible, again they suffered transformation into some unnecessary ornamental form of words. But the idea persisted. A consciousness of the possibility of finding and establishing the laws of the higher world was never lost. Mystical philosophy never regarded the logic of Aristotle as all-embracing and all-powerful. It built its system outside of logic or above logic, unconsciously going along those paths of thought paved in remote antiquity.

The higher logic existed before deductive and inductive logic was formulated. This higher logic may be called intuitive logic—the logic of infinity, the logic of ecstasy.

Not only is this logic possible, but it exists, and has existed from time immemorial; it has been formulated many times; it has entered into philosophical systems as their key—but for some strange reason has not been recognized as logic.

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It is possible to deduce the system of this logic from many philosophical systems. The most precise and complete formulation of the law of higher logic I find in the writing of Plotinus, in his On Intelligible Beauty. I shall quote this passage in the succeeding chapter.

I have called this system of higher logic Tertium Organum because for us it is the third canon—third instrument—of thought after those of Aristotle and Bacon. The first was the Organon, the second, Novum Organum. But the third existed earlier than the first.

Man, master of this instrument, of this key, may open the door of the world of causes without fear.

The axioms which Tertium Organum embraces cannot be formulated in our language. If we attempt to formulate them in spite of this, they will produce the impression of absurdities. Taking the axioms of Aristotle as a model, we may express the principal axiom of the new logic in our poor earthly language in the following manner:

or

or,

But these axioms are in effect absolutely impossible. They are not the axioms of higher logic, they are merely attempts to express the axioms of this logic in concepts. In reality the ideas of higher logic are inexpressible in concepts. When we encounter such an inexpressibility it means that we have touched the world of causes.

The logical formula: A is both A and Not-A, corresponds to the mathematical formula: A magnitude can be greater or less than itself.

The absurdity of both these propositions shows that they cannot refer to our world. Of course absurdity, as such, is indeed not an index of the attributes of noumena, but the attributes of noumena will certainly be expressed in what are absurdities to us. To hope to find in the world of causes anything logical from our standpoint is just as useless as to think that the world of things can exist in

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accordance with the laws of a world of shadows or stereometry according to the laws of planimetry.

To master the fundamental principles of higher logic means to master the fundamentals of the understanding of a space of higher dimensions, or of the world of the wondrous.

In order to approach to a clear understanding of the relations of the multi-dimensional world, we must free ourselves from all the "idols" of our world, as Bacon calls them, i.e., from all obstacles to correct receptivity and reasoning. Then we shall have taken the most important step toward an inner affinity with the world of the wondrous.

A two-dimensional being, in order to approach to an understanding of the three-dimensional world, already should have become a three-dimensional being before it can rid itself of its "idols," i.e., of its conventional—converted into axiomatic—ways of feeling and thinking, which create for it the illusion of two-dimensionality.

What is it exactly from which the two-dimensional being must liberate itself?

First of all—and most important—from the assurance that that which it sees and senses really exists; from this will come the consciousness of the incorrectness of its perception of the world, and then the idea that the real, new world must exist in quite other forms—new, incomparable, incommensurable with relation to the old ones. Then the two-dimensional being must overcome its sureness of the correctness of its categories. It must understand that things which seem to it different and separate from one another may be parts of some to it incomprehensible whole, or that they have much in common which it does not perceive; and that things which seem to it one and indivisible are in reality infinitely complex and multifarious.

The mental growth of the two-dimensional being must proceed along the path of the recognition of those common properties of objects, unknown to it before, which are the result of their similar origin or similar functions, incomprehensible from the point of view of a plane.

When once the two-dimensional being has admitted the possibility of the existence of hitherto unknown common properties of objects, which before seemed different, then it has already approached to our own understanding of the world. It has approached to our

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logic, has begun to understand the collective name, i.e., a word used not as a proper noun, but as an appellate noun—a word expressing a concept.

The "idols" of the two-dimensional being, hindering the development of its consciousness, are those proper nouns, which it has itself given to all the objects surrounding it. For such a being each object has its own proper noun, corresponding to its perception of the object; common names, corresponding to concepts, it knows not of. Only by getting rid of these idols, by understanding that the names of things can be not only proper, but common ones as well, will it be possible for it to advance farther, to develop mentally, to approach the human understanding of the world. Take the most simple sentence:

[paragraph continues] For the two-dimensional being this will be an absurdity, and it will represent the idea to itself after this fashion:

In other words, every one of our logical propositions will be an absurdity to it. Why this is so is clear. Such a being has no concepts; the proper nouns which constitute the speech of such a being have no plurals. It is easy to understand that any plural of our speech will seem to it an absurdity.

