Logic: Deductive and Inductive

by Carveth Read, M.A.

“Chapter 23”

Additional Information
  • Year Published: 1914
  • Language: English
  • Country of Origin: England
  • Source: Read C. (1914). Logic: Deductive and Inductive.London, England; Simpkin, Marshall, Hamilton, Kent & Co. LTD.
  • Readability:
    • Flesch–Kincaid Level: 8.0
  • Word Count: 5,239




Section 1. Ordinary words may need definition, if in the course of exposition or argument their meaning is liable to be mistaken. But as definition cannot give one the sense of a popular word for all occasions of its use, it is an operation of great delicacy. Fixity of meaning in the use of single words is contrary to the genius of the common vocabulary; since each word, whilst having a certain predominant character, must be used with many shades of significance, in order to express the different thoughts and feelings of multitudes of men in endlessly diversified situations; and its force, whenever it is used, is qualified by the other words with which it is connected in a sentence, by its place in the construction of the sentence, by the emphasis, or by the pitch of its pronunciation compared with the other words.

Clearly, the requisite of a scientific language, ‘that every word shall have one meaning well defined,’ is too exacting for popular language; because the other chief requisite of scientific language cannot be complied with, ‘that there be no important meaning without a name.’ ‘Important meanings,’ or what seem such, are too numerous to be thus provided for; and new ones are constantly arising, as each of us pursues his business or his pleasure, his meditations or the excursions of his fancy. It is impossible to have a separate term for each meaning; and, therefore, the terms we have must admit of variable application.

An attempt to introduce new words is generally disgusting. Few men have mastered the uses of half the words already to be found in our classics. Much more would be lost than gained by doubling the dictionary. It is true that, at certain stages in the growth of a people, a need may be widely felt for the adoption of new words: such, in our own case, was the period of the Tudors and early Stuarts. Many fresh words, chiefly from the Latin, then appeared in books, were often received with reprobation and derision, sometimes disappeared again, sometimes established their footing in the language: see The Art of English Poetry (ascribed to Puttenham), Book III. chap. 4, and Ben Jonson’s Poetaster, Act. V. sc. I. Good judges did not know whether a word was really called for: even Shakespeare thought ‘remuneration’ and ‘accommodate’ ridiculous. But such national exigencies rarely arise; and in our own time great authors distinguish themselves by the plastic power with which they make common words convey uncommon meanings.

Fluid, however, as popular language is and ought to be, it may be necessary for the sake of clear exposition, or to steady the course of an argument, to avoid either sophistry or unintentional confusion, that words should be defined and discriminated; and we must discuss the means of doing so.

Section 2. Scientific method is applicable, with some qualifications, to the definition of ordinary words. Classification is involved in any problem of definition: at least, if our object is to find a meaning that shall be generally acceptable and intelligible. No doubt two disputants may, for their own satisfaction, adopt any arbitrary definition of a word important in their controversy; or, any one may define a word as he pleases, at the risk of being misunderstood, provided he has no fraudulent intention. But in exposition or argument addressed to the public, where words are used in some of their ordinary senses, it should be recognised that the meaning of each one involves that of many others. For language has grown with the human mind, as representing its knowledge of the world: this knowledge consists of the resemblances and differences of things and of the activities of things, that is, of classes and causes; and as there is such order in the world, so there must be in language: language, therefore, embodies an irregular classification of things with their attributes and relations according to our knowledge and beliefs. The best attempt (known to me) to carry out this view is contained in Roget’s Thesaurus, which is a classification of English words according to their meanings: founded, as the author tells us, on the models of Zoology and Botany, it has some of the requisites of a Logical Dictionary.

Popular language, indeed, having grown up with a predominantly practical purpose, represents a very imperfect classification philosophically considered. Things, or aspects, or processes of things, that have excited little interest, have often gone unnamed: so that scientific discoverers are obliged, for scientific purposes, to invent thousands of new names. Strong interests, on the other hand, give such a colour to language, that, where they enter, it is difficult to find any indifferent expressions. Consistency being much prized, though often the part of a blockhead, inconsistency implies not merely the absence of the supposed virtue, but a positive vice: Beauty being attractive and ugliness the reverse, if we invent a word for that which is neither, ‘plainness,’ it at once becomes tinged with the ugly. We seem to love beauty and morality so much as to be almost incapable of signifying their absence without expressing aversion.

