each object as an aggregate of qualities, and acquires the power of dwelling at will upon one or other of those qualities to the exclusion of the rest. Logical abstraction, in short, comes into play, and the mind becomes capable of reasoning, not merely about objects which are physically complete and concrete, but about things which may be thought of separately in the mind though they exist not separately in nature. We can think of the hardness of a rock, or the colour of a flower, and thus produce abstract notions, denoted by abstract terms, which will form a subject for further consideration.

At the same time arise general notions and classes of objects. We cannot fail to observe that the quality hardness exists in many objects, for instance in many fragments of rock; mentally joining these together, we create the class hard object, which will include, not only the actual objects examined, but all others which may happen to agree with them, as they agree with each other. As our senses cannot possibly report to us all the contents of space, we cannot usually set any limits to the number of objects which may fall into any such class. At this point we begin to perceive the power and generality of thought, which enables us in a single act to treat of indefinitely or even infinitely numerous objects. We can safely assert that whatever is true of any one object coming under a class is true of any of the other objects so far as they possess the common qualities implied in their belonging to the class. We must not place a thing in a class unless we are prepared to believe of it all that is believed of the class in general; but it remains a matter of important consideration to decide how far and in what manner we can safely undertake thus to assign the place of objects in that general system of classification which constitutes the body of science.

Twofold Meaning of General Names.

Etymologically the meaning of a name is that which we are caused to think of when the name is used. Now every general name causes us to think of some one or more of the objects belonging to a class; it may also cause us to think of the common qualities possessed by those objects,

A name is said to denote the object of thought to which it may be applied; it implies at the same time the possession of certain qualities or circumstances. The objects denoted form the extent of meaning of the term; the qualities implied form the intent of meaning. Crystal is the name of any substance of which the molecules are arranged in a regular geometrical manner. The substances or objects in question form the extent of meaning; the circumstance of having the molecules so arranged forms the intent of meaning.

When we compare general terms together, it may often be found that the meaning of one is included in the meaning of another. Thus all crystals are included among material substances, and all opaque crystals are included among crystals; here the inclusion is in extension. We may also have inclusion of meaning in regard to intension. For, as all crystals are material substances, the qualities implied by the term material substance must be among those implied by crystal. Again, it is obvious that while in extension of meaning opaque crystals are but a part of crystals, in intension of meaning crystal is but part of opaque crystal. We increase the intent of meaning of a term by joining to it adjectives, or phrases equivalent to adjectives, and the removal of such adjectives of course decreases the intensive meaning. Now, concerning such changes of meaning, the following all-important law holds universally true :- When the intent of meaning of a term is increased the extent is decreased; and vice versa, when the extent is increased the intent is decreased. In short, as one is increased the other is decreased.

This law refers only to logical changes. The number of steam-engines in the world may be undergoing a rapid increase without the intensive meaning of the name being altered. The law will only be verified, again, when there is a real change in the intensive meaning, and an adjective may often be joined to a noun without making a change. Elementary metal is identical with metal; mortal man with man; it being a property of all metals to be elements, and of all men to be mortals.

There is no limit to the amount of meaning which a term may have. A term may denote one object, or many, or an infinite number; it may imply a single quality, if such

there be, or a group of any number of qualities, and yet the law connecting the extension and intension will infallibly apply. Taking the general name planet, we increase its intension and decrease its extension by prefixing the adjective exterior; and if we further add nearest to the earth, there remains but one planet, Mars, to which the name can then be applied. Singular terms, which denote a single individual only, come under the same law of meaning as general names. They may be regarded as general names of which the meaning in extension is reduced to a minimum. Logicians have erroneously asserted, as it seems to me, that singular terms are devoid of meaning in intension, the fact being that they exceed all other terms in that kind of meaning, as I have elsewhere tried to show.1

Abstract Terms.

Comparison of objects, and analysis of the complex resemblances and differences which they present, lead us to the conception of abstract qualities. We learn to think of one object as not only different from another, but ast differing in some particular point, such as colour, or weight, or size. We may then convert points of agreement or difference into separate objects of thought which we call qualities and denote by abstract terms. Thus the term redness means something in which a number of objects agree as to colour, and in virtue of which they are called red. Redness forms, in fact, the intensive meaning of the term red.

