(a) According to Hamilton, abstraction is not properly a positive act; it is merely the negation of attention. Concentrated attention on a single point leads to an abstraction of consciousness from others in an object. Abstraction should not be applied to that on which attention is concentrated. Here we prescind, rather than abstract. Of the qualities A, B, and C, we prescind A in abstracting from B and C.

Further, abstraction in this sense, as performed on individual objects, gives only an individual notion. "The notion of the figure of the desk before me is an abstract idea-an idea that makes part of the total notion of that body, and on which I have concentrated my attention, in order to consider it exclusively. This idea is abstract, but it is at the same time individual; it represents the figure of this particular desk, and not the figure of any other body."-(Met., L. ii. 278.) There are thus individual abstract notions, and abstract general notions.

§ 105. This gives rise to the distinction between Abstract and Concrete Terms or names. Humanity is said to be abstract; and man is said to be concrete. Redness is abstract; red is concrete. The difference is said to be that the latter, the concrete noun, indicates an attribute or attributes in or with a being, something existing or conceived as existing; whereas the abstract noun is applied to the mere attribute or attributes. Now I think that this is more a distinction of language than of thought. It is true that human, man, coloured, imply directly something to which these attributes belong; but humanity, colour, imply equally, if not so directly, an object to which they belong, or subject in which they inhere. We cannot realise to thought the attributes implied in the abstract term humanity, without thinking of man in which they are embodied. So far as language goes, humanity indicates attributes a step further removed from the concrete than man, but that is all. If we actually give meaning either to the notions humanity or man, we must equally embody them in a definite concrete image or object. Mere abstract thought is an impossibility. The abstract exists only in the term; it is not actual thought; it is the mere possibility of our realising thought.

§ 106. No doubt we do make abstract terms the subjects of propositions. We speak of virtue, duty, humanity, as right, obligatory, worthy. But we have a tendency to make abstractions realities, and to think that these by themselves may people the universe; whereas it is our thought of them which gives them life-even meaning. In this point of view, the individual object alone is the real-the abstract is a mere

passing show or dim shadow of the individual as the real, imperfectly representing the fact of our experience. Neither the abstract nor the general, as in thought, is the real for us; by these we mean at the furthest to imply that there are beings, definite realities of space and time, and that these realities have certain mutual relations or attributes. The very fact of our giving attributes to things means that they are, and that they are diverse as well; for all similarity or likeness implies that the things known as similar are also diverse diverse in their true existence as individuals of space and time. Otherwise similarity would be meaningless; there would be not similarity, but simple identity. But it is things or beings, otherwise different, which we hold together by the bond of resemblance.

§ 107. An abstract idea is thus primarily that of a quality or attribute, and it may be regarded as opposed to the concrete when it forms one of the qualities of a lower notion. Thus in the scale, organisation is abstract in respect of animal, for it is higher up and enters into the lower animal as a determining element or quality. The abstract is thus always a less determinate notion than the concrete, the lower or concrete being fuller as it were of attributes or qualities. In this way the abstract quality is at the root of the generic idea.

§ 108. The course of inquiry which has now been pursued, in regard to the nature and formation of notions, has a direct bearing on a question much debated by psychologists and philologists, I refer to the origin of our class-knowledge; in other words, the primum cognitum. The question is, What do we first apprehend-the individual object or the general idea?

(1.) We have already found that our knowledge of objects is at first vague and indefinite; (2.) we classify them according to certain very general resemblances, as of time and place; (3.) we are attracted by certain striking features in the objects, which we exclusively attend to; and (4.) we generalise, or transform these abstracted features into general ideas; (5.) we then look upon numerically different objects as possessing or embodying this attribute or those attributes. We thus in the end individualise objects by distinguishing them as members of a class, or as possessing this or that definite attribute. It is really in virtue of the general idea or notion

that we regard objects as distinguished from each other, as belonging to this class of things and not to that. So that our general knowledge is the means of setting the objects of our experience in the precise light of individual objects, as special instances of general notions.

