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fer from Mr. Stewart. But wide, indeed, is the CHAP. difference between them, with respect to the nature of demonstration. Mr. S. maintains, “ that demonstrative evidence belongs only to mathematics. It is not founded on absolute or unalterable truths, but on definitions or hypotheses ; and implies nothing more than the necessary connection between the premises which we assume, and the conclusions which we deduce from them. The word “ demonstration” cannot, therefore, be applied to reasonings concerning matters of fact, which, how convincing soever they may be, afford only the highest degree of probability.”99 From this very limited notion of the subject, he seems, however, afterwards to depart; and, in speaking of the Pythagorean or Copernican system of astronomy, he says,
" that the discoveries of the last century afforded many
in support of their common opinion by that learned writer;" adding “ From the perusal of Dr. G.'s wonderful work, I have now the satisfaction to discover, that the conjectures I had been led to draw from these scanty materials, are completely confirmed by the opinion of an author, who is probably better qualified than any preceding commentator, to decide on this subject.” In conversing, August last, in Paris, with Baron Cuvier, the illustrious successor of Buffon, and far his superior in exact science, he said, it is ridiculous to think that Aristotle did not employ induction in the physical sciences, when he always employs it with such signal success in the moral. On the contrary, he appeared to this excellent judge, to be the greatest collector of facts from his own observation, that perhaps ever existed; and always to reason from them, consequentially. He was unacquainted, indeed, with many facts and many instruments which time has brought to light ; but how wonderfully he supplied the want of them, is proved in my New Analysis, p. 147. third edit.
99 Compare Elements, vol. ii. p. 151. et seq., & p. 251.
CHAP. new proofs of a direct and even a demonstrative
But, waving this apparent inconsistency, I would observe that Aristotle's account of demonstration is altogether different. Its object, according to him, is not conditional or
hypothetic, but absolute and immutable truth. Analyt. From principles deserving those epithets, he dePosterior.
duces, by the cogency of clear argument, conclusions demonstratively certain; thus preparing, in the preliminary books, for example, of what have been called his metaphysicks, the way to what he himself calls his first philosophy, or theology ; and rearing, on accurate and firm definitions of cause and effect, mind and matter, his glorious demonstrations of the being and attributes of Deity. Descending from this sublime speculation, he investigates, in other treatises, truths not demonstrative, indeed, but by no means purely hypothetical. It is thus that, in his physicks, his problems, his meteorology, and in his history of animals, taken in the largest acceptation of that title, as containing not only history, but the philosophy of that history, he draws innumerable conclusions more or less probable, according to the different degrees of evidence belonging to his premises; and passing from physical science to the moral world, and the practical affairs of life, deduces from definitions carefully established on facts, the duties and interests of men, whether considered as individuals, or as members of the same commu
100 Elements, vol. ü. p. 421.
nity. Such are his important reasonings on ethics CHA P. and politics, and also on the subject of rhetoric, which he observes is a natural adjunct to politics, since it serves as one of the main instruments by which the managers of free states are enabled to guide and govern them. Having thus delineated an encyclopédia of science, under the heads of God, man, and nature, Aristotle analysed the intellectual operations by which all this had been effected, and recomposed them into the form called syllogism. He anticipates and scorns the vain boast of his pretended followers, of teaching men to argue and to reason.98 He protests no less distinctly against the perverse use which, after the example of even his best 99 Greek commentators, the schoolmen made of his syllogism. To see the justness of a conclusion, the movement of thought quicker than lightning, needs not to be expanded verbally into all the various steps of an argument. In most cases this is unnecessary,
it would be awkward ; in some it would be intolerable.
The modern oppugners of abused syllogism have, therefore, a great authority on their side, namely, Aristotle himself. He says explicitly, that some sciences100 need not its aid; and that even in those matters 101 which Lord Bacon allows to be its proper and legitimate province, it ought
98 Rhetoric sub initio.
99 See Johannes Philoponus, υπομνημα εις τα περι ψυχης βιβλια. 1. äi. edit. Venet. 1535.
100 Anlyt. Poster. I. i. c. 10. évias perlou etisnuas, k.T.A.
101 The affairs of civil life and arts, consisting in talk and opinion Bacon, Novum Organum in Præfat.
CHAP. to be employed sparingly.102 When any proposi..
tion is so obvious, that it cannot fail to occur spontaneously, it would savour of the rustic or the pedant103 to declare it : but expressed or understood, the elements of syllogism are essential to all demonstration, for all reasoning whatever, implies a subject about which we reason, premises from which we reason, and a conclusion that is drawn from them. 104
If Mr. S. had not too much despised logic, to Objection
be a proficient in that art, he would not have found fault with Aristotle's phraseology in di. viding syllogisms into demonstrative and dialectical.
« 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 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 syllogism 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 Aris102 Rhetoric, l. iii. cap. 18. p. 389. edit. Buhle. et pasim.
105 I have resolved the epithet poptikov because it implies both notions.
104 Analyt. Poster. 1. 1. c. 10. p. 270. edit. Buhle. 105 Elements, vol.ii. p. 249.
totle himself annexed to the distinction ; for he CHAP. tells us, that it does not refer to the form of syl
I. logisms, but to the 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 that 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 connection between the conclusion and the premises, than the certainty or the necessity of the truths which the premises assume."106 This reason is a very illogical one. In every legitimate syllogism, the conclusion is indeed necessarily connected with the premises ; but, as every syllogism must consist of premises, as well as of a conclusion, nothing more than a dialectical or probable syllogism can be the result of dialectical or probable premises.
A demonstrative syllogism, therefore, requires premises that are necessary and certain; since, in the words of Aristotle, these qualities could not
106 Elem. vol. ii. p. 250.