The mental process which Logic deals with, viz. the investigation of truth by means of evidence, is always a process of Induction. Since Induction is simply the extension to a class of something observed to be true of certain members of it, Observation is the first preliminary to it. It is, therefore, right to consider, not indeed how or what to observe (for this belongs to the art of Education), but under what conditions observation is to be relied on. The sole condition is, that the supposed observation should really be an observation, and not an inference, whereas it is usually a compound of both, there being, in our propositions, besides observation which relates only to the sensations, an inference from the sensations to the objects themselves. Thus so-called errors of sense are only erroneous inferences from sense. The sensations themselves must be genuine; but, as they generally arise on a certain arrangement of outward objects being present to the organs, we, as though by instinct, infer this arrangement even when not existing. The sole object, then, of the logic of observation, is to separate the inferences from observation from theobservations themselves, the only thing really observed by the mind (to waive the metaphysical problem as to theperceptionof objects) being its own feelings or states of consciousness, outward, viz. Sensations, and inward, viz. Thoughts, Emotions, and Volitions.
As in the simplest observation much is inference, so, in describing an observed fact, we not merely describe the fact, but are always forced to class it, affirming the resemblance, in regard of whatever is the ground of the name being given, between it and all other things denoted by the name. The resemblance is sometimes perceived by direct comparison of the objects together; sometimes (as, e.g. in the description of the earth's figure as globular and so forth) it is inferred through intermediate marks, i.e. deductively. When a hypothesis is made (e.g. by Kepler, as to the figure of the earth's orbit), and then verified by comparison with actual observations, Dr. Whewell calls the process Colligation of Facts by appropriate Conceptions, and affirms it to be the whole of Induction. But this also is only description, being really the ordinary process of ascertaining resemblance by a comparison of phenomena; and, though subsidiary to Induction, it is not itself Induction at all.
Abstract Ideas, that is, General Conceptions, certainly do exist, however Metaphysics may decide asto their composition. Theyrepresentin our minds the whole classes of things called by the general names; and, being implied in the mental operation whereby classes 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, andsuperinduced, 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, toconnect. 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 ofcomparison 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 termcomparisonexpresses as well their origin as (and this far more exactly than toconnector tosuperinduce) their function.
Dr. Whewell says that conceptions must beappropriateandclear. 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 beclearin the following sense; that is to say, asufficient numberof facts must have beencarefully observed, and accuratelyremembered. It is also a condition (and one implied in the latter qualities) of clearness, that the conception should bedeterminate, 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 withpreviously 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.
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 association, 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 thirdnecessarycondition. 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 therewere 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 areindispensable, are the abstract names of attributes; but, in fact, men have always given general names to objects also.
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 class 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, stilldenotethe things of which it is currently affirmed. To effect this double object (which is called, though improperly, definingnot the name but the thing), he must select from theattributes in which the denoted objects agree, choosing, as the common properties are always many, and, in akind, innumerable, those which are familiarly predicated of the class, 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 class, 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 assumed the form of a battle of definitions; such definitions being not arbitrary, but made with a view to some tacitly assumed principle needing expression.
We ought, if possible, to define in consonance with the denotation. But sometimes this is impossible, through the name having accumulatedtransitiveapplications, 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. Thesetransitiveapplications, even when found to correspond in different languages, may have arisen, not from any common quality in the objects, but from some association of ideas founded on the common nature and condition of mankind. When the association is so natural and habitual as to become virtually indissoluble, thetransitivemeanings are apt to coalesce in one complex conception; and every new transition becomes a more comprehensive generalisation of the term inquestion. 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 asCause(Efficient, Material, Formal, and FinalCause),the Good,the Fit.
When a term is applied to many different objects agreeingallonly inonequality (e.g. thingsbeautiful, inagreeableness), thoughmostagree 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 cluster 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 everoscillating 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. Theselfishtheory 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.