Again, the erroneous theories of mankind have often found their way into popular speech, and their terms have remained there long after the rejection of the beliefs they embodied: as–lunatic, augury, divination, spell, exorcism: though, to be sure, such words may often be turned to good account, besides the interest of preserving their original sense. Language is a record as well as an index of ideas.

Language, then, being essentially classificatory, any attempt to ascertain the meaning of a word, far from neglecting its relations to others, should be directed toward elucidating them.

Every word belongs to a group, and this group to some other larger group. A group is sometimes formed by derivation, at least so far as different meanings are marked merely by inflections, as short, shorter, shorten, shortly; but, for the most part, is a conflux of words from many different sources. Repose, depose, suppose, impose, propose, are not nearly connected in meaning; but are severally allied in sense much more closely with words philologically remote. Thus repose is allied with rest, sleep, tranquillity; disturbance, unrest, tumult; whilst depose is, in one sense, allied with overthrow, dismiss, dethrone; restore, confirm, establish; and, in another sense, with declare, attest, swear, prove, etc. Groups of words, in fact, depend on their meanings, just as the connection of scientific names follows the resemblance in character of the things denoted.

Words, accordingly, stand related to one another, for the most part, though very irregularly, as genus, species, and co-ordinate species. Taking repose as a genus, we have as species of it, though not exactly co-ordinate with one another, tranquillity with a mental differentia (repose of mind), rest, whether of mind or body, sleep, with the differentia of unconsciousness (privative). Synonyms are species, or varieties, wherever any difference can be detected in them; and to discriminate them we must first find the generic meaning; for which there may, or may not, be a single word. Thus, equality, sameness, likeness, similarity, resemblance, identity, are synonyms; but, if we attend to the ways in which they are actually used, perhaps none of them can claim to be a genus in relation to the rest. If so, we must resort to a compound term for the genus, such as ‘absence of some sort of difference.’ Then equality is absence of difference in quantity; sameness is often absence of difference in quality, though the usage is not strict: likeness, similarity, and resemblance, in their actual use, perhaps, cannot be discriminated; unless likeness be the more concrete, similarity the more abstract; but they may all be used compatibly with the recognition of more or less difference in the things compared, and even imply this. Identity is the absence of difference of origin, a continuity of existence, with so much sameness from moment to moment as is compatible with changes in the course of nature; so that egg, caterpillar, chrysalis, butterfly may be identical for the run of an individual life, in spite of differences quantitative and qualitative, as truly as a shilling that all the time lies in a drawer.

Co-ordinate Species, when positive, have the least contrariety; but there are also opposites, namely, negatives, contradictories and fuller contraries. These may be regarded as either co-ordinate genera or the species of co-ordinate genera. Thus, repose being a genus, not-repose is by dichotomy a co-ordinate genus and is a negative and contradictory; then activity (implying an end in view), motion (limited to matter), disturbance (implying changes from a state of calm), tumult, etc., are co-ordinate species of not-repose, and are therefore co-ordinate opposites, or contraries, of the species of repose.

As for correlative words, like master and slave, husband and wife, etc., it may seem far-fetched to compare them with the sexes of the same species of plants or animals; but there is this resemblance between the two cases, that sexual names are correlative, as ‘lioness,’ and that one sex of a species, like a correlative name, cannot be defined without implying the other; for if a distinctive attribute of one sex be mentioned (as the lion’s mane), it is implied that the other wants it, and apart from this implication the species is not defined: just as the definition of ‘master’ implies a ‘slave’ to obey.

Common words, less precise than the terms of a scientific nomenclature, differ from them also in this, that the same word may occur in different genera. Thus, sleep is a species of repose as above; but it is also a species of unconsciousness, with co-ordinate species swoon, hypnotic state, etc. In fact, every word stands under as many distinct genera, at least, as there are simple or indefinable qualities to be enumerated in its definition.

