20. Fixity of Connotation.—It has been already pointed out that subjective intension is variable. A given name will almost certainly call up in the minds of different persons different ideas; and even in the case of the same person it will probably do so at different times. The question may be raised how far the same is true of connotation. It has been implied in the preceding section that the scientific use of a name may differ 29 from its use in everyday discourse; and there can be no doubt that as a matter of fact different people may by the same name intend to signify different things, that is to say, they would include different attributes in the connotation of the name. It is, moreover, not unfrequently the case that some of us may be unable to say precisely what is the meaning that we ourselves attach to the words we use.
At the same time a clear distinction ought to be drawn between subjective intension and connotation in respect of their variability. Subjective intension is necessarily variable; it can never be otherwise. Connotation, on the other hand, is only variable by accident; and in so far as there is variation language fails of its purpose. “Identical reference,” as Mr Bosanquet puts it, “is the root and essence of the system of signs which we call language” (Logic, I. p. 16). It is only by some conventional agreement which shall make language fixed that scientific discussions can be satisfactorily carried on; and there would be no variation in the connotation of names in the case of an ideal language properly employed. In dealing with reasonings from the point of view of logical doctrine, it is, therefore, no unreasonable assumption to make that in any given argument the connotation of the names employed is fixed and definite; in other words, that every name employed is either used in its ordinary sense and that this is precisely determined, or else that, the name being used with a special meaning, such meaning is adhered to consistently and without equivocation.
21. Extension and Denotation.—The terms extension and denotation are usually employed as synonymous, but there will be some advantage in drawing a certain distinction between them. We shall find that when names are regarded as the subjects of propositions there is an implied reference to some universe of discourse, which may be more or less limited. For example, we should naturally understand such propositions as all men are mortal, no men are perfect, to refer to all men who have actually existed on the earth, or are now existing, or will exist hereafter, but we should not understand them to refer to all fictitious persons or all beings possessing the essential characteristics of men whom we are able to conceive or imagine. 30 The meaning of universe of discourse will be further illustrated [subsequently]. The only reason for introducing the conception at this point is that we propose to use the term denotation or objective extension rather than the term extension simply when there is an explicit or implicit limitation to the objects actually to be found in some restricted universe. By the subjective extension of a general name, on the other hand, we shall understand the whole range of objects real or imaginary to which the name can be correctly applied, the only limitation being that of logical conceivability. Every name, therefore, which can be used in an intelligible sense will have a positive subjective extension, but its denotation in a universe which is in some way restricted by time, place, or circumstance may be zero.[27]
[27] The value of the above distinction may be illustrated by reference to the divergence of view indicated in the following quotation from Mr Monck, who uses the terms denotation and extension as synonymous: “It is a matter of accident whether a general name will have any extension (or denotation) or not. Unicorn, griffin, and dragon are general names because they have a meaning, and we can suppose another world in which such beings exist; but the terms have no extension, because there are no such animals in this world. Some logicians speak of these terms as having an extension, because we can suppose individuals corresponding to them. In this way every general term would have an extension which might be either real or imaginary. It is, however, more convenient to use the word extension for a real extension (past, present, or future) only” (Introduction to Logic, p. 10). It should be added, in order to prevent possible misapprehension, that by universe of discourse, as used in the text, we do not necessarily mean the material universe; we may, for example, mean the universe of fairy-land, or of heraldry, and in such a case, unicorn, griffin, and dragon may have denotation (in our special sense), as well as subjective extension, greater than zero. What is the particular universe of reference in any given proposition will generally be determined by the context. For logical purposes we may assume that it is conventionally understood and agreed upon, and that it remains the same throughout the course of any given argument. As Dr Venn remarks, “We might include amongst the assumptions of logic that the speaker and hearer should be in agreement, not only as to the meaning of the words they use, but also as to the conventional limitations under which they apply them in the circumstances of the case” (Empirical Logic, p. 180).
In the sense here indicated, denotation is in certain respects the correlative of comprehension rather than of connotation. For in speaking of denotation we are, as in the case of comprehension, taking an objective standpoint; and there is, moreover, in the case of comprehension, as in that of denotation, a 31 tacit reference to some particular universe of discourse. Since, however, denotation is generally speaking determined by connotation, there is one very important respect in which connotation and denotation are still correlatives.
22. Dependence of Extension and Intension upon one another.[28]—Taking any class-name X, let us first suppose that there has been a conventional agreement to use it wherever a certain selected set of properties P1, P2, … Pm, are present. This set of properties will constitute the connotation of X, and will, with reference to a given universe of discourse,[29] determine the denotation of the name, say, Q1, Q2, … Qy ; that is, Q1, Q2, … Qy, are all the individuals possessing in common the properties P1, P2, … Pm.
[28] This section may be omitted on a first reading.
[29] It will be assumed in the remainder of this section that we are throughout speaking with reference to a given universe of discourse.
These properties may not, and almost certainly will not, exhaust the properties common to Q1, Q2, … Qy. Let all the common properties be P1, P2, … Px ; they will include P1, P2, … Pm, and in all probability more besides, and will constitute the comprehension of the class-name.
Now it will always be possible in one or more ways to make out of Q1, Q2, … Qy, a selection Q1, Q2, … Qn, which shall be precisely typical of the whole class;[30] that is to say, Q1, Q2, … Qn will possess in common those attributes and only those attributes (namely, P1, P2, … Px) which are possessed in common by Q1, Q2, … Qy.[31] Q1, Q2, … Qn may be called the exemplification or 32 extensive definition of X. The reason for selecting the name extensive definition will appear in a moment. It will sometimes be convenient correspondingly to speak of the connotation of a name as its intensive definition.