some degree of doubt. As certain as death-as certain as the rising of the sun-are proverbial modes of expression in all countries; and they are, both of them, borrowed from events which, in philosophical language, are only probable or contingent. In like manner, the existence of the city of Pekin, and the reality of Cæsar's assasination, which the philosopher classes with probabilities, because they rest solely upon the evidenee of testimony, are universally classed with certainties by the rest of mankind; and in any case but the statement of a logical theory, the application to such truths of the word probable, would be justly regarded as an impropriety of speech. This difference between the technical meaning of the word probability, as employed by logicians, and the notion usually attached to it in the business of life, together with the erroneous theories concerning the nature, of demonstration, which I have already endeavored to refute,-have led many authors of the highest name, in some of the most important arguments which can employ human reason, to overlook that irresistible evidence which was placed before their eyes, in search of another mode of proof altogether unattainable in moral inquiries, and which, if it could be attained, would not be less liable to the cavils of sceptics.

But although, in philosophical language, the epithet probable be applied to events which are acknowledged to be certain, it is also applied to those events which are called probable by the vulgar. The philosophical meaning of the word, therefore, is more comprehensive than the popular; the former denoting that particular species of evidence of which contingent truths admit ; the latter being confined to such degrees of this evidence as fall short of the highest. These different degrees of probability the philosopher considers as a series, beginning with bare possibility, and terminating in that apprehended infallibility with which the phrase moral certainty is synonymous. To this last term of the series, the word probable is, in its ordinary acceptation, plainly inapplicable.

The satisfaction which the astronomer derives from the exact coincidence, in point of time between his theoretical predictions concerning the phenomena of the heavens, and the corresponding events when they actually occur, does not imply the smallest doubt, on his part, of the constancy of the laws of nature. It resolves partly into the pleasure of arriving at the knowledge of the same truth or of the same fact by different media; but chiefly into the gratifying assurance which he thus receives, of the correctness of his principles, and of the competency of the human faculties to these sublime investigations. What exquisite delight must La Place have felt, when, by deducing from the theory of gravitation, the cause of the acceleration of the moon's mean motion—an acceleration which proceeds at the rate of little more than 11" in a century, he accounted, with such mathematical precision, for all

the recorded observations of her place from the infancy of astronomical science! It is from the length and abstruseness, however, of the reasoning process, and from the powerful effect produced on the imagination, by a calculus which brings into immediate contrast with the immensity of time, such evanescent elements as the fractional parts of a second, that the coincidence between the computation and the event appears in this instance so peculiarly striking. In other respects, our confidence in the future result rests on the same principle with our expectation that the sun will rise tomorrow at a particular instant; and, accordingly, now that the correctness of the theory has been so wonderfully verified by a comparison with facts, the one event is expected with no less assurance than the other.

With respect to those inferior degrees of probability to which, in common discourse, the meaning of that word is exclusively confined, it is not my intention to enter into any discussions. The subject is of so great extent, that I could not hope to throw upon it any lights satisfactory either to my reader or to myself, without encroaching upon the space destined for inquiries more intimately connected with the theory of our reasoning powers. One set of questions, too, arising out of it, I mean those to which mathematical calculations have been applied by the ingenuity of the moderns, involve some very puzzling metaphysical difficulties, the consideration of which would completely interrupt the train of our present speculations. I proceed, therefore, in continuation of those in which we have been lately engaged, to treat of other topics of a more general nature, tending to illustrate the logical procedure of the mind in the discovery of scientific truth. As an introduction to these, I propose to devote one whole chapter to some miscellaneous strictures and reflections on the logic of the schools.

CHAPTER III.

OF THE ARISTOTELIAN LOGIC.

SECTION I.

Of the demonstrations of the Syllogistic Rules given by Aristotle and his Commentators.

