ter, where the premises are meant to express truths or facts, (supported, on the most favourable supposition, by a very high degree of probability,) the conclusion must necessarily partake of that uncertainty in which the premises are involved. But what I am chiefly anxious at present to impress on the minds of my readers, is the substance of the two following propositions: 27-first, That dialectical syllogisms (provided they be not sophistical) are not less demonstratively conclusive, so far as the process of reasoning is concerned, than those to which this latter epithet is restricted by Aristotle; and, secondly, That it is to the process of reasoning alone, and not to the premises on which it proceeds, that Aristotle's demonstrations exclusively refer. The sole object, therefore, of these demonstrations, is (as I already remarked) not to strengthen, by new proofs, principles which were doubtful, or to supply new links to a chain of reasoning which was imperfect, but to confirm one set of demonstrations by means of another. The mistakes into which some of my readers might have been led by the contrast which Aristotle's language implies between dialectical syllogisms, and those which he honours with the title of demonstrative, will, I trust, furnish a sufficient apology for the length of this explanation. Having enlarged so fully on the professed aim of Aristotle's demonstrations, I shall despatch, in a very few pages, what I have to offer on the manner in which he has carried his design into effect. If the design be as unphilosophical as I have endeavoured to shew that it is, the apparatus contrived for its execution can be considered in no other light than as an object of literary curiosity. A process of reasoning which pretends to demonstrate the legitimacy of a conclusion which, of itself, by its own intrinsic evidence, irresistibly commands the assent, must, we may be perfectly assured, be at bottom unsubstantial and illusory, how specious soever it may at first sight appear. Supposing all its inferences to be strictly just, it can only bring us round again to the point from whence we set out. The very acute strictures of Dr. Reid, in his Analysis of Aristotle's Logic, on this part of the Syllogistic Theory, render it superfluous for me, on the present occasion, to enter into any details upon the subject. To this small, but valuable tract, therefore, I beg leave to refer my readers; contenting myself with a short extract, which contains a general and compendious view of the conclusion each drawn, and of the argument used to prove it, in each of the three figures of syllogisms. 2. 66 "In the first figure, the conclusion affirms or denies something of a certain species or individual; and the argument to prove this "conclusion is, That the same thing may be affirmed or denied of "the whole genus to which that species or individual belongs. "In the second figure, the conclusion is, That some species or "individual does not belong to such a genus; and the argument is, "That some attribute common to the whole genus does not belong "to that species or individual. "In the third figure, the conclusion is, That such an attribute be- . longs to part of a genus; and the argument is, That the attribute "in question belongs to a species or individual which is part of that genus. 26 66 "I apprehend that, in this short view, every conclusion that falls "within the compass of the three figures, as well as the mean of "proof, is comprehended. The rules of all the figures might be ea"sily deduced from it; and it appears that there is only one principle of reasoning in all the three; so that it is not strange, that a "syllogism of one figure should be reduced to one of another figure. "The general principle in which the whole terminates, and of "which every categorical syllogism is only a particular application, geneal "is this, That what is affirmed or denied of the whole genus may “be affirmed or denied of every species and individual belonging to miniple "it This is a principle of undoubted certainty indeed, but of no "great depth. Aristotle and all the logicians assume it as an ax"iom, or first principle, from which the syllogistic system, as it 66 were, takes its departure; and after a tedious voyage, and great "expense of demonstration, it lands at last in this principle, as its "ultimate conclusion. O curas hominum! O quantum est in rebus " inane !""* When we compare this mockery of science with the unrivalled powers of the inventor, it is scarcely possible to avoid suspecting, that he was anxious to conceal its real poverty and nakedness, under the veil of the abstract language in which it was exhibited. It is observed by the author last quoted, that Aristotle hardly ever gives examples of real syllogisms to illustrate his rules; and that his commentators, by endeavouring to supply this defect, have only brought into contempt the theory of their master. "We acknow"ledge (says he) that this was charitably done, in order to assist the "conception in matters so very abstract; but whether it was pru"dently done for the honour of the art, may be doubted." One thing is certain, that when we translate any of Aristotle's demonstrations from the general and enigmatical language in which he states it, into more familiar and intelligible terms, by applying it to a particular example, the mystery at once disappears, and resolves into some self-evident or identical puerility. It is surely a strange mode of proof, which would establish the truth of what is obvious, and what was never doubted of, by means of an argument which appears quite unintelligible, till explained and illustrated