Analysis of Mr. Mill's System of Logic Part 7

_This Chapter is a digression._

Abstract Ideas, that is, General Conceptions, certainly do exist, however Metaphysics may decide as to their composition. They _represent_ in our minds the whole cla.s.ses of things called by the general names; and, being implied in the mental operation whereby cla.s.ses are formed, viz. in the comparison of phenomena, to ascertain in what they agree, cannot be dispensed with in induction, since such a comparison is a necessary preliminary to an induction, and more than two objects cannot well be compared without a type, in which capacity conceptions serve.

But, though implied in the comparison, it does not follow that, as Dr.

Whewell supposes, they must have existed in the mind prior to comparison. Sometimes, but only sometimes, they are pre-existent to the comparison of the particular facts in question, being, as was Kepler's hypothesis of an ellipse, familiar conceptions borrowed from different facts, and _superinduced_, to use Dr. Whewell's expression, on the facts in question. But even such conceptions are the results of former comparisons of individual facts. And much more commonly (and these are the more difficult cases in science) conceptions are not pre-existent even in this sense; but they have to be got (e.g. the Idea of Polarity) by abstraction, that is, by comparison, from among the very phenomena which they afterwards serve to arrange, or, as Dr. Whewell says, to _connect_. They seem to be pre-existent; but this is only because the mind keeps ever forming conceptions from the facts, which at the time are before it, and then tentatively applies these conceptions (which it is always remodelling, dropping some which are found not to suit after-found facts, and generalising others by a further effort of abstraction) as types of comparison for phenomena subsequently presented to it; so that, being found in these later stages of the comparison already in the mind, they appear in the character simply of types, and not as being also themselves results of comparison. Really they are always both; and the term _comparison_ expresses as well their origin as (and this far more exactly than to _connect_ or to _superinduce_) their function.

Dr. Whewell says that conceptions must be _appropriate_ and _clear_.

They must, indeed, be appropriate relatively to the purpose in view (for appropriateness is only relative); but they cannot avoid being appropriate (though one may be more so than another) if our comparison of the objects has led to a conception corresponding to any real agreement in the facts: the ancients' and schoolmen's conceptions were often absolutely inappropriate, because grounded on only apparent agreement. So, again, they must be _clear_ in the following sense; that is to say, a _sufficient number_ of facts must have been _carefully observed_, and accurately _remembered_. It is also a condition (and one implied in the latter qualities) of clearness, that the conception should be _determinate_, that is, that we should know precisely what agreements we include in it, and never vary the connotation except consciously.

Activity, carefulness, and accuracy in the observing and comparing faculties are therefore needed; the first quality to produce appropriateness, and the latter two, clearness. Moreover, _scientific imagination_, i.e. the faculty of mentally arranging known elements into new combinations, is necessary for forming true conceptions; and the mind should be stored with previously acquired conceptions, kindred to the subject of inquiry, since a comparison of the facts themselves often fails to suggest the principle of their agreement; just as, in seeking for anything lost, we often have to ask ourselves in what places it may be hid, that we may search for it there.

CHAPTER III.

NAMING AS SUBSIDIARY TO INDUCTION.

As reasoning is from particulars to particulars, and consists simply in recognising one fact as a mark of another, or a mark of a mark of another, the only necessary conditions of the exertion of the reasoning power are senses, to perceive that two facts are conjoined; and a.s.sociation, as the law by which one of the two facts raises up the idea of the other. The existence of artificial signs is not a third _necessary_ condition. It is only, however, the rudest inductions (and of such even brutes are capable) that can be made without language or other artificial signs. Without such we could avail ourselves but little of the experience of others; and (except in cases involving our intenser sensations or emotions) of none of our own long past experience. It is only through the medium of such permanent signs that we can register uniformities; and the existence of uniformities is necessary to justify an inference, even in a single case, and they can be ascertained once for all.

