TERTIUM ORGANUM

THE THIRD CANON OF THOUGHT
A KEY TO THE ENIGMAS OF THE WORLD

And sware . . . that there should be time no longer.
Revelation 10: 6

That ye, being rooted and grounded in love, may be able to comprehend with all
saints what is the breadth, the length, the depth and the height.
St Paul's Epistle to the Ephesians 3: 17, 18


CONTENTS

FOREWORD

CHAPTER 1 What do we know and what do we not know? Our known data and our unknown data. Unknown quantities taken as known quantities. Matter and motion. What does positivist philosophyarrive at? Identity of the unknown quantities: x = y, y = x. What do we actually know? The existence of consciousness in us and of the world outside us. Dualism or monism? Subjective and objective cognition. Where do the causes of sensations lie? Kant's system. Time and space. Mach's observation. What the physicist actually works with.

CHAPTER 2 A new view of Kant's problem. Hinton's books. 'Space-sense' and its evolution. A system for developing the sense of the fourth dimension by means of exercises with different coloured cubes. The geometrical concept of space. Three perpendiculars. Why are there only three? Can everything existing be measured by three perpendiculars? Physical and metaphysical facts. Signs of existence. The reality of ideas. The insufficient evidence of the existence of matter and motion. Matter and motion are only logical concepts, like 'good' and 'evil'.

CHAPTER 3 What can we learn about the fourth dimension by studying geometrical relationships within our space? What should be the relationship of a three-dimensional body to a fourdimensional one? A four-dimensional body as the trace of the movement of a three-dimensional body in a direction not contained in it. A four-dimensional body as composed of an infinite number of three-dimensional bodies. A three-dimensional body as a section of a four-dimensional one. Parts of bodies and whole bodies in three and in four dimensions. Incommensurability of a three-dimensional and a fourdimensional body. A material atom as a section of a fourdimensional line.

CHAPTER 4 In what direction may the fourth dimension lie? What is motion? Two kinds of movement - movement in space and movement in time -contained in every motion. What is time? Present past and future. Wundt on sense-cognition. Groping through life. Why we do not see the past and the future. A new extension in space and motion in that space. Two ideas contained in the concept of time. Time as the fourth dimension of space. Impossibility of understanding the idea of the fourth dimension without the idea of motion. The idea of motion and 'time-sense'. 'Time-sense' as the limit (surface) of space sense. Riemann's idea of the translation of time into space in the fourth dimension. Hinton on
the law of surfaces. 'Ether' as a surface.

CHAPTER 5 Four-dimensional space. 'Time-body' -Linga Sharira. Form of the human body from birth to death. Incommensurability of a three-dimensional and a four-dimensional body. Newton's fluents. Unreality of constant magnitudes in our world. Right and left hand in three-dimensional and a four-dimensional space. Differences between three-dimensional and fourdimensional space. Not two different spaces, but two different modes of perception of one and the same world.

CHAPTER 6 Methods of investigating the problem of higher dimensions. Analogy between imaginary worlds of different dimensions. One-dimensional world on a line. 'Space' and 'time' of a onedimensional being. Two-dimensional world on a plane. 'Space' and 'time', 'ether', 'matter' and 'motion' of a two-dimensional being. Reality and illusion on a plane. Impossibility of seeing an'angle'. An 'angle' as motion. Incomprehensibility, for a twodimensional being of the functions of the objects of our world. Phenomena and noumena of a two-dimensional being. How could a plane being understand the third dimension?

CHAPTER 7 Impossibility of a mathematical definition of dimensions. Whydoes mathematics not feel dimensions? The entirely conventional character of the designation of dimensions by powers. The possibility of representing all the powers on a line. Kant and Lobachevsky. The difference between non-Euclidean geometry and metageometry. Where should we seek the explanation of the three-dimensionality of the world, if Kant's ideas are correct? Are not the three-dimensional conditions of the world to be found in our perceiving apparatus, in our mind?

CHAPTER 8 Our perceiving apparatus. Sensation. Representation Concept.Art as the language of the future. To what extent does the threedimensionality of the world depend on the properties of our perceiving apparatus? What could prove this dependence? Where could we find a real confirmation of this dependence? Psychology of animals. In what does it differ from the human? Reflex. Irritability of the cell. Instinct. Pleasure - pain. Emotional thinking. Absence of concepts. Language of animals. Logic of animals. Different levels of intelligence in animals. The goose, the cat, the dog and the monkey.

