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Unfortunately the continuity of immobility consists in not moving; how therefore it is to produce motion remains more mysterious than ever. And however infinitely small the parts into which Herr Dühring minces his transition from complete non-motion to universal motion, and however long the duration he assigns to it, we have not got a ten-thousandth part of a millimetre further. Without an act of creation we can never get from nothing to something, even if the something were as small as a mathematical differential.

Contains within itself a contradiction, and in fact an absurd contradiction. It is clear that an infinity which has an end but no beginning is neither more nor less infinite than that which has a beginning but no end. The slightest dialectical insight should have told Herr Dühring that beginning and end necessarily belong together, like the north pole and the south pole, and that if the end is left out, the beginning just becomes the end -- the one end which the series has; and vice versa. The whole deception would be impossible but for the mathematical usage of working with infinite series.

And this was the first thing to be proved. -- With regard to the second, if the opposite is again assumed, then the world must be an infinite given total of co-existent things. htm (22 of 88) [23/08/2000 17:35:50] 1877: Anti-Duhring -- "Philosophy" certain limits of an intuition, in any other way than by means of the synthesis of its parts, and can conceive the total of such a quantum only by means of a completed synthesis, or by the repeated addition of a unit to itself. Accordingly, to conceive the world, which fills all spaces, as a whole, the successive synthesis of the parts of an infinite world would have to be looked upon as completed; that is, an infinite time would have to be regarded as elapsed in the enumeration of all co-existing things.

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