But generalisation is not only from individuals to species. We may apply abstraction to the common terms denoting species, and ascend to a class still higher. The words dog, sheep, cow, lion, horse, each denote a common notion obtained by abstraction and generalisation, from the individuals of which they are respectively predicable; and as in these we discover attributes common to all of them, we may resume the former process, and divest these classes of their respective formal characteristics, and express the notion comprehending all the marks in which they resemble each other by the common term, quadruped. Generalisation may evidently be carried to almost any extent by considering common nouns (for instance, quadruped) as singular; for by omitting their points of difference, we arrive at new aggregates, expressed by more general terms. Thus from quadruped we may arrive at the more general term, animal, and from animal we may obtain the still more general term, corporeal being. By proceeding in this way, laying aside points of difference, and considering only points of resemblance, we arrive ultimately at substance or being, the highest possible generalisation.

It will be seen from the foregoing, that abstraction is in a certain sense analytic in its character; for by it we separate mentally all the attributes and marks of a whole. Generalisation is, on the other hand, synthetic in its nature; for by it we collect into classes all such attributes or marks of wholes as have common points of resemblance or agreement.

It is not requisite that the individuals from which we obtain a common or general notion should co-exist. Succession in point of time is sufficient, e. g., We could have the common notion king, if only one had existed at a given time, in the same manner as we have the common notion Pope, which is founded on the points of agreement noted in a succession of individual Popes. We can reason about either of them without necessarily referring to any one individual king or Pope.

The process of abstraction, and the use of common terms, are subordinate to that arrangement and classification, without which our knowledge could not be applied to much practical use. The elements of our knowledge are almost unlimited, both in number and variety; and on this account classification becomes an unavoidable necessity. After we have abstracted and generalised accurately, we can make the results the objects of separate examination. We may, for instance, contemplate at pleasure, number, form, weight, colour, motion, attraction, heat, electricity, &c.; and the results are related to some of the most important sciences with which mankind are conversant.

It follows that the only limit to our power of forming classes is the capability of tracing differences upon which to ground distinctions; and the only rule that requires to be observed, is to make the classification subservient to our convenience, whether for the purpose of recording or examining.

Common terms expressive of a class are nouns substantive; as, field, flower, city, rock, tower, desert, &c.; but points of difference, whether essential or accidental, are denoted by adjectives, and the use of the adjective is to limit the meaning of the noun to certain individuals. Of themselves, adjectives have no independent meaning; they merely indicate or connote attributes, whether of objects, of attributes, or of feelings. By means of adjectives, instead of requiring a separate noun substantive for each object to be denoted, one noun-substantive, coupled with appropriate adjectives, will serve to denote many objects. Thus we say, tall man, short man, amiable man, active man, useful man, &c. So of colours, we call them bright, dark, pleasing, gloomy, vivid, lively, &c.; and

a It is the employment of the power of generalising that constitutes the characteristic distinction between the higher and the lower animals. The highest form of instinct can neither form nor comprehend a general notion. It cannot go beyond the knowledge of an individual and its accidents.

of characters, we say they are just, cruel, decided, vacillating, sagacious, reflecting, &c.; and of affections, we say they are intense, moderate, absorbing, divided, lasting.

It may not be out of place to refer here briefly to the furious controversy which long existed between the sects of Realists and Nominalists, regarding the nature of Universals, and which only terminated when a more important question -the Reformation-diverted their attention from it. Porphyry, in his treatise on the predicables, probably originated the strife by the following passage:-'Whether,' he says, genus or species are substances, or exist in bare thought alone, or, supposing them to be substances, whether they are material or immaterial, and, again, whether they exist separately or in composition with sensible objects, I must decline discussing. The subject is profound, and needs a separate and more detailed inquiry.'

Averroës may be regarded as the founder of the Realists, although his view of the matter was but a species of neoPlatonism. He held that genus and species were substances, but left it matter of doubt whether these substances existed apart from matter, or whether they were to be considered as always present in the concrete. Among the schoolmen, long

a Reid states the Platonic doctrine of ideas summarily as follows:-' Plato and his masters held that there are objects of intellect of a superior order and nature which are permanent and immutable. These are ideas, or universal natives, of which the objects of sense are only the images and shadows. To these ideas they ascribed the most magnificent attributes. Of man, of a rose, of a circle, and of every species of things, they believed that there is one idea or form, which existed from eternity, before any individual of the species was formed; that the idea is the exemplar or pattern, according to which the Deity formed the individual species; that every individual of the species participates of this idea, which constitutes its essence. Thus the idea of every species, though one and immutable, might be considered in their different views or respects-first, as having an eternal existence before there was any individual species; secondly, as existing in every individual of that species without division or multiplication, and making the essence of the species; and, thirdly, as an object of intellect and science in man.-Int. Powers, essay 5, cap. 6.

before Nominalism took its rise, this doctrine was generally considered heterodox. They acquiesced in it only in conceiving the Universal to be an actual existence. They held that genera and species were really existing things-that they existed actually as substances, and not merely as conceptions of the mind-that there was an universal man existing as one and the same in Socrates and Plato, and all the individuals of the species-and that the various individuals are formed by the addition of accidents to the species.

Roscelin of Compeigne founded the sect of the Nominalists. He held that universals were nothing but names. Roscelin was followed by Abelard, who held an intermediate view between absolute nominalism and realism. He believed

universals to be conceptions, but without an independent and objective reality. In order, however, that these conceptions should be formed and retained in the mind, they must rest on the signs of language; but he made conceptions turn on the proposition, while Roscelin made them turn on the simple term. His doctrine, however, continued vague and assailable until the days of Occam, whose opinions correspond with that of modern conceptualists." He held that genera and species existed, but existed only in the mind-that every universal is really a singular in itself, and therefore is only a universal in virtue of its signification, which is a sign of many things.b The following is a specimen of his reasoning:—' If the realist opinion,' he remarks, were true, God could not annihilate one individual without destroying all; for to annihilate one individual, he must destroy all that is of its essence. Consequently, he must destroy the universal which exists both in it and in other individuals; and these could not continue to exist when deprived of a part of their substance, such as the universal is supposed to be.'

a Aristotle has been claimed as a realist, a conceptualist, and a nominalist. b Nullum universale est aliqua substantia extra animam existens, Occam.

SECTION II.

EXTENSION AND COMPREHENSION.

The extension of a term means the number of individual things of which severally that term may be predicated; in other words, it regards the number of species into which a genus, or the number of individuals into which a species may be divided. Thus of the term flower the parts of extension are violet, lily, blue-bell, daisy, buttercup, &c., because of all these and of as many more as answer to the description, the term flower may be predicated. For as we have seen, common terms denote a whole class, and any individual in that class; and may therefore be predicated of all or any one of these individuals.

The parts of extension of a genus are consequently the species contained under it, and of a species the individuals contained under it.

The comprehension-otherwise called the intension-of a term means all the simple notions which, taken together, make up the more complex notion signified by the term; in other words, it is the aggregate of all the known properties of a genus, species, or individual, to which it may be applied. Thus the notions of substance, body, life, sensation, and reason, are the parts of comprehension of the term man.

By keeping in view what is meant by the extension, and what by the comprehension of a term, it will be seen that a singular term has the least extension of all; for it can only be predicated of the one individual thing to which it belongs, while, on the contrary, a singular term has a greater comprehension than a term denoting a class, i. e., a common term.

Of common terms some have a wider and some a more restricted extension, according to the number of things to which they may be applied in the same sense. Common