by an instance perfectly similar to the very thing to be proved. "If A (says Aristotle) is attributed to every B, and B to every "C, it follows necessarily, that A may be attributed to every C."t * This axiom is called, in scholastic language, the dictum de omni et de nullo. † Analyt. Prior. cap. iv. It is obvious, that Aristotle's symbolical demonstrations might be easily thrown into the form of symbolical syllogisms. The circumstance which induced him to prefer the former mode of statement, was, probably, that he might avoid the appearance of reasoning in a circle, by employing the syllogistic theory to demonstrate itself. It is curious how it should have escaped him, that, in attempting to shun this fallacy, he had fallen into ano19 VOL. II. Such is the demonstration given of the first mode of the first figure; and it is obviously nothing more than the axiom, called the dictum de omni, concealed under the disguise of an uncouth and cabalistical phraseology. The demonstrations given of the other legitimate modes are all of the same description. In disproving the illegitimate modes, he proceeds after a similar manner; condescending, however, in general, to supply us, by way of example, with three terms, such as bonum, habitus, prudentia; album, equus, cygnus ;-which three terms, we are left, for our own satisfaction, to form into illegitimate syllogisms of the particular figure and mode which may be under consideration. The manifest inconclusiveness of every such syllogism, he seems to have thought, might assist readers of slower apprehension in perceiving more easily the import of the general proposition. The inconclusiveness, for instance, of those modes of the first figure, in which the major is particular, is thus stated and explained. "If A is or is not in some "B, and B in every C, no conclusion follows. Take for the terms "inthe affirmative case, good, habit, prudence; and in the negative, 11* good, habit, ignorance.' With respect to such passages as this, Dr. Reid has perfectly expressed my feeling, when he says; That "the laconic style of the author, the use of symbols not familiar, "and, in place of giving an example, his leaving us to form one from "three assigned terms, give such embarrassment to a reader, that he " is like one reading a book of riddles." Can it be reasonably supposed, that so great an obscurity in such a writer was not the effect of some systematical design? From the various considerations already stated, I might perhaps, without proceeding farther, be entitled to conclude, that Aristotle's demonstrations amount to nothing more than to a specious and imposing parade of words; but the innumerable testimonies to their validity, from the highest names, and the admiration in which they continue to be held by men of distinguished learning, render it necessary for me, before dismissing the subject, to unfold a little more completely some parts of the foregoing argument. It may probably appear to some of my readers superfluous to yllogism remark, after the above-cited specimens of the reasonings in ques tion, that not one of these demonstrations ever carry the mind dan not forward, a single step, from one truth to another; but merely from a general axiom to some of its particular exemplifications. Nor is this any, mind all; they carry the mind in a direction opposite to that in which its outh judgments are necessarily formed. The meaning of a general to another axiom, it is well known, is seldom, if ever intelligible, till it has ther exactly of the same description;-that of employing an argument in the common form to demonstrate the legitimacy of syllogisms, after having represented a syllogistic analysis as the only infallible test of the legitimacy of a demonstration. Analyt. Prior. cap. iv. + Dr. Gillies has attempted a vindication of the use which Aristotle, in his demonstrations, has made of the letters of the alphabet. For some remarks on this attempt, see Note (L.) been illustrated by some example; whereas Aristotle, in all his demonstrations, proceeds on the idea, that the truth of an axiom, particular in particular instances, is a logical consequence of its truth, as enun- comunion ciated in general terms. Into this mistake, it must be owned, he not an inf was not unnaturally led by the place which is assigned to axioms at спи рот the beginning of the elements of geometry, and by the manner in a genera which they are afterwards referred to in demonstrating the propo- axion. sitions. "Since A (it is said) is equal to B, and B to C, A is equal "to C; for, things which are equal to one and the same thing, are equal "to one another." This place, I have little doubt, has been occupied by mathematical axioms, as far back, at least, as the foundation of the Pythagorean school; and Aristotle's fundamental axiom will be found to be precisely of the same description. Instead, therefore, of saying, with Dr. Gillies, that "on the basis of one single "truth Aristotle has reared a lofty and various structure of abstract 66 science," it would be more correct to say that the whole of this science is comprised or implied in the terms of one single axiom. Nor must it be forgotten (if we are to retain Dr. Gillies's metaphor) that the structure may, with much more propriety, be considered as the basis of the axiom, than the axiom of the structure. When it is recollected, that the greater part of our best philosophers (and among the rest Dr. Reid) still persevere, after all that Locke has urged on the opposite side of the question, in considering axioms as the ground-work of mathematical science, it will not appear surprising, that Aristotle's