DIVISIONS OF CONCEPTS AND TERMS. 55 



applicational reference simply ; to call the objective extension of a term i.e. 

 all the actual individual things to which the term is correctly applicable^ 

 by the name of denotation; and to describe its conventional extension i.e. 

 all the objects to which the term is actually applied by a given speaker in a 

 given context within a possibly restricted universe of discourse as forming 

 the application* of the term (corresponding roughly to what ancient 

 logicians called Suppositio*}. 



The multitude of purely, intrinsically, logically possible or conceiv 

 able objects in any realm is simply indefinite. And although there is an 

 intelligible sense in which we may conceive a proportionate variation in the 

 indefinite multitudes making up such purely possible classes the indefinite 

 multitude of possible men being less than the indefinite multitude of possible 

 animals, or than the indefinite multitude of possible human hands, and these ten 

 times less than the indefinite multitude of possible human fingers, and soon, 

 yet we do not see the utility, in logic, of giving any special title, as Dr. Keynes 

 does (op. cit., p. 30), whether extension or denotation, to the range of such 

 purely or intrinsically possible objects of thought. These titles should be 

 reserved for things supposed to exist actually in some real or imaginary 

 realm, at some real or imaginary time, and to be, at the time of predica 

 tion, at least adequately capable of existing in their proper realm in the sense 

 that if they either actually have not existed or do not exist, they at least will 

 (and not merely may} exist in it. The word &quot;exist&quot; here evidently implies 

 mere membership of a class in any realm, real or imaginary. 



34. RELATION BETWEEN INTENSION AND EXTENSION. Since 

 intension refers to attributes and extension to the objects posses 

 sing those attributes, it is obvious that, generally speaking, accord 

 ing as the former is increased the latter is diminished and vice versa 

 in any related series of general concepts ; that, for instance, in the 

 series of concepts expressed by the terms, figure, plane figure, 

 rectilinear plane figure, quadrilateral, parallelogram, rectangle, 

 square, the intension gradually increases while the extension 

 decreases ; and that in the series, man, animal, living thing, 

 material thing, thing, the intension progressively decreases while 



1 Dr. VENN (op. cit., p. 178) limits denotation to the objects actually existing at 

 the point of time at which the term is used : so that the names of extinct animals 

 would have now no denotation ; while that of the term man, for example, would 

 change with every human birth and death. We prefer not to make such a limitation. 



a Thus, what the term denotes its denotation depends on, and is the correlative 

 of, its connotation, and is objective in the sense that it is determined by this latter 

 and cannot be limited by any further subjective or conventional arrangement made or 

 implied by the speaker; while the application of the term the collection of objects 

 to which the speaker intends actually to apply it within a restricted universe of 

 discourse, is conventional in the sense of being expressly or tacitly determined by 

 the speaker. This usage differs from that of Dr. Keynes (op. cit., p. 30), who gives 

 the title of &quot; subjective extension&quot; to &quot;the whole range of objects real or imagin 

 ary to which the name can be directly applied, the only limitation being that of 

 logical conceivability.&quot; 



3 C/. JOSEPH, op. cit., p. 14. 