CHAPTER 9 Perception of the world by man and by animals. Illusions of animals and their lack of control over perceptions. A world of moving planes. Angles and curves as motion. Third dimension as motion. The two-dimensional appearance, for animals, of our three-dimensional world. Animals as real two-dimensional beings. Lower animals as one-dimensional beings. Time and space of a snail. Time-sense as a nebulous spacesense. Time and space of a dog. Change of the world with a change of the mental apparatus. Proof of Kant's problem. Three-dimensional world as an illusory representation.

CHAPTER 10 Spatial understanding of time. Four-dimensional angles and curves in our life. Does motion exist in the world or not? Mechanical motion and 'life'. Biological phenomena as manifestations of motion proceeding in higher space. Evolution of space-sense. Growth of space-sense and diminution of timesense. Translation of time-sense into space-sense. Handicaps presented by our concepts, our language. The need to find a method of expressing time-concepts spatially. Science on the fourth dimension. A four-dimensional body. Four-dimensional sphere.

CHAPTER 11 Science and the problem of the fourth dimension. Paper read by Professor N. A. Oumoff at the Mendeleev Convention in 1911, 'The Characteristic Features and Problems of Contemporary Natural-scientific Thought*. New physics. Electro-magnetic theory. Principles of relativity. The works of Einstein and Minkowsky. Simultaneous existence of the past and the future. The eternal Now. Van Manen's book on occult experiences. Diagram of a four-dimensional figure.

CHAPTER 12 Analysis of phenomena. What determines for us different orders of phenomena? Methods and forms of the transition of phenomena of one order into another. Phenomena of motion. Phenomena of life. Phenomena of consciousness. The central question of our perception of the world: which kind of phenomena is primary and produces the others? Can motion lie at the beginning of everything? Laws of the transformation of energy. Simple transformation and the liberation of latent energy. Different liberating forces of different kinds of phenomena. The force of mechanical energy, the force of a living cell and the force of an idea. Phenomena and noumena of our world.

CHAPTER 13 The apparent and the hidden side of life. Positivism as the study of the phenomenal aspect of life. What constitutes the 'two-dimensionality' of positivist philosophy? Envisaging everything on one plane, in one physical sequence. Streams flowing under the earth. What can the study of life, as a phenomenon, give? The artificial world which science builds for itself. The non-existence, in actual fact, of completed and isolated phenomena. A new sense of the world.

CHAPTER 14 The voices of stones. The wall of a church and the wall of a prison. The mast of a ship and a gallows. The shadow of a hangman and the shadow of a saint. The soul of a hangman and the soul of a saint. The different combinations of phenomena known to us in higher space. The connectedness of phenomena which seem to us separate, and the difference between phenomena which appear to be similar. How should we approach the noumenal world? The understanding of things outside the categories of time and space. The reality of a great many 'figures of speech'. The occult understanding of energy. The letter of a Hindu occultist. Art as the cognition of the noumenal world. What we see and what we do not see. Plato's dialogue about the cave.

CHAPTER 15 Occultism and love. Love and death. Different attitudes to problems of death and problems of love. What is lacking in our understanding of love? Love as an everyday and a psychological phenomenon. Possibility of a religious understanding of love. The creative force of love. The negation of love. Running away from love. Love and mysticism. The 'miraculous' in love. Nietzsche and Edward Carpenter on love.

CHAPTER 16 The phenomenal and the noumenal side of man. 'Man in himself.' How do we know the inner side of man? Can we know of the existence of consciousness in conditions of space not analogous to ours? Brain and consciousness. Unity of the world. Logical impossibility of a simultaneous existence of
spirit and matter. Either all is spirit or all is matter. Rational and irrational actions in nature and in man's life. Can rational actions exist side by side with irrational? The world as an accidentally produced mechanical toy. The impossibility of consciousness in a mechanical universe. The impossibility of mechanicalness if consciousness exists. The fact of human consciousness interfering with the mechanical system. The consciousness of other cross-sections of the world. How can we know about them? Kant on 'spirits'. Spinoza on the cognition of the invisible world. Necessity for the intellectual definition of what is possible and what is impossible in the noumenal world.

