# Lit2Go

## Deductive Logic

### by George William Joseph Stock, M.A.

#### Part 1: Chapter 3

• Year Published: 1888
• Language: English
• Country of Origin: England
• Source: Stock, G. W. J. (1888). Deductive Logic. Oxford, England; Pembroke College.
• Flesch–Kincaid Level: 11.0
• Word Count: 6,701
• Genre: Informational
• Keywords: math, math history

PART I.—OF TERMS.

CHAPTER III.

Of the Division of Terms.

86. The following scheme presents to the eye the chief divisions of terms.

Term
Division of terms according to their place in thought.
Subject-Term
Attributive

according to the kind of thing signified.
Abstract
Concrete

according to Quantity in Extension.
Singular
Common

according to Quality.
Positive
Privative
Negative

according to number of meanings.
Univocal
Equivocal

according to number of things involved in the name.
Absolute
Relative

according to number of quantities.
Connotative
Non-connotative

Subject-term and Attributive.

87. By a Subject-term is meant any term which is capable of standing by itself as a subject, e.g. ‘ribbon,’ ‘horse.’

88. Attributives can only be used as predicates, not as subjects, e.g. ‘cherry-coloured,’ ‘galloping.’ These can only be used in conjunction with other words (syncategorematically) to make up a subject. Thus we can say ‘A cherry-coloured ribbon is becoming,’ or ‘A galloping horse is dangerous.’

89. Attributives are contrivances of language whereby we indicate that a subject has a certain attribute. Thus, when we say ‘This paper is white,’ we indicate that the subject ‘paper’ possesses the attribute whiteness. Logic, however, also recognises as attributives terms which signify the non-possession of attributes. ‘Not-white’ is an attributive equally with ‘white.’

90. An Attributive then may be defined as a term which signifies the possession, or non-possession, of an attribute by a subject.

91. It must be carefully noticed that attributives are not names of attributes, but names of the things which possess the attributes, in virtue of our knowledge that they possess them. Thus ‘white’ is the name of all the things which possess the attribute whiteness, and ‘virtuous’ is a name; not of the abstract quality, virtue, itself, but of the men and actions which possess it. It is clear that a term can only properly be said to be a name of those things whereof it can be predicated. Now, we cannot intelligibly predicate an attributive of the abstract quality, or qualities, the possession of which it implies. We cannot, for instance, predicate the term ‘learned’ of the abstract quality of learning: but we may predicate it of the individuals, Varro and Vergil. Attributives, then, are to be regarded as names, not of the attributes which they imply, but of the things in which those attributes are found.

92. Attributives, however, are names of things in a less direct way than that in which subject-terms may be the names of the same things. Attributives are names of things only in predication, whereas subject-terms are names of things in or out of predication. The terms ‘horse’ and ‘Bucephalus’ are names of certain things, in this case animals, whether we make any statement about them or not: but the terms ‘swift’ and ‘fiery’ only become names of the same things in virtue of being predicable of them. When we say ‘Horses are swift’ or ‘Bucephalus was fiery,’ the terms ‘swift’ and ‘fiery’ become names respectively of the same things as ‘horse’ and ‘Bucephalus.’ This function of attributives as names in a secondary sense is exactly expressed by the grammatical term ‘noun adjective.’ An attributive is not directly the name of anything. It is a name added on in virtue of the possession by a given thing of a certain attribute, or, in some cases, the non-possession.

93. Although attributives cannot be used as subjects, there is nothing to prevent a subject-term from being used as a predicate, and so assuming for the time being the functions of an attributive. When we say ‘Socrates was a man,’ we convey to the mind the idea of the same attributes which are implied by the attributive ‘human.’ But those terms only are called attributives which can never be used except as predicates.

94. This division into Subject-terms and Attributives may be regarded as a division of terms according to their place in thought. Attributives, as we have seen, are essentially predicates, and can only be thought of in relation to the subject, whereas the subject is thought of for its own sake.

Abstract and Concrete Terms.

95. An Abstract Term is the name of an attribute, e.g. whiteness [Footnote: Since things cannot be spoken of except by their names, there is a constantly recurring source of confusion between the thing itself and the name of it. Take for instance ‘whiteness.’ The attribute whiteness is a thing, the word ‘whiteness’ is a term.], multiplication, act, purpose, explosion.

