§ 359. If definition thus consists in referring a thing to a class, we see a further reason why the summum genus of all things cannot be defined.
§ 360. We have said that definition is useful in enabling us to distinguish things from one another in our minds: but this must not be regarded as the direct object of the process. For this object may be accomplished without giving a definition at all, by means of what is called a Description. By a description is meant an enumeration of accidents with or without the mention of some class-name. It is as applicable to proper names as to common terms. When we say 'John Smith lives next door on the right-hand side and passes by to his office every morning at nine o'clock,' we have, in all probability, effectually distinguished John Smith from other people: but living next, &c., cannot be part of the intension of John Smith, since John Smith may change his residence or abandon his occupation without ceasing to be called by his name. Indirectly then definition serves the purpose of distinguishing things in the mind, but its direct object is to unfold the intension of terms, and so impart precision to our thoughts by setting plainly before us the meaning of the words we are using.
§ 361. But when we say that definition is unfolding the intension of terms, it must not be imagined that we are bound in defining to unfold completely the intension of terms. This would be a tedious, and often an endless, task. A term may mean, or convey to the mind, a good many more attributes than those which are stated in its definition. There is no limit indeed to the meaning which a term may legitimately convey, except the common attributes of the things denoted by it. Who shall say, for instance, that a triangle means a figure with three sides, and does not mean a figure with three angles, or the surface of the perpendicular bisection of a cone? Or again, that man means a rational, and does not mean a speaking, a religious, or an aesthetic animal, or a biped with two eyes, a nose, and a mouth? The only attributes of which it can safely be asserted that they can form no part of the intension of a term are those which are not common to all the things to which the name applies. Thus a particular complexion, colour, height, creed, nationality cannot form any part of the intension of the term 'man.' But among the attributes common to a class we cannot distinguish between essential and unessential, except by the aid of definition itself. Formal logic cannot recognise any order of priority between the attributes common to all the members of a class, such as to necessitate our recognising some as genera and differentiae and relegating others to the place of properties or inseparable accidents.
§ 362. The art of giving a good definition is to seize upon the salient characteristics of the thing defined and those wherefrom the largest number of other attributes can be deduced as consequences. To do this well requires a special knowledge of the thing in question, and is not the province of the formal logician.
§ 363. We have seen already, in treating of the Heads of Predicables (§ 325), that the difference between genus and difference on the one hand and property on the other is wholly relative to some assumed definition. Now definitions are always to a certain extent arbitrary, and will vary with the point of view from which we consider the thing required to be defined. Thus 'man' is usually contrasted with 'brute,' and from this point of view it is held a sufficient definition of him to say that he is 'a rational animal,' But a theologian might be more anxious to contrast man with supposed incorporeal intelligences, and from this point of view man would be defined as an 'embodied spirit.'
§ 364. In the two definitions just given it will be noticed that we have really employed exactly the same attributes, only their place as genus and difference has been reversed. It is man's rational, or spiritual, nature which distinguishes him from the brutes: but this is just what he is supposed to have in common with incorporeal intelligences, from whom he is differentiated by his animal nature.
[Illustration]
This illustration is sufficient to show us that, while there is no absolute definition of anything, in the sense of a fixed genus and difference, there may at the same time be certain attributes which permanently distinguish the members of a given class from those of all other classes.
§ 365. The above remarks will have made it clear that the intension of a term is often much too wide to be conveyed by any definition; and that what a definition generally does is to select certain attributes from the whole intension, which are regarded as being more typical of the thing than the remainder. No definition can be expected to exhaust the whole intension of a term, and there will always be room for varying definitions of the same thing, according to the different points of view from which it is approached.
§ 366. Names of attributes lend themselves to definition far more easily than names of substances. The reason of this is that names of attributes are primarily intensive in force, whereas substances are known to us in extension before they become known to us in intension. There is no difficulty in defining a term like 'triangle' or 'monarchy,' because these terms were expressly invented to cover certain attributes; but the case is different with such terms as 'dog,' 'tree,' 'plant,' 'metal,' and other names of concrete things. We none of us have any difficulty in recognising a dog or tree, when we see them, or in distinguishing them from other animals or plants respectively. We are therefore led to imagine that we know the meaning of these terms. It is not until we are called upon for a definition that we discover how superficial our knowledge really is of the common attributes possessed by the things which these names denote.