sophisticating it, as Wolf did, by the vain attempt of deducing the first principles of geometry from supposed deeper grounds of ontology, it behoved the metaphysician rather to examine whether the only province of knowledge, which man has succeeded in erecting into a pure science, might not furnish materials, or at least hints, for establishing and pacifying the unsettled, warring, and embroiled domain of philosophy. An imitation of the mathematical method had indeed been attempted with no better success than attended the essay of David to wear the armour of Saul. Another use however is possible and of far greater promise, namely, the actual application of the positions which had so wonderfully enlarged the discoveries of geometry, mutatis mutandis, to philosophical subjects. Kant having briefly illustrated the utility of such an attempt in the questions of space, motion, and infinitely small quantities, as employed by the mathematician, proceeds to the idea of negative quantities and the transfer of them to metaphysical investigation. Opposites, he well observes, are of two kinds, either logical, that is, such as are absolutely incompatible; or real, without being contradictory. The former he denominates Nihil negativum irrepraesentabile, the connection of which produces nonsense. A body in motion is something-- Aliquid cogitabile; but a body, at one and the same time in motion and not in motion, is nothing, or, at most, air articulated into nonsense. But a motory force of a body in one direction, and an equal force of the same body in an opposite direction is not incompatible, and the result, namely, rest, is real and representable. For the purposes of mathematical calculus it is indifferent which force we term negative, and which positive, and consequently we appropriate the latter to that, which happens to be the principal object in our thoughts. Thus if a man's capital be ten and his debts eight, the subtraction will be the same, whether we call the capital negative debt, or the debt negative capital. But in as much as the latter stands practically in reference to the former, we of course represent the sum as 10-8. It is equally clear that two equal forces acting in opposite directions, both being finite and each distinguished from the other by its direction only, must neutralize or reduce each other to inaction. Now the transcendental philosophy demands; first, that two forces should be conceived which counteract each other by their essential nature; not only not in consequence of the accidental direction of each, but as prior to all direction, nay, as the primary forces from which the conditions of all possible directions are derivative and deducible: secondly, that these forces should be assumed to be both alike infinite, both alike indestructible. The problem will then be to discover the result or product of two such forces, as distinguished from the result of those forces which are finite, and derive their difference solely from the
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