96. A Concrete Term is the name of a substance, e.g. a man, this chair, the soul, God.

97. Abstract terms are so called as being arrived at by a process of Abstraction. What is meant by Abstraction will be clear from a single instance. The mind, in contemplating a number of substances, may draw off, or abstract, its attention from all their other characteristics, and fix it only on some point, or points, which they have in common. Thus, in contemplating a number of three-cornered objects, we may draw away our attention from all their other qualities, and fix it exclusively upon their three-corneredness, thus constituting the abstract notion of ‘triangle.’ Abstraction may be performed equally well in the case of a single object: but the mind would not originally have known on what points to fix its attention except by a comparison of individuals.

98. Abstraction too may be performed upon attributes as well as substances. Thus, having by abstraction already arrived at the notion of triangle, square, and so on, we may fix our attention upon what these have in common, and so rise to the higher abstraction of ‘figure.’ As thought becomes more complex, we may have abstraction on abstraction and attributes of attributes. But, however many steps may intervene, attributes may always be traced back to substances at last. For attributes of attributes can mean at bottom nothing but the co-existence of attributes in, or in connection with, the same substances.

99. We have said that abstract terms are so called, as being arrived at by abstraction: but it must not be inferred from this statement that all terms which are arrived at by abstraction are abstract. If this were so, all names would be abstract except proper names of individual substances. All common terms, including attributives, are arrived at by abstraction, but they are not therefore abstract terms. Those terms only are called abstract, which cannot be applied to substances at all. The terms ‘man’ and ‘human’ are names of the same substance of which Socrates is a name. Humanity is a name only of certain attributes of that substance, namely those which are shared by others. All names of concrete things then are concrete, whether they denote them individually or according to classes, and whether directly and in themselves, or indirectly, as possessing some given attribute.

100. By a ‘concrete thing’ is meant an individual Substance conceived of with all its attributes about it. The term is not confined to material substances. A spirit conceived of under personal attributes is as concrete as plum-pudding.

101. Since things are divided exhaustively into substances and attributes, it follows that any term which is not the name of a thing capable of being conceived to exist by itself, must be an abstract term. Individual substances can alone be conceived to exist by themselves: all their qualities, actions, passions, and inter-relations, all their states, and all events with regard to them, presuppose the existence of these individual substances. All names therefore of such things as those just enumerated are abstract terms. The term ‘action,’ for instance, is an abstract term. For how could there be action without an agent? The term ‘act’ also is equally abstract for the same reason. The difference between ‘action’ and ‘act’ is not the difference between abstract and concrete, but the difference between the name of a process and the name of the corresponding product. Unless acts can be conceived to exist without agents they are as abstract as the action from which they result.

102. Since every term must be either abstract or concrete, it may be asked—Are attributives abstract or concrete? The answer of course depends upon whether they are names of substances or names of attributes. But attributives, it must be remembered, are never directly names of anything, in the way that subject-terms are; they are only names of things in virtue of being predicated of them. Whether an attributive is abstract or concrete, depends on the nature of the subject of which it is asserted or denied. When we say ‘This man is noble,’ the term ‘noble’ is concrete, as being the name of a substance: but when we say ‘This act is noble,’ the term ‘noble’ is abstract, as being the name of an attribute.

103. The division of terms into Abstract and Concrete is based upon the kind of thing signified. It involves no reference to actual existence. There are imaginary as well as real substances. Logically a centaur is as much a substance as a horse.

Terms.

104. A Singular Term is a name which can be applied, in the same sense, to one thing only, e.g. ‘John,’ ‘Paris,’ ‘the capital of France,’ ‘this pen.’

105. A Common Term is a name which can be applied, in the same sense, to a class of things, e.g. ‘man,’ ‘metropolis,’ ‘pen.’

In order that a term may be applied in the same sense to a number of things, it is evident that it must indicate attributes which are common to all of them. The term ‘John’ is applicable to a number of things, but not in the same sense, as it does not indicate attributes.

106. Common terms are formed, as we have seen already ( 99), by abstraction, i. e. by withdrawing the attention from the attributes in which individuals differ, and concentrating it upon those which they have in common.

107. A class need not necessarily consist of more than two things. If the sun and moon were the only heavenly bodies in the universe, the word ‘heavenly body’ would still be a common term, as indicating the attributes which are possessed alike by each.

