OF TERMS AND THEIR DENOTATION
Sec. 1. In treating of Deductive Logic it is usual to recognise three
divisions of the subject: first, the doctrine of Terms, words, or other
signs used as subjects or predicates; secondly, the doctrine of
Propositions, analysed into terms related; and, thirdly, the doctrine of
the Syllogism in which propositions appear as the grounds of a
conclusion.
The terms employed are either letters of the alphabet, or the words of
common language, or the technicalities of science; and since the words
of common language are most in use, it is necessary to give some account
of common language as subserving the purposes of Logic. It has been
urged that we cannot think or reason at all without words, or some
substitute for them, such as the signs of algebra; but this is an
exaggeration. Minds greatly differ, and some think by the aid of
definite and comprehensive picturings, especially in dealing with
problems concerning objects in space, as in playing chess blindfold,
inventing a machine, planning a tour on an imagined map. Most people
draw many simple inferences by means of perceptions, or of mental
imagery. On the other hand, some men think a good deal without any
continuum of words and without any imagery, or with none that seems
relevant to the purpose. Still the more elaborate sort of thinking, the
grouping and concatenation of inferences, which we call reasoning,
cannot be carried far without language or some equivalent system of
signs. It is not merely that we need language to express our reasonings
and communicate them to others: in solitary thought we often depend on
words--'talk to ourselves,' in fact; though the words or sentences that
then pass through our minds are not always fully formed or articulated.
In Logic, moreover, we have carefully to examine the grounds (at least
the proximate grounds) of our conclusions; and plainly this cannot be
done unless the conclusions in question are explicitly stated and
recorded.
Conceptualists say that Logic deals not with the process of thinking
(which belongs to Psychology) but with its results; not with conceiving
but with concepts; not with judging but with judgments. Is the concept
self-consistent or adequate? Logic asks; is the judgment capable of
proof? Now, it is only by recording our thoughts in language that it
becomes possible to distinguish between the process and the result of
thought. Without language, the act and the product of thinking would be
identical and equally evanescent. But by carrying on the process in
language and remembering or otherwise recording it, we obtain a result
which may be examined according to the principles of Logic.
Sec. 2. As Logic, then, must give some account of language, it seems
desirable to explain how its treatment of language differs from that of
Grammar and from that of Rhetoric.
Grammar is the study of the words of some language, their classification
and derivation, and of the rules of combining them, according to the
usage at any time recognised and followed by those who are considered
correct writers or speakers. Composition may be faultless in its
grammar, though dull and absurd.
Rhetoric is the study of language with a view to obtaining some special
effect in the communication of ideas or feelings, such as
picturesqueness in description, vivacity in narration, lucidity in
exposition, vehemence in persuasion, or literary charm. Some of these
ends are often gained in spite of faulty syntax or faulty logic; but
since the few whom bad grammar saddens or incoherent arguments divert
are not carried away, as they else might be, by an unsophisticated
orator, Grammar and Logic are necessary to the perfection of Rhetoric.
Not that Rhetoric is in bondage to those other sciences; for foreign
idioms and such figures as the ellipsis, the anacoluthon, the oxymoron,
the hyperbole, and violent inversions have their place in the
magnificent style; but authors unacquainted with Grammar and Logic are
not likely to place such figures well and wisely. Indeed, common idioms,
though both grammatically and rhetorically justifiable, both correct and
effective, often seem illogical. 'To fall asleep,' for example, is a
perfect English phrase; yet if we examine severally the words it
consists of, it may seem strange that their combination should mean
anything at all.
But Logic only studies language so far as necessary in order to state,
understand, and check the evidence and reasonings that are usually
embodied in language. And as long as meanings are clear, good Logic is
compatible with false concords and inelegance of style.
