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deny myself the pleasure of enriching my book with a few of his observations.

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"It is the distinguishing characteristic of a lively and vigorous conception, to push its speculative conclusions somewhat beyond their just limits. Hence, in the logical discussions of this estima ble writer, these maxims (stated without any explanation or restriction,) That the study of a science is nothing more than the ac quisition of a language; and, that a science properly treated is only a language well contrived.' Hence the rash assertion, "That mathematics possess no advantage over other sciences, but what they derive from a better phraseology; and that all of these might attain to the same characters of simplicity and of certainty, if we knew how to give them signs equally perfect.'" (Des Signes et de l'Art de Penser, &c., Introd. pp. xx. xxi.)

"The same task which must have been executed by those who contributed to the first formation of a language, and which is exe cuted by every child when he learns to speak it, is repeated over in the mind of every adult when he makes use of his mother tongue; for it is only by the decomposition of his thoughts that he can learn to select the signs which he ought to employ, and to dispose them in a suitable order. Accordingly, those external actions which we call speaking or writing, are always accompanied with a philosophical process of the understanding, unless we content ourselves, as too often happens, with repeating over mechanically what has been said by others. It is in this respect that languages, with their forms and rules, conducting (so to speak) those who use them, into the path of a regular analysis; tracing out to them, in a well-ordered discourse, the model of a perfect decomposition, may be regarded in a certain sense, as analytical methods.-But I stop short: Condillac to whom this idea belongs, has developed it too well to leave any hope of improving upon his statement."

"In

In a note upon this passage, however, M. De Gerando has cer tainly improved not a little on the statement of Condillac. asserting," says he, "that languages may be regarded as analytical methods, I have added the qualifying phrase, in a certain sense, for the word method cannot be employed here with exact propriety. Languages furnish the occasions and the means of analysis; that is to say, they afford us assistance in following that method; but they are not the method itself. They resemble signals or finger-posts placed on a road to enable us to discover our way; aud if they help us to analyze, it is because they are themselves the results, and, as it were, the monuments of an analysis which has been previously made; nor do they contribute to keep us in the right path, but in proportion to the degree of judgment with which that analysis has been conducted." (Ibid. pp. 158, 159, Tom. i.)

I was the more solicitous to introduce these excellent remarks, as I suspect that I have myself indirectly contributed to propagate in this country the erroneous opinion which it is their object to

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 which, while they remain uncorrected, will forever prevent us from reaching the summit of things intellectual, by the aid of a calculus adapted to moral as well as to intellectual science." (Wallisii Opera, p. 633.)*

In these extracts from Leibnitz, as well as in that quoted from Condillac, in the beginning of this article, the essential distinction between mathematics and the other sciences, 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 whole 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. (Philosophical Essays, p. 153, et seq.) 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

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.

the logical deduction expressed in words, another logical process of a far nicer and more difficult nature;-that of fixing, with a ra pidity which escapes our memory, the precise sense of every word which is ambiguous by the relation in which it stands to the gener al scope of the argument. In proportion as the language of science becomes more and more exact, the difficulty of this task will be gradually diminished; but let the improvement be carried to any conceivable extent, not one step will have been gained in accelerat ing that era, so sanguinely anticipated by Leibnitz and Condillac, when our reasonings in morals and politics shall resemble, in their mechanical regularity, and in their demonstrative certainty, the investigations of algebra. The improvements which language re ceives, in consequence of the progress of knowledge, consisting rather in a more precise distinction and classification of the various meanings of words, than in a reduction of these meanings in point of number, the task of mental induction and interpretation may be rendered more easy and unerring; but the necessity of this task can never be superseded, till every word which we employ shall be as fixed and invariable in its signification as an algebraical character or as the name of a geometrical figure.

In the mean time, the intellectual superiority of one man abore another, in all the different branches of moral and political philo sophy, will be found to depend chiefly on the success with which he has cultivated these silent habits of inductive interpretationmuch more, in my opinion, than on his acquaintance with those rules which form the great objects of study to the professed logi cian. In proof of this, it is sufficient for me to remind my readers, that the whole theory of syllogism proceeds on the supposi tion that the same word is always to be employed precisely in the same sense, (for otherwise, the syllogism would be vitiated by con sisting of more than three terms;) and, consequently, it takes for granted, in every rule which it furnishes for the guidance of our reasoning powers, that the nicest and by far the most difficult part of the logical process has been previously brought to a successful termination.