THE great variety of speculations which, in the present state of science, the Aristotelian logic naturally suggests to a philosophical

* I allude more particularly to the doubts started on this subject by D'Alembert, in his Opuscules Mathématiques; and in his Mélanges de Litterature.

inquirer, lays me, in this chapter, under the necessity of selecting a few leading questions, bearing immediately upon the particular objects which I have in view. In treating of these, I must, of course suppose my readers to possess some previous acquaintance with the subject to which they relate; but it is only such a general knowledge of its outlines and phraseology, as, in all universities, is justly considered as an essential accomplishment to those who receive a liberal education.

I begin with examining the pretensions of the Aristotelian logic to that pre-eminent rank which it claims among the sciences; professing, not only to rest all its conclusions on the immovable basis of demonstration, but to have reared this mighty fabric on the narrow ground-work of a single axiom. "On the basis," says the latest of his commentators, " of one simple truth, Aristotle has reared a lofty and various structure of abstract science, clearly expressed and fully demonstrated." (Analysis of Aristotle's works, by Dr. Gillies, vol. i. p. 83, 2nd edit.) Nor have these claims been disputed by mathematicians themselves. "In logica," says Dr. Wallis, "strictura syllogismi demonstratione nititur pure mathematicâ."* And, in another passage: "Sequitur institutio logica, communi usui accommodata.-Quo videant Tirones, syllogismorum leges strictissimis demonstrationibus plane mathematicis ita fundatas, ut consequentias habeant irrefragabiles, quæque offuciis fallaciisque detegendis sint accommodatæ." Dr. Reid, too, although he cannot be justly charged, on the whole, with any undue reverence for the authority of Aristotle, has yet, upon one occasion, spoken of his demonstrations with much more respect than they appear to me entitled to. "I believe," says he, "it will be difficult,in any science, to find so large a system of truths of so very abstract and so general a nature, all fortified by demonstration, and all invented and perfected by one man. It shows a force of genius, and labor of investigation, equal to the most arduous attempts." (Analysis of Aristotle's Logict.)

As the fact which is so confidently assumed in these passages would, if admitted, completely overturn all I have hitherto said concerning the nature both of axioms and of demonstrative evidence, the observations which follow seem to form a necessary sequel to some of the preceding discussions. I acknowledge, at the same time, that my chief motive for introducing them, was a wish to counteract the effect of those triumphant panegyrics upon Aristotle's Organon, which of late have been pronounced by some

* See the Monitum prefixed to the Miscellaneous Treatises annexed to the third volume of Dr Wallis's Mathematical works.

1 Preface to the same volume.

That Dr. Reid, however, was perfectly aware that these demonstrations are more specious than solid, may be safely inferred from a sentence which afterwards occurs in the same tract. "When we go without the circle of the mathematical sciences, I know nothing in which there seems to be so much demonstration as in that part of logic which treats of the figures and modes of syllogisms."

writers, whose talents and learning justly add much weight to their literary opinions; and an anxiety to guard the rising generation against a waste of time and attention upon a study so little fitted, in my judgment, to reward their labor.

The first remark which I have to offer upon Aristotle's demonstrations, is, that they proceed on the obviously false supposition of its being possible to add to the conclusiveness and authority of demonstrative evidence. One of the most remarkable circumstances which distinguishes this from that species of evidence which is commonly called moral or probable, is, that it is not susceptible of degrees; the process of reasoning of which it is the result, being either good for nothing, or so perfect and complete in itself, as not to admit of support from any adventitious aid. Every such process of reasoning, it is well known, may be resolved into a series of legitimate syllogisms, exhibiting separately and distinctly, in a light as clear and strong as language can afford, each successive link of the demonstration. How far this conduces to render the demonstration more convincing than it was before, is not now the question. Some doubts may reasonably be entertained upon this head, when it is considered, that, among the various expedients employed by mathematical teachers to assist the apprehension of their pupils, none of them have ever thought of resolving a demonstration, as may always be easily done, into the syllogisms of which it is composed. But, abstracting altogether from this consideration, and granting that a demonstration may be rendered more manifest and satisfactory by being syllogistically stated; upon what principle can it be supposed possible, after the demonstration has been thus analyzed and expanded, to enforce and corroborate, by any subsidiary reasoning, that irresistible conviction which demonstration. necessarily commands?