Sec. 3. Terms are either Simple or Composite: that is to say, they may
consist either of a single word, as 'Chaucer,' 'civilisation'; or of
more than one, as 'the father of English poetry,' or 'modern civilised
nations.' Logicians classify words according to their uses in forming
propositions; or, rather, they classify the uses of words as terms, not
the words themselves; for the same word may fall into different classes
of terms according to the way in which it is used. (Cf. Mr. Alfred
Sidgwick's _Distinction and the Criticism of Beliefs_, chap. xiv.)
Thus words are classified as Categorematic or Syncategorematic. A word
is Categorematic if used singly as a term without the support of other
words: it is Syncategorematic when joined with other words in order to
constitute the subject or predicate of a proposition. If we say _Venus
is a planet whose orbit is inside the Earth's_, the subject, 'Venus,'
is a word used categorematically as a simple term; the predicate is a
composite term whose constituent words (whether substantive, relative,
verb, or preposition) are used syncategorematically.
Prepositions, conjunctions, articles, adverbs, relative pronouns, in
their ordinary use, can only enter into terms along with other words
having a substantive, adjectival or participial force; but when they are
themselves the things spoken of and are used substantively (_suppositio
materialis_), they are categorematic. In the proposition, _'Of' was used
more indefinitely three hundred years ago than it is now_, 'of' is
categorematic. On the other hand, all substantives may be used
categorematically; and the same self-sufficiency is usually recognised
in adjectives and participles. Some, however, hold that the
categorematic use of adjectives and participles is due to an ellipsis
which the logician should fill up; that instead of _Gold is heavy_, he
should say _Gold is a heavy metal_; instead of _The sun is shining_,
_The sun is a body shining_. But in these cases the words 'metal' and
'body' are unmistakable tautology, since 'metal' is implied in gold and
'body' in sun. But, as we have seen, any of these kinds of word,
substantive, adjective, or participle, may occur syncategorematically in
connection with others to form a composite term.
Sec. 4. Most terms (the exceptions and doubtful cases will be discussed
hereafter) have two functions, a denotative and a connotative. A term's
denotative function is, to be the name or sign of something or some
multitude of things, which are said to be called or denoted by the term.
Its connotative function is, to suggest certain qualities and
characteristics of the things denoted, so that it cannot be used
literally as the name of any other things; which qualities and
characteristics are said to be implied or connoted by the term. Thus
'sheep' is the name of certain animals, and its connotation prevents its
being used of any others. That which a term directly indicates, then,
is its _Denotation_; that sense or customary use of it which limits the
Denotation is its _Connotation_ (ch. iv.). Hamilton and others use
'Extension' in the sense of Denotation, and 'Intension' or
'Comprehension' in the sense of Connotation. Now, terms may be
classified, first according to what they stand for or denote; that is,
according to their _Denotation_. In this respect, the use of a term is
said to be either Concrete or Abstract.
A term is Concrete when it denotes a 'thing'; that is, any person,
object, fact, event, feeling or imagination, considered as capable of
having (or consisting of) qualities and a determinate existence. Thus
'cricket ball' denotes any object having a certain size, weight, shape,
colour, etc. (which are its qualities), and being at any given time in
some place and related to other objects--in the bowler's hands, on the
grass, in a shop window. Any 'feeling of heat' has a certain intensity,
is pleasurable or painful, occurs at a certain time, and affects some
part or the whole of some animal. An imagination, indeed (say, of a
fairy), cannot be said in the same sense to have locality; but it
depends on the thinking of some man who has locality, and is definitely
related to his other thoughts and feelings.
A term is Abstract, on the other hand, when it denotes a quality (or
qualities), considered by itself and without determinate existence in
time, place, or relation to other things. 'Size,' 'shape,' 'weight,'
'colour,' 'intensity,' 'pleasurableness,' are terms used to denote such
qualities, and are then abstract in their denotation. 'Weight' is not
something with a determinate existence at a given time; it exists not
merely in some particular place, but wherever there is a heavy thing;
and, as to relation, at the same moment it combines in iron with
solidity and in mercury with liquidity. In fact, a quality is a point of
agreement in a multitude of different things; all heavy things agree in
weight, all round things in roundness, all red things in redness; and an
abstract term denotes such a point (or points) of agreement among the
things denoted by concrete terms. Abstract terms result from the
analysis of concrete things into their qualities; and conversely a
concrete term may be viewed as denoting the synthesis of qualities into
an individual thing. When several things agree in more than one quality,
there may be an abstract term denoting the union of qualities in which
they agree, and omitting their peculiarities; as 'human nature' denotes
the common qualities of men, 'civilisation' the common conditions of
civilised peoples.