108. This being so, it follows that the division of terms into singular and common is as exhaustive as the preceding ones, since a singular term is the name of one thing and a common term of more than one. It is indifferent whether the thing in question be a substance or an attribute; nor does it matter how complex it may be, so long as it is regarded by the mind as one.

109. Since every term must thus be either singular or common, the members of the preceding divisions must find their place under one or both heads of this one. Subject-terms may plainly fall under either head of singular or common: but attributives are essentially common terms. Such names as ‘green,’ ‘gentle,’ ‘incongruous’ are applicable, strictly in the same sense, to all the things which possess the attributes which they imply.

110. Are abstract terms then, it may be asked, singular or common? To this question we reply—That depends upon how they are used. The term ‘virtue,’ for instance, in one sense, namely, as signifying moral excellence in general, without distinction of kind, is strictly a singular term, as being the name of one attribute: but as applied to different varieties of moral excellence—justice, generosity, gentleness and so on—it is a common term, as being a name which is applicable, in the same sense, to a class of attributes. Similarly the term ‘colour,’ in a certain sense, signifies one unvarying attribute possessed by bodies, namely, the power of affecting the eye, and in this sense it is a singular term: but as applied to the various ways in which the eye may be affected, it is evidently a common term, being equally applicable to red, blue, green, and every other colour. As soon as we begin to abstract from attributes, the higher notion becomes a common term in reference to the lower. By a ‘higher notion’ is meant one which is formed by a further process of abstraction. The terms ‘red,’ ‘blue,’ ‘green,’ etc., are arrived at by abstraction from physical objects; ‘colour’ is arrived at by abstraction from them, and contains nothing, but what is common to all. It therefore applies in the same sense to each, and is a common term in relation to them.

111. A practical test as to whether an abstract term, in any given case, is being used as a singular or common term, is to try whether the indefinite article or the sign of the plural can be attached to it. The term ‘number,’ as the name of a single attribute of things, admits of neither of these adjuncts: but to talk of ‘a number’ or ‘the numbers, two, three, four,’ etc., at once marks it as a common term. Similarly the term ‘unity’ denotes a single attribute, admitting of no shades of distinction: but when a writer begins to speak of ‘the unities’ he is evidently using the word for a class of things of some kind or other, namely, certain dramatical proprieties of composition.

Proper Names and Designations.

112. Singular terms may be subdivided into Proper Names and Designations.

113. A Proper Name is a permanent singular term applicable to a thing in itself; a Designation is a singular term devised for the occasion, or applicable to a thing only in so far as it possesses some attribute.

114. ‘Homer’ is a proper name; ‘this man,’ ‘the author of the Iliad’ are designations.

115. The number of things, it is clear, is infinite. For, granting that the physical universe consists of a definite number of atoms-neither one more nor one less-still we are far from having exhausted the possible number of things. All the manifold material objects, which are made up by the various combinations of these atoms, constitute separate objects of thought, or things, and the mind has further an indefinite power of conjoining and dividing these objects, so as to furnish itself with materials of thought, and also of fixing its attention by abstraction upon attributes, so as to regard them as things, apart from the substances to which they belong.

116. This being so, it is only a very small number of things, which are constantly obtruding themselves upon the mind, that have singular terms permanently set apart to denote them. Human beings, some domestic animals, and divisions of time and place, have proper names assigned to them in most languages, e.g. ‘John,’ ‘Mary,’ ‘Grip,’ ‘January,’ ‘Easter,’ ‘Belgium,’ ‘Brussels,’ ‘the Thames,’ ‘Ben-Nevis.’ Besides these, all abstract terms, when used without reference to lower notions, are of the nature of proper names, being permanently set apart to denote certain special attributes, e.g. ‘benevolence,’ ‘veracity,’ ‘imagination,’ ‘indigestibility, ‘retrenchment.’

117. But the needs of language often require a singular term to denote some thing which has not had a proper name assigned to it. This is effected by taking a common term, and so limiting it as to make it applicable, under the given circumstances, to one thing only. Such a limitation may be effected in English by prefixing a demonstrative or the definite article, or by appending a description, e.g. ‘this pen,’ ‘the sofa,’ ‘the last rose of summer.’ When a proper name is unknown, or for some reason, unavailable, recourse may be had to a designation, e.g. ‘the honourable member who spoke last but one.’

Collective Terms.

