In our anticipations of astronomical phenomena, as well as in those which we form concerning the result of any familiar experiment in physics, philosophers are accustomed to speak of the event as only probable; although our confidence in its happening is not less complete, than if it rested on the basis of mathematical demonstration. The word probable, therefore, when thus used, does not imply any deficiency in the proof, but only marks the particular nature of that proof, as contradistinguished from another species of evidence. It is opposed, not to what is certain, but to what admits of being demonstrated after the manner of mathematicians. This differs widely from the meaning annexed to the same word in popular discourse; according to which, whatever event is said to be probable, is understood to be expected with 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 assassination, which the philosopher classes with probabilities, because they rest solely upon the evidence 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 endeavoured 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 to-morrow 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.

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

CHAPTER THIRD.

OF THE ARISTOTELIAN LOGIC.

SECTION I.

Of the Demonstrations of the Syllogistic Rules given by Aristotle and his Commen

tators.

THE great variety of speculations which, in the present state of science, the Aristotelian logic naturally suggests to a philosophical 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 acccomplishment 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 immoveable basis of demonstration, but to have reared this mighty fabric on the narrow groundwork 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."* Nor have these claims been disputed by mathematicians themselves. "In logicâ," says Dr. Wallis, "structura syllogismi demonstratione nititur pure mathematicâ." And, in another passage: " Sequitur institutio logica, communi usui accommodata.-Quo videant tirones, syllogis

Analysis of Aristotle's Works by Dr. Gillies, Vol. I. p. 83, 2d edit.

† See the Monitum prefixed to the Miscellaneous Treatises annexed to the third Volume of Dr. Wallis's Mathematical Works.

morum 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." +

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 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 sus

Preface to the third Volume of Dr. Wallis's Mathematical Works.

† Analysis of Aristotle's Logic.

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."