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After this strong and explicit assertion of the priority of Aristotle's claim to the opinion which we are here told philosophers begin very generally to adopt,” it is to be hoped, that M. De Gerando will be in future allowed to enjoy the undisputed honour of having seen a little farther into this fundamental article of logic than the Stagirite himself.

of antiquity, whose opinions, when they are stated in any terms but his own, are to be received with so great distrust.

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chanism, may render the operations of reason steady and visible, and, in their effects on the minds of others, irresistible."*

And after which he proceeds thus : “Our common algebra, which we justly value so highly, is no more than a branch of that general art which I have here in view. But, such as it is, it puts it out of our power to commit an error, even although we should wish to do 80; while it exhibits truth to our eyes like a picture stamped on paper by means of a machine. It must at the same time be recollected, that algebra is indebted for whatever it accomplishes in the demonstration of general theorems to the suggestions of a higher science; a science which I I have been accustomed to call characteristical combination; very different, however, in its nature from that which these words are likely, at first, to suggest to the hearer. The marvellous utility of this art I hope to illustrate, both by precepts and examples, if I shall be so fortunate as to enjoy health and leisure.

“ It is impossible for me to convey an adequate idea of it in a short description. But this I may venture to assert, that no instrument (or organ) could easily be imagined of a more powerful efficacy for promoting the improvement of the human understanding ; and that, supposing it to be adopted, as the common method of philosophizing, the time would very soon arrive, when we should be able to form conclusions concerning God and the Mind, with not less certainty than we do at present concerning figures and numbers.R”

*“Quod velut mechanica ratione fixam et visibilem et (ut ita dicam) irresistibilem reddat rationem."

+ Wallisii Opera, Vol. III. p. 627.

The following passage is translated from another letter of Leibnitz to the same correspondent :

“The matter in question depends on another of much higher moment; I mean, on a general and true art of combination, of the extensive influence of which I do not know that any person has yet been fully aware. This, in truth, does not differ from that sublime analysis, into the recesses of which Des Cartes himself, as far as I can judge, was not able to penetrate. But, in order to carry it into execution, an alphabet of human thoughts must be previously formed ; and for the invention of this alphabet, an analysis of axioms is indispensably necessary. I am not, however, surprised, that nobody has yet sufficiently considered it ; for we are, in general, apt to neglect what is easy; and to take many things for granted, from their apparent evidence ; faults, while they remain uncorrected, will for ever prevent us from reaching the summit of things intellectual, by the aid of a calculas adapted to moral as well as to mathematical science."*

In these extracts from Leibnitz, as well as in that quoted from Condillac, in the beginning of this article, the èssential distinction between mathematics and the other sci

* Wallisii Opera, Vol. III. p. 633. As these reveries of this truly great man are closely connected with the subsequent history of logical speculation in more than one country of Europe, I have been induced to incorporate them, in an English version, with my own disquisitions. Some expressions, which, I am sensible, are not altogether agreeable to the idiom of our language, might have been easily avoided, if I had not felt it incumbent on me, in translating an author whose meaning, in this instance, I was able but very imperfectly to comprehend, to deviate as little as possible from his own words.

ences, in point of phraseology, is entirely overlooked. In the former science, where the use of an ambiguous word is impossible, it may be easily conceived how the solution of a problem may be reduced to something resembling the operation of a mill, the conditions of the problem, when once translated from the common language into that of algebra, disappearing entirely from the view; and the subsequent process being almost mechanically regulated by general rules, till the final result is obtained. In the latter the nhole of the words about which our reasonings are conversant, admit, more or less, of different shades of meaning; and it is only by considering attentively the relation in which they stand to the immediate context, that the precise idea of the author in any particular instance is to be ascertained. In these sciences, accordingly, the constant and unremitting exercise of the attention is indispensably necessary, to prevent us, at every step of our progress, from going astray.

On this subject I have made various remarks in a volume lately published ; to which I beg leave here to refer, in order to save the trouble of unnecessary repetitions. * From what I have there said, I trust it appears that, in following any train of reasoning, beyond the circle of the mathematical sciences, the mind must necessarily carry on along with the logical deduction expressed in words, another logical process of a far nicer and more difficult nature ;-that of fixing, with a rapidity which escapes our memory, the precise sense of every word which is ambiguous, by the relation in which it stands to the general

Philosophical Essays, p. 153. et seq.

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