it was not till they had first added a religious to the purely speculative element, which they at last introduced to such an extent, that they charged each the other with having committed the sin against the Holy Ghost! Newton and Leibnitz had neither the excuse nor the guilt of this superadded provocation.* However paradoxical apparently may be the phraseology of Leibnitz, in his first expositions of the Differential Calculus, respecting his infinitesimal quantities, (as, that there are quantities infinitely less than quantities infinitely little, and that of two quantities infinitely great, one may be infinitely greater than the other,) it is plain that he soon worked his own conceptions completely clear, and gave his abbreviated expressions their true interpretation. The explanations of Leibnitz are, in fact, often so perspicuous, * One other unjust statement of Dr. Guhrauer's, we cannot pass unnoticed. The unhappy controversy on the Calculus commenced, it is well known, by some slight skirmishes in the year 1699, when Fatio insinuated, that the applause which Leibnitz was receiving for his Differential Calculus, (first given to the world by him in 1684,) would be more justly bestowed on Newton-its first inventor. Dr. Guhrauer is pleased to intimate that Newton was privy to Fatio's attack, and prompted it. This is most unjust, as it is in express contradiction to Newton's assertion, that he knew nothing of Fatio's intention, and was no party to it. In several other places Dr. G. insinuates, that it is easy to see that Newton was behind the curtain in the early attacks on Leibnitz (vol. i. p. 303.), though he did not choose to appear in the controversy himself. Whether it was wise or not in Newton to stand so long aloof-whether it was in sullen pride or real magnanimity -from confidence in his claims, or dislike of controversy-certain it is, that, during all the earlier stages of the dispute, he remained silent; and being so, no man has a right to charge on him, without explicit evidence, the language of his adherents, whose just pride in the reputation of their countryman is quite sufficient to account both for the rashness of their zeal, and the intemperance of their expressions. that they ought to have satisfied every objector; and to have prevented the elegant and ingenious nonsense which Bishop Berkeley ventured upon, in regard to them, more than thirty years after, in his 'Analyst.' Thus, among many other places, in an explanatory letter to M. Varignon, in 1701, Leibnitz says:— 'Je ne me souviens pas assez des expressions dont je puis m'être servi; mais mon dessein a été de marquer qu'on n'a pas besoin de faire dépendre l'analyse mathématique des controverses métaphysiques, ni d'assurer qu'il y a dans la nature des lignes infiniment petites à la rigueur, en comparaison des nôtres, ni par conséquent qu'il y a des lignes infiniment plus grandes que les nôtres. C'est pourquoi afin d'éviter ces subtilités j'ai crû que pour rendre le raisonnement sensible à tout le monde, il suffisait d'expliquer ici l'infini par l'incomparable, c'est-à-dire, de concevoir des quantités incomparablement plus grandes ou plus petites que les nôtres; ce qui fournit autant qu'on veut de dégrés d'incomparables, puisque ce qui est incomparablement plus petit, entre inutilement en ligne de compte à l'égard de celui qui est incomparablement plus grand que lui. C'est ainsi qu'une parcelle de matière magnétique, qui passe à travers du verre, n'est pas comparable avec un grain de sable, ni ce grain avec le globe de la terre, ni ce globe avec le firmament.' Dr. Guhrauer is very severe on the 'narrowness of mind' implied in Newton's concealing his Fluxions under ciphers, in his correspondence with Leibnitz; and contrasts it with the frank and manly conduct of the latter, when, in his reply to Newton's second letter, he communicated the principles of his Calculus to his rival. It ought, at all events, to reconcile Dr. Guhrauer to Newton's procedure, that it formed, in fact, the safeguard of Leibnitz's claims; for had Newton disclosed his secret, it would have been impossible to establish them. We must here conclude, though we could have wished to add a few observations on several other matters;-on Leibnitz's religious opinions*, and theological controversies-especially with Clarke, Bossuet, and Pelisson, -on his political and diplomatic life, in which, with his accustomed versatility, he seems to have been as much at his ease as in literature and science †, -on the influence he exerted on Literature * Of Leibnitz's reputed adoption of the doctrines of Romanism, we have said nothing. It is certain that if he adopted he never avowed them, nor