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crystal is but part of opaque crystal. We increase the intent of meaning of a term by joining adjectives, or phrases equivalent to adjectives, to it, 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 versâ, 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 all men to be mortals.

There is no limit to the amount of meaning which a term may have. 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 a.

Abstract Terms.

Comparison of different 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 as 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 called qualities, and denoted 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 can in addition imply. The adjective 'red' is the name of red objects, but it implies the possession by them of the quality redness; but this latter term has one single meaning-the quality alone. Thus it arises that abstract terms are incapable of number or plurality. Red objects are numerically distinct each from each, and there are a multitude of such objects; but redness is a single existence 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,

a J. S. Mill, 'System of Logic,' Book I. chap. ii. section 5. Jevons' 'Elementary Lessons in Logic,' pp. 41-43; 'Pure Logic,' p. 6. See also Shedden's 'Elements of Logic,' London, 1864, pp. 14, &c.

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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 or unity. In virtue of this unity we acquire the power of treating all instances of such quality as we may treat any one. We possess, in short, general knowledge.

Substantial Terms.

Logicians appear to have taken very little notice of a large 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 physically independent of other bodies.

It is only when we break up, by actual mechanical division, the uniform whole which forms the meaning of a substantial term, that we introduce the notion of number. Piece of gold is a term capable of plurality; for there may be an endless variety of pieces discriminated

from each other, either by their various shapes and sizes, or, in the absence of such marks, by occupying simultaneously different parts of space. In substance they are one; as regards the properties of space they are many. We need not further pursue this distinction between unity and plurality until we come to consider the principles of number in a subsequent chapter.

Collective Terms.

We must clearly distinguish between the collective and the general meaning 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 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 or circumstances which are true alike of the whole and its parts. Thus a number of organ pipes tuned in unison produce an aggregate of sound which is of exactly the same

pitch as each separate sound. In the case of substantial terms, certain qualities may be present equally in each minutest part as in the whole. The chemical nature of the largest mass of pure carbonate of lime in existence is the same as the nature of the smallest particle. In the case of abstract terms, again, we cannot draw a distinction between whole and part; what is true of redness in any case is always true of redness, so far as it is merely red.

Synthesis of Terms.

We continually combine simple terms together so as to form new terms of more complex meaning. Thus, to increase the intension of meaning of a term we write it with an adjective or a phrase of adjectival nature. By joining brittle' to 'metal,' we obtain a combined term, 'brittle metal,' which denotes a certain portion of the metals, namely such as are selected on account of possessing the quality of brittleness. As we have already seen, 'brittle metal' possesses less extension and greater intension than metal. Nouns, prepositional phrases, participial phrases and subordinate propositions may also be added to terms so as to increase their intension and decrease their extension.

In our symbolic language we need some mode of indicating this junction of terms, and the most convenient device will be the simple juxtaposition of the distinct letter-terms. Thus if A mean brittle, and B mean metal, then AB will mean brittle metal. Nor need there be any limit to the number of letters thus joined together, or the complexity of the notions which they may represent. Thus if we take the letters

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