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 constituents of the connotation; but also from the incorporation in the connotation, in addition to these, and often, finally, to theexclusionof them altogether, of other circumstances at first only casually associated with it. These collateral associations 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.paganandvillain, 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 anyset 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 termbirds. But, as ideas of our pleasures and pains and their supposed causes, cling, most of all, by association 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 ofquestion-beggingnames 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.
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 assertions 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 everykind.
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 isenoughfor adescriptiveterminology, 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 associatedimmediately, 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 identity of which in different persons cannot be determined, cannot be exactlydescribed. 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 classes which we artificially construct in virtue of those properties). For, although a definition would often convey the meaning, both time and space are saved, perspicuity promoted, and the attention excited and concentrated, by giving a brief and compact name to each of the newgeneral 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 classes which are marked out from neighbouring classes by definite properties to be arrived at by abstraction, there are classes, viz.kinds, distinguished severally by an unknown multitude of independent properties (and about which classes therefore many assertions will be made), there must be a name for everykind. That is, besides a terminology, there must be a nomenclature, i.e. a collection of the names of all the lowestkinds, orinfimæ species. The Linnæan 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 akind; 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 thepracticalvalidity of the reasoning depends on the hypothesis that no counteracting cause has interfered with the truth of the premisses. We can assure 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 analogies 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 theformulaswhich 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 circumstances.
Every name which connotes an attribute thereby divides, but only incidentally, all things, known and unknown, real and imagined, into two classes, viz. those which have, and those which have not the attribute. But sometimes the naming itself is but the secondary and subsidiary, and the classification, the primary object. The general problem of such classification 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 arereal thingsexclusively, butallreal 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 classification; but those best suited are properties which are causes, or, next, as the cause of a class'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 classification so grounded is scientific; the same also is not technical or artificial, but natural, and emphaticallynatural(as compared with classifications in an inferior degree alsonatural, which are based on properties important with reference to the reasoner's special practical objects), when the classification 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 classification, thatit groups together things of like general aspect; but this is not asine quâ non: a group may benaturaleven if based on veryunobviousproperties, 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 unobvious ones which form the real basis.
As the first principle ofnaturalclassification is that the classes must be so formed that the objects composing each may have as many properties in common as possible to serve as predicates, allkindsshould have places among thenaturalgroups, since the common properties ofkinds, and, therefore, the general assertions that can be made about them, are innumerable. Butkindsare too few to make up the whole of a classification: other classes also may be eminentlynatural, though marked out from each other only by a definite number of properties. Of neither sort ofnaturalgroups is Dr. Whewell's theorystrictlytrue, viz. that everynaturalgroup 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 class, 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 aboutnaturalgroups so often state matters as being true not in all cases, but only in most. Now, there is a truth, but only apartial truth, in this doctrine. It is this: in formingnaturalgroups, species which want certain of the class-characters, some one, and others another, are classed 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 (andmust, when the classification is made expressly with a view to a special inductive enquiry) refer mentally, not as a substitute for, but in illustration of the definition of the group, to some standard specimen which hasallthe characters well developed. But not the less, therefore, are allnatural, equally with all artificial, groups framed with distinct reference to certain definite characters. In the case ofkinds, a few characters are chosen as marks of the rest. In the case of othernaturalgroups, the formation of the larger groups, into which we collect theinfimæ species, is suggested indeed by resemblance to types (since we form each such larger group round a selectedkindwhich serves as its exemplar); but the group itself, when formed, is determined by definite characters.
Class 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 ofkinds, when the word indicates by its very formation the properties it connotes. But this is seldom possible. For, though akind-name connotes not all thekind-properties, but some onlywhich 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 thekind'snearest natural affinities. For instance, in the binary Nomenclature of Botany and of Zoology, the name of every species consists of the name of thenaturalgroup 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 thekind's characterssecured, 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?