It furnishes no valid reply to this objection, to allege, that mathematicians often employ themselves in inventing different demonstra tions of the same theorem; for, in such instances, their attempts do not proceed from any anxiety to swell the mass of evidence, by finding (as in some other sciences) a variety of collateral arguments all bearing with their combined force, on the same truth :their only wish is, to discover the easiest and shortest road by which

From a passage indeed in a memoir by Leibnitz, printed in the sixth volume of the Acta Eruditorum, it would seem, that a commentary of this kind, on the first six books of Euclid, had been actually carried into execution by two writers, whose names he mentions. "Firma autem demonstratio est, quæ præscriptam a logica formam servat, non quasi semper ordinatis scholarum more syllogismis opus sit (quales Christianus Herlinus et Conradus Dasypodius in sex priores Euclidis libros exhibuerunt) sed ita saltem ut argumentatio concludat vi forme," &c. &c. Acta Eruditor. Lips. vol. i. p. 285. Venet. 1740.

I have not seen either of the works alluded to in the above sentence, and, upon less respectable authority, should have scarcely conceived it to be credible, that any person, capable of understanding Euclid, had ever seriously engaged in such an undertaking. It would have been difficult to devise a more effectual expedient for exposing to the meanest understanding, the futility of the syllogistic theory.

the truth may be reached. In point of simplicity, and of what geometers call elegance, these various demonstrations may differ widely from each other; but in point of sound logic, they are all precisely on the same footing. Each of them shines with its own intrinsic light alone; and the first which occurs (provided they be all equally understood) commands the assent not less irresistibly than the last.

The idea, however, on which Aristotle proceeded, in attempting to fortify one demonstration by another, bears no analogy whatever to the practice of mathematicians in multiplying proofs of the same theorem: nor can it derive the slightest countenance from their example. His object was not to teach us how to demonstrate the same thing in a variety of different ways; but to demonstrate, by abstract reasoning, the conclusiveness of demonstration. By what means he set about the accomplishment of his purpose, will afterwards appear. At present, I speak only, of his design; which if the foregoing remarks be just, it will not be easy to reconcile with correct views, either concerning the nature of evidence, or the theory of the human understanding.

For the sake of those who have not previously turned their attention to Aristotle's Logic, it is necessary, before proceeding farther, to take notice of a peculiarity (and, as appears to me, an impropriety,) in the use which he makes of the epithets demonstrative and dialectical, to mark the distinction between the two great classes into which he divides syllogisms; a mode of speaking which, according to the common use of language, would seem to imply, that one species of syllogisms may be more conclusive and cogent than another. That this is not the case, is almost self-evident: for if a syllogism be perfect in form, it must, of necessity, be not only conclusive but demonstratively conclusive. Nor is this, in fact, the idea which Aristotle himself annexed to the distinction; for he tells us, that it does not refer to the form of syllogisms, but to their matter; or, in plainer language, to the degree of evidence accompanying the premises on which they proceed.* In the two books of his last Analytics, accordingly, he treats of syllogisms which are said to be demonstrative, because their premises are certain; and in his Topics, of what he calls dialectical syllogisms, because their premises are only probable. Would it not have been a clearer and juster mode of stating this distinction, to have applied the epithets demonstrative and dialectical to the truth of the conclusions resulting from these two classes of syllogisms, instead of applying

*To the same purpose also Dr. Wallis: "Syllogismus Topicus, (qui et Dialecticus dici solet) talis haberi solet syllogismus (seu syllogismorum series) qui firmam potius præsumptionem, seu opinionem valde probabilem creat, quam absolutam certitudinem. Non quidem ratione Formæ, (nam syllogismi omnes, si in justa forma, sunt demonstrativi; hoc est, si præmissæ veræ sint, vera erit et conclusio,) sed ratione materiæ, seu Præmissarum; quæ ipsæ, utplurimum, non sunt absolute certæ, et universaliter veræ; sed saltem probabiles, atque utplurimum veræ.”Wallis, Logica, lib. iii. cap. 23.