General names are not, as some have argued, a mere contrivance to economise words. For, if there were a name for every individual object, but no general names, we could not record one uniformity, or the result of a single comparison. To effect this, all indeed, that are _indispensable_, are the abstract names of attributes; but, in fact, men have always given general names to objects also.

CHAPTER IV.

THE REQUISITES OF A PHILOSOPHICAL LANGUAGE, AND THE PRINCIPLES OF DEFINITION.

Concrete general names (and the meaning of abstract names depends on the concrete) should have a fixed and knowable connotation. This is easy enough when, as in the case of new technical names, we choose the connotation for ourselves; but it is hard when, as generally happens with names in common use, the same name has been applied to different objects, from only a vague feeling of resemblance. For, then, after a time, general propositions are made, in which predicates are applied to those names; and these propositions make up a loose connotation for the cla.s.s name, which, and the abstract at about this same period formed from it, are consequently never understood by two people, or by the same person at different times, in the same way. The logician has to fix this fluctuating connotation, but so that the name may, if possible, still _denote_ the things of which it is currently affirmed. To effect this double object (which is called, though improperly, defining _not the name but the thing_), he must select from the attributes in which the denoted objects agree, choosing, as the common properties are always many, and, in a _kind_, innumerable, those which are familiarly predicated of the cla.s.s, and out of them, if possible, or otherwise, even in preference to them, the ones on which depend, or which are the best marks of, those thus familiarly predicated. To do this successfully, presumes a knowledge of all the common properties of the cla.s.s, and the relations between them of causation and dependence. Hence the discussion of non-verbal definitions (which Dr. Whewell calls the Explication of Conceptions) is part of the business of discovery. Hence, too, disputes in science have often a.s.sumed the form of a battle of definitions; such definitions being not arbitrary, but made with a view to some tacitly a.s.sumed principle needing expression.

We ought, if possible, to define in consonance with the denotation. But sometimes this is impossible, through the name having acc.u.mulated _transitive_ applications, in its gradual extension from one object, in relation to which it connotes one property, to another which resembles the former, but in quite a different attribute. These _transitive_ applications, even when found to correspond in different languages, may have arisen, not from any common quality in the objects, but from some a.s.sociation of ideas founded on the common nature and condition of mankind. When the a.s.sociation is so natural and habitual as to become virtually indissoluble, the _transitive_ meanings are apt to coalesce in one complex conception; and every new transition becomes a more comprehensive generalisation of the term in question. In such cases the ancients and schoolmen did not suspect, what otherwise they carefully watched for, viz. ambiguities: not Plato, though his Comparisons and Abstractions preparatory to Induction are perfect; not even Bacon, in his speculations on Heat. Hence have sprung the various vain attempts to trace a common idea in all the uses of a word, such as _Cause_ (Efficient, Material, Formal, and Final _Cause_), _the Good_, _the Fit_.

When a term is applied to many different objects agreeing _all_ only in _one_ quality (e.g. things _beautiful_, in _agreeableness_), though _most_ agree in something besides, it is better to exclude part of the denotation than of the connotation, however indistinct: else language ceases to keep alive old experience, alien perhaps to present tendencies. In any case, words are always in danger of losing part of their connotation. For, just one or two out of a complex cl.u.s.ter of ideas, and sometimes merely the look or sound of the word itself, is often all that is absolutely necessary for the suggesting another set of ideas to continue the process of thought; and consequently, some metaphysicians have even fancied that all reasoning is but the mechanical use of terms according to a certain form. If persons be not of active imaginations, the only antidote against the propensity to let slip the connotation of names, is the habit of predicating of them the properties connoted; though even the propositions themselves, as may be seen from the way in which maxims of Religion, Ethics, and Politics are used, are often repeated merely mechanically, not being questioned, but also not being felt. Much of our knowledge recorded in words is ever oscillating between its tendency, in consequence of different generations attending exclusively to different properties in names, to become partially dormant, and the counter-efforts of individuals, at times, to revive it by tracing the forgotten properties historically in the almost mechanically repeated formulas of propositions; and, when they have been there rediscovered, promulgating them, not as discoveries, but with authority as what men still profess to believe.