118. The division of terms into singular and common being, like those which have preceded it, fundamental and exhaustive, there is evidently no room in it for a third class of Collective Terms. Nor is there any distinct class of terms to which that name can be given. The same term may be used collectively or distributively in different relations. Thus the term ‘library,’ when used of the books which compose a library, is collective; when used of various collections of books, as the Bodleian, Queen’s library, and so on, it is distributive, which, in this case, is the same thing as being a common term.

119, The distinction between the collective and distributive use of a term is of importance, because the confusion of the two is a favourite source of fallacy. When it is said ‘The plays of Shakspeare cannot be read in a day,’ the proposition meets with a very different measure of acceptance according as its subject is understood collectively or distributively. The word ‘all’ is perfectly ambiguous in this respect. It may mean all together or each separately—two senses which are distinguished in Latin by ‘totus’ or ‘cunctus,’ for the collective, and ‘omnis’ for the distributive use.

120. What is usually meant however when people speak of a collective term is a particular kind of singular term.

121. From this point of view singular terms may be subdivided into Individual and Collective, by an Individual Term being meant the name of one object, by a Collective Term the name of several considered as one. ‘This key’ is an individual term; ‘my bunch of keys’ is a collective term.

122. A collective term is quite as much the name of one thing as an individual term is, though the thing in question happens to be a group. A group is one thing, if we choose to think of it as one. For the mind, as we have already seen, has an unlimited power of forming its own things, or objects of thought. Thus a particular peak in a mountain chain is as much one thing as the chain itself, though, physically speaking, it is inseparable from it, just as the chain itself is inseparable from the earth’s surface. In the same way a necklace is as much one thing as the individual beads which compose it.

123. We have just seen that a collective term is the name of a group regarded as one thing: but every term which is the name of such a group is not necessarily a collective term. ‘London,’ for instance, is the name of a group of objects considered as one thing. But ‘London’ is not a collective term, whereas ‘flock,’ ‘regiment,’ and ‘senate’ are. Wherein then lies the difference? It lies in this—that flock, regiment and senate are groups composed of objects which are, to a certain extent, similar, whereas London is a group made up of the most dissimilar objects—streets and squares and squalid slums, fine carriages and dirty faces, and so on. In the case of a true collective term all the members of the group will come under some one common name. Thus all the members of the group, flock of sheep, come under the common name ‘sheep,’ all the members of the group ‘regiment’ under the common name, ‘soldier,’ and so on.

124. The subdivision of singular terms into individual and collective need not be confined to the names of concrete things. An abstract term like ‘scarlet,’ which is the name of one definite attribute, may be reckoned ‘individual,’ while a term like ‘human nature,’ which is the name of a whole group of attributes, would more fitly be regarded as collective.

126. The main division of terms, which we have been discussing, into singular and collective, is based upon their Quantity in Extension. This phrase will be explained presently.

126. We come now to a threefold division of terms into Positive, Privative and Negative. It is based upon an implied two-fold division into positive and non-positive, the latter member being subdivided into Privative and Negative.

Term
_______________|_______________
|                               |
Positive                     Non-Positive
_____________|____________
|                          |
Privative                   Negative
If this division be extended, as it sometimes is, to terms in general, a positive term must be taken to mean only the definite, or comparatively definite, member of an exhaustive division in accordance with the law of excluded middle ( 25). Thus ‘Socrates’ and ‘man’ are positive, as opposed to ‘not-Socrates’ and ‘not-man.’

127. The chief value of the division, however, and especially of the distinction drawn between privative and negative terms, is in relation to attributives.

From this point of view we may define the three classes of terms as follows:

A Positive Term signifies the presence of an attribute, e.g.: ‘wise,’ ‘full.’

A Negative Term signifies merely the absence of an attribute, e.g. ‘not-wise,’ ‘not-full.’

A Privative Term signifies the absence of an attribute in a subject capable of possessing it, e.g. ‘unwise,’ ‘empty’. [Footnote: A privative term is usually defined to mean one which signifies the absence of an attribute where it was once possessed, or might have been expected to be present, e.g. ‘blind.’ The utility of the slight extension of meaning here assigned to the expression will, it is hoped, prove its justification.]