Every general name, if used as a concrete term, has, or may have, a
corresponding abstract term. Sometimes the concrete term is modified to
form the abstract, as 'greedy--greediness'; sometimes a word is adapted
from another language, as 'man--humanity'; sometimes a composite term is
used, as 'mercury--the nature of mercury,' etc. The same concrete may
have several abstract correlatives, as 'man--manhood, humanity, human
nature'; 'heavy--weight, gravity, ponderosity'; but in such cases the
abstract terms are not used quite synonymously; that is, they imply
different ways of considering the concrete.
Whether a word is used as a concrete or abstract term is in most
instances plain from the word itself, the use of most words being pretty
regular one way or the other; but sometimes we must judge by the
context. 'Weight' may be used in the abstract for 'gravity,' or in the
concrete for a measure; but in the latter sense it is syncategorematic
(in the singular), needing at least the article 'a (or the) weight.'
'Government' may mean 'supreme political authority,' and is then
abstract; or, the men who happen to be ministers, and is then concrete;
but in this case, too, the article is usually prefixed. 'The life' of
any man may mean his vitality (abstract), as in "Thus following life in
creatures we dissect"; or, the series of events through which he passes
(concrete), as in 'the life of Nelson as narrated by Southey.'
It has been made a question whether the denotation of an abstract term
may itself be the subject of qualities. Apparently 'weight' may be
greater or less, 'government' good or bad, 'vitality' intense or dull.
But if every subject is modified by a quality, a quality is also
modified by making it the subject of another; and, if so, it seems then
to become a new quality. The compound terms 'great weight,' 'bad
government,' 'dull vitality,' have not the same denotation as the simple
terms 'weight, 'government,' 'vitality': they imply, and may be said to
connote, more special concrete experience, such as the effort felt in
lifting a trunk, disgust at the conduct of officials, sluggish movements
of an animal when irritated. It is to such concrete experiences that we
have always to refer in order fully to realise the meaning of abstract
terms, and therefore, of course, to understand any qualification of
them.
Sec. 5. Concrete terms may be subdivided according to the number of things
they denote and the way in which they denote them. A term may denote one
thing or many: if one, it is called Singular; if many, it may do so
distributively, and then it is General; or, as taken all together, and
then it is Collective: one, then; any one of many; many in one.
Among Singular Terms, each denoting a single thing, the most obvious are
Proper Names, such as Gibraltar or George Washington, which are merely
marks of individual things or persons, and may form no part of the
common language of a country. They are thus distinguished from other
Singular Terms, which consist of common words so combined as to restrict
their denotation to some individual, such as, 'the strongest man on
earth.'
Proper Terms are often said to be arbitrary signs, because their use
does not depend upon any reason that may be given for them. Gibraltar
had a meaning among the Moors when originally conferred; but no one now
knows what it was, unless he happens to have learned it; yet the name
serves its purpose as well as if it were "Rooke's Nest." Every Newton
or Newport year by year grows old, but to alter the name would cause
only confusion. If such names were given by mere caprice it would make
no difference; and they could not be more cumbrous, ugly, or absurd than
many of those that are given 'for reasons.'
The remaining kinds of Singular Terms are drawn from the common
resources of the language. Thus the pronouns 'he,' 'she,' 'it,' are
singular terms, whose present denotation is determined by the occasion
and context of discourse: so with demonstrative phrases--'the man,'
'that horse.' Descriptive names may be more complex, as 'the wisest man
of Gotham,' which is limited to some individual by the superlative
suffix; or 'the German Emperor,' which is limited by the definite
article--the general term 'German Emperor' being thereby restricted
either to the reigning monarch or to the one we happen to be discussing.
