therefore, of saying, with Dr. Gillies, that "on the basis of one single truth Aristotle has reared a lofty and various structure of abstract 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 shown; 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 impos

sible that the former should be certain. Agreeing there fore, with Aristotle, in considering axioms as the basis of all demonstrative science, he was led, at the same time, in conformity with the doctrine 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 Aristotle; for, while he tells us, that there is no demonstration but of eternal truths,* he asserts, that the first principles which are the foundation of all demonstration, are got by induction from the informations of sense. In what manner this apparent contradiction is to be reconciled, I leave to the consideration of his future commentators.

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

ων

* Φανερὸν δὲ καὶ, ἐὰν ὦσιν αἱ προτάσεις καθόλου ἐξ ὧν ὁ συλλογισμός, ὅτι ἀναγκὴ καὶ τὸ συμπέρασμα αίδιον εἶναι τῆς τοιαύτης ἀποδείξεως, καὶ τῆς (ἁπλῶς εἰπεῖν) ἀποδείξεως· οὐκ ἔστιν ἄρα ἀπόδειξις τῶν φθαρτῶν, οὐδ ̓ ἐπιστήμη ἁπλῶς, ἀλλ ̓ οὕτως, ὥσπερ κατὰ συμβεβηκός.—Analyt. Post. Lib. i. cap. viii.

† ̓ Εκ μὲν οὖν αἰσθήσεως γίγνεται μνήμη. ἐκ δὲ μνήμης πολλάκις τοῦ αὐτοῦ γινομένης, ἐμπειρία. αἱ γὰρ πολλαὶ μνῆμαι τῷ ἀριθμῷ, ἐμπειρία μία ἔστιν· ἐκ δ ̓ ἐμπειρίας ἡ ἐκ παντὸς ἠρεμήσαντος τοῦ καθόλου ἐν τῇ ψυχῇ, τοῦ ἑνὸς παρὰ τὰ πολλὰ, ὃ ἂν ἐν ἅπασιν ἓν ἕνῇ ἐκείνοις τὸ αὐτὸ, τεχνῆς ἀρχὴ καὶ ἐπιστήμης. ἐὰν γὲ περὶ γένεσιν, τεχνῆς· ἐὰν δὲ περὶ τὸ ὂν, ἐπιστήμης. (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. His 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.

Ancient Metaphysics, Vol. V. pp. 184, 185.

§ It may perhaps be asked, Is not this the very mode of philosophizing recommend

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these tenets has been eagerly claimed as a discovery of Aristotle, by some of the most zealous admirers of his logical demonstrations.*

In this point of view, Lord Monboddo has certainly conducted, with greater skill, his defence of the syllogistic theory; inasmuch as he has entirely abandoned the important conclusions of Aristotle concerning the natural progress of human knowledge; and has attempted to entrench himself in (what was long considered as one of the most inaccessible fastnesses of the Platonic philosophy) the very ancient theory, which ascribes to general ideas an existence necessary and eternal. Had he, upon this occasion, after the example of Aristotle, confined himself solely to abstract principles, it might not have been an easy task to refute, to the satisfaction

ed by Bacon, first to proceed analytically from particulars to generals, and Gen to reason synthetically from generals to particulars? My reply to this quesity are tion which will not puzzle any person at all acquainted with the surges, Is lay, till I shall have an opportunity, in the progress of my work, of tota essential difference between the meanings annexed to the word indic Aristotelian and in the Baconian logic.-Upon the present occasion is ee observe, that Bacon's plan of investigation was never supposed to ex 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 won the trines ascribed to Aristotle, which appear not a little at varance * The following passages (which I am led to select for their cor econ present argument) strike me as not only widely different, tot coryers tory, in their import.

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According to Aristotle, definitions are the foundasssa de al se enca

fountains are pure only when they originate in an arr.

patient comparison of the perceptible quaites of intere
"Demonstrative truth can apply only to those things which nece

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of common readers, his metaphysical arguments. Fortunately, however, he has favored us with some examples and illustrations, which render this undertaking quite unnecessary; and which, in my opinion, have given to the cause which he was anxious to support, one of the most deadly blows which it has ever received. The following panegyric in particular, on the utility of logic, while it serves to show that, in admiration of the Aristotelian demonstrations, he did not yield to Dr. Gillies, forms precisely such a comment as I myself could have wished for, on the leading propositions which I have now been attempting to establish.

"In proof of the utility of logic,” * says Lord Monboddo, "I will give an example of an argument to prove that man is a substance; which argument, put into the syllogistic form, is this:

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Every Animal is a Substance;
Every Man is an Animal;

Therefore every Man is a Substance.

"There is no man, I believe, who is not convinced of the truth of the conclusion of this syllogism: But how he is convinced of this, and for what reason he believes it to be true, no man can tell, who has not learned, from the logic of Aristotle, to know what a proposition, and what a syllogism is. There he will learn, that every proposition affirms or denies something of some other thing. What is affirmed or denied is called the Predicate; and that of which it is affirmed or denied, is called the Subject. The predicate being a more general idea than the subject of which it is predicated, must contain or include it, if it be an affirmative proposition; or if it be a negative proposition, it must exclude it. This is the nature of propositions: And as to syllogism, the use of it is to prove any proposition that is not self-evident. And this is done by finding out what is called a middle term; that is, a term connected with both the predicate and the subject of the proposition to be proved. Now, the proposition to be pro here is, that man is a substance; or, in other wor substance can be predi

of ancient philosophy than Mr. Locke did, it will be necessary to explain in what sense one idea can be said to contain another, or the idea less general can be said to be a part of the more general. And, in the first place, it is not in the sense that one body is said to be a part of another, or the greater body to contain the lesser; nor is it as one number is said to contain another; but it is virtually or potentially that the more general idea contains the less general. In this way the genus contains the species; for the genus may be predicated of every species under it, whether existing or not existing; so that virtually it contains all the specieses under it, which exist or may exist. And not only does the more general contain the less general, but (what at first sight may appear surprising) the less general contains the more general, not virtually or potentially, but actually. Thus, the genus animal contains virtually man, and every other species of animal either existing or that may exist: But the genus animal is contained in man, and in other animals actually; for man cannot exist without being in actuality, and not potentially only an animal."*

If we have recourse to Dr. Gillies for a little more light upon this question, we shall meet with a similar disappointment. According to him, the meaning of the phrases in question is to be sought for in the following definition of Aristotle: "To say that one thing is contained in another, is the same as saying, that the second can be predicated of the first in the full extent of its signification; and one term is predicated of another in the full extent of its signification, when there is no particular denoted by the subject, to which the predicate does not apply."