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refert, modo meminerimus, per solam Virium notionem intelligibiliter explicari."
DES CARTES, speaking as a naturalist, and in imitation of Ar.. chimedes, said, give me matter and motion, and I will construct you the universe. We must of course understand him to have meant; I will render the construction of the universe intelligible. In the same sense the transcendental philosopher says; grant me a nature having two contrary forces, the one of which tends to expand infinitely, while the other strives to apprehend or find itself in this infinity, and I will cause the world of intelligences with the whole system of their representations to rise up before you. Every other science pre-supposes intelligence as already existing and complete: the philosopher contemplates it in its growth, and as it were represents its history to the mind from its birth to its maturity.
2 Leibnitz. Op T. ii., P. ii., p. 53.-T. iii., p. 321.
[The first sentence of this quotation is from the treatise of Leibnitz De Ipsa Natura, sive de Vi insita Actionibusque creaturarum, § 8, ed. Erdmann. P. i., p. 157:-the second is from his Specimen Dynamicum, pro admirandis Naturæ legibus circa corporum Vires, et mutuas Actiones detegendis et ad suas causas revocandis. Ex Actis Erudit., Lips., ann. 1695. In the second extract, Mr. C. has substituted the word phantasiæ for imaginationi, and, in the beginning of the last sentence, rerum for formam. He quoted from the edition of Lud. Dutens, a Frenchman resident in Britain, as I learn from Erdmann's Preface, in which it is mentioned that neither his collection nor that of Raspe, who added posthumous, works of Leibnitz, contains all his philosophical writings, and that both the one and the other frustro a bibliopolis quæres, imo in publicis bibliothecis desiderabis. The former however is at the British Museum, presented by himself in 1800. The new edition comprehends only the philosophical works, the Specimen Dynamicum is classed among the mathematical,but, as Erdmann himself observes, it is often very difficult to judge utrum scriptio aliqua philosophicæ indolis sit an non sit. See Appendix S. S.C.] 3 Synesii Episcop. Hymn. iii., l. 231.
[This first paragraph of Chap. xiii., with the exception of the second sentence, is freely translated from Transsc. Id. first § of Section C., p. 147 S. C.]
The venerable sage of Koenigsburg has preceded the march of this master-thought as an effective pioneer in his essay on the introduction of negative quantities into philosophy, published 1763. In this he has shown, that instead of assailing the science of mathematics by metaphysics, as Berkeley did in his ANALYST," or of 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 armor of Saul. Another use however is possible and of fär
[Versuch den Begriff der negativen Grössen in die Weltweisheit einzuführen. An attempt towards introducing the idea of negative magnitudes into philosophy, 1763. Works, vol. i., p. 19. S C.]
[The Analyst was published soon after Berkeley's promotion to the see of Cloyne, March 17, 1734. It is said that the Bishop addressed it to Dr. Halley on learning from Mr Addison that he who dealt so much in demonstration," had brought Dr. Garth into a state of general scepticism or even unbelief on religious subjects, as appeared in the latter's last illness. It's whole title is "The Analyst; or, a Discourse addressed to an infidel Mathematician: wherein it is examined whether the object, principles and inferences of the modern Analysis are more distinctly conceived, or more evidently deduced, than religious mysteries and points of faith." He endeavored to show that the doctrine of fluxions furnished a strong example of mathematical uncertainty and fallacy.]
7 [Cousin represents Wolf as having improved the Leibnitzian philoso. phy by qualifying it in some directions and filling it up in others. He seems to consider his mathematical method as at once his strength and his weakness-for he says-" Son mérite principal consiste dans l'unité, la solidité, et l'enchainement systématique qu'il sut donner à tout l'ensemble à l'aide de la méthode appelée mathématique, méthode qui, selon lui, n'étoit autre chose que l'application la plus parfaite des lois du raisonnement." Then after enumerating the defects of his philosophy he sums them up thus-“ Enfin” il “négligea la distinction des caractères propres qui séparent la philosophie et les mathématiques dans leur forme et leur matière." (Manuel., vol. ii., 175-6.) I suppose that no man before Kant's day had seen this distinction so clearly, and laid it down so determinately, did the sage of Koenigsburg. S. C.]
