§ 349. Hence proper names do not admit of definition, except just in so far as they do possess some slight degree of intension: Thus we can define the term 'John' only so far as to say that 'John' is the name of a male person. This is said with regard to the original intension of proper names; their acquired intension will be considered later.
§ 350. Again, since definition is unfolding the intension of a term, it follows that those terms will not admit of being defined whose intension is already so simple that it cannot be unfolded further. Of this nature are names of simple attributes, such as greenness, sweetness, pleasure, existence. We know what these things are, but we cannot define them. To a man who has never enjoyed sight, no language can convey an idea of the greenness of the grass or the blueness of the sky; and if a person were unaware of the meaning of the term 'sweetness,' no form of words could convey to him an idea of it. We might put a lump of sugar into his mouth, but that would not be a logical definition.
§ 351. Thus we see that, for a thing to admit of definition, the idea of it must be complex. Simple ideas baffle definition, but at the same time do not require it. In defining we lay out the simpler ideas which are combined in our notion of something, and so explain that complex notion. We have defined 'triangle,' when we analyse it into 'figure' and 'contained by three lines.' Similarly we have defined 'substance' when we analyse it into 'thing' and 'which can be conceived to exist by itself.'
§ 352. But when we get to 'thing' we have reached a limit. The Summum Genus, or highest class under which all things fall, cannot be defined any more than a simple attribute; and for the very good reason that it connotes nothing but pure being, which is the simplest of all attributes. To say that a thing is an 'object of thought' is not really to define it, but to explain its etymology, and to reclaim a philosophical term from its abuse by popular language, in which it is limited to the concrete and the lifeless. Again, to define it negatively and to say that a thing is 'that which is not nothing' does not carry us any further than we were before. The law of contradiction warrants us in saying as much as that.
§ 353. Definition is confined to subject-terms, and does not properly extend to attributives. For definition is of things through names, and an attributive out of predication is not the name of anything. The attributive is defined, so far as it can be, through the corresponding abstract term.
§ 354. Common terms, other than attributives, ought always to admit of definition. For things are distributed by the mind into classes owing to their possessing certain attributes in common, and the definition of the class-name can be effected by detailing these attributes, or at least a sufficient number of them.
§ 355. It is different with singular terms. Singular terms, when abstract, admit of definition, in so far as they are not names of attributes so simple as to evade analysis. When singular terms are concrete, we have to distinguish between the two cases of proper names and designations. Designations are connotative singular terms. They are formed by limiting a common term to the 'case in hand.' Whatever definition therefore fits the common term will fit also the designation which is formed from it, if we add the attributes implied by the limitations. Thus whatever definition fits the common term 'prime minister' will fit also the singular term 'the present prime minister of England' by the addition to it of the attributes of place and time which are indicated by the expression. Such terms as this have a definite amount of intension, which can therefore be seized upon and expounded by a definition.
§ 356. But proper names, having no original intension of their own, cannot be defined at all; whereas, if we look upon them from the point of view of their acquired intension, they defy definition by reason of the very complexity of their meaning. We cannot say exactly what 'John' and 'Mary' mean, because those names, to us who know the particular persons denoted by them, suggest all the most trifling accidents of the individual as well as the essential attributes of the genus.
§ 357. Definition serves the practical purpose of enabling us mentally to distinguish, or, as the name implies, 'mark off' the thing defined from all other things whatsoever. This may seem at first an endless task, but there is a short cut by which the goal may be reached. For, if we distinguish the thing in hand from the things which it is most like, we shall, 'a fortiori,' have distinguished it from things to which it bears a less resemblance.
§ 358. Hence the first thing to do in seeking for a definition is to fix upon the class into which the thing to be defined most naturally falls, and then to distinguish the thing in question from the other members of that class. If we were asked to define a triangle, we would not begin by distinguishing it from a hawser, but from a square and other figures with which it is more possible to confound it. The class into which a thing falls is called its Genus, and the attribute or attributes which distinguish it from other members of that class are called its Difference.