16. The Extension and the Intension of Names.[18]—Every concrete general name is the name of a real or imaginary class of objects which possess in common certain attributes; and there are, therefore, two aspects under which it may be regarded. We may consider the name (i) in relation to the objects which are called by it; or (ii) in relation to the qualities belonging to those objects. It is desirable to have terms by which to refer to this broad distinction without regard to further refinements of meaning; and the terms extension and intension will accordingly be employed to express in the most general way these two aspects of names respectively.[19]
[18] We may speak also of the extension and the intension of concepts. In the discussion, however, of questions concerning extension and intension, it is essential to recognise the part played by language as the instrument of thought. Hence it seems better to start from names rather than from concepts. Neglect to consider names explicitly in this connexion has been responsible for much confusion.
[19] It is usual to employ the terms comprehension and connotation as simply synonymous with intension, and denotation as synonymous with extension. We shall, however, presently find it convenient to differentiate the meanings of these terms. The force of the terms extension and intension in the most general sense might perhaps also be expressed by the pair of terms application and implication.
The extension of a name then consists of objects of which the name can be predicated; its intension consists of properties which can be predicated of it. For example, by the extension of plane triangle we mean a certain class of geometrical figures, and by its intension certain qualities belonging to such figures. 23 Similarly, by the extension of man is meant a certain class of material objects, and by its intension the qualities of rationality, animality, &c., belonging to these objects.
17. Connotation, Subjective Intension, and Comprehension.—The term intension has been used in the preceding section to express in the most general way that aspect of general names under which we consider not the objects called by the names but the qualities belonging to those objects. Taking any general name, however, there are at least three different points of view from which the qualities of the corresponding class may be regarded; and it is to a want of discrimination between these points of view that we may attribute many of the controversies and misunderstandings to which the problem of the connotation of names has given rise.
(1) There are those qualities which are essential to the class in the sense that the name implies them in its definition. Were any of this set of qualities absent the name would not be applicable; and any individual thing lacking them would accordingly not be regarded as a member of the class. The standpoint here taken may be said to be conventional, since we are concerned with the set of characteristics which are supposed to have been conventionally agreed upon as determining the application of the name.
(2) There are those qualities which in the mind of any given individual are associated with the name in such a way that they are normally called up in idea when the name is used. These qualities will include the marks by which the individual in question usually recognises or identifies an object as belonging to the class. They may not exhaust the essential qualities of the class in the sense indicated in the preceding paragraph, but on the other hand they will probably include some that are not essential to it. The standpoint here taken is subjective and relative. Even when there is agreement as to the actual meaning of a name, the qualities that we naturally think of in connexion with it may vary both from individual to individual, and, in the case of any given individual, from time to time.
We may consider as a special case under this head the 24 complete group of attributes known at any given time to belong to the class. All these attributes can be called up in idea by any person whose knowledge of the class is fully up to date; and this group may, therefore, be regarded as constituting the most scientific form of intension from the subjective point of view.
(3) There is the sum-total of qualities actually possessed in common by all members of the class. These will include all the qualities included under the two preceding heads,[20] and usually many others in addition. The standpoint here taken is objective.[21]
[20] It is here assumed, as regards the qualities mentally associated with the name, that our knowledge of the class, so far as it extends, is correct.