ing to Aristotle, constituting the true scientific view of a thing-and all the real knowledge consequently of the properties of the thing depending on the right limitation of this notion-some exact method of arriving at definitions which should express these limitations, and serve as the principles of sciences, became indispensable in such a system of philosophy. But in order to attain such definitions, a process of induction was required,—not merely an induction of that kind, which is only a peculiar form of syllogism, enumerating all the individuals implied in a class instead of the whole class collectively, but an induction of a philosophical character, and only differing from the induction of modern philosophy so far as it is employed about language. We shall endeavour to show this more fully. There are, then, two kinds of induction treated of by Aristotle. The first, that of simple enumeration." (After explaining with ordinary accuracy the first, in fact the only, species of induction, he proceeds :)" But there is also a higher kind of induction employed by Aristotle, and pointed out by him expressly in its subserviency to the exact notions of things, by its leading to the right definitions of them in words. As it appears that words, in a dialectical point of view, are classes more or less comprehensive of observations on things, it is evident that we must gradually approximate towards a definition of any individual notion, by assigning class within class, until we have narrowed the extent of the expression as far as language will admit. (Analyt. Post. ii. c. 13, § 21.) The first definitions of any object are vague, founded on some obvious resemblance which it exhibits compared with other objects. This point of resemblance we abstract in thought, and it becomes, when expressed in language, a genus or class, under which we regard the object as included. A more attentive examination suggests to us less obvious points of resemblance between this object and some of those with which we had classed it before. Thus carrying on the analysis-and by the power of abstraction giving an independent existence to those successive points of resemblance-we obtain subaltern genera or species, or subordinate classes included in that original class with which the process of abstraction commenced. As these several classifications are relative to each other, and dependent on the class with which we first commenced, the definition of any notion requires a successive enumeration of the several classes in the line of abstraction, and hence is said technically to consist of genus and differentia; the genus being the first abstraction, or class to which the object is first referred, and the differentia being the subordinate classes in the same line of abstraction. Now, the process by which we discover these successive genera, is strictly one of philosophical induction. As in the philosophy of nature in general, we take certain facts as the basis of enquiry, and proceed by rejection and exclusion of principles involved in the enquiry, until at last-there appearing no ground for further rejection-we conclude that we are in possession of the true principle of the object examined; so, in the philosophy of language, we must proceed by a like rejection and exclusion of notions implied in the general term with which we set out, until we reach the very confines of that notion of it with which our enquiry is concerned. This exclusion is effected in language, by annexing to the general term denoting the class to which the object is primarily referred, other terms not including under them those other objects or notions to which the

general term applies. For thus, whilst each successive term in the definition, in itself, extends to more than the object so defined,—yet all viewed together do not; and this their relative bearing on the one point constitutes the being of the things. This is thus illustrated by Aristotle :-' If we are enquiring,' he says, 'what magnanimity is, we must consider the instances of certain magnanimous persons whom we know, what one thing they all have so far forth as they are such; as, if Alcibiades was magnanimous, or Achilles, or Ajax ;-what one thing they all have; say, impatience under insult; for one made war, another raged, the other slew himself. Again, in the instances of others, as of Lysander or Socrates—if here it is, to be unaltered by prosperity or adversity;—taking these two cases, I consider, what this apathy in regard to events, and impatience under insult, have the same in them. If, now, they have nothing the same, there must be two species of magnanimity.'" (P. 513.)

Mr Hampden afterwards states, inter alia, that the induction of Aristotle, "having for its object to determine accurately in words the notion of the being of things, proceeds, according to the nature of language, from the general, and ends in the particular; whereas the investigation of a law of nature proceeds from the particular, and ends in the general. Dialectical induction is synthetical, whilst philosophical induction is analytical in the result." On this ground, he explains the meaning of the term (Taywyn), and defends the Induction of Aristotle against its disparagement by Lord Bacon.

We had imagined, that every compend of logic explained the two grand methods of Investigating the Definition; but upon looking into the Oxford treatises on this science, we were surprised to find, that this, among other important matters, had in all of them been overlooked. This may, in part, enable us to surmise, how Mr Hampden could have so misconceived so elementary a point, as to have actually reversed the doctrine, not only of Aristotle, but of all other philosophers. A few words will be sufficient to illustrate the nature of the error.

In the thirteenth chapter (Pacian division) of the second book of the Posterior Analytics, Aristotle treats of the manner of hunting out, as he terms it, the essential nature (Tò Tí EoT, quidditas) of a thing, the enunciation of which nature constitutes its definition. This may be attempted in two contrary ways.— By the one, we may descend from the category, or higher genus of the thing to be defined, dividing and subdividing, through the opposite differences, till we reach the genus under which it is proximately contained; and this last genus, along with the specific difference by which the genus is divided, will be the defini

tion required. By the other, we may ascend from the singulars, contained under the thing to be defined, (which is necessarily an universal,) by an exclusion of their differences, until we attain an attribution common to them all, which attribution will supply the definition sought.-The former of these is, after Plato, called by Aristotle, and logicians in general, the method of Division; the higher genus being regarded as the (universal) whole, the subaltern genera and species as the (subject) parts into which it is divided. The extension here determines the totality.-The latter, which is described but not named by Aristotle, is variously denominated by his followers. Some, as his Greek commentators, taking the totality as determined by the comprehension, view the singulars as so many (essential) wholes, of which the common attribute or definition is a part, and accordingly call this mode of hunting up the essence the Analytic; others again, regarding the genus as the whole, the species and individuals as the parts, style it the Compositive, or Synthetic, or Collective:* while others, in fine, looking simply to the order of the process itself, from the individual to the general, name it the Inductive. These last we shall imitate.