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Where are our "idols?" From what shall we liberate ourselves in order to pass to an understanding of the multi-dimensional world?

First of all we must get rid of our assurance that we see and sense that which exists in reality, and that the real world is like the world which we see—i.e., we must rid ourselves of the illusion of the material world. We must understand mentally all the illusoriness of the world perceived by us in space and time, and know that the real world cannot have anything in common with it; to understand that it is impossible to imagine the real world in terms of form; and finally we must perceive the conditionality of the axioms

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of our mathematics and logic, related as they are to the unreal phenomenal world.

In mathematics the idea of infinity will help us to do this. The unreality of finite magnitudes in comparison with infinite ones is obvious. In logic let us dwell upon the idea of monism, i.e., the fundamental unity of everything which exists, and consequently recognize the impossibility of constructing any axioms, which involve the idea of opposites—of theses and antitheses—upon which our logic is built.

The logic of Aristotle and of Bacon is at bottom dualistic. If we really deeply assimilate the idea of monism, we shall dethrone the "idol" of this logic.

The fundamental axioms of our logic reduce themselves to identity and contradiction, just as do the axioms of mathematics. At the bottom of them all lies the admission of our general axiom, namely, that every given something has something opposite to it; therefore every proposition has its anti-proposition, every thesis has its anti-thesis. To the existence of any thing is opposed the non-existence of that thing. To the existence of the world is opposed the non-existence of the world. Object is opposed to subject; the objective world to the subjective; the I is opposed to the Not-I; to motion—immobility; to variability—constancy; to unity—heterogeneity; to truth—falsehood; to good—evil. And in conclusion, to every A in general is opposed Not-A.

The recognition of the reality of these divisions is necessary for the acceptance of the fundamental axioms of the logic of Aristotle and Bacon, i.e., the absolute and incontestable recognition of the duality of the world—of dualism. The recognition of the unreality of these divisions and that of the unity of all opposites is necessary for the comprehension of higher logic.

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At the very beginning of this book the existence of THE WORLD and of THE PSYCHE was admitted, i.e., the reality of the dual division of everything existent, because all other opposites are derived from this opposition.

Duality is the condition of our knowledge of the phenomenal (three-dimensional) world; this is the instrument of our knowledge

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of phenomena. But when we come to the knowledge of the noumenal world (or the world of many dimensions), this duality begins to hinder us, appears as an obstacle to knowledge.

Dualism is the chief "idol"; let us free ourselves from it.

The two-dimensional being, in order to comprehend the relations of things in three dimensions and our logic, must renounce its "idol"—the absolute singularity of objects which permits it to call them solely by their proper names.

We, in order to comprehend the world of many dimensions, must renounce the idol of duality.

But the application of monism to practical thought meets the in-surmountable obstacle of our language. Our language is incapable of expressing the unity of opposites, just as it cannot express spatially the relation of cause to effect. Therefore we must reconcile ourselves to the fact that all attempts to express super-logical relations in our language will seem absurdities, and really can only give hints at that which we wish to express.

Thus the formula,

or,

representing the principal axioms of higher logic, expressed in our language of concepts, sounds absurd from the standpoint of our usual logic, and is not essentially true.

Let us therefore reconcile ourselves to the fact that it is impossible to express super-logical relations in our language as it is at present constituted.

The formula, "A is both A and Not-A" is untrue because in the world of causes there exists no opposition between "A" and "Not-A." But we cannot express their real relation. It would be more correct to say:

But this also would be untrue, because "A" is not only all, but also an arbitrary part of all, and at the same time a given part.

This is exactly the thing which our language cannot express. It

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is to this that we must accustom our thought, and train it along these lines.

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We must train our thought to the idea that separateness and inclusiveness are not opposed in the real world, but exist together and simultaneously without contradicting one another. Let us understand that in the real world one and the same thing can be both a part and the whole, i.e., that the whole, without changing, can be its own part; understand that there are no opposites in general, that everything is a certain image of all.

And then, beginning to understand all this, we shall grasp the separate ideas concerning the essentials of the "noumenal world," or the world of many dimensions in which we really live.