demonstrations should have so long continued to maintain their ground in books of logic. That this idea is altogether erroneous, in so far as mathematics is concerned, has been already sufficiently shewn; the whole of that science resting ultimately, not on axioms, but on definitions or hypotheses. By those who have examined my reasonings on this last point, and who take the pains to combine them with the foregoing remarks, I trust it will be readily allowed, that the syllogistic theory furnishes no exception to the general doctrine concerning demonstrative evidence, which I formerly endeavoured to establish; its pretended demonstrations being altogether nugatory, and terminating at last (as must be the case with every process of thought involving no data but what are purely axiomatical) in the very proposition from which they originally set out. The idea, that all demonstrative science must rest ultimately on axioms, has been borrowed, with many other erroneous maxims, from the logic of Aristotle; but is now, in general, stated in a manner much more consistent (although perhaps not nearer to the truth) than in the works of that philosopher. According to Dr. Reid, the degree of evidence which accompanies our conclusions, is necessarily determined by the degree of evidence which accompanies our first principles; so that, if the latter be only probable, it is perfectly impossible that the former should be certain. Agreeing, therefore, with Aristotle, in considering axioms as the basis of all demonstrative science, he was led, at the same time, in conformity with the doc trine just mentioned, to consider them as eternal and immutable truths, which are perceived to be such by an intuitive judgment of the understanding. This, however, is not the language of AristoI'm consistentle; for, while he tells us, that there is no demonstration but of * eternal truths, he asserts, that the first principles which are the cyny lan- foundation of all demonstration, are got by induction from the insnage vistotle. is to be reconciled, I leave to the consideration of his future com mentators. For my own part, I cannot help being of opinion with Lord Monboddo (who certainly was not wanting in a due respect for the authority of Aristotle) that the syllogistic theory would have accorded much better with the doctrine of Plato concerning general ideas, than with that held on the same subject by the founder of the Peripatetic school. To maintain that, in all demonstration, we argue from generals to particulars, and, at the same time, to assert, that the necessary progress of our knowledge is from particulars to generals, by a gradual induction from the informations of sense, do not appear, to an ordinary understanding, to be very congruous parts of the same system ;§ and yet the last of these tenets has been eagerly claimed as a discovery of Aristotle, by some of the most zealous admirers of his logical demonstrations.|| * Φανερον δε και, ταν ωσιν ὡς προτάσεις καθόλου εξ ὧν ὁ συλλογισμός, ότι ανάγκη και το συμπέρασμα αίδιον είναι της τοιαυτης αποδείξεως, και της άπλως ειπείν) αποδείξεως ουκ εστιν αρα αποδειξις των φθαρτων, ουδ' επιστημη άπλως, αλλ' ούτως, ώσπερ κατα συμβεβηκος. Analy. Post. Lib. i cap. vii. It is clear, if the propositions of which the syllogism is composed, are universal, that the conclusion of a demonstration of this kind, and indeed of demonstration generally, must be universally true. It is not then a demonstration of truths not eternal, nor know. ledge, speaking simply, but only accidentally.] + Εκ μεν ουν αισθησεως γίγνεται μνημη. εκ δε μνημης πολλακις του αυτού γενομένης, εμπειρία. άρ 223 πολλαι μνημει του αριθμώ, εμπειρια μια εστιν. εκ δ' εμπειρίας η εκ παντός ηρεμήσαντος του καθόλου εν τη ψυχη του ένος παρά τα πολλα, ὁ αν εν άπασιν ἐν ένη εκείνοις το αυτό, τέχνης αρχή και επιστήμης. σαν μεν περί γενεσιν τέχνης, αν δε περί το ον, επιστημης. (Analyt. Post, Lib. ii. cap. xix.) The whole chapter may be read with advantage by those who wish for a fuller explanation of Aristotle's opinion on this question. illustration of the intellectual process by which general principles are obtained from the perceptions of sense, and from reiterated acts of memory resolving into one experience, is more particularly deserving of attention. His [Remembrance arises from perception, but from memory often repeated, experience; for many remembrances form but one experience. But from the experience of each single action taken universally in the mind, of one thing from many, what is in all the same, arise art and science; if it concerns production, of art; if knowledge of what already exists, of science.] Ancient Metaphysics, Vol. V pp. 184 185. It may perhaps be asked, Is not this the very mode of philosophizing recommended by Bacon, first, to proceed analytically from particulars to generals, and then to reason synthetically from generals to particulars My reply to this question (a question which will not puzzle any person at all acquainted with the subject) I must delay, till I shall have an opportunity, in the progress of my work of pointing out the essential difference between the meanings annexed to the word induction, in the Aristotelian, and in the Baconian legic.-Upon the present occasion, it is sufficient to observe, that Bacon's plan of investigation was never supposed to be applicable to the discovery of principles which are necessary and eternal. See Dr. Gillies's Analysis of Aristotle's works, passim. In this learned, and on the whole very instructive performance, I find several doctrines ascribed to Aristotle, which appear not a little at variance with each other. The follow |