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… - Petr Uspensky

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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 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.