128. Thus a privative term stands midway in meaning between the other two, being partly positive and partly negative—negative in so far as it indicates the absence of a certain attribute, positive in so far as it implies that the thing which is declared to lack that attribute is of such a nature as to be capable of possessing it. A purely negative term conveys to the mind no positive information at all about the nature of the thing of which it is predicated, but leaves us to seek for it among the universe of things which fail to exhibit a given attribute.

A privative term, on the other hand, restricts us within a definite sphere. The term ‘empty’ restricts us within the sphere of things which are capable of fulness, that is, if the term be taken in its literal sense, things which possess extension in three dimensions.

129. A positive and a negative term, which have the same matter, must exhaust the universe between them, e.g. ‘white’ and ‘not-white,’ since, according to the law of excluded middle, everything must be either one or the other. To say, however, that a thing is ‘not-white’ is merely to say that the term ‘white’ is inapplicable to it. ‘Not-white’ may be predicated of things which do not possess extension as well as of those which do. Such a pair of terms as ‘white’ and ‘not-white,’ in their relation to one another, are called Contradictories.

130. Contrary terms must be distinguished from contradictory. Contrary terms are those which are most opposed under the same head. Thus ‘white’ and ‘black’ are contrary terms, being the most opposed under the same head of colour. ‘Virtuous’ and ‘vicious’ again are contraries, being the most opposed under the same head of moral quality.

131. A positive and a privative term in the same matter will always be contraries, e.g. ‘wise’ and ‘unwise,’ ‘safe’ and ‘unsafe’: but contraries do not always assume the shape of positive and privative terms, but may both be positive in form, e.g. ‘wise’ and ‘foolish,’ ‘safe’ and ‘dangerous.’

132. Words which are positive in form are often privative in meaning, and vice versa. This is the case, for instance, with the word ‘safe,’ which connotes nothing more than the absence of danger. We talk of a thing involving ‘positive danger’ and of its being ‘positively unsafe’ to do so and so. ‘Unhappy,’ on the other hand, signifies the presence of actual misery. Similarly in Latin ‘inutilis’ signifies not merely that there is no benefit to be derived from a thing, but that it is positively injurious. All such questions, however, are for the grammarian or lexicographer, and not for the logician. For the latter it is sufficient to know that corresponding to every term which signifies the presence of some attribute there may be imagined another which indicates the absence of the same attribute, where it might be possessed, and a third which indicates its absence, whether it might be possessed or not.

133. Negative terms proper are formed by the prefix ‘not-’ or ‘non-,’ and are mere figments of logic. We do not in practice require to speak of the whole universe of objects minus those which possess a given attribute or collection of attributes. We have often occasion to speak of things which might be wise and are not, but seldom, if ever, of all things other than wise.

134. Every privative attributive has, or may have, a corresponding abstract term, and the same is the case with negatives: for the absence of an attribute, is itself an attribute. Corresponding to ‘empty,’ there is ‘emptiness’; corresponding to ‘not-full’ there may be imagined the term ‘not-fulness.’

135. The contrary of a given term always involves the contradictory, but it involves positive elements as well. Thus ‘black’ is ‘not-white,’ but it is something more besides. Terms which, without being directly contrary, involve a latent contradiction, are called Repugnant, e.g. ‘red’ and ‘blue.’ All terms whatever which signify attributes that exclude one another may be called Incompatible.

136. The preceding division is based on what is known as the Quality of terms, a positive term being said to differ in quality from a non-positive one.

Univocal and Equivocal Terms.

137. A term is said to be Univocal, when it has one and the same meaning wherever it occurs. A term which has more than one meaning is called Equivocal. ‘Jam-pot,’ ‘hydrogen’ are examples of univocal terms; ‘pipe’ and ‘suit’ of equivocal.

138. This division does not properly come within the scope of logic, since it is a question of language, not of thought. From the logician’s point of view an equivocal term is two or more different terms, for the definition in each sense would be different.

139. Sometimes a third member is added to the same division under the head of Analogous Terms. The word ‘sweet,’ for instance, is applied by analogy to things so different in their own nature as a lump of sugar, a young lady, a tune, a poem, and so on. Again, because the head is the highest part of man, the highest part of a stream is called by analogy ‘the head.’ It is plainly inappropriate to make a separate class of analogous terms. Rather, terms become equivocal by being extended by analogy from one thing to another.

Absolute and Relative Terms.