The object of Classification generally is to bring our ideas of objects into the order best fitted for prosecuting inductive enquiries into the laws of the phenomena generally. But a Classification which aims at facilitating an inductive enquiry into the laws of some special phenomenon, must be based on that phenomenon itself. The requisites of such a classification are, first, the bringing into one class allkindsof things which exhibit the phenomenon; next,the arranging them in aseries, according to the degrees in which they exhibit it. Such a classification has been largely applied in Comparative Anatomy and Physiology (and these alone), since there has been found a recognisable difference in the degree in which animals possess one main phenomenon, viz. Animal Life.
This arrangement of the instances, whence the law is to be collected, in a series, is that which is always implied in and is a condition ofanyapplication of the method, viz. that of Concomitant Variations, which must be used when conjoined circumstances cannot easily be separated by experiment. But sometimes (and it is so in Zoology) the law of the subject of the special enquiry (e.g. Animal Life) has such influence over the general character of the objects, that all other differences among them seem mere modifications of it; and then the classification required for the special purpose becomes the determining principle of the classification of the same objects for general purposes.
To recognise the identity of phenomena which thus differ only in degree, we must assume a type-species. This will be thatkindwhich has the class-properties in their greatest intensity (and, therefore, most easily studied with all their effects); and we must conceive the other varieties as instances of degeneracy from that type.
The divisions of the series must be determined by the principles ofnaturalgrouping in general (that is, in effect, by natural affinity); in subordination, however, to the principle of a natural series; that is, in the same group must not be placed thingswhich ought to occupy different points of the general scale.
Zoology affords the onlycompleteexample of the true principles of rational classification, whether as to the formation of groups or of series. Yet the same principles are applicable to all cases (to art and business as well as science) where the various parts of a wide subject have to be brought into mental co-ordination.
The habit of reasoning well is the only complete safeguard against reasoning ill, that is, against drawing conclusions with insufficient evidence, a practice which the various contradictory opinions, particularly about the phenomena relating to Man, show to be even now common, and that too among the most enlightened. But, to be able to explain an error is a necessary condition of seeing the truth; for, 'Contrariorum eadem est Scientia.' Consequently, a work on Logic must classify Fallacies, that is, the varieties of Apparent Evidence; for theycanbe classified, though not in respect of their negative quality of being either not evidence at all, or inconclusive, yet in respect of the positive property they have ofappearingto be evidence.
As Logic has been here treated as embracing the whole reasoning process, so it must notice the fallacies incident to any part of it (not to Ratiocination merely), whether arising from faulty Induction, or from faulty Ratiocination, or from dispensing wholly with either or both of them. It does not treat of errors from negligence, or from inexpertness in usingright methods, nor does it treat of errors from moral causes, viz. Indifference to truth, or Bias by our wishes or our fears; for the moral causes are but theremoteandpredisposing, not theexcitingcauses of opinions; and therefore inferences from them, since they must always involve the intellectual operation of admitting insufficient evidence as sufficient, really come under a classification of the things which wronglyappearevidence to theunderstanding.
Fallacies may be arranged, with reference either to the cause which makes them (erroneously) appear evidence, or to the particular kind of evidence they simulate. The following classification is grounded on both these considerations jointly.
The business of Logic is, not to enumerate false opinions, but to enquire what property in the facts led to them, that is, what peculiarity of relation between two facts made us suppose them habitually conjoined or disjoined, and thus regard the presence or absence of the one as evidence of that of the other. For every such property in the facts, or our mode of considering them, there is a corresponding class of Fallacies.
As the supposed habitual connexion or repugnance of two facts may be admitted, either as a self-evident and axiomatic truth, or as itself an inference, the first great division is into Fallacies of SimpleInspection orà prioriFallacies, and Fallacies, of Inference. But there is also an intermediate class. For, sometimes an inference is erroneous through our not conceiving what our premisses precisely are, and from our therefore substituting new premisses for the old, or a new conclusion for the one we undertook to prove; and this is called the Fallacy of Confusion. Under this head, indeed, of Fallacies of Confusion, might strictly be brought almost any fallacy, though falling also under some other head: for, some of the links in an argument, especially if sophistical, are sure to be suppressed; and, it being left doubtful which is the proposition to be supplied, we can seldom tell with certainty underwhichclass the fallacy absolutely comes. It is, however, convenient to reserve the nameFallacy of Confusionfor cases where Confusion is thesolecause of the error.
