Chapter XXI (part 5)

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 . p. 262 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: A is both A and Not-A . or Everything is both A and Not-A . or, Everything is All . 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.