Now, in the chapter referred to, Aristotle considers and contrasts these two methods.-In regard to Division (§ 8-20) he shows on the one hand, (against Plato, who is not named,) that this process is not to be viewed as having any power of demonstration or argument; † and on the other (against Speusippus, as

* "In one respect," says Aristotle," the Genus is called a part of the Species; in another, the Species a part of the Genus."-(Metaph. L. v. c. 25, t. 30. Compare Phys. L. iv. c. 5 (3) t. 23; and Porph. Intr. c. 3, § 39.) In like manner, the same method, viewed in different relations, may be styled either Analysis or Synthesis. This, however, has not been acknowledged; nor has it even attracted notice, that different logicians and philosophers, though severally applying the terms only in a single sense, are still at cross purposes with each other. One calls Synthesis what another calls Analysis,-one calls Progression what another calls Regression; and this both in ancient and modern times. We ourselves think it best to regulate the use of these terms by reference to the notion of a whole and parts, of any kind. This we do, and do professedly. Mr Hampden, but probably without intending it, does the same: in one part of the passage we have quoted, speaking of Division, (his logical induction,) as an "analysis;" in another, describing it as "synthetical." [The total omission of the distinction of Comprehension and Extension (though this be the very turning point of logic), by former Oxford logicians, is remarkable in itself, and has been the cause, as is here exemplified, of much error and confusion. Dr Whately, indeed, not only overlooks the distinction, but he often reverses the language in which it is logically expressed.] This he had elsewhere done; Pr. Analyt. 1. i. c. 31, Post. Analyt. 1. ii. c. 5, et alibi.

we learn from Eudemus, through the Greek expositors), that it is not wholly to be rejected as worthless, being useful, in subserviency always to the other method of induction, to ensure,-that none of the essential qualities are omitted,-that these qualities alone are taken,—and that they are properly subordinated and arranged. In reference to the Inductive method, which is to be considered as the principal, he explains its nature, and delivers various precepts for its due application. (§ 7, 21, ets.)

This summary will enable the reader to understand Mr Hampden's perversion of Aristotle's doctrine.-In the first place: that gentleman is mistaken, in supposing that the philosopher applies the term Induction to any method of investigating the definition discussed by him in the chapter in question. The word does not once occur.-In the second place: he is still farther deceived, in thinking that Aristotle there bestows that name on a descent from the universal to the particular; whereas, in his philosophy -indeed in all philosophies-it exclusively pertains to an ascent from the particular to the universal.-In the third place: he is wrong, in imagining that Aristotle there treats only of a single method, for he considers and contrasts two methods, not only different, but opposed.*-In the fourth place: he is mistaken, in understanding as applied to one contrary, the observations which Aristotle applies, and which are only applicable, in expounding the reverse. For example: he quotes in the note, as pertinent to Division, words of the original relative to Induction; and the instance (from the definition of Magnanimity) adduced to elucidate the one method, is in reality employed by Aristotle to explain the other.-In the fifth place: his error is enhanced, by seeing in his own single method the subordinate of Aristotle's two; and in lauding, as a peculiarly important part of the Aristotelic philosophy, a process in the exposition of which Aristotle has no claim to originality, and to which he himself, here and

* Mr Hampden's error, we suspect, originates in the circumstance that Pacius (whom Duval follows in the Organon) speaks, in his analytic argument of the chapter, of a methodus divisiva and a methodus inductiva; and that Mr Hampden, using Duval's edition, in his extemporaneous study of the subject, not previously aware that there are two opposite methods of investigating the definition, took up the notion that these were merely a twofold expression for the same thing. Mr Hampden is an able man: but to understand Aristotle in any of his works, he must be understood in all; and to be understood in all, he must be long and patiently studied by a mind disciplined to speculation, and familiar with the literature of philosophy.

elsewhere, justly attributes only an inferior importance.—In the sixth place in contradiction equally of his whole philosophy and of the truth of nature, the Stagirite is made to hold that our highest abstractions are first in the order of time; that our process of classification is encentric, not eccentric; that a child generalises substance and accident before egg and white.

"The

Mr Hampden's statement of the Inductive method being thus the reverse of truth, it is needless to say that the etymological explanation he has hazarded of the term (maywyn) must be erroneous. But even more erroneous is the pendant by which he attempts to illustrate his interpretation of that term. ȧmaуwyn, Abduction spoken of by Aristotle, (Anal. Prior. ii. c. 25,) is just the reverse, a leading away, by the terms successively brought from the more accurate notion conveyed by a former one." The Abduction, here referred to, is no more such a "leading away "-than it is a theft. It is a kind of syllogismof what nature we cannot longer trespass on the patience of our readers by explaining. For the same reason we say nothing of some other errors we had remarked in Mr Hampden's account of that branch of the Aristotelic philosophy which we have been now considering.