15 The use of the same term as both abstract and concrete in the manner above described must be distinguished from the not unfrequent case of quite another kind in which a name originally abstract changes its meaning and comes to be used in the sense of the corresponding concrete; as, for example, when we talk of the Deity meaning thereby God, not the qualities of God. Compare Jevons, Elementary Lessons in Logic, pp. 21, 22.
19 It must be admitted that this result is paradoxical. As yielding a division of names that is non-exclusive, it is also unscientific. There are two ways of avoiding this difficulty.
In the first place, we may further modify our definitions and say that an abstract name is the name of anything which can be regarded as an attribute of something else (whether it is or is not itself a subject of attributes), while a concrete name is the name of that which cannot be regarded as an attribute of something else. This distinction is simple and easy of application, it is in accordance with popular usage, and it satisfies the condition that the members of a division shall be mutually exclusive. But it may be doubted whether it has any logical value.
A second way of avoiding the difficulty is to give up for logical purposes the distinction between concrete and abstract names, and to substitute for it a distinction between the concrete and the abstract use of names. A name is then used in a concrete sense when the thing called by the name is contemplated as a subject of attributes, and in an abstract sense when the thing called by the name is contemplated as an attribute of subjects. It follows from what has been already said that some names can be used as concrete only, while others can be used either as abstract or as concrete. This solution is satisfactory from the logical point of view, since logic is concerned not with names as such, but with the use of names in propositions. It may be added that as logicians we have very little to do with the abstract use of names, A consideration of the import of propositions will shew that when a name appears either as the subject or as the predicate of a non-verbal proposition its use is always concrete.
13. Can Abstract Names be subdivided into General and Singular?—The question whether any abstract names can be considered general has given rise to much difference of opinion amongst logicians. On the one hand, it is argued that all 20 abstract names must necessarily be singular, since an attribute considered purely as such and apart from its concrete manifestations is one and indivisible, and cannot admit of numerical distinction.16 On the other hand, it is urged that some abstracts must certainly be considered general since they are names of attributes of which there are various kinds or subdivisions; and in confirmation of this view it is pointed out that we frequently write abstracts in the plural number, as when we say, “Redness and yellowness are colours,” “Patience and meekness are virtues.”17
16 This represents the view taken by Jevons. See Principles of Science, 2, § 3.
17 Compare Mill, Logic, i. 2, § 4.
The solution of the question really depends upon our use of the term abstract.
If we adopt the definition given in the last paragraph but one of the preceding section, and include under abstract names the names of attributes which are themselves the subjects of attributes, these latter attributes possibly varying in different instances, then there can be no doubt that some abstracts are general; for they are the names of a class of things which, while having something in common, are also distinguishable inter se.
So far, however, as the question is raised in regard to the abstract (as distinguished from the concrete) use of names in the manner indicated in the last paragraph of the preceding section, we are led to the conclusion that it is only when names are used in a concrete sense that they can be considered general. For it is clear that the name of an attribute can be described as general only in so far as the attribute is regarded as exhibiting characteristics which vary in different instances, only in so far, that is to say, as it is itself a subject of attributes; and when the attribute is so regarded, the name is used in a concrete, not an abstract, sense.
Take the propositions, “Some colours are painfully vivid,” “All yellows are agreeable,” “Some courage is the result of ignorance,” “Some cruelty is the result of fear,” “All cruelty is detestable.” The subjects of these propositions are certainly 21 general. According to the definition given in the last paragraph but one of the preceding section they are also abstract. If, however, in place of distinguishing between abstract and concrete names per se, we distinguish between the abstract and the concrete use of names as proposed in the last paragraph of the preceding section, then the terms in question are all used in a concrete, not an abstract, sense.
EXERCISES.
14. Discuss Mill’s statement that “names are names of things, not of our ideas,” with special reference to the following names: dodo, mermaid, chimaera, toothache, jealousy, idea. [C.]
15. Discuss the logical characteristics of adjectives. [K.]
CHAPTER II.
EXTENSION AND INTENSION.
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.
21 When the objective standpoint is taken, there is an implied reference to some particular universe of discourse, within which the class denoted by the name is supposed to be included. The force of this remark will be made clearer at a subsequent stage.
In seeking to give a precise meaning to connotation, we may start from the above classification. It suggests three distinct senses in which the term might possibly be used, and as a matter of fact all three of these senses have been selected by different logicians, sometimes without any clear recognition of divergence from the usage of other writers. It is desirable that we should be quite clear in our own minds in which sense we intend to employ the term.