The danger is, lest the formula itself be dismissed by clear-headed narrow-minded logicians, and the connotation fixed by them (in order that the denotation may be extended) in accordance with the present use of the term. Then, if the truths be at any time rediscovered, the prejudice is against them as novelties. The _selfish_ theory of morals partly fell because the inconsistency of received formulas with it prompted a reconsideration of its basis. What would have been the result if the formulas attaching odium to selfishness, praise to self-sacrifice, had been dismissed, if this indeed had been possible!

Language, in short, is the depositary of all experience, which, being the inheritance of posterity, we have a right to vary, but none to curtail. We may improve the conclusions of our ancestors; we should not let drop any of their premisses; we may alter a word's connotation; but we must not destroy part of it.

CHAPTER V.

THE NATURAL HISTORY OF THE VARIATION IN THE MEANING OF TERMS.

The connotation of names shifts not only by reason of gradual inattention to some of the common properties, which, if language were ruled by convention alone, would be in their entirety both the perpetual and the sole const.i.tuents of the connotation; but also from the incorporation in the connotation, in addition to these, and often, finally, to the _exclusion_ of them altogether, of other circ.u.mstances at first only casually a.s.sociated with it. These collateral a.s.sociations are the cause why there are so few exact synonymes; and why the dictionary meaning, or Definition, is so bad a guide to its uses, as compared with its history, since the latter explains the law of the succession by showing the causes which determined the successive uses.

Two counter-movements are always going on in language. One is generalisation, by which words are ever losing part of their connotation, and becoming more general. This arises, partly from men, such as historians and travellers, using words, especially those expressing complicated mental and social facts strange to them, in a loose sense, in ignorance of the true connotation; partly, from known things multiplying faster than names for them; partly, also, from the wish to give people some notion of a new object by reference to a known thing resembling it however slightly. The other movement is specialisation; and by it words (even the same words which, as, e.g.

_pagan_ and _villain_, later get generalised in a new direction) are ever taking a fresh connotation, through their denotation being diminished. Specialisations often occur even in scientific nomenclature, a word which expressed general characters becoming confined to a specific substance in which these characters are predominant. So it is when any set of persons has to think of one species oftener than of any other contained in the genus: e.g. some sportsmen mean partridges by the term _birds_. But, as ideas of our pleasures and pains and their supposed causes, cling, most of all, by a.s.sociation to what they have been once connected with, the great source of specialisation is the addition of the ideas of agreeableness or painfulness, and approbation or censure, to the connotation. And hence arises the fallacy of _question-begging_ names referred to later on.

It is the business of logicians not to ignore, for they cannot prevent, transformations of terms in common use, but to trace and embody them, and men's half unconscious reasons for them, in distinct definitions.

CHAPTER VI.

TERMINOLOGY AND NOMENCLATURE.

Not only must words have a fixed and knowable meaning; but also, no important meaning should be without its word: that is, there should be a name for everything which we have often to make a.s.sertions about. There should be, therefore, first, names suited to describe all the individual facts; secondly, a name for every important common property detected by comparing those facts; and, thirdly, a name for every _kind_.

First, it conduces to brevity and clearness to have separate names for the oft-recurring combinations of feelings; but, as these can be defined without reference back to the feelings themselves, it is _enough_ for a _descriptive_ terminology, if there be a name for every variety of elementary feeling, since none of these can be defined, or indicated to a person, except either by his having the sensation itself, or being referred through a known mark to his remembrance of it. The meaning of the name when given to a feeling is fixed, in the first instance, by convention, and must be a.s.sociated _immediately_, not through the usage of ordinary language, with the feeling, so that it may at once recall the latter. But even among the elementary feelings, those purely mental, and also sensations, such as those from disease, the ident.i.ty of which in different persons cannot be determined, cannot be exactly _described_. It is only the impressions on the outward senses, or those inward feelings connected uniformly with outward objects (and, consequently, sciences, such as botany, conversant with outward objects), which are susceptible of an exact descriptive language.

