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, (Ï 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 Í 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,' "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."

ceptible 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 analysed 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 demonstrations 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

*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 logicâ 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 formæ," &c. &e.—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 scarcely have 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.

VOL. II.

23

same truth;-their only wish is, to discover the easiest and shortest road by which 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 accompany