Instead of the definite, the indefinite article may be used to make
general terms singular, as 'a German Emperor was crowned at Versailles'
(_individua vaga_).
Abstract Terms are ostensively singular: 'whiteness' (e.g.) is one
quality. But their full meaning is general: 'whiteness' stands for all
white things, so far as white. Abstract terms, in fact, are only
formally singular.
General Terms are words, or combinations of words, used to denote any
one of many things that resemble one another in certain respects.
'George III.' is a Singular Term denoting one man; but 'King' is a
General Term denoting him and all other men of the same rank; whilst the
compound 'crowned head' is still more general, denoting kings and also
emperors. It is the nature of a general term, then, to be used in the
same sense of whatever it denotes; and its most characteristic form is
the Class-name, whether of objects, such as 'king,' 'sheep,' 'ghost'; or
of events, such as 'accession,' 'purchase,' 'manifestation.' Things and
events are known by their qualities and relations; and every such
aspect, being a point of resemblance to some other things, becomes a
ground of generalisation, and therefore a ground for the need and use of
general terms. Hence general terms are far the most important sort of
terms in Logic, since in them general propositions are expressed and,
moreover (with rare exceptions), all predicates are general. For,
besides these typical class-names, attributive words are general terms,
such as 'royal,' 'ruling,' 'woolly,' 'bleating,' 'impalpable,'
'vanishing.'
Infinitives may also be used as general terms, as '_To err is human_';
but for logical purposes they may have to be translated into equivalent
substantive forms, as _Foolish actions are characteristic of mankind_.
Abstract terms, too, are (as I observed) equivalent to general terms;
'folly' is abstract for 'foolish actions.' '_Honesty is the best
policy_' means _people who are honest may hope to find their account in
being so_; that is, in the effects of their honest actions, provided
they are wise in other ways, and no misfortunes attend them. The
abstract form is often much the more succinct and forcible, but for
logical treatment it needs to be interpreted in the general form.
By antonomasia proper names may become general terms, as if we say _'A
Johnson' would not have written such a book_--i.e., any man of his
genius for elaborate eloquence.
A Collective Term denotes a multitude of similar things considered as
forming one whole, as 'regiment,' 'flock,' 'nation': not distributively,
that is, not the similar things severally; to denote them we must say
'soldiers of the regiment,' 'sheep of the flock,' and so on. If in a
multitude of things there is no resemblance, except the fact of being
considered as parts of one whole, as 'the world,' or 'the town of
Nottingham' (meaning its streets and houses, open spaces, people, and
civic organisation), the term denoting them as a whole is Singular; but
'the world' or 'town of Nottingham,' meaning the inhabitants only, is
Collective.
In their strictly collective use, all such expressions are equivalent to
singular terms; but many of them may also be used as general terms, as
when we speak of 'so many regiments of the line,' or discuss the
'plurality of worlds'; and in this general use they denote any of a
multitude of things of the same kind--regiments, or habitable worlds.
Names of substances, such as 'gold,' 'air,' 'water,' may be employed as
singular, collective, or general terms; though, perhaps, as singular
terms only figuratively, as when we say _Gold is king_. If we say with
Thales, '_Water is the source of all things_,' 'water' seems to be used
collectively. But substantive names are frequently used as general
terms. For example, _Gold is heavy_ means 'in comparison with other
things,' such as water. And, plainly, it does not mean that the
aggregate of gold is heavier than the aggregate of water, but only that
its specific gravity is greater; that is, bulk for bulk, any piece of
gold is heavier than water.
Finally, any class-name may be used collectively if we wish to assert
something of the things denoted by it, not distributively but
altogether, as that _Sheep are more numerous than wolves_.