did he ever join the Romish communion. If the unfinished manuscript, called the Systema Theologicum,' (not so entitled by him,) really expresses his views, it is, as Dr. Guhrauer observes, in opposition to all his other writings, and to his whole life also.' Dr. Guhrauer's remarks on its origin and purport may be found in vol. ii. pp. 32–34. He also treats the whole question of Leibnitz's opinions on this subject very ably in vol. i. pp. 340-358. It is at the same time certain, that Leibnitz's tolerant temper, the eclecticism of his philosophy, - which always disposed him to find points of reconciliation in opposing systems, whether those of Aristotle and Descartes, or of Rome and Luther, his reverence for antiquity, cherished by his profound historical researches-all predisposed him to regard the differences between Romanists and Protestants as far less important than they are. In the attempt to negotiate a reconciliation between them, he expended no small portion of his time and energies; and, in his controversy with Bossuet, he sometimes makes far too liberal concessions for that object. It is not a little curious, and highly characteristic, that he always flattered himself that he was in possession of a metaphysical solution of the doctrine of Transubstantiation. In this instance, at least, he verified a naïve assertion he was accustomed to make respecting himself, 'That to him, unlike the generality of people, all difficult things were easy, and all easy things difficult.' † Of this, a proof rendered more especially remarkable by long subsequent events, is furnished in a Memorial addressed by him to Louis XIV., proposing that memorable plan for keeping some of the chief nations of Europe in check, which Buonaparte afterwards attempted to realise; namely, the conquest and colonisa as the centre of all the literary commerce of the age an influence which Mr. Stewart has so justly ap preciated, and finely illustrated, in his well-known 'Dissertation.' But on all these topics our space compels us to be silent, while on others we gladly content ourselves with referring to the admirable criticisms of the last-mentioned writer, and his other illustrious coadjutors, Sir James Mackintosh and Professor Playfair, in their associated Dissertations on the History of Metaphysical, Ethical, Mathematical, and Physical Science. In each of these, Leibnitz is made, so to speak, to re-enter; for while few other names appear in more than one of them, he is of sufficient importance to be subjected to a fresh examination in all. So various, indeed, are the phases of his character and genius, so numberless his accomplishments, that we may apply to him the well-known lines. of Dryden, divested of the satire which was designed in their original application ́ A man so various that he seem'd to be tion of Egypt. Of this posthumous piece, an English translation was published in London, in 1803, which seems now entirely forgotten. * Prefixed to the seventh edition of the Encyclopædia Britannica. 234 GENIUS AND WRITINGS OF PASCAL.* So much has been written of late years respecting Pascal, and so much that is worth reading, that we should scarcely have been induced to make him the subject of present criticism, had it not been for the appearance of the remarkable volumes of M. Faugère. It seems strange to say, that the most popular work of an author who has been dead nearly two hundred years, and who has obtained a world-wide reputation * 'Edinburgh Review,' Jan. 1847. 1. Des Pensées de Pascal. Rapport à l'Académie Française sur la nécessité d'une nouvelle édition de cet ouvrage. Par M. V. COUSIN. 8vo. Paris: 1843. 2. Pensées, Fragments, et Lettres de Blaise Pascal: publiés pour la première fois conformément aux manuscrits originaux, en grande partie inédits. Par M. PROSPER FAUGÈRE. 2 vols. 8vo. Paris: 1844. The greater [This essay has been twice translated into French. part of it first appeared in the 'Révue Britannique,' the conductors of which have conferred a similar honour on several others contained in these volumes. M. Faugère, the editor of the 'Pensées,' having, as he thought, and not unreasonably, ground for complaint at the omission of certain passages, in which his labours had been applauded, published a new translation of the whole. As far as the author is able to judge, it is an admirable specimen of skill and fidelity in the very difficult operation of intellectual transfusion. It may be as well also to mention, that, since the appearance of the present essay, an entirely new translation of nearly the whole of Pascal's writings-all, in fact, except his strictly scientific writings-has been published by G. Pearce, Esq.] |