Cases, then, where there is more or less ground for the error inthe nature of the apparent evidence itself, the evidence being assumed to be of a certain sort, and a false conclusion being drawn from it, may be classed as Fallacies of Inference. According as the apparent evidence consists of particular facts, or of foregone generalisations, we call the errors Fallacies of Induction or of Deduction. Each of these classes, again, may be subdivided into two species, according as the apparent evidence is either false, or, though true, inconclusive. Such subdivisions of the Fallacy of Induction are respectively called, in the former case, Fallacies of Observation (including cases where the facts are not directly observed, but inferred), and, in the latter, Fallacies of Generalisation. Among Fallacies of Deduction, those which proceedon false premisses have no specific name, for they must fall under one of the other heads of Fallacies; but those, the premisses of which, though true, do not support the conclusion, compose a subdivision, which may be specified as Fallacies of Ratiocination.
There must be someà prioriknowledge, some propositions to be received without proof; for there cannot be a chain suspended from nothing. What these are is disputed, one school recognising as ultimate premisses only the facts of our subjective consciousness, e.g. Sensations, while Ontologists hold that the mind intuitively, and not through experience, recognises as realities other existences, e.g. Substances, which are suggested by, though not inferrible from, those facts of consciousness. But, as both schools, in fact, allow that the mind infers therealityfrom theideaof a thing, and that it may do this unduly, there results a class of Fallacies resting on the tacit assumption that the objects in nature have the same order as our ideas of them. Hence not only arose the vulgar belief that facts which make us think of an event are omens foreboding (e.g. lucky or unlucky names), or even causing its occurrence; but even men of science both did and do fall into this Fallacy. The following dogmas express the different forms of this error:—
1. α [Greek: a].Things which we cannot help thinking of together must coexist; thus Descartes held that, because existence is involved (though really only by the thinker himself) in the idea of a geometrical figure, a thing like the idea must exist. β [Greek: b].Whatever is inconceivable is false.The latter proposition has been defended by drawing a distinction between the principle, and its possibly wrong application to facts, e.g. to Antipodes; but how can we ever know that it has been rightly applied? Coleridge, again, has distinguished between the unimaginable, which he thinks may possibly be true, and the inconceivable, which he thinks cannot be; but Antipodes were imaginable at the same period when they were inconceivable. In fact, as even to Newton it seemed inconceivable, that a thing should act where it is not (e.g. that the sun should act upon the earth without the medium of an ether), simply because his mind was not familiar with the idea, so itmaybe withourincapability (if not, indeed, resulting merely from our limited faculties) ofconceiving, e.g. that matter cannot think; that space is infinite; thatex nihilo nihil fit. Leibnitz's tenet that allnaturalphenomena must be explicableà priori, and the further assumption by some that Nature always acts by the simplest, i.e. by the most easily conceivable means (and that, therefore, e.g. the heavenly bodies have a circular movement), exhibit vividly this Fallacy of Simple Inspection.
2.Whatever can be thought of apart, or has a separate name, exists apart as a separate entity, e.g. Nature, Time, qualities, as e.g. Whiteness, and, worst of all, the Substantiæ Secundæ. Mysticism is thishabit of ascribing objective existence to the subjective creations of the mind, and reasoning from them to the things themselves.
3.A fact must follow a certain law, because we see no reason for its deviating from it in one way rather than in another.This, which is the same as the Principle of the Sufficient Reason, has been used to prove the Law of Inertia (the very point to be proved, viz. that only external force can be a sufficient reason for motionin a particular direction, being assumed), and also the First Law of Motion, the argument being, in the latter case, that a moving body, if it donotcontinue of itself to move uniformly in a straight line, must deviate right or left, and that there isno reasonfor its going one way more than the other: to which the answer is, that, apart from experience, we could not know whether or not there were a reason. Geometers often fall into this Fallacy.