Secondly, there must also be a separate name for every important common property recognised through that comparison of observed instances which is preparatory to induction (including names for the cla.s.ses which we artificially construct in virtue of those properties). For, although a definition would often convey the meaning, both time and s.p.a.ce are saved, perspicuity promoted, and the attention excited and concentrated, by giving a brief and compact name to each of the new _general conceptions_, as Dr. Whewell calls them, that is, the new results of abstraction. Thenceforward the name nails down and clenches the unfamiliar combination of ideas, and suggests its own definition.

Thirdly, as, besides the artificial cla.s.ses which are marked out from neighbouring cla.s.ses by definite properties to be arrived at by abstraction, there are cla.s.ses, viz. _kinds_, distinguished severally by an unknown mult.i.tude of independent properties (and about which cla.s.ses therefore many a.s.sertions will be made), there must be a name for every _kind_. That is, besides a terminology, there must be a nomenclature, i.e. a collection of the names of all the lowest _kinds_, or _infimae species_. The Linnaean arrangements of plants and animals, and the French of chemistry, are nomenclatures. The peculiarity of a name which belongs to a nomenclature is, not that its meaning resides in its denotation instead of its connotation (for it resides in its connotation, like that of other concrete general names); but that, besides connoting certain attributes which its definition explains, it also connotes that these attributes are distinctive of a _kind_; and this fact its definition cannot explain.

A philosophical language, then, must possess, first, precision, and next (the subject of the present chapter), completeness. Some have argued that, in addition, names are fitted for the purposes of thought in proportion as they approximate to mere symbols in compactness, through meaninglessness, and capability of use as counters without reference to the various objects which, though utterly different, they may thus at different times equally well represent. Such are, indeed, the qualities enabling us to employ the figures of arithmetic and the symbols of algebra perfectly mechanically according to general technical rules.

But, in the first place, in our direct inductions, at all events, depending as they do on our perception of the particulars of the agreement and difference of the phenomena, we could never dispense with a distinct mental image of the latter. Further, even in deduction, though a syllogism is conclusive from its mere form, if the terms are unambiguous, yet the _practical_ validity of the reasoning depends on the hypothesis that no counteracting cause has interfered with the truth of the premisses. We can a.s.sure ourselves of this only by studying the phenomena at every step. For it is only in geometry and algebra that there is no danger from the Composition of Causes, or the superseding of one set of laws by another; and that, therefore, the propositions are categorically true. In sciences in general, then, the object should be, so far from keeping individualising peculiarities out of sight, to contrive the greatest possible obstacles to a merely mechanical use of language: we should carefully keep alive a consciousness of its meaning, by referring, by aid of derivation and the a.n.a.logies between the ideas of the roots and the derivatives, to the origin of words; and as words, however philosophically constructed, are always tending, like coins, to have their inscription worn off, we should be ever stamping them afresh.

This we shall effect, if we contemplate habitually, not the _formulas_ which record the laws of the phenomena (for, if so, the formulas will themselves progressively lose their meaning), but the phenomena whence the laws were collected; and we must conceive these phenomena in the concrete, and clothe them in circ.u.mstances.

CHAPTER VII.

CLa.s.sIFICATION, AS SUBSIDIARY TO INDUCTION.

Every name which connotes an attribute thereby divides, but only incidentally, all things, known and unknown, real and imagined, into two cla.s.ses, viz. those which have, and those which have not the attribute.

But sometimes the naming itself is but the secondary and subsidiary, and the cla.s.sification, the primary object. The general problem of such cla.s.sification is, to provide that things shall be thought of in such groups, and the groups in such an order, as will best promote the remembrance and ascertainment of their laws. Its subjects are _real things_ exclusively, but _all_ real things, since, to place one object in a group, we ought to know the divisions of nature at large.