Section 3. Partially similar to a scientific nomenclature, ordinary language has likewise a terminology for describing things according to their qualities and structure. Such is the function of all the names of colours, sounds, tastes, contrasts of temperature, of hardness, of pleasantness; in short, of all descriptive adjectives, and all names for the parts and processes of things. Any word connoting a quality may be used to describe many very different things, as long as they agree in that quality.

But the quality connoted by a word, and treated as always the same quality, is often only analogically the same. We speak of a great storm, a great man, a great book; but great is in each case not only relative, implying small, and leaving open the possibility that what we call great is still smaller than something else of its kind, but it is also predicated with reference to some quality or qualities, which may be very different in the several cases of its application. If the book is prized for wisdom, or for imagination, its greatness lies in that quality; if the man is distinguished for influence, or for courage, his greatness is of that nature; if the storm is remarkable for violence, or for duration, its greatness depends on that fact. The word great, therefore, is not used for these things in the same sense, but only analogically and elliptically. Similarly with good, pure, free, strong, rich, and so on. ‘Rest’ has not the same meaning in respect of a stone and of an animal, nor ‘strong’ in respect of thought and muscle, nor ‘sweet’ in respect of sugar and music. But here we come to the border between literal and figurative use; every one sees that figurative epithets are analogical; but by custom any figurative use may become literal.

Again, many general names of widely different meaning, are brought together in describing any concrete object, as an animal, or a landscape, or in defining any specific term. This is the sense of the doctrine, that any concrete thing is a conflux of generalities or universals: it may at least be considered in this way; though it seems more natural to say, that an object presents these different aspects to a spectator, who, fully to comprehend it, must classify it in every aspect.

Section 4. The process of seeking a definition may be guided by the following maxims:

(1) Find the usage of good modern authors; that is (as they rarely define a word explicitly), consider what in various relations they use it to denote; from which uses its connotation may be collected.

(2) But if this process yield no satisfactory result, make a list of the things denoted, and of those denoted by the co-ordinate and opposite words; and observe the qualities in which the things denoted agree, and in which they differ from those denoted by the contraries and opposites. If ‘civilisation’ is to be defined, make lists of civilised peoples, of semi-civilised, of barbarous, and of savage: now, what things are common to civilised peoples and wanting in the others respectively? This is an exercise worth attempting. If poetry is to be defined, survey some typical examples of what good critics recognise as poetry, and compare them with examples of bad ‘poetry,’ literary prose, oratory, and science. Having determined the characteristics of each kind, arrange them opposite one another in parallel columns. Whoever tries to define by this method a few important, frequently occurring words, will find his thoughts the clearer for it, and will collect by the way much information which may be more valuable than the definition itself, should he ever find one.

(3) If the genus of a word to be defined is already known, the process may be shortened. Suppose the genus of poetry to be belles lettres (that is, ‘appealing to good taste’), this suffices to mark it off from science; but since literary prose and oratory are also belles lettres, we must still seek the differentia of poetry by a comparison of it with these co-ordinate species. A compound word often exhibits genus and difference upon its face: as ‘re-turn,’ ‘inter-penetrate,’ ‘tuning-fork,’ ‘cricket-bat’; but the two last would hardly be understood without inspection or further description. And however a definition be discovered, it is well to state it per genus et differentiam.

(4) In defining any term we should avoid encroaching upon the meaning of any of the co-ordinate terms; for else their usefulness is lessened: as by making ‘law’ include ‘custom,’ or ‘wealth’ include ‘labour’ or ‘culture.’

(5) If two or more terms happen to be exactly synonymous, it may be possible (and, if so, it is a service to the language) to divert one of them to any neighbouring meaning that has no determinate expression. Thus, Wordsworth and Coleridge took great pains to distinguish between Imagination and Fancy, which had become in common usage practically equivalent; and they sought to limit ‘imagination’ to an order of poetic effect, which (they said) had prevailed during the Elizabethan age, but had been almost lost during the Gallo-classic, and which it was their mission to restore. Co-ordinate terms often tend to coalesce and become synonymous, or one almost supersedes the other, to the consequent impoverishment of our speech. At present proposition (that something is the fact) has almost driven out proposal (that it is desirable to co-operate in some action). Even good writers and speakers, by their own practice, encourage this confusion: they submit to Parliament certain ‘propositions’ (proposals for legislation), or even make ‘a proposition of marriage.’ Definition should counteract such a tendency.