4.The differences in nature must correspond to our received distinctions(in names and classifications). Thus, the Greeks thought that, by determining the meanings of words, they ascertained facts. Aristotle usually starts with 'We say thus or thus.' So, with theDoctrine of Contrarieties, in which the Pythagoreans and others assumed that oppositions in language imply similar ones in nature. Hence, too, the ancient belief in the essential difference between the laws of things terrestrial and things celestial, and in man's incapability of imitating nature's works. Bacon's error (which vitiates his inductive system) was analogous, in looking (either through his eagerness for practical results, or a lingering belief that causes were the sole object of philosophy) for the causeof given effects rather than the effects of a given cause. Hence sprang his tacit assumption (and that in enquiries into the causes of a thing's sensible qualities, where it was especially fatal), that in all cases, e.g. of heat or cold, theforma, or set of conditions, isonething. A similar notion, viz. that each property of gold, as of other things, has its oneforma, produced the belief in Alchemy.
5. The conditions of a phenomenon often do resemble the phenomenon itself, e.g. in cases of Motion, Contagion, Feelings; but it is a Fallacy to suppose thatthey must or probably will. By this fancied law men guided their conjectures. Thus, theDoctrine of Signatureswas, that substances showed their uses as medicines by external resemblance, either to their supposed effect, or to the disease. So, the Cartesians, and even Leibnitz, argued, that nothing physical but previous motion could account for motion, explaining the human body's voluntary motions by Nervous Vibrations or by Animal Spirits. Hence, too, the inference that there is a correspondence between the physical qualities of the cause, and like or like-named ones, either of the phenomenon (e.g. between sharp particles and a sharp taste), or of its effects (e.g. between the redness of Mars, and fire and slaughter as results of that planet's influence). In metaphysics, the Epicureans' doctrine ofspecies sensibiles, and the moderns' ofperception through ideas, arose from this fallacy (combined with another, viz. that a thing cannot act where it is not). Again, the conditions of a thing are sometimes spoken of even as though they were the thing itself. Thus, in the Novum Organon, heat (i.e. really the conditions of thefeeling of it) is called a kind of motion; and Darwin, in his Zoonomia, after describingideaas a kind ofnotion of external things, defines it asa motion of the fibres. Cousin says: 'Tout ce qui est vrai de l'effet est vrai de la cause,' though, the reversemightbe true; and Coleridge affirms, asan evident truth, that mind and matter, as having no common property, cannot act on each other. The same fallacy led Leibnitz to hispre-established harmony, and Malebranche to hisoccasional causes. So, Cicero argues that mental pleasures, if arising from the bodily, could not, as they do, exceed their cause; and Descartes, that the Efficient Cause must have all the perfections of the effect. Conversely Descartes, too, and persons who assail, e.g. the Principle of Population by reference to Divine benevolence (thus implying that, because God is perfect, therefore whattheythink perfection must obtain in nature), assume that effects must resemble their causes.
A fallacy of Observation (the first of the three fallacies of Proof) may be either negative or positive.
1. The former, which is called Non-observation, is a case, not of a positive mis-estimate of evidence, or of the proper faculties (whether the senses or reason) not having been employed, but simply of the non-employment of any of the faculties. It arises α ([Greek: a]) from neglect of instances. Sometimes this iswhen there is a stronger motive to remember the instances on the one side, and the observers have neglected the principle of the Elimination of Chance. Hence (the mind, as Bacon says, being more moved by affirmative than by negative instances) the belief in predictions, e.g. about the weather, because they occasionally turn out correct; and the credit of the proverb, that 'Fortune favours fools,' since the cases of a wise man's success through luck are forgotten in his more numerous successes through genius. But a preconceived opinion is thechiefcause why opposing instances are overlooked. Hence originate the errors about physical facts (e.g. of Copernicus's foes, and friends, too, about the falling stone), andà fortiori, on moral, social, and religious subjects, where yet stronger feelings are involved.
