Hence Number, so far from being the derivative of Time and Space, founds, at the bottom, in the self-definition and social recognition of intelligent beings, and so finds _a priori_ a valid expression in Time and in Space, as well as in every other primitive and spontaneous form in which intelligence utters itself. The Pythagorean doctrine of the rank of Number in the scale of realities is only one remove from the truth: though the numbers are indeed not the Prime Beings, they do enter into the essential nature of the Prime Beings; are, so to speak, the organ of their definite reality and identity, and for that reason go forward into the entire defining procedure by which these intelligences organize their world of experiences. And the popular impression that Time and Space are derivatives from Number, is in one aspect the truth, rather than the doctrine of Kant is; for though they are not mere generalizations and abstractions from numbered dates and durations, places and extents, they do exist as relating-principles which minds simply _put_, as the conditions _of perceptive experiences_; which by the nature of intelligence they must number in order to have and to master; while Number itself, the contrast of One and Many, enters into the very being of minds, and therefore still holds in Time and in Space, which are the organs, or _media_, not of the whole being of the mind, but only of that region of it constituted by sensation,--the material, the disjunct, the empirical. Besides, the logical priority of Number is implied in the fact that minds in putting Time and Space _a priori_ must count them as two, since they discriminate them with complete clearness, so that it is impossible to work up Space out of Time (as Berkeley and Stuart Mill so adroitly, but so vainly, attempted to do), or Time out of Space (as Hegel, with so little adroitness and such patent failure, attempted to do). No; there Time and Space stand, fixed and inconfusable, incapable of mutual transmutation, and thus the ground of an abiding difference between the inner or psychic sense-world and the outer or physical, between the subjective and the (sensibly) objective. By means of them, the world of minds discerns and bounds securely between the privacy of each and the publicity, the life "out of doors," which is common to all; between the cohering isolation of the individual and the communicating action of the society. Indeed, as from this attained point of view we can now clearly see, the real ground of the difference between Time and Space, and hence between subjective perception and the objective existence of physical things, is in the fact that a mind, in _being_ such,--in its very act of self-definition,--correlates itself with a _society_ of minds, and so, to fulfill its nature, in so far as this includes a world of experiences, must form its experience socially as well as privately, and hence will put forth a condition of sensuous communication, as well as a