§ 109. In reply, accordingly, to the question now proposed of the primum cognitum-I agree with those who hold, in opposition to a certain class of philosophers, that we do not at first know individual objects in their true character as individuals. Our knowledge of all objects is at first vague and indefinite; and the first step towards clear or definite knowledge is when we attend to the striking feature of an object, when, in a word, we begin to abstraet. The knowledge we gain by abstraction is further transformed into the general by an increasing experience of new objects with a feature similar to that in the object we originally observed. Having reached the point of a general idea, we now have a clear and distinct apprehension of objects as individuals,— as the members of different and definite classes. So that our knowledge may be viewed as progressing from the dimness of the indefinite, through the abstract, to the clearness of general and individual vision.

§ 110. This view, however, is not less opposed to the doctrine which makes our knowledge begin with the definitely general, and which has been attributed to Leibnitz, among other philosophers. It seems to me impossible, from the nature of the case, to maintain with truth that our knowledge begins with the general idea. This involves the conception of a plurality of individual objects, possessing a common feature. These objects are necessarily already in our experience, and intelligence, dealing with them, forms the general idea. It would, indeed, I believe, be more correct to say that in a sense our thought begins at once with the general and the individual, that the two dawn on consciousness together; that as we are elaborating the concept out of individuals, we are also making these themselves distinct objects of consciousness. In truth, as we do not think the individual apart from the general, or the general apart from the individual, this process of a double or twofold evolution of intelligence really takes place. Perfected or matured thought really commences with the general idea and the individual instance of it at one and the same time.

§ 111. The doctrine now advanced thus supersedes the whole of the old controversy regarding the primum cognitum. And I hold that this view applies very emphatically, not only to our general ideas but to our universal ideas as well. We have no universal ideas in any proper sense of the word before the particular. We have no idea of Being before we apprehend some being, or being in a definite form. Nor have we the universal ideas of unity, identity, quantity, quality, relation, and so on, before the particulars or perceptions in which they are embodied. Chronologi

cally, these, the universal and the particular, are realised together, and each is necessary to the other, though they have different sources in the mind. And I hold it especially wrong to say that the universal develops into the particular, or that the particular is evolved out of it. This is a meaningless statement. It supposes the universal to be first in thought, whereas it has no meaning at all, unless it is along with the particular in thought. There is a logical concomitance between the two, but there is no logical or ideal priority; and this is needed for evolution. A theory of this sort which constantly charges abstraction on the opposite view, is itself abstraction run mad.

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CHAPTER X.

THE CONCEPT-ITS CHARACTERISTICS SPECIALLY CONSIDERED.

§ 112. The general characteristics of the Concept or Notion, viewed as the product of Abstraction and Generalisation, may be stated as follows:

(1.) The Concept is Representative.

(2.) It is Partial or Inadequate.

(3.) It is a knowledge of Relation, which is not picturable. (4.) It has two sides or aspects-that of Comprehension and

that of Extension.

(5.) It is perfected by being expressed in a Term.

§ 113. As the sum of notes or marks in which a plurality of objects agree, it is a Notion; as that by means of which several are grasped as one, or as the ideal unity of several objects, it is a Concept-holding in one through the common quality or qualities. Its first and essential function is, therefore, the power of representing any one of the individual objects, actual or possible, which may possess the quality or qualities it contains.

§ 114. To this it should be added, as Esser has observed, that a concept is properly the representation of an object not merely through marks which distinguish it from other objects in general, but through its distinctive marks, that is, those marks which distinguish it from the objects which come nearest to it. The distinctive marks of an object are those which make it to be this, not that—that is, they are peculiar and essential. E.g., the concept of a square is not simply that of a four-sided figure, for this does not distinguish it from an oblong or a rhombus; but of a four-sided figure which has all its sides equal, and all its angles right angles.