(i) According to Mill’s usage, which is that adopted in the following pages, the conventional standpoint is taken when we speak of the connotation of a name. On this view, we do not mean by the connotation of a class-name all the qualities possessed in common by the class; nor do we necessarily mean those particular qualities which may be mentally associated with the name; but we mean just those qualities on account of the possession of which any individual is placed in the class and called by the name. In other words, we include in the connotation of a class-name only those attributes upon which the classification is based, and in the absence of any of which the name would not be regarded as applicable. For example, although all equilateral triangles are equiangular, equiangularity is not on this view included in the connotation of equilateral 25 triangle, since it is not a property upon which the classification of triangles into equilateral and non-equilateral is based; although all kangaroos may happen to be Australian kangaroos, this is not part of what is necessarily implied by the use of the name, for an animal subsequently found in the interior of New Guinea, but otherwise possessing all the properties of kangaroos, would not have the name kangaroo denied to it; although all ruminant animals are cloven-hoofed, we cannot regard cloven-hoofed as part of the meaning of ruminant, and (as Mill observes) if an animal were to be discovered which chewed the cud, but had its feet undivided, it would certainly still be called ruminant.
(ii) Some writers who regard proper names as connotative appear to include in the connotation of a name all those attributes which the name suggests to the mind, whether or not they are actually implied by it. And it is to be observed in this connexion that a name may in the mind of any given individual be closely associated with properties which even the same individual would in no way regard as implied in the meaning of the name, as, for instance, “Trinity undergraduate” with a blue gown. This interpretation of connotation is, therefore, clearly to be distinguished from that given in the preceding paragraph.
We may further distinguish the view, apparently taken by some writers, according to which the connotation of a class-name at any given time would include all the properties known at that time to belong to the class.
(iii) Other writers use the term in still another sense and would include in the connotation of a class-name all the properties, known and unknown, which are possessed in common by all members of the class. Thus, Mr E. C. Benecke writes,—“Just as the word ‘man’ denotes every creature, or class of creatures, having the attributes of humanity, whether we know him or not, so does the word properly connote the whole of the properties common to the class, whether we know them or not. Many of the facts, known to physiologists and anatomists about the constitution of man’s brain, for example, are not involved in most men’s idea of the brain; the possession 26 of a brain precisely so constituted does not, therefore, form any part of their meaning of the word ‘man.’ Yet surely this is properly connoted by the word…. We have thus the denotation of the concrete name on the one side and its connotation on the other, occupying perfectly analogous positions. Given the connotation,—the denotation is all the objects that possess the whole of the properties so connoted. Given the denotation,—the connotation is the whole of the properties possessed in common by all the objects so denoted” (Mind, 1881, p. 532). Jevons uses the term in the same sense. “A term taken in intent (connotation) has for its meaning the whole infinite series of qualities and circumstances which a thing possesses. Of these qualities or circumstances some may be known and form the description or definition of the meaning; the infinite remainder are unknown” (Pure Logic, p. 6).22
22 Bain appears to use the term in an intermediate sense, including in the connotation of a class-name not all the attributes common to the class but all the independent attributes, that is, all that cannot be derived or inferred from others.
While rejecting the use of the term connotation in any but the first of the above mentioned senses, we shall find it convenient to have distinctive terms which can be used with the other meanings that have been indicated. The three terms connotation, intension, and comprehension are commonly employed almost synonymously, and there will certainly be a gain in endeavouring to differentiate their meanings. Intension, as already suggested, may be used to indicate in the most general way what may be called the implicational aspect of names; the complex terms conventional intension, subjective intension, and objective intension will then explain themselves. Connotation may be used as equivalent to conventional intension ; and comprehension as equivalent to objective intension. Subjective intension is less important from the logical standpoint, and we need not seek to invent a single term to be used as its equivalent.23
23 For anyone who is given the meaning of a name but knows nothing of the objects denoted by the name, subjective intension coincides with connotation. Were the ideal of knowledge to be reached, subjective intension would coincide with comprehension.
27 Conventional intension or connotation will then include only those attributes which constitute the meaning of a name;24 subjective intension will include those that are mentally associated with it, whether or not they are actually signified by it; objective intension or comprehension will include all the attributes possessed in common by all members of the class denoted by the name. We might perhaps speak more strictly of the connotation of the name itself, the subjective intension of the notion which is the mental equivalent of the name, and the comprehension of the class which is denoted by the name.25
24 It is to be observed that in speaking of the connotation of a name we may have in view either the signification that the name bears in common acceptation, or some special meaning assigned to it by explicit definition for some scientific or other specific purpose.
25 The distinctions of meaning indicated in this section will be found essential for clearness of view in discussing certain questions to which we shall pass on immediately; in particular, the questions whether connotation and denotation necessarily vary inversely, and whether proper names are connotative.
