Chapter XXI (part 1)

p. 254 CHAPTER XXI Man's transition to a higher logic. The necessity for rejecting everything "real." "Poverty of the spirit." The recognition of the infinite alone as real. Laws of the infinite. Logic of the finite—the Organon of Aristotle and the Novum Organum of Bacon. Logic of the infinite— Tertium Organum . The higher logic as an instrument of thought, as a key to the mysteries of nature, to the hidden side of life, to the world of noumena. A definition of the world of noumena on the basis of all the foregoing. The impression of the noumenal world on an unprepared consciousness. "The thrice unknown darkness in the contemplation of which all knowledge is re-solved into ignorance." 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. p. 255 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.