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Such also is the problem of the infinite divisibility of matter, which, as Kant has shown, can be denied and affirmed successively by arguments equally plausible and irrefutable. Antinomy simply expresses a fact, and forces itself imperatively on the mind; contradiction, properly speaking, is an absurdity.
The free divisibility of the soil always involved the risk of an insolvent agricultural proletariate; and under such circumstances, when all burdens were increasing and all means of deliverance were foreclosed, distress and despair could not but spread with fearful rapidity among the agricultural middle class. Relations of the Social Question to the Question between Orders
Those foolish persons who deify all rather than admit a God recoil before the infinite divisibility of matter which is in the nature of imponderable forces. Locke and Condillac retarded by fifty years the immense progress which natural science is now making under the great principle of unity due to Geoffroy de Saint-Hilaire.
For in order to form a just notion of these animals, we must have a distinct idea representing every part of them, which, according to the system of infinite divisibility, is utterly impossible, and, recording to that of indivisible parts or atoms, is extremely difficult, by reason of the vast number and multiplicity of these parts.
So that, as modern physics and optics have enabled us not to conceive merely, but to actually realize, the vastness of spatial extension, side by side with subtile tenuity and extreme divisibility of matter, so the labor, enthusiasm, and perseverance of thirty years, stimulated by the insight of a rare and master mind, and aided by lenses of steadily advancing perfection, have enabled the student of life-forms not simply to become possessed of an inconceivably broader, deeper, and truer knowledge of the great world of visible life, of which he himself is a factor, but also to open up and penetrate into a world of minute living things so ultimately little that we cannot adequately conceive them, which are, nevertheless, perfect in their adaptations and wonderful in their histories.
The other important features of Edison's discovery relate to the divisibility of the current, and its control and regulation in volume by the operator. These matters were fully mastered in the Edison invention, and the apparatus rendered as completely subject to management as are the other varieties of illuminating agencies. It were vain to speculate upon the future of electric lighting.
Of this mutual complaisance I cannot give a more evident instance than in the doctrine of infinite divisibility, with the examination of which I shall begin this subject of the ideas of space and time.
But the question is to know whether a movement can be considered as a numerical multiplicity. Virtual divisibility there is, no doubt, but not actual division; divisibility is indefinite, whereas an actual division, if it respects the inner articulations of reality, is bound to halt at a limited number of phases.
And having no more reason to set bounds to those repeated ideas than we have to set bounds to number, we have that indeterminable idea of immensity. Infinite Divisibility.
The true answer to the statement of the Materialist, the answer which we feel in our hearts, on the very expression of the plurality and divisibility of feeling, is that it assumes what, far from admitting, we cannot even understand, and that, with every effort of attention which we can give to our mental analysis, we are as incapable of forming any conception of what is meant by the quarter of a doubt, or the half of a belief, as of forming to ourselves an image of a circle without a central point, or of a square without a single angle."
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