18. Sigwart’s distinction between Empirical, Metaphysical, and Logical Concepts.—Sigwart observes that in speaking of concepts we ought to distinguish between three meanings of the word. These three meanings of “concept” he describes as follows.26
26 Logic, I. p. 245. This and future references to Sigwart are to the English translation of his work by Mrs Bosanquet.
(1) By a concept may be meant a natural psychological production,—the general idea which has been developed in the natural course of thought. Such ideas are different for different people, and are continually in process of formation; even for the individual himself they change, so that a word does not always keep the same meaning even for the same person. Strictly speaking, it is only by a fiction which neglects individual peculiarities that we can speak of the concepts corresponding to the terms used in ordinary language.
(2) In contrast with this empirical meaning the concept may be viewed as an ideal; it is then the mark at which we aim in our endeavour to attain knowledge, for we seek to find in it an adequate copy of the essence of things. 28
(3) Between these two meanings of the word, which may be called the empirical and the metaphysical, there lies the logical. This has its origin in the logical demand for certainty and universal validity in our judgments. All that is required is that our ideas should be absolutely fixed and determined, and that all who make use of the same system of denotation should have the same ideas.
This threefold distinction may be usefully compared with that drawn in the preceding section. Sigwart is approaching the question from a different point of view, but it will be observed that his three “meanings of concept” correspond broadly with subjective intension, objective intension, and conventional intension respectively.
It may be added that Mr Bosanquet’s distinction (Logic, I. pp. 41 to 46) between the objective reference of a name (its logical meaning) and its content for the individual mind (the psychical idea) appears to some extent to correspond to the distinction between connotation and subjective intension.
19. Connotation and Etymology.—The connotation of a name must not be confused with its etymology. In dealing with names from the etymological or historical point of view we consider the circumstances in which they were first imposed and the reasons for their adoption; also the successive changes, if any, in their meaning that have subsequently occurred. In making precise the connotation to be attached to a name we may be helped by considering its etymology. But we must clearly distinguish between the two; in finally deciding upon the connotation to be assigned to a name for any particular scientific purpose, we may indeed find it necessary to depart not merely from its original meaning, but also from its current meaning in everyday discourse.
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.
30 It may chance to be necessary to make Q1, Q2, … Qn coincide with Q1, Q2, … Qy. But this must be regarded as the limiting case; usually a smaller number of individuals will be sufficient.
31 Mr Johnson points out to me that in pursuing this line of argument certain restrictions of a somewhat subtle kind are necessary in regard to what may be called our “universe of attributes.” The “universe of objects” which is what we mean by the “universe of discourse,” implies individuality of object and limitation of range of objects ; and if we are to work out a thoroughgoing reciprocity between attributes and objects, we must recognise in our “universe of attributes” restrictions analogous to the above, namely, simplicity of attribute and limitation of range of attributes. By “simplicity of attribute” is meant that the universe of attributes must not contain any attribute which is a logical function of any other attribute or set of attributes. Thus, if A, B are two attributes recognised in our universe, we must not admit such attributes as X (= A and B), or Y (= A or B), or Z (= not-A). We may indeed have a negatively defined attribute, but it must not be the formal contradictory of another or formally involve the contradictory of another. The following example will shew the necessity of this restriction. Let P1, P2, P3, be selected as typical of the whole class P1, P2, P3 P4, P5, P6; and let A1 be an attribute possessed by P1 alone, A2 an attribute possessed by P2 alone, and so on. Then if we recognise A1 or A2 or A3 as a distinct attribute, it is at once clear that P1, P2, P3 will no longer be typical of the whole class; and the same result follows if not-A4 is recognised as a distinct attribute. Similarly, without the restriction in question any selection (short of the whole) would necessarily fail to be typical of the whole class. As a concrete example, suppose that we select from the class of professional men a set of examples that have in common no attribute except those that are common to the whole class. It may turn out that our examples are all barristers or doctors, but none of them solicitors. Now if we recognise as a distinct attribute being “either a barrister or a doctor,” our selected group will thereby have an extra common attribute not possessed by every professional man. The same result will follow if we recognise the attribute “non-solicitor.” Not much need be added as regards the necessity of some limitation in the range of attributes which are recognised. The mere fact of our having selected a certain group would indeed constitute an additional attribute, which would at once cause the selection to fail in its purpose, unless this were excluded as inessential. Similarly, such attributes as position in space or in time &c. must in general be regarded as inessential. For example, I might draw on a sheet of paper a number of triangles sufficiently typical of the whole class of triangles, but for this it would be necessary to reject as inessential the common property which they would possess of all being drawn on a particular sheet of paper.
