66

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 honor of having seen a little farther into this fundamental article of logic than the Stagirite himself.

III.

Continuation of the Subject.-Visionary Theories of some Logicians, occasioned by their Inattention to the Essential Distinction between Mathematics and other Sci

ences.

IN a passage already quoted from De Gerando, he takes notice of what he justly calls a rash assertion of Condillac," that mathematics possess no advantage over other sciences, but what they derive from a better phraseology; and that all of them might attain to the same characters of simplicity and of certainty, if we knew how to give them signs equally perfect."

Leibnitz seems to point at an idea of the same sort, in those obscure and enigmatical hints (not altogether worthy, in my opinion, of his powerful and comprehensive genius) which he has repeatedly thrown out, about the miracles to be effected by a new art of his own invention; to which art he sometimes gives the name of

well arranged.' The influence," I have added, " which these very enlightened and philosophical views have already had on the doctrines of chemistry, cannot fail to be known to most of my readers."

When this paragraph was first written, I was fully aware of the looseness and indistinctness of Lavoisier's expressions; but as my only object in introducing the quotation was to illustrate the influence of general logical principles on the progress of particular sciences, I did not think it necessary, in the introduction to my work, to point out in what manner Condillac's propositions were to be limited and corrected. I am truly happy, for the sake of M. De Gerando, that I happened to transcribe them in the same vague and very exceptionable terms in which I found them sanctioned by the names of Condillac, and of one of the most illustrious of his disciples. It will not, I hope, be considered as altogether foreign to the design of this note, if I remark further, how easy it is for a translator of Aristotle (in consequence of the unparalleled brevity which he sometimes affects) to accommodate the sense of the original, by the help of paraphrastical clauses, expressed in the phraseology of modern science, to every progressive step in the history of human knowledge. In truth, there is not one philosopher of antiquity, whose opinions, when they are stated in any terms but his own, are to be received with so great distrust.

The unsoundness of Condillac's assertion, that the art of reasoning is nothing more than a language well arranged, was, I believe, first pointed out by M. Prevost. See some acute and decisive objections to this proposition in his Treatise Des Signes, &c. Paris, An. VIII. p. 20.

VOL. II.

13

Ars Combinatoria Characteristica, and sometimes of Ars Combinatoria Generalis ac Vera. In one of his letters to Mr. Oldenburg, he speaks of a plan he had long been meditating, of treating of the science of mind by means of mathematical demonstrations. "Many wondeful things," he adds, "of this kind have occurred to me; which, at some future period, I shall explain to the public with that logical precision which the subject requires."* In the same letter, he intimates his belief in the possibility of inventing an art, "which, with an exactitude resembling that of mechanism, may render the operations of reason steady and visible, and, in their effects on the minds of others, irresistible."† 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 so; 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 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 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

"Multa in hoc genere mira a me sunt observata, quæ aliquando, quo par est rigore, exposita dabo."

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

should be able to form conclusions concerning God and the Mind, with not less certainty than we do at present concerning figures and numbers." *

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 for ever prevent us from reaching the summit of things intellectual, by the aid of a calculus 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 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

* Wallisti Opera, Vol. III. p. 621.

† 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.

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.* 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 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 accelerating 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 receives, 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 philosophy, will be found to depend chiefly on the success with which he has cultivated these silent habits of inductive interpretation,-much more, in my opinion, than on his acquaintance with those rules which form the great objects of study to the professed logician. In proof of this, it is sufficient for me to remind my readers, that the whole theory of syllogism' proceeds on the supposition that the same word is always to be employed precisely in the same sense, (for otherwise, the syllogism would be vitiated by consisting 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 mechanism of speech, none has hitherto attended to the far more wonderful 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 than the very surface of the subject; being all of them confined to that 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.*

* Those who are interested in this discussion, will enter more completely into my