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 irrepræsentabile, the connexion of which produces nonsense. A body in notion 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. 10 Now the transcendental philosophy demands; first,
[Kant says in his Preface to the Versuch already referred to. ase which may be made of mathematics in philosophy consists either in an imitation of the method or in the real application of their positions to the objects of philosophy." He shows the ill success of the former attempt, and that the troublesome non liquet would not yield to all this pomp of demonstration. S. C.]
9 [Ibid., 1. Absch., Works I., 25-33. Mr. C. repeats the teaching of the Versuch, in language of his own, till he comes to the application, “It is equally clear," &c. S. C.]
10 [The reader may compare the rest of the paragraph and the following one with the doctrine of the Transse. Id., especially the section entitled
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 circumstance of their direction. When we have formed a scheme or outline of these two different kinds of force, and of their different results by the process of discursive reasoning, it will then remain for us to elevate the thesis from notional to actual, by contemplating intuitively this one power with its two inherent indestructible yet counteracting forces, and the results or generations to which their inter-penetration gives existence, in the living principle and in the process of our own self-consciousness. By what instrument this is possible the solution itself will discover, at the same time that it will reveal to and for whom it is possible. Non omnia possumus omnes. There is a philosophic, no less than a poetic genius, which is differenced from the highest perfection of talent, not by degree but by kind.
The counteraction then of the two assumed forces does not depend on their meeting from opposite directions; the power which acts in them is indestructible; it is therefore inexhaustibly re-ebullient; and as something must be the result of these two forces, both alike infinite, and both alike indestructible; and as rest or neutralization cannot be this result; no other conception is possible, but that the product must be a tertium aliquid, or finite generation. Consequently this conception is necessary Now this tertium aliquid can be no other than an inter-penetration of the counteracting powers, partaking of both
Thus far had the work been transcribed for the press, when I received the following letter from a friend, whose practical judg
Deduction der productiven Anschauung, pp. 156-185. But the sentences of the B. L. are not the same with those of Schelling, nor is the applica tion of the analogy suggested by Kant made in the Transsc. Id. S. C.]
ment I have had ample reason to estimate and revere, and whose taste and sensibility preclude all the excuses which my self-love might possibly have prompted me to set up in plea against the decision of advisers of equal good se se, but with less tact and feeling.
"You ask my opinion concerning your Chapter on the Imagination, both as to the impressions it made on myself, and as to those which I think it will make on the Public, i. e. that part of the public, who, from the title of the work and from its forming a sort of introduction to a volume of poems, are likely to constitute the great majority of your readers.
"As to myself, and stating in the first place the effect on my understanding, your opinions and method of argument were not only so new to me, but so directly the reverse of all I had ever been accustomed to consider as truth, that even if I had comprehended your premises sufficiently to have admitted them, and had seen the necessity of your conclusions, I should still have been in that state of mind, which in your note on Chap. IV., you have so ingeniously evolved, as the antithesis to that in which a man is, when he makes a bull. In your own words, I should have felt as if I had been standing on my head.
The effect on my feelings, on the other hand, I cannot better represent, than by supposing myself to have known only our light airy modern chapels of ease, and then for the first time to have been placed, and left alone, in one of our largest Gothic cathedrals in a gusty moonlight night of autumn. Now in glimmer, and now in gloom;' often in palpable darkness not without a chilly sensation of terror; then suddenly emerging into broad yet visionary lights with colored shadows of fantastic shapes, yet all decked with holy insignia and mystic symbols; and ever and anon coming out full upon pictures and stone-work images of great men, with whose names I was familiar, but which looked upon me with countenances and an expression, the most dissimilar to all I had been in the habit of connecting with those names. Those whom I had been taught to venerate as almost super-human in magnitude of intellect, I found perched in little