(6) We must avoid the temptation to extend the denotation of a word so far as to diminish or destroy its connotation; or to increase its connotation so much as to render it no longer applicable to things which it formerly denoted: we should neither unduly generalise, nor unduly specialise, a term. Is it desirable to define education so as to include the ‘lessons of experience’; or is it better to restrict it as implying a personal educator? If any word implies blame or praise, we are apt to extend it to everything we hate or approve. But coward cannot be so defined as to include all bullies, nor noble so as to include every honest man, without some loss in distinctness of thought.

The same impulses make us specialise words; for, if two words express approval, we wish to apply both to whatever we admire and to refuse both to whatever displeases us. Thus, a man may resolve to call no one great who is not good: greatness, according to him, connotes goodness: whence it follows that (say) Napoleon I. was not great. Another man is disgusted with greatness: according to him, good and great are mutually exclusive classes, sheep and goats, as in Gray’s wretched clench: “Beneath the good how far, yet far above the great.” In feet, however ‘good’ and ‘great’ are descriptive terms, sometimes applicable to the same object, sometimes to different: but ‘great’ is the wider term and applicable to goodness itself and also to badness; whereas by making ‘great’ connote goodness it becomes the narrower term. And as we have seen (Section 3), such epithets may be applicable to objects on account of different qualities: good is not predicated on the same ground of a man and of a horse.

(7) In defining any word, it is desirable to bear in mind its derivation, and to preserve the connection of meaning with its origin; unless there are preponderant reasons for diverting it, grounded on our need of the word to express a certain sense, and the greater difficulty of finding any other word for the same purpose. It is better to lean to the classical than to the vulgar sense of ‘indifferent,’ ‘impertinent,’ ‘aggravating,’ ‘phenomenal.’

(8) Rigorous definition should not be attempted where the subject does not admit of it. Some kinds of things are so complex in their qualities, and each quality may manifest itself in so many degrees without ever admitting of exact measurement, that we have no means of marking them off precisely from other things nearly allied, similarly complex and similarly variable. If so we cannot precisely define their names. Imagination and fancy are of this nature, civilisation and barbarism, poetry and other kinds of literary expression. As to poetry, some think it only exists in metre, but hardly maintain that the metre must be strictly regular: if not, how much irregularity of rhythm is admissible? Others regard a certain mood of impassioned imagination as the essence of poetry; but they have never told us how great intensity of this mood is requisite. We also hear that poetry is of such a nature that the enjoyment of it is an end in itself; but as it is not maintained that poetry must be wholly impersuasive or uninstructive, there seems to be no means of deciding what amount or prominence of persuasion or instruction would transfer the work to the region of oratory or science. Such cases make the method of defining by the aid of a type really useful: the difficulty can hardly be got over without pointing to typical examples of each meaning, and admitting that there may be many divergences and unclassifiable instances on the border between allied meanings.

Section 5. As science began from common knowledge, the terms of the common vocabulary have often been adopted into the sciences, and many are still found there: such as weight, mass, work, attraction, repulsion, diffusion, reflection, absorption, base, salt, and so forth. In the more exact sciences, the vague popular associations with such words are hardly an inconvenience: since those addicted to such studies do not expect to master them without undergoing special discipline; and, having precisely defined the terms, they acquire the habit of thinking with them according to their assigned signification in those investigations to which they are appropriate. It is in the Social Sciences, especially Economics and Ethics, that the use of popular terminology is at once unavoidable and prejudicial. For the subject-matters, industry and the conduct of life, are every man’s business; and, accordingly, have always been discussed with a consciousness of their direct practical bearing upon public and private interests, and therefore in the common language, in order that everybody may as far as possible benefit by whatever light can be thrown upon them. The general practice of Economists and Moralists, however, shows that, in their judgment, the good derived from writing in the common vocabulary outweighs the evil: though it is sometimes manifest that they themselves have been misled by extra-scientific meanings. To reduce the evil as much as possible, the following precautions seem reasonable:

(1) To try to find and adopt the central meaning of the word (say rent or money) in its current or traditionary applications: so as to lessen in the greater number of cases the jar of conflicting associations. But if the central popular meaning does not correspond with the scientific conception to be expressed, it may be better to invent a new term.

