Deductive Logic Part 4

-- 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 cla.s.s 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 cla.s.s 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, const.i.tute 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 a.s.signed 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 a.s.signed to it. This is effected by taking a common term, and so limiting it as to make it applicable, under the given circ.u.mstances, 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 cla.s.s of Collective Terms. Nor is there any distinct cla.s.s 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 Quant.i.ty 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 cla.s.ses 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 a.s.signed 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 a.s.sume 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.