The fallacy of Non-observation may occur β ([Greek: b]) from neglect, not of the material instances wholly, but of some material facts in them, e.g. in cases of cures by quack remedies (such as Kenelm Digby's 'sympathetic powder'), of some attendant fact (as exclusion of air from a wound, rest, regimen, and the like) which really worked the cure. Sometimes the neglected fact is one ascertainable, not by the senses, but by reasoning, which has been overlooked. Thus, Cousin's argument that, if the sole end of punishment were to prevent crime by intimidating intending criminals, the punishment of the innocent, indiscriminately with the guilty, would have the same effect, ignores the fact that the innocent would then be equally intimidated, and so the punishment would be of no use as an example to criminals. So, in Political Economy, where the effects of a cause often consist of two setsof phenomena, the one obvious, the other deeper under the surface, and exactly contrary, the latter is often neglected. This was why the rapidly spent capital of the prodigal was supposed formerly to employ more labour than the invested savings of the parsimonious, and the purchase of native goods to encourage native industry more than the purchase of foreign.
2. The error in Mal-observation, which is thepositivekind of Mis-observation, is not the overlooking facts, but the seeing them wrong. It arises from mistaking what is in fact inference (as muchmustbe, whenever we try to observe or to describe) for perception, which is infallible evidence of what is really perceived. The Anti-Copernicans, when they appealed to common sense, made this mistake. So do untrained persons generally in describing facts, especially natural phenomena (e.g. apothecaries and nurses in stating symptoms), and that, too, in proportion to their ignorance. We might expect this, since usually the actual perceptions of the senses (e.g. the colour and extension) are not of interest, except as marks whence to draw inferences about something else (e.g. about the body, to which these qualities belong). Painters, therefore, to know what the sensation actually was, have to go through a special training. But this confusion of inference with perception is still more likely in highly abstract subjects; and, consequently, in these, mere, and often false inferences, have continually been regarded as intuitive judgments.
This class includes whatever errors of generalisation are not mere blunders, but arise from some wrong general conception of the inductive process. Only a few kinds can be noted. 1. Under this Fallacy come generalisations whichcannotbe established by experience, e.g. inferences from the order in the Solar System to other and unknown parts of the universe; and also, except when a particular effect would contradict either the laws of number and extension, or the universal law of causality, all inferences from the fact thatwehave never known of a particular effect to its impossibility. 2. Those generalisations also are fallacious which resolve, either, as in early Greece, all things into one element, or, as often in modern times, impressions on the senses, differing in quality, and not merely in degree, into the same; e.g. heat, light, and (through vibrations) sensation, into motion; mental, into nervous states; and vital phenomena, into mechanical or chemical processes. In these theories, one fact has its laws applied to another. It may possibly be a condition of that other; but even then the mode in which the new fact is actually produced would have to be explained by its own law, and not by that of the condition. 3. Again, generalisations got by Simple Enumeration, fall under this Fallacy. That sort of Induction 'precariò concludit,' says Bacon, 'et periculo exponitur ab instantiâ contradictoriâ, ... ex his tantummodò quæ præsto sunt pronuncians.' The ancients used it; and inquestions relating to man and society, it is still employed bypracticalmen. By it men arrived at the various examples of the formula,Whatsoever has never been(e.g. a State without artificial distinctions of rank; negroes as civilised as the white race)will never be; which, being inductions without elimination, could at most form the ground only of the lowest empirical laws. Higher empirical laws can be got, when a phenomenon presents (as no negation can) a series of regular gradations, since something may then be inferred from the observed as to the unobservable terms of the series. Such is the law of man's necessary progression, in contradiction to the above formula. But even this better generalisation is similarly, though not as grossly, fallacious as the preceding, when, though not itself a cause, but only a summary expression for the general result of all the causes, it is accepted asthelaw of human changes, past and even future. So, empirical generalisations, from