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servations 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.




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 inquirer, lays me, in this chapter, under the necessity of selecting a

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

Claims of Aristotle's Login.

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."* Nor have these claims been disputed by "mathematicians themselves. (1) In logica (says Dr. Wallis) struc"tura syllogismi demonstratione nititur pure mathematicâ." And, in another passage: "(2) Sequitur institutio logica, communi usui ac"commodata. Quo videant Tirones, syllogismorum leges strictissi"mis demonstrationibus plane mathematicis ita fundatas, ut conse"quentias habeant irrefragabiles, quaeque offuciis fallaciisque dete"gandis sint accommodatae." 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 per"fected by one man. It shows a force of genius, and labour of in"vestigation 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,

• 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.

Preface to the same volume.

Analysis of Aristotle's Logic.

That Dr. Reid, however, was perfectly aware that these demonstrations are more spe cious than solid, may be safely inferred from a sentence which afterwards occurs in the "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."

same tract.

(1) In logic the structure of the syllogism is supported by demonstration purely mathe matical.

(2) Next follows, the institution of logic, accommodated to general use.-By this the young student may perceive, that the laws of syllogisms are so founded on the strictest mathematical demonstrations, as to furnish conclusions the most certain, and adapted to detect all sophisms and fallacies.


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 for this excOrganon, 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 labour.


The first remark which I have to offer Aristotle's demon

strations, is, That they proceed on the obviously false supposition impossible

of its being possible to add to the conclusiveness and authority off innov demonstrative evidence. One of the most remarkable circumstances weight of

which this from that species of evidence which is com

monly called moral or probable, is, that it is not susceptible of de- dim: Euid: grees; 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?

•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 be mentions. "Firma autem demonstratio est, quae praescriptam a logica formam servat, non quasi semper ordinatis scholarum more syllogismis opus sit (quales Christianus Her linus et Conradus Dasypadius in sex priores Euclidis libros exhibuerunt) sed ita saltem ut argumentatio concludat vi formae," &c. &c. Acta Eruditor. Lips. Vol. I. p. 285. Venit. 1740.

[It is a clear demonstration, which preserves the form prescribed by logic, not as if there was always need of syllogisms arranged in order, after the method of the schools, (such as C. Herlinus and C Dasypadius have exhibited in the six first books of Euclid,) but so that the reasoning is conclusive according to the form.]

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.

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 demonstra not proceed from any anxiety to swell the mass of evidence, by tion of y finding (as in some other sciences) a variety of collateral arguments, all bearing, with their combined force, on the same truth;—their same thior: 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.


Why Diff:

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 exDemonstrat ample. His object was not to teach us how to demonstrate the same thing in a variety of different ways; but to demonstrate, by conclusive abstract reasoning, the conclusiveness of demonstration. By what ness of de- means he set about the accomplishment of his purpose, will aftermonstration wards 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.

Meaning of

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 dialecDemonstratical, to mark the distinction between the two great classes into which he divides syllogisms; a mode of speaking which, according tive dial to the common use of language, would seem to imply, that one spetural sylla: cies 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 Distinction in perfect in form, it must, of necessity, be not only conclusive, but demonstratively conclusive. is in fact, the idea which Ariscorrect, why totle 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,


To the same purpose also Dr. Wallis: "Syllogismus Topicus (qui et Dialecticus dici solet) talis haberi solet syllogismus (seu syllogismorum series) qui firman) potius praesump tionem seu opinionem valde probabilem creat, quam absolutam certitudinem. Non quidein ratione Formae, (nam syllogismi omnes, si in justa forma, sunt demonstrativi; hoc est, si praemissae verae sint, vera erit et conclusio,) sed ratione Materiae seu Praemissarum; quae ipsae, utplurimum, non sunt absolute certae, et universaliter verae; sed saltem probabiles, atque utplurimum verae." Wallis, Logica, Lib. iii. cap. 23.

(4 Topical, which is called also a Dialectical Syllogism, is usually a syllogism or series of ayilogisms, which creates rather a strong presumption, or a very probable opinion,

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 them to the syllogisms themselves? The phrase demonstrative syllogism certainly seems, at first sight, to express rather the complete and necessary connexion between the conclusion and the premises, than the certainty or the necessity of the truths which the premises assume.

To this observation it may be added, (in order to prevent any misapprehensions from the ambiguity of language,) that Aristotle's idea of the nature of demonstration is essentially different from that which I have already endeavoured to explain. "In all demonstra"tion," (says Dr. Gillies, who, in this instance, has very accurately and clearly stated his author's doctrine,)" the first principles must be "necessary, immutable, and therefore eternal truths, because those "qualities could not belong to the conclusion, unless they belonged to “the premises, which are its causes."* According to the account of de-xirst prinmonstrative or mathematical evidence formerly given, the first princi-p ples on which it rests are not eternal and immutable truths, but defi- monst: veoson: nitions or hypotheses; and therefore, if the epithet demonstrative be understood, in our present argument, as descriptive of that pecu-mouth but liar kind of evidence which belongs to the distinction

of dr

not stemal

between demonstrative aud dialectical syllogisms is reduced to this; definitions.

that in the former, where all that is asserted is the necessary connexion between the conclusion and the premises, neither the one nor the other of these can with propriety be said to be either true or false, because both of them are entirely hypothetical: in the lat

than absolute certainty. Not on account of its Form (for all syllogisms, if in proper form, are demonstrative; that is, if the premises are true the conclusion will be also true) but on account of their matter or premises, which themselves, for the most part, are not abso lutely certain and universally true; but at best probable and true for the most part.]

Aristotle's Ethics and Politics, &c. By Dr. Gillies. Vol. I. p. 96.

I am much at a loss how to reconcile this account of demonstrative evidence with the view which is given by Dr Gillies of the nature of syllogism, and of the principles on which the syllogistic theory is founded. In one passage, (p. 81.) he tells us, that Aris totle invented the syllogism, to prevent imposition arising from the abuse of words:" in a second (p. 83) that "the simple truth on which Aristotle has reared a lofty and various structure of abstract science, clearly expressed and fully demonstrated-is itself founded in the natural and universal texture of language:" in a third, (p. 86.) that “the doctrines of Aristotle's Organon have been strangely perplexed by confounding the grammatical principles on which that work is built with mathematical axioms." Is it possible to suppose, that Aristotle could have ever thought of applying to mere grammatical principles, to truths founded in the natural and universal texture of language-the epithets of neces» sary, immulable, and eternal?

I am unwilling to lengthen this note, otherwise it might be easily shewn, how utterly irreconcileable, in the present instance, are the glosses of this ingenious commentator with the text of his author. Into some of these glosses it is probable that he has been uncon sciously betrayed, by his anxiety to establish the claim of his favourite philosopher to the important speculations of Locke on the abuse of words, and to those of some later writers on language considered as an instrument of thought.

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