§ 145. It is a nice question whether the abstract names of relations should themselves be considered relative terms. Difficulties will perhaps be avoided by confining the expression 'relative _term_' to names of concrete things. 'Absolute,' it must be remembered, is a mere negative of 'relative,' and covers everything to which the definition of the latter does not strictly apply. Now it can hardly be said that 'rule' is a name given to a certain abstract thing with direct reference to some other thing, namely, subjection. Rather 'rule' and 'subjection' are two names for identically the same series of facts, according to the side from which we look at them. 'Ruler' and 'subject,' on the other hand, are names of two distinct substances, but each involving a reference to the other.
§ 146. This division then may be said to be based on the number of things involved in the name.
§ 147. Before explaining this division, it is necessary to treat of what is called the Quantity of Terms.
§ 148. A term is possessed of quantity in two ways--
§ 149. The Extension of a term is the number of things to which it applies.
§ 150. The Intension of a term is the number of attributes which it implies.
§ 151. It will simplify matters to bear in mind that the intension of a term is the same thing as its meaning. To take an example, the term 'man' applies to certain things, namely, all the members of the human race that have been, are, or ever will be: this is its quantity in extension. But the term 'man' has also a certain meaning, and implies certain attributes--rationality, animality, and a definite bodily shape: the sum of these attributes constitutes its quantity in intension.
§ 152. The distinction between the two kinds of quantity possessed by a term is also conveyed by a variety of expressions which are here appended.
Extension = breadth = compass = application = denotation.
Intension = depth = comprehension = implication = connotation.
Of these various expressions, 'application' and 'implication' have the advantage of most clearly conveying their own meaning. 'Extension' and 'intension,' however, are more usual; and neither 'implication' nor 'connotation' is quite exact as a synonym for 'intension.' (§ 164.)