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 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 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 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 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