Any property may be the basis for a cla.s.sification; but those best suited are properties which are causes, or, next, as the cause of a cla.s.s's chief peculiarities seldom serves as its diagnostic, any effect which is a sure mark both of the cause and of the other effects. Only a cla.s.sification so grounded is scientific; the same also is not technical or artificial, but natural, and emphatically _natural_ (as compared with cla.s.sifications in an inferior degree also _natural_, which are based on properties important with reference to the reasoner's special practical objects), when the cla.s.sification is based on those properties which would most impress one who knew all the properties, but was not interested particularly in any one. Further, it is a great recommendation of a cla.s.sification, that it groups together things of like general aspect; but this is not a _sine qua non_: a group may be _natural_ even if based on very _un.o.bvious_ properties, provided these are marks of many other properties, though certainly then there should be also some more obvious property to act as a mark of the un.o.bvious ones which form the real basis.

As the first principle of _natural_ cla.s.sification is that the cla.s.ses must be so formed that the objects composing each may have as many properties in common as possible to serve as predicates, all _kinds_ should have places among the _natural_ groups, since the common properties of _kinds_, and, therefore, the general a.s.sertions that can be made about them, are innumerable. But _kinds_ are too few to make up the whole of a cla.s.sification: other cla.s.ses also may be eminently _natural_, though marked out from each other only by a definite number of properties. Of neither sort of _natural_ groups is Dr. Whewell's theory _strictly_ true, viz. that every _natural_ group is not determined by definition, that is, by definite characters which can be expressed in words, but is fixed by Type. He explains that a type is an example of any cla.s.s, for instance, a species of a genus, which possesses all the characters and properties of the genus in a marked way; that round this type-species are grouped all the other species, which, though deviating from it in various directions and degrees, yet are of closer affinity to it than to the centre of any other group; and that this is the reason why propositions about _natural_ groups so often state matters as being true not in all cases, but only in most. Now, there is a truth, but only a partial truth, in this doctrine. It is this: in forming _natural_ groups, species which want certain of the cla.s.s-characters, some one, and others another, are cla.s.sed with those (the majority) that have them all, because they are more like (that is, in fact, have more of the common characters of) that particular group than of any other. On account of the feeling of vagueness hence engendered, we certainly, in deciding if an object belong to the group, do generally (and _must_, when the cla.s.sification is made expressly with a view to a special inductive enquiry) refer mentally, not as a subst.i.tute for, but in ill.u.s.tration of the definition of the group, to some standard specimen which has _all_ the characters well developed.

But not the less, therefore, are all _natural_, equally with all artificial, groups framed with distinct reference to certain definite characters. In the case of _kinds_, a few characters are chosen as marks of the rest. In the case of other _natural_ groups, the formation of the larger groups, into which we collect the _infimae species_, is suggested indeed by resemblance to types (since we form each such larger group round a selected _kind_ which serves as its exemplar); but the group itself, when formed, is determined by definite characters.

Cla.s.s names should by the mode of their construction help those who have learnt about the thing, to remember it, and those who have not learnt, now to learn, by being merely told the name. This is best effected, in the case of _kinds_, when the word indicates by its very formation the properties it connotes. But this is seldom possible. For, though a _kind_-name connotes not all the _kind_-properties, but some only which serve as sure marks of the rest, even these have been found too many to be included conveniently in a name (except in Elementary Chemistry, where every compound substance has one distinctive index-property, viz.

the chemical composition). A subsidiary resource is to point out the _kind's_ nearest natural affinities. For instance, in the binary Nomenclature of Botany and of Zoology, the name of every species consists of the name of the _natural_ group next above, with a word added expressive of some quality in the nature or mode of discovery, or what not, of the particular species itself. By this device (obtaining at present only in Botany and Zoology), as well is the expression, in the name, of many of the _kind's characters_ secured, as the use of names economised, and the memory relieved. Except for some such plan, what hope of naming the 60,000 known species of Plants?

CHAPTER VIII.