In such case the higher logic, even with its imperfect formulæ, as they appear in our rough language of concepts, represents in spite of this a powerful instrument of knowledge of the world, our only means of preservation from deceptions.

The application of this instrument of thought gives the key to the mysteries of nature, to the world as it is.

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Let us endeavor to enumerate those properties of THE WORLD OF CAUSES which result from all the foregoing.

It is first of all necessary to reiterate that it is impossible to express in words the properties of the world of causes. Every thought expressed about them in our ordinary language will be false. That is, we may say in relation to the "real" world that "every spoken thought is a lie." It is possible to speak about it only conditionally. by hints, by symbols. And if one interprets literally anything said about it, nothing but absurdity results. Generally speaking, everything said in words regarding the world of causes is likely to seem absurd, and is in reality its mutilation. The truth it is impossible to express; it is possible only to give a hint at it, to give an impulse to thought. But everyone must discover the truth for himself. "Another's truth" is worse than a lie, because it is two lies. This explains why truth very often can be expressed only by means of

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paradox, or even in the form of a lie. Because, in order to speak of truth without a lie, we should know some other language—ours is unsuitable.

What then are we able to say about the world of many dimensions, about the world of noumena, or world of causes?

1. In that world "TIME" must exist spatially, i.e. temporal events must exist and not happen—exist before and after their manifestation, and be located in one section, as it were. Effects must exist simultaneously with causes. That which we name the law of causality cannot exist there, because time is a necessary condition for it. There cannot be anything which is measured by years, days, hours—there cannot be before, now, after. Moments of different epochs, divided by great intervals of time, exist simultaneously, and may touch one another. Along with this, all the possibilities of a given moment, even those opposite to one another, and all their results up to infinity, must be actualized simultaneously with a given moment, but the length of a moment can be different on different planes.

2. There is nothing measurable by our measures, nothing commensurable with our objects, nothing greater or less than our objects. There is nothing situated on the right or left side, above or below one of our objects. There can be nothing similar to our objects, lines or figures and at the same time exist. Different points in our space, divided for us by enormous distances, may meet there. "Distance" or "proximity" are there defined by inner "affinity" or "remoteness," by sympathy or antipathy, i.e., by properties which seem to us to be subjective.

3. There is neither matter nor motion. There is nothing that could possibly be weighed or photographed, or expressed in the formulæ of physical energy. There is nothing which has form, color or odor—nothing possessing the properties of physical bodies. Nevertheless, the properties of the world of causes, granted an understanding of certain laws, can be considered in enumerated categories.

4. There is nothing dead or unconscious. Everything lives, everything breathes, thinks, feels; everything is conscious, and everything speaks.

5. In that world the axioms of our mathematics cannot be applied,

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because there is nothing finite. Everything there is infinite and, from our standpoint, variable.

6. The laws of our logic cannot act there. From the standpoint of our logic, that world is illogical. This is the realm the laws of which are expressed in Tertium Organum.

7. The separateness of our world does not exist there. Everything is the whole. And each particle of dust, without mentioning of course every life and every conscious being, lives a life which is one with the whole and includes the whole within itself.

8. In that world the duality of our world cannot exist. There being is not opposed to non-being. Life is not opposed to death. On the contrary, the one includes the other within itself. The unity and multiplicity of the I; the I and the Not-I; motion and immobility; union and separateness; good and evil; truth and falsehood—all these divisions are impossible there. Everything subjective is objective, and everything objective is subjective. That world is the world of the unity of opposites.

9. The sensation of the reality of that world must be accompanied by the sensation of the unreality of this one. At the same time the difference between real and unreal cannot exist there, just as the difference between subjective and objective cannot exist.

10. That world and our world are not two different worlds. The world is one. That which we call our world is merely our incorrect perception of the world: the world seen by us through a narrow slit. That world begins to be sensed by us as the wondrous, i.e., as something opposite to the reality of this world, and at the same time this, our earthly world, begins to seem unreal. The sense of the wondrous is the key to that world.

11. But everything that can be said about it will not define our relation to that world until we come to understand that even comprehending it we will not be able to grasp it as a whole, i.e., in all its variety of relations, but can think of it only in this or that aspect.

12. Everything that is said about the world of causes refers also to the All. But between our world and the All there may be many transitions.

Footnotes

258:1 "The Ancient Wisdom," by Annie Besant, Introd. p. 23, Theosophical Publishing Society, London.

258:2 Although it should be remembered that we see only three out of seven colors of the solar spectrum.