present to past time, and from the character of one nation to that of another, are similarly fallacious when employed as causal laws. 4. This Fallacy occurs, not only when an empirical is confounded with a causal law, but when causation is inferred improperly. The mistake sometimes lies in inferringà posteriorithat one fact must be the cause of another (e.g. the National Debt, or some special institution, of England's prosperity), because of their casual conjunction; at other times, in assumingà priorithat one of several coexisting agents is the sole cause, and then deducing the effects from it exclusively. The latter is properly False Theory. It has been exemplified in medicine by the tracing of all diseases by one school, to viscidityof the blood, by another, to the presence of some acid or alkali, and, in politics, by the assumption that some special form of government or society is absolutely good. 5. In False Analogies (which fall under this Fallacy) there is no pretence of a conclusive induction. The argument from Analogy is the inferring, in the absence of evidence either way, that an object resembles a second object in one point, because it is seen to resemble it in another point, which either is not known to be connected with the first by causation (as, that the planets must be inhabited because they obey the same astronomical laws with the earth, which is), or which is known to be, not, indeed, its cause or its effect, but either one of a set of conditions, which together are its cause, or an occasional effect of its cause. Now, persons (usually from poverty, not from luxuriance, of imagination) often overrate the weight of true analogies; but the fallacy specially consists in inferring resemblance in one point from resemblance in another, when the evidence is not only not in favour of, but even positively against the connection of the two by way of causation. It is so in the argument in favour of absolutism, on the ground of its resemblance to paternal government in the one point of irresponsibility, as though the assumed benefits of paternal rule flowed from this quality. Similarly fallacious are the inferences, through analogies, from the liability to decay of bodies natural to that of bodies politic; from the supposed need of aprimum mobilein nature to that of an irresponsible power in a state; and from the effects of a decrease of a country's corn to the effects of a decrease of its gold (the utility of which, but not of corn, depends on itsvalue, and its value on its scarcity). Such, also, were the Pythagorean inferences that there is a music of the spheres, because the intervals between the planets have the same proportion as the divisions of the monochord; and, again, that the movements of the stars as beingdivinemust be regular, because so are those even of orderlymen. So, Aristotle and other ancients supposed perfection to obtain in all natural facts, because it appeared to exist in some; and so, the Stoics tried to prove the equality of all crimes by reference to various similes and metaphors (as, that the man held half an inch below the surface will be drowned as certainly as the man at the bottom of the sea; and that want of skill is shown as much in steering a straw-laden boat as a treasure galleon on to the rocks). But, in fact, the connection by causation between the known and the inferred resemblance, which isassumedby these metaphors, is the very thing which they are brought to prove. The real use of such cases of analogy as metaphors is that they serve, not as an argument, but as an assertion that one exists. Though they cannot prove, they sometimes suggest the proof, and point to a case in which the same grounds for a conclusion have been found adequate. Such are d'Alembert's classification of successful politicians as either eagles or serpents; and the statement, as an argument for education, that, in waste land weeds will spring up; and such isnotBacon's inference from the levity of floating straw to the worthlessness of theextantscientific works of the ancients.
The great source of fallacious generalisation is bad classification, by which things with no, or no important, common properties, are grouped together.Worst is it, when a word which commonly signifies some definite fact is applied to other facts only slightly similar. Bacon (who has himself thus erred in his enquiries into heat) specifies, as examples of this, the various applications (got, by unscientific abstraction, from the original sense) of the word 'wet,' to flame, air, dust, and glass, as well as to water. The application by Plato, Aristotle, and other ancients, of the terms Generation, Corruption, and κἱνησις [Greek: kinêsis] to many heterogeneous phenomena, with a mixture of the ideas belonging to them severally, caused many perplexities, which may be noticed under Fallacies of Confusion.