140. An Absolute term is a name given to a thing without reference to anything else.

141. A Relative term is a name given to a thing with direct reference to some other thing.

142. ‘Hodge’ and ‘man’ are absolute terms. ‘Husband’ ‘father,’ ‘shepherd’ are relative terms. ‘Husband’ conveys a direct reference to ‘wife,’ ‘father’ to ‘Child,’ ‘shepherd’ to ‘sheep.’ Given one term of a relation, the other is called the correlative, e.g. ‘subject’ is the correlative of ‘ruler,’ and conversely ‘ruler’ of ‘subject.’ The two terms are also spoken of as a pair of correlatives.

143. The distinction between relative and absolute applies to attributives as well as subject-terms. ‘Greater,’ ‘near, ‘like,’ are instances of attributives which everyone would recognise as relative.

144. A relation, it will be remembered, is a kind of attribute, differing from a quality in that it necessarily involves more substances than one. Every relation is at bottom a fact, or series of facts, in which two or more substances play a part. A relative term connotes this fact or facts from the point of view of one of the substances, its correlative from that of the other. Thus ‘ruler’ and ‘subject’ imply the same set of facts, looked at from opposite points of view. The series of facts itself, regarded from either side, is denoted by the corresponding abstract terms, ‘rule ‘and ‘subjection.’

145. It is a nice question whether the abstract names of relations should themselves be considered relative terms. Difficulties will perhaps be avoided by confining the expression ‘relative term‘ to names of concrete things. ‘Absolute,’ it must be remembered, is a mere negative of ‘relative,’ and covers everything to which the definition of the latter does not strictly apply. Now it can hardly be said that ‘rule’ is a name given to a certain abstract thing with direct reference to some other thing, namely, subjection. Rather ‘rule’ and ‘subjection’ are two names for identically the same series of facts, according to the side from which we look at them. ‘Ruler’ and ‘subject,’ on the other hand, are names of two distinct substances, but each involving a reference to the other.

146. This division then may be said to be based on the number of things involved in the name.

Connotative and Non-Connotative Terms.

147. Before explaining this division, it is necessary to treat of what is called the Quantity of Terms.

Quantity of Terms.

148. A term is possessed of quantity in two ways—

(1) In Extension;

(2) In Intension.

149. The Extension of a term is the number of things to which it applies.

150. The Intension of a term is the number of attributes which it implies.

151. It will simplify matters to bear in mind that the intension of a term is the same thing as its meaning. To take an example, the term ‘man’ applies to certain things, namely, all the members of the human race that have been, are, or ever will be: this is its quantity in extension. But the term ‘man’ has also a certain meaning, and implies certain attributes—rationality, animality, and a definite bodily shape: the sum of these attributes constitutes its quantity in intension.

152. The distinction between the two kinds of quantity possessed by a term is also conveyed by a variety of expressions which are here appended.

Extension = breadth = compass = application = denotation.

Intension = depth = comprehension = implication = connotation.

Of these various expressions, ‘application’ and ‘implication’ have the advantage of most clearly conveying their own meaning. ‘Extension’ and ‘intension,’ however, are more usual; and neither ‘implication’ nor ‘connotation’ is quite exact as a synonym for ‘intension.’ ( 164.)

153. We now return to the division of terms into connotative and non-connotative.

154. A term is said to connote attributes, when it implies certain attributes at the same time that it applies to certain things distinct therefrom. [Footnote: Originally ‘connotative’ was used in the same sense in which we have used ‘attributive,’ for a word which directly signifies the presence of an attribute and indirectly applies to a subject. In this, its original sense, it was the subject which was said to be connoted, and not the attribute.]

155. A term which possesses both extension and intension, distinct from one another, is connotative.

156. A term which possesses no intension (if that be possible) or in which extension and intension coincide is non-connotative.

157. The subject-term, ‘man,’ and its corresponding attributive, ‘human,’ have both extension and intension, distinct from one another. They are therefore connotative. But the abstract term, ‘humanity,’ denotes the very collection of attributes, which was before connoted by the concrete terms, ‘man’ and ‘human.’ In this case, therefore, extension and intension coincide, and the term is non-connotative.

158. The above remark must be understood to be limited to abstract terms in their singular sense. When employed as common terms, abstract terms possess both extension and intension distinct from one another. Thus the term ‘colour’ applies to red, blue, and yellow, and at the same time implies (i.e. connotes), the power of affecting the eye.