(2) To define the term with sufficient accuracy to secure its clear and consistent use for scientific purposes.

(3) When a popular term has to be used in a sense that departs from the ordinary one in such a way as to incur the danger of misunderstanding, to qualify it by some adjunct or “interpretation-clause.”

The first of these rules is not always adhered to; and, in the progress of a science, as subtler and more abstract relations are discovered amongst the facts, the meaning of a term may have to be modified and shifted further and further from its popular use. The term ‘rent,’ for example, is used by economists, in such a sense that they have to begin the discussion of the facts it denotes, by explaining that it does not imply any actual payment by one man to another. Here, for most readers, the meaning they are accustomed to, seems already to have entirely disappeared. Difficulties may, however, be largely overcome by qualifying the term in its various relations, as produce-rents, ground-rents, customary rents, and so forth, (Cf. Dr. Keynes’ Scope and Method of Political Economy, chap. 5.)

Section 6. Definitions affect the cogency of arguments in many ways, whether we use popular or scientific language. If the definitions of our terms are vague, or are badly abstracted from the facts denoted, all arguments involving these terms are inconclusive. There can be no confidence in reasoning with such terms; since, if vague, there is nothing to protect us from ambiguity; or, if their meaning has been badly abstracted, we may be led into absurdity–as if ‘impudence’ should be defined in such a way as to confound it with honesty.

Again, it is by definitions that we can best distinguish between Verbal and Real Propositions. Whether a term predicated is implied in the definition of the subject, or adds something to its meaning, deserves our constant attention. We often persuade ourselves that statements are profound and important, when, in fact, they are mere verbal propositions. “It is just to give every man his due”; “the greater good ought to be preferred to the less”; such dicta sound well–indeed, too well! For ‘a man’s due’ means nothing else than what it is just to give him; and ‘the greater good’ may mean the one that ought to be preferred: these, therefore, are Truisms. The investigation of a definition may be a very valuable service to thought; but, once found, there is no merit in repeating it. To put forward verbal or analytic propositions, or truisms, as information (except, of course, in explaining terms to the uninstructed), shows that we are not thinking what we say; for else we must become aware of our own emptiness. Every step forward in knowledge is expressed in a real or synthetic proposition; and it is only by means of such propositions that information can be given (except as to the meaning of words) or that an argument or train of reasoning can make any progress.

Opposed to a truism is a Contradiction in Terms; that is, the denying of a subject something which it connotes (or which belongs to its definition), or the affirming of it something whose absence it connotes (or which is excluded by its definition). A verbal proposition is necessarily true, because it is tautologous; a contradiction in terms is necessarily false, because it is inconsistent. Yet, as a rhetorical artifice, or figure, it may be effective: that ‘the slave is not bound to obey his master’ may be a way of saying that there ought to be no slaves; that ‘property is theft,’ is an uncompromising assertion of the communistic ideal. Similarly a truism may have rhetorical value: that ‘a Negro is a man’ has often been a timely reminder, or even that “a man’s a man.” It is only when we fall into such contradiction or tautology by lapse of thought, by not fully understanding our own words, that it becomes absurd.

