DIVISIONS OF CONCEPTS AND TERMS. 61 



division of concepts and terms into general and singular (28) is 

 exhaustive, or whether perhaps there may not be certain classes 

 of terms which have no extension at all, i.e. which do not de 

 note things at all (30). Extension in general we have under 

 stood to mean the reference of our concepts and terms to things. 

 If, therefore, we have concepts which represent as their objects 

 attributes apart from all reference to things and we undoubtedly 

 have such concepts, purely abstract and potentially applicable to 

 things, though not actually applied to things by the mind, and if 

 we have abstract terms which express the attributes conceived in 

 this way, then consistency would demand that we deny such con 

 cepts and terms aU extension and recognize for them only one kind 

 of meaning, viz. implicational or intensive meaning. It would 

 seem that we cannot with propriety speak of the extension or 

 denotation of such concepts and terms at all any more than we 

 can speak with propriety of the intension or connotation of a 

 certain other class of terms to which we shall presently refer, and 

 which have only the applicational or extensive kind of meaning. 



Hence we must recognize a division of terms into those which 

 have extension and those which have not : into Denotative Terms 

 and Non-denotative Terms. And if we compare this division with 

 that given above (28) into general and singular terms we can 

 now see that the latter division is not an exhaustive division, 

 since it can have reference only to terms that have extension, i.e. 

 to denotative terms, not to non-denotative ones. 



When logicians discuss the question whether abstract terms are singular 

 or general, they do not imply any reference of these latter to things : they 

 are thinking exclusively of a sphere or system of abstract attributes (35), call 

 ing those attributes general which they can analyse into different kinds or 

 varieties, and those others singular which they cannot further analyse. So, 

 colour, virtue, etc., would be general, while perhaps squareness, yellowness, 

 equality, might be instanced as singular. It will be noticed, however, that 

 this distinction into singular and general, as applied to abstract terms, has not 

 the same meaning as it had above (28) : there it concerned exclusively the 

 reference of our concepts and terms to individual things ; here it refers to 

 the relations of abstract attributes to one another. And, furthermore, deno 

 tation is the reference not of a wider class to its sub-classes or varieties, but 

 to all the individual members of that wider class. For this reason also the 

 use of the term denotation in the present connexion is inappropriate. 1 



We see no sufficient reason to deny that concepts of purely possible or 

 logically conceivable objects of thought such as the objects thought of in 

 pure mathematics are general (as also the terms we may invent to express 



l Cf. JOSEPH, op. cit., p. 135. 