159. Since all terms are names of things, whether substances or attributes, it is clear that all terms must possess extension, though the extension of singular terms is the narrowest possible, as being confined to one thing.

160. Are there then any terms which possess no intension? To ask this, is to ask—Are there any terms which have absolutely no meaning? It is often said that proper names are devoid of meaning, and the remark is, in a certain sense, true. When we call a being by the name ‘man,’ we do so because that being possesses human attributes, but when we call the same being by the name, ‘John,’ we do not mean to indicate the presence of any Johannine attributes. We simply wish to distinguish that being, in thought and language, from other beings of the same kind. Roughly speaking, therefore, proper names are devoid of meaning or intension. But no name can be entirely devoid of meaning. For, even setting aside the fact, which is not universally true, that proper names indicate the sex of the owner, the mere act of giving a name to a thing implies at least that the thing exists, whether in fact or thought; it implies what we may call ‘thinghood’: so that every term must carry with it some small amount of intension.

161. From another point of view, however, proper names possess more intension than any other terms. For when we know a person, his name calls up to our minds all the individual attributes with which we are familiar, and these must be far more numerous than the attributes which are conveyed by any common term which can be applied to him. Thus the name ‘John’ means more to a person who knows him than ‘attorney,’ ‘conservative,’ ‘scamp,’ of ‘vestry-man,’ or any other term which may happen to apply to him. This, however, is the acquired intension of a term, and must be distinguished from the original intension. The name ‘John’ was never meant to indicate the attributes which its owner has, as a matter of fact, developed. He would be John all the same, if he were none of these.

162. Hitherto we have been speaking only of christening-names, but it is evident that family names have a certain amount of connotation from the first. For when we dub John with the additional appellation of Smith, we do not give this second name as a mere individual mark, but intend thereby to indicate a relationship to other persons. The amount of connotation that can be conveyed by proper names is very noticeable in the Latin language. Let us take for an example the full name of a distinguished Roman—Publius Cornelius Scipio AEmilianus Africanus minor. Here it is only the praenomen, Publius, that can be said to be a mere individual mark, and even this distinctly indicates the sex of the owner. The nomen proper, Cornelius, declares the wearer of it to belong to the illustrious gens Cornelia. The cognomen, Scipio, further specifies him as a member of a distinguished family in that gens. The agnomen adoptivum indicates his transference by adoption from one gens to another. The second agnomen recalls the fact of his victory over the Carthaginians, while the addition of the word ‘minor’ distinguishes him from the former wearer of the same title. The name, instead of being devoid of meaning, is a chapter of history in itself. Homeric epithets, such as ‘The Cloud-compeller,’ ‘The Earth-shaker’ are instances of intensive proper names. Many of our own family names are obviously connotative in their origin, implying either some personal peculiarity, e.g. Armstrong, Cruikshank, Courteney; or the employment, trade or calling of the original bearer of the name, Smith, Carpenter, Baker, Clark, Leach, Archer, and so on; or else his abode, domain or nationality, as De Caen, De Montmorency, French, Langley; or simply the fact of descent from some presumably more noteworthy parent, as Jackson, Thomson, Fitzgerald, O’Connor, Macdonald, Apjohn, Price, Davids, etc. The question, however, whether a term is connotative or not, has to be decided, not by its origin, but by its use. We have seen that there are some proper names which, in a rough sense, may be said to possess no intension.

163. The other kind of singular terms, namely, designations ( 113) are obviously connotative. We cannot employ even the simplest of them without conveying more or less information about the qualities of the thing which they are used to denote. When, for instance, we say ‘this table,’ ‘this book,’ we indicate the proximity to the speaker of the object in question. Other designations have a higher degree of intension, as when we say ‘the present prime minister of England,’ ‘the honourable member who brought forward this motion to-night.’ Such terms have a good deal of significance in themselves, apart from any knowledge we may happen to possess of the individuals they denote.

164. We have seen that, speaking quite strictly, there are no terms which are non-connotative: but, for practical purposes, we may apply the expression to proper names, on the ground that they possess no intension, and to singular abstract terms on the ground that their extension and intension coincide. In the latter case it is indifferent whether we call the quantity extension or intension. Only we cannot call it ‘connotation,’ because that implies two quantities distinct from one another. A term must already denote a subject before it can be said to connote its attributes.

165. The division of terms into connotative and non-connotative is based on their possession of one quantity or two.