CHAPTER 17 A living and intelligent universe. Different forms and lines of intelligence. Animated nature. Souls of stones and souls of trees. The soul of a forest. The human 'I' as a collective intelligence. Man as a complex being. 'Mankind' as a being. The soul of the world. The face of Mahadeva. Professor James on the animated world. Fechner's ideas. Zendavesta. The living Earth.

CHAPTER 18 Intelligence and life. Life and knowledge. Intellect and emotions. Emotion as an instrument of knowledge. The evolution of emotions from the standpoint of knowledge. Pure and impure emotions. Personal and super-personal emotions. The elimination of self-element as a means of approach to true knowledge. 'Be as little children. . . .' 'Blessed are the pure in heart. . . .' The value of morality from the standpoint of knowledge. The defects of intellectualism 'Dreadnoughts' as the crown of intellectual culture. The dangers of moralism. Moral aestheticism. Religion and art as organized forms of emotional knowledge. The knowledge of GOD and the knowledge of BEAUTY.

CHAPTER 19 The intellectual method. Objective knowledge. The limits of objective knowledge. Possibility of expanding knowledge by the application of the psychological method. New forms of knowledge. The ideas of Plotinus. Different forms of consciousness. Steep (potential state of consciousness). Dreams (consciousness enclosed within itself, reflected from itself). Waking consciousness (dualistic sensation of the world). Ecstasy ('going out of oneself). 'Turiya' (the absolute consciousness of all as of oneself). 'The drop absorbing the ocean.' 'Nirvana.'

CHAPTER 20 The sensation of infinity. The first test of a Neophyte. Intolerable sadness. Loss of everything real. What would an animal experience on becoming a man? Transition to a new logic. Our logic as based on the observation of laws of the phenomenal world. Its unsuitability for the study of the noumenal world. The need of a new logic. Analogous axioms in logic and mathematics. TWO MATHEMATICS. The mathematics of real magnitudes (infinite and variable); and mathematics of unreal imaginary magnitudes (finite and constant). Transfinite numbers - numbers lying BEYOND INFINITY. The possibility of different infinities.

CHAPTER 21 Necessity of abandoning our phenomenal logic for a noumenal approach. Science must recognize that only through poetry and mysticism do we approach the world of causes. Preparation through faith and love are necessary to overcome the terror of infinity. The real meaning of 'Poor in spirit'. The Organon of Aristotle, the Novum Organum of Bacon and Tertium Organum which, though often forgotten, existed before the others and is a key to the hidden side of life. Necessity of discarding our twodimensional 'idols' and attempting to enumerate the properties of the world of causes.

CHAPTER 22 'Theosophy' of Max Müller. Ancient India. Philosophy of the Vedânta. Tat tvam asi. Perception by expanded consciousness as a reality. Mysticism of different ages and peoples. Similarity of experiences. Tertium Organum as a key to mysticism. Signsof the noumenal world. Treatise of Plotinus. 'On IntelligibleBeauty' as a system of higher logic which is not understood. Illumination of Jacob Boehme. 'A harp of many strings, of which each string is a separate instrument, while the whole is only one harp.' Mysticism of the Philokalia, St Avva Dorotheus and others. Clement of Alexandria. Lao-Tzu and Chuang-Tzu. Light on the Path and The Voice of the Silence. Mohammedan mystics. Poetry of the Sufis. Mystical states under narcotics. The Anaesthetic Revelation. Professor James's experiments. Dostoyevsky on 'time' (The Idiot). Influence of nature on the soul of man.

CHAPTER 23 Cosmic Consciousness of Dr Bucke. The three forms of consciousness according to Bucke. Simple consciousness, or the consciousness of animals. Self-consciousness, or the consciousness of men. Cosmic consciousness. In what is it expressed? Sensation, representation, concept, higher MORAL concept -creative understanding. Men of cosmic consciousness. The fall of Adam. The knowledge of good and evil. Christ and the salvation of man. Comments on Dr Bucke's book. Birth of the new humanity. Two races. SUPERMAN. TABLE OF
THE FOUR FORMS OF MANIFESTATION OF CONSCIOUSNESS.

CONCLUSION




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