(b) The second limit of Definition is the impossibility of exhausting infinity, which would be necessary in order to convey the meaning of the name of any individual thing or person.  For, as we saw in chap. iv., if in attempting to define a proper name we stop short of infinity, our list of qualities or properties may possibly be found in two individuals, and then it becomes the definition of a class-name or general name, however small the actual class.  Hence we can only give a Description of that which a proper name denotes, enumerating enough of its properties to distinguish it from everything else as far as our knowledge goes.

Sec. 8.  The five Predicables (Species, Genus, Difference, Proprium, Accident) may best be discussed in connection with Classification and Definition; and in giving an account of Classification, most of what has to be said about them has been anticipated.  Their name, indeed, connects them with the doctrine of Propositions; for Predicables are terms that may be predicated, classified according to their connotative relation to the subject of a proposition (that is, according to the relation in which their connotation stands to the connotation of the subject):  nevertheless, the significance of the relations of such predicates to a subject is derivative from the general doctrine of classification.

For example, in the proposition ‘X is Y,’ Y must be one of the five sorts of predicables in relation to X; but of what sort, depends upon what X (the subject) is, or means.  The subject of the proposition must be either a definition, or a general connotative name, or a singular name.

If X be a definition, Y must be a species; for nothing but a general name can be predicated of a definition:  and, strictly speaking, it is only in relation to a definition (as subject) that species can be a predicable; when it is called Species predicabilis (1).

If X be a connotative name, it is itself a species (Species subjicibilis); and the place of the subject of a proposition is the usual one for species.  The predicate, Y, may then be related to the species in three different ways.  First, it may be a definition, exactly equivalent to the species;—­in fact, nothing else than the species in an explicit form, the analysis of its connotation.  Secondly, the predicate may be, or connote, some part only of the definition or connotation of the species; and then it is either genus (2), or difference (3).  Thirdly, the predicate may connote no part of the definition, and then it is either derivable from it, being a proprium (4), or not derivable from it, being an accident (5).  These points of doctrine will be expanded and illustrated in subsequent pages.

If X be a singular name, deriving connotation from its constituent terms (chap. iv.  Sec. 2), as ‘The present Emperor of China,’ it may be treated as a Species subjicibilis.  Then that he is ‘an absolute monarch,’ predicates a genus; because that is a genus of ‘Emperor,’ a part of the singular name that gives it connotation.  That he wears a yellow robe is a proprium, derivable from the ceremonial of his court.  That he is thirty years of age is an accident.