We have then, with reference to X,
(1) Connotation:
P1 … Pm ;
(2) Denotation:
Q1 … Qn … Qy ;
(3) Comprehension:
P1 … Pm … Px ;
(4) Exemplification:
Q1 … Qn.
Of these, either the connotation or the exemplification will suffice to mark out or completely identify the class, although they do not exhaust either all its common properties or all the individuals contained in it. In other words, whether we start from the connotation or from the exemplification, the denotation and the comprehension will be the same.32
32 It will be observed that connotation and exemplification are distinguished from comprehension and denotation in that they are selective, while the latter pair are exhaustive. In making our selection our aim will usually be to find the minimum list which will suffice for our purpose.
33 For a concrete illustration of the above, the term metal may be taken. From the chemical point of view a metal may be defined as an element which can replace hydrogen in an acid and thus form a salt. This then is the connotation of the name. Its denotation consists of the complete list of elements fulfilling the above condition now known to chemists, and possibly of others not yet discovered.33 The members of the whole class thus constituted are, however, found to possess other properties in common besides those contained in the definition of the name, for example, fusibility, the characteristic lustre termed metallic, a high degree of opacity, and the property of being good conductors of heat and electricity. The complete list of these properties forms the comprehension of the name. Now a chemist would no doubt be able from the full denotation of metal to make a selection of a limited number of metals which would be precisely typical of the whole class;34 that is to say, his selected list would possess in common only such properties as are common to the whole class. This selected class would constitute the exemplification of the name.
33 It is necessary to distinguish between the known extension of a term and its full denotation, just as we distinguish between the known intension of a term and its full comprehension.
34 He would take metals as different from one another as possible, such as aluminium, antimony, copper, gold, iron, mercury, sodium, zinc.
We have so far assumed that (1) connotation or intensive definition has first been arbitrarily fixed, and that this has successively determined (2) denotation, (3) comprehension, and—with a certain range of choice—(4) exemplification. But it is clear that theoretically we might start by arbitrarily fixing (i) the exemplification or extensive definition ; and that this would successively determine (ii) comprehension, (iii) denotation, and then—again with a certain range of choice35—(iv) connotation.
35 It is ordinarily said that “of the denotation and connotation of a term one may, both cannot, be arbitrary,” and this is broadly true. It is possible, however, to make the statement rather more exact. Given either intensive or extensive definition, then both denotation and comprehension are, with reference to any assigned universe of discourse, absolutely fixed. But different intensive definitions, and also different extensive definitions, may sometimes yield the same results; and it is therefore possible that, everything else being given, connotation or exemplification may still be within certain limits indeterminate. For example, given the class of parallel straight lines, the connotation may be determined in two or three different ways; or, given the class of equilateral equiangular triangles, we may select as connotation either having three equal sides or having three equal angles. Again, given the connotation of metal, it would no doubt be possible to select in more ways than one a limited number of metals not possessing in common any attributes which are not also possessed by the remaining members of the class.
34 It is interesting from a theoretical point of view to note the possibility of this second order of procedure; and this order may, moreover, be said to represent what actually occurs—at any rate in the first instance—in certain cases, as, for example, in the case of natural groups in the animal, vegetable, and mineral kingdoms. Men form classes out of vaguely recognised resemblances long before they are able to give an intensive definition of the class-name, and in such a case if they are asked to explain their use of the name, their reply will be to enumerate typical examples of the class. This would no doubt ordinarily be done in an unscientific manner, but it would be possible to work it out scientifically. The extensive definition of a name will take the form: X is the name of the class of which Q1, Q2, … Qn are typical. This primitive form of definition may also be called definition by type.36
36 It is not of course meant that when we start from an extensive definition, we are classing things together at random without any guiding principle of selection. No doubt we shall be guided by a resemblance between the objects which we place in the same class, and in this sense intension may be said always to have the priority. But the resemblance may be unanalysed, so that we may be far more familiar with the application of the class-name than with its implication; and even when a connotation has been assigned to the name, it may be extensively controlled, and constantly subject to modification, just because we are much more concerned to keep the denotation fixed than the connotation.
In this connexion the names of simple feelings which are incapable of analysis may be specially considered. For the names of ultimate elements, there is, says Sigwart,37 no definition; we must assume that everyone attaches the same meaning to them. To such names we may indeed be able to assign a proximate genus, as when we say “red is a colour”; but we 35 cannot add a specific difference. It is, however, only an intensive definition that is wanting in these cases; and the deficiency is supplied by means of an extensive definition. The way in which we make clear to others our use of such a term as “red” is by pointing out or otherwise indicating various objects which give rise in us to the feeling. Thus “red” is the colour of field poppies, hips and haws, ordinary sealing-wax, bricks made from certain kinds of clay, &c. This is nothing more or less than an extensive definition as above defined.