The Experience of Previous Generations
Beyond Axiomatic Statement
The World and the Psyche
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See also:The Kybalion
Natural Law in the Spiritual World
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.
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. And as soon as we begin to think in terms other 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 [see Chapter VIII and Chapter IX Ed.] that to an animal, i.e., to a two-dimensional being, thinking not by concepts but by perceptions, our logical ideas must seem absurd.
The logical relations in the world of many dimensions seem equally absurd to us. We have no reason to hope that the relations of the world of causes shall be logical from our point of view. On the contrary, it may be said that everything logical is phenomenal. From our standpoint, nothing can be logical there. All that is there [i.e., in the "world of many dimensions" Ed.] 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 towards 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 formulae. 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 naοve 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 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 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 an unknown world. 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 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 recognise the expansion of the real world far beyond the limits of any "infinite sphere" or of our logic, i.e., must recognise 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. But this transition to the wondrous is impossible without recognising the reality of new logical relations which are absurd and impossible from the standpoint of our logic.
The laws of our logic are the laws of our receptivity of the three-dimensional world, or rather, the laws of our three-dimensional receptivity of the world.
If we desire to escape from the three-dimensional world and go further, we must first 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.
We must throw off the chains of our logic. This is the first, the great, the chief liberation towards which humanity must strive. Man, throwing off the chains of "three-dimensional" logic, has already penetrated, in thought, into another world. Not only is this transition possible, but it is accomplished constantly. Although we are unhappily not entirely conscious of our rights in "another world", and often sacrifice these rights through regarding ourselves as limited to this earthly world, nevertheless paths 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 and many magical formulae before which these doors open by themselves. But we have not understood either the purpose of these keys or the meaning of the formulae. Also, we have 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.
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 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 described as a "Thrice-unknown darkness in contemplation of which all knowledge is resolved into ignorance". Annie Besant: Introduction to The Ancient Wisdom
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, he as yet sensed only chaos: the old had 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 still attracted by the life left behind. The world which it saw only for an instant becomes but a dream, a vision, the creation of imagination; but the familiar old world, too, is never thereafter the same: it is too narrow; there isn't enough room in it. The awakening consciousness can no longer live the free life of the beast. It already knows something different: it hears new voices, even though the body still holds it. And the animal does not know whither or how it can escape from the body or from itself.
A man on the threshold of a new world experiences this 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.
In theosophical literature and in books on occultism, it is often asserted that on entering into the "astral" world, man begins to see new colours which are not in the solar spectrum. [Although it should be remembered that we see only three out of seven colours in the solar spectrum. PDO] In this symbolism of the new colours 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, unknown and inaccessible to man in the life of everyday.
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?
How 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, symbolise 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" whilst on the other side he is still deeply immersed in "matter", i.e., in illusion, in unreality, and believes too much in the reality of the unreal.
Speaking generally, the sensation of light, of life, of consciousness penetrating everything, of happiness, gives a new world. But to the unprepared mind, such a world 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 old, familiar world.
And in order not to experience horror from the loss of the old world, it is necessary to have renounced it voluntarily through either 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, deceitful, illusory, mayavic. One must reconcile oneself to this unreality; one must 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.
The most profound philosophical truth is expressed in the beautiful evangelical symbol: Blessed are the poor in spirit: for theirs is the kingdom of heaven. Matthew, 5:3.
These words become clear in the sense of a renunciation 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 renunciation of matter; such "poverty" is his when a man has no earth under his feet, no sky above his head.
Foxes have holes, and birds of the air have nests, but the Son of man hath not where to lay his head. Matthew, 8:20.
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 he renounces them because he discerns the true substance that he is striving towards 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 was the purposes 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.
We have seen that mathematics has already found a 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 absurd 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, from the standpoint of the mathematics of finite and constant numbers, only that which seems absurd can be the truth.
Logic now goes along the same path. It must renounce itself, come to perceive the necessity for its own annihilation, so that out of it a new and higher logic can arise.
In his Critique of Pure Reason, Kant proved the possibility of transcendental logic.
Before Bacon, before Aristotle, the formulae of this higher logic, opening the doors of mystery, were given in the ancient Hindu scriptures. But the meaning of these formulae 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 or 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 it has not been recognised as logic.
It is possible to deduce the system of this logic from many philosophical systems. I find the most precise and complete formulation of the law of higher logic 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 were the Organon, the second, Novum Organum. But the third existed earlier than the first.
Man, master of this instrument, of this key, may without fear open the door of 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 accordance with the laws of a world of shadows 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 towards an inner affinity with the world of the wondrous.
In order to approach an understanding of the three-dimensional world, a two-dimensional being should already 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 exactly is it from which the two-dimensional being must liberate itself?
First, and most important, it must give up the assurance that what 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 certainty 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, previously unknown to it, which are the result of their similar origin or similar functions, incomprehensible from the point of view of a plane.
Once the two-dimensional being has admitted the possibility of the existence of hitherto unknown common properties of objects which previously seemed different, then it has already approached to our own three-dimensional understanding of the world. It has approached to our 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 also common, will it be possible for it to advance further, to develop mentally, to approach the human understanding of the world.
Take that the most simple sentence: John and Peter are both men.
For the two-dimensional being this will be an absurdity, and it will represent the idea to itself after this fashion: John and Peter are both Johns and Peters.
In other words, every one of our logical propositions will be an absurdity to the two-dimensional being. Why this is so is clear. Such a being has no concepts; the proper nouns which constitute its speech have no plurals. It is easy to understand that any plural of our speech will to it seem absurd.
First of all we must get rid of our assurance that what we see and sense 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 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 recognise 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 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 antithesis. 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.
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.
Duality is the condition of our knowledge of the phenomenal (three-dimensional) world; this is the instrument of our knowledge 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.
In order to comprehend the relations of things in three dimensions and the axioms of our logic, the two-dimensional being must renounce its "idol" the absolute singularity of objects which permits it to call them solely by their proper names.
In order to comprehend the world of many dimensions, we must renounce the idol of duality.
But the application of monism to practical thought meets the insurmountable 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 supra-logical relations in our language will seem absurdities, and can really only give hints at that which we wish to express.
Thus the formula,
Let us therefore reconcile ourselves to the fact that it is impossible to express supra-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: "A is All".
But this too 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 is to this that we must accustom our thought, and train it along these lines.
Then, beginning to understand all this, we shall grasp the separate ideas concerning the essentials of the "noumenal world", the world of many dimensions in which we really live.
In such case the higher logic, even with its imperfect formulae 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.
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 is impossible to express; it is possible only to 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 can very often be expressed only by means of paradox, or even in the form of a lie. 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?