In treating of a different question, I have elsewhere remarked, that although many authors have spoken of the wonderful mechan ism of speech, no one has hitherto attended to the far more won derful mechanism which it puts into action behind the scene. A similar observation will be found to apply to what is commonly called the art of reasoning. The scholastic precepts which profess to teach it, reach no deeper that the very surface of the subject; being all of them confined to than part of the intellectual process which is embodied in the form of verbal propositions. On the most favorable supposition which can be formed with respect to them, they are superfluous and nugatory; but, in many cases, it is to be apprehended, that they interfere with the right conduct of the understanding by withdrawing the attention from the cultivation

of that mental logic on which the soundness of our conclusions essentially depends, and in the study of which, although some general rules may be of use, every man must be, in a great measure, his own master.*

In the practical application of the foregoing conclusions, it can not fail to occur, as a consideration equally obvious, and important, that, in proportion as the objects of our reasoning are removed from the particular details with which our senses are conversant, the difficulty of these latent inductive processes must be increased. This is the real source of that incapacity for general speculation, which Mr. Hume has so well described as a distinguishing characteristic of uncultivated minds. "General reasonings seem intricate, merely because they are general; nor is it easy for the bulk of mankind to distinguish, in a great number of particulars, that common circumstance in which they all agree, or to extract it, pure and unmixed, from the other superfluous circumstances. Every judgment or conclusion with them is particular. They cannot enlarge their views to those universal propositions which comprehend under them an infinite number of individuals, and include a whole science in a single theorem. Their eye is confounded with such an extensive prospect, and the conclusions deduced from it, even though clearly expressed, seem intricate and obscure." (Essay on Commerce.)

Difficult, however, and even impossible as the task of general speculation is to the bulk of mankind, it is nevertheless true, that it is the path which leads the cautious and skillful reasoner to all his most certain, as well as most valuable conclusions in morals and in politics. If a theorist, indeed, should expect, that these conclusions are in every particular instance to be realized, he would totally misapprehend their nature and application; inasmuch as they are only to be brought to an experimental test, by viewing them on an extensive scale, and continuing our observations during a long period of time. "When a man deliberates," says Mr. Hume, "concerning his conduct in any particular affair, and forms schemes in politics, trade, economy, or any business in life, he never ought to draw his arguments too fine, or connect too long a chain of consequences together. Something is sure to happen that will disconcert his reasoning, and produce an event different from what he expected. But when we reason upon general subjects, one may justly affirm, that our speculations can scarcely ever be too fine, provided they be just; and that the difference between a common man and a man of genius is chiefly seen in the shallowness or depth of the principles on which they proceed." The same author afterwards excellently observes, "That general principles, however intricate they may seem, must always prevail, if they be just and

Those who are interested in this discussion, will enter more completely into my views, if they take the trouble to combine what is here stated with some observations I have introduced in the First Part, chap. iv. sec. 2.

the logical deduction expressed in words, another logical process of a far nicer and more difficult nature;-that of fixing, with a ra pidity which escapes our memory, the precise sense of every word which is ambiguous by the relation in which it stands to the gener al scope of the argument. In proportion as the language of sei ence becomes more and more exact, the difficulty of this task will be gradually diminished; but let the improvement be carried to any conceivable extent, not one step will have been gained in accelerat ing that era, so sanguinely anticipated by Leibnitz and Condillac, when our reasonings in morals and politics shall resemble, in their mechanical regularity, and in their demonstrative certainty, the investigations of algebra. The improvements which language re ceives, in consequence of the progress of knowledge, consisting rather in a more precise distinction and classification of the various meanings of words, than in a reduction of these meanings in point of number, the task of mental induction and interpretation may be rendered more easy and unerring; but the necessity of this task can never be superseded, till every word which we employ shall be as fixed and invariable in its signification as an algebraical character or as the name of a geometrical figure.

In the mean time, the intellectual superiority of one man above another, in all the different branches of moral and political philo sophy, will be found to depend chiefly on the success with which he has cultivated these silent habits of inductive interpretationmuch more, in my opinion, than on his acquaintance with those rules which form the great objects of study to the professed logi cian. In proof of this, it is sufficient for me to remind my read ers, that the whole theory of syllogism proceeds on the supposi tion that the same word is always to be employed precisely in the same sense, (for otherwise, the syllogism would be vitiated by con sisting of more than three terms;) and, consequently, it takes for granted, in every rule which it furnishes for the guidance of our reasoning powers, that the nicest and by far the most difficult part of the logical process has been previously brought to a successful termination.

In treating of a different question, I have elsewhere remarked, that although many authors have spoken of the wonderful mechan ism of speech, no one has hitherto attended to the far more won derful mechanism which it puts into action behind the scene. A similar observation will be found to apply to what is commonly called the art of reasoning. The scholastic precepts which profess to teach it, reach no deeper that the very surface of the subject; being all of them confined to than part of the intellectual process which is embodied in the form of verbal propositions. On the most favorable supposition which can be formed with respect to them, they are superfluous and nugatory; but, in many cases, it is to be apprehended, that they interfere with the right conduct of the nderstanding by withdrawing the attention from the cultivation

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