Abstract terms are strongly distinguished from general terms by possessing only one kind of meaning; for as they denote qualities there is nothing which they cannot in addition imply. The adjective "red" is the name of red objects, but it implies the possession by them of the quality

1 Jevons' Elementary Lessons in Logic, pp. 41-43; Pure Logic, p. 6. See also J. S. Mill, System of Logic, Book I. chap. ii. section 5, and Shedden's Elements of Logic, London, 1864, pp. 14, &c. Professor Robertson objects (Mind, vol. i. p. 210) that I confuse singular and proper names; if so, it is because I hold that the same remarks apply to proper names, which do not seem to me to differ logically from singular names.

redness; but this latter term has one single meaning-the quality alone. Thus it arises that abstract terms are incapadle of plurality. Red objects are numerically distinct each from each, and there are multitudes of such objects; but redness is a single quality which runs through all those objects, and is the same in one as it is in another. It is true that we may speak of rednesses, meaning different kinds or tints of redness, just as we may speak of colours, meaning different kinds of colours. But in distinguishing kinds, degrees, or other differences, we render the terms so far concrete. In that they are merely red there is but a single nature in red objects, and so far as things are merely coloured, colour is a single indivisible quality. Redness, so far as it is redness merely, is one and the same everywhere, and possesses absolute oneness. In virtue of this unity we acquire the power of treating all instances of such quality as we may treat any one. We possess, li short, general knowledge.

Substantial Terms.

Logicians appear to have taken little notice of a class of terms which partake in certain respects of the character of abstract terms and yet are undoubtedly the names of concrete existing things. These terms are the names of substances, such as gold, carbonate of lime, nitrogen, &c. We cannot speak of two golds, twenty carbonates of lime, or a hundred nitrogens. There is no such distinction between the parts of a uniform substance as will allow of a discrimination of numerous individuals. The qualities of colour, lustre, malleability, density, &c., by which we recognise gold, extend through its substance irrespective of particular size or shape. So far as a substance is gold, it is one and the same everywhere; so that terms of this kind, which I propose to call substantial terms, possess the peculiar unity of abstract terms. Yet they are not abstract; for gold is of course a tangible visible body, entirely concrete, and existing independently of other bodies.

It is only when, by actual mechanical division, we break up the uniform whole which forms the meaning of a substantial term, that we introduce number. Piece of gold

is a term capable of plurality; for there may be a great many pieces discriminated either by their various shapes and sizes, or, in the absence of such marks, by simultaneously occupying different parts of space. In substance they are one; as regards the properties of space they are many.1 We need not further pursue this question, which involves the distinction between unity and plurality, until we consider the principles of number in a subsequent chapter.

Collective Terms.

We must clearly distinguish between the collective and the general meanings of terms. The same name may be used to denote the whole body of existing objects of a certain kind, or any one of those objects taken separately. Man" may mean the aggregate of existing men, which we sometimes describe as mankind; it is also the general name applying to any man. The vegetable kingdom is the name of the whole aggregate of plants, but "plant itself is a general name applying to any one or other plant. Every material object may be conceived as divisible into parts, and is therefore collective as regards those parts. The animal body is made up of cells and fibres, a crystal of molecules; wherever physical division, or as it has been called partition, is possible, there we deal in reality with a collective whole. Thus the greater number of general terms are at the same time collective as regards each individual whole which they denote.

It need hardly be pointed out that we must not infer of a collective whole what we know only of the parts, nor of the parts what we know only of the whole. The relation of whole and part is not one of identity, and does not allow of substitution. There may nevertheless be qualities which are true alike of the whole and of its parts. A number of organ-pipes tuned in unison produce an aggregate of sound which is of exactly the same pitch as each

1 Professor Robertson has criticised my introduction of "Substantial Terms" (Mind, vol. i. p. 210), and objects, perhaps correctly, that the distinction if valid is extra-logical. I am inclined to think, however, that the doctrine of terms is, strictly speaking, for the most part extra-logical.