Deductive Logic

_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 a.n.a.logous Terms. The word 'sweet,' for instance, is applied by a.n.a.logy 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 a.n.a.logy 'the head.' It is plainly inappropriate to make a separate cla.s.s of a.n.a.logous terms. Rather, terms become equivocal by being extended by a.n.a.logy 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 Quant.i.ty of Terms.

_Quant.i.ty of Terms._

-- 148. A term is possessed of quant.i.ty 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 quant.i.ty 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 const.i.tutes its quant.i.ty in intension.

-- 152.

Extension = breadth = compa.s.s = 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 s.e.x 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 relations.h.i.+p 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 aemilia.n.u.s Africa.n.u.s minor. Here it is only the praenomen, Publius, that can be said to be a mere individual mark, and even this distinctly indicates the s.e.x of the owner. The nomen proper, Cornelius, declares the wearer of it to belong to the ill.u.s.trious 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 t.i.tle. 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 quant.i.ty extension or intension. Only we cannot call it 'connotation,' because that implies two quant.i.ties 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 quant.i.ty or two.

CHAPTER IV.

_Of the Law of Inverse Variation of Extension and Intension._