Real Propositions comprise the predication of Propria and Accidentia. Accidentia, implying a sort of empirical law, can only be established by direct induction. But propria are deduced from (or rather by means of) the definition with the help of real propositions, and this is what is called ‘arguing from a Definition.’ Thus, if increasing capacity for co-operation be a specific character of civilisation, ‘great wealth’ may be considered as a proprium of civilised as compared with barbarous nations. For co-operation is made most effectual by the division of labour, and that this is the chief condition of producing wealth is a real proposition. Such arguments from definitions concerning concrete facts and causation require verification by comparing the conclusion with the facts. The verification of this example is easy, if we do not let ourselves be misled in estimating the wealth of barbarians by the ostentatious “pearl and gold” of kings and nobles, where 99 per cent. of the people live in penury and servitude. The wealth of civilisation is not only great but diffused, and in its diffusion its greatness must be estimated.

To argue from a definition may be a process of several degrees of complexity. The simplest case is the establishing of a proprium as the direct consequence of some connoted attribute, as in the above example. If the definition has been correctly abstracted from the particulars, the particulars have the attributes summarised in the definition; and, therefore, they have whatever can be shown to follow from those attributes. But it frequently happens that the argument rests partly on the qualities connoted by the class name and partly on many other facts.

In Geometry, the proof of a theorem depends not only upon the definition of the figure or figures directly concerned, but also upon one or more axioms, and upon propria or constructions already established. Thus, in Euclid’s fifth Proposition, the proof that the angles at the base of an isosceles triangle are equal, depends not only on the equality of the opposite sides, but upon this together with the construction that shows how from the greater of two lines a part may be cut off equal to the less, the proof that triangles that can be conceived to coincide are equal, and the axiom that if equals be taken from equals the remainders are equal. Similarly, in Biology, if colouring favourable to concealment is a proprium of carnivorous animals, it is not deducible merely from their predatory character or any other attribute entering into the definition of any species of them, but from their predatory character together with the causes summarised in the phrase ‘Natural Selection’; that is, competition for a livelihood, and the destruction of those that labour under any disadvantages, of which conspicuous colouring would be one. The particular coloration of any given species, again, can only be deduced by further considering its habitat (desert, jungle or snowfield): a circumstance lying wholly outside the definition of the species.

The validity of an argument based partly or wholly on a definition depends, in the first place, on the existence of things corresponding with the definition–that is, having the properties connoted by the name defined. If there are no such things as isosceles triangles, Euclid’s fifth Proposition is only formally true, like a theorem concerning the fourth dimension of space: merely consistent with his other assumptions. But if there be any triangles only approximately isosceles, the proof applies to them, making allowance for their concrete imperfection: the nearer their sides approach straightness and equality the more nearly equal will the opposite angles be.

Again, as to the things corresponding with terms defined, according to Dr. Venn, their ‘existence’ may be understood in several senses: (1) merely for the reason, like the pure genera and species of Porphyry’s tree; the sole condition of whose being is logical consistency: or (2) for the imagination, like the giants and magicians of romance, the heroes of tragedy and the fairies of popular superstition; whose properties may be discussed, and verified by appeal to the right documents and authorities (poems and ballads): or (3) for perception, like plants, animals, stones and stars. Only the third class exist in the proper sense of the word. But under a convention or hypothesis of existence, we may argue from the definition of a fairy, or a demigod, or a dragon, and deduce various consequences without absurdity, if we are content with poetic consistency and the authority of myths and romances as the test of truth.

In the region of concrete objects, whose properties are causes, and neither merely fictions nor determinations of space (as in Geometry), we meet with another condition of the validity of any argument depending on a definition: there must not only be objects corresponding to the definition, but there must be no other causes counteracting those qualities on whose agency our argument relies. Thus, though we may infer from the quality of co-operation connoted by civilisation, that a civilised country will be a wealthy one, this may not be found true of such a country recently devastated by war or other calamity. Nor can co-operation always triumph over disadvantageous circumstances. Scandinavia is so poor in the gifts of nature favourable to industry, that it is not wealthy in spite of civilisation: still, it is far wealthier than it would be in the hands of a barbarous people. In short, when arguing from a definition, we can only infer the tendency of any causal characteristics included in it; the unqualified realisation of such a tendency must depend upon the absence of counteracting causes. As soon as we leave the region of pure conceptions and make any attempt to bring our speculations home to the actual phenomena of nature or of human life, the verification of every inference becomes an unremitting obligation.