These fallacies (to which the nameFallacyis commonly applied exclusively) would generally be detected if the arguments were set out formally; and the value of the syllogistic rules is, that they force the reasoner to be aware what it is that he is really asserting. The frequent errors in processes such as Conversion and Opposition, which are in appearance, though not in reality, inferences from premisses, may for convenience be here referred to. Such are the simple conversion of an universal affirmative; the corresponding error in a hypothetical proposition of inferring the truth of the antecedent from that of the consequent; and the confusing of a contrary with a contradictory, which amounts, in practice, to mistaking the reverse of wrong for right. But fallacies of Ratiocination properly lie in syllogisms. Theycommonly resolve themselves, when in a single syllogism, into the having more than three terms, whether covertly, as through an undistributed middle, or an illicit process, or avowedly. But the most dangerous and the commonest of these fallacies arise in a chain of argument fromchanging the premisses. One of the obscurer forms of this is the fallacya dicto secundum quid(i.e. with a qualification, or condition, expressed, or, more usually, understood)ad dictum simpliciter. Thus, the Mercantile Theory was in favour of prohibiting all trade which tends to carry out more money than it brings in, on the ground that money is riches, though it is so only if the money can befreelyspent. Such, too, was the argument (used to support the doctrine that tithes fall on the landlord) that, because now the rent of tithe-free land exceeds that of tithed land, the rent from the latter would be increased by the abolition of all tithes. There was a similar fallacy in the use of the maxim, that individuals are the best judges of their pecuniary interests, against Mr. Wakefield's scheme for concentrating settlers. Cases in which the condition oftimeis dropped, fall under this same particular fallacy, as, when the maxim that prices always find their level, is construed as meaning that they are alwaysattheir level. It is the same with the reasoning (especially in political and social subjects), upon principles, which are true in the absence of all modifying causes, as though no such causescouldexist. Other analogous fallacies are thosea dicto simpliciter ad dictum secundum quid(the converse of the preceding), anda dicto secundum quid ad dictum secundum alterum quid.
Under this head come all fallacies which arise, not so much from a false estimate of the probative force of known evidence, as from an indistinct conception what the evidence is.
1. Thus, where there is an ambiguous middle, or a term used in different senses in the premisses and in the conclusion, the argument proceeds as though there were evidence to the point, when, in fact, there is none. This error does not occur much in direct inductions, since the things themselves are there present to the senses or memory; but chiefly, in Ratiocination, where we are deciphering our own or others' notes. The ambiguity arises very often from assuming that a word corresponds precisely in meaning with the root itself (e.g.representative), or with cognate words from the same root, calledparonymouswords (as,artful, withart). Other examples of ambiguities are; 'Money,' which, meaning both the currency and also capital seeking investment, is often thought to be scarce in the former sense, because scarce in the latter; 'Influence of Property,' which, signifying equally the influence of respect for the power for good, and of fear of the power for evil, which is possessed by the rich, is represented as being assailed under its former form when attacked really only under the latter; 'Theory,' which, because applied popularly to the accounting for an effect apart from facts, is ridiculed, even when expressing, as it properly does, the result of philosophical inductionfrom experience; 'The Church,' which refers (as in the question of the inviolability ofChurchproperty) sometimes to the clergy alone, sometimes to all its members; 'Good,' in the Stoic argument that virtue, as alonegood(in the Stoic sense), must therefore include freedom and beauty, because these aregood(in the popular sense). So, the meaning of 'I' shifts fromthe laws of my naturetomy will, in Descartes'à prioriargument for the being of a God, viz. that there must be an external archetype whence I got the conception, for ifI(i.e.the laws of my nature) made it,I(i.e.my will, and not, as it should consistently be,the laws of my nature) could unmake it; butI(i.e.my will) cannot. In the Free-Will controversy, 'I' is used ambiguously for volitions, actions, and mental dispositions, and 'Necessity' both forCertaintyand forCompulsion. From the application of 'same,' 'one,' 'identical,' which primarily refer to a single object, to several objects becausesimilar, grew up (for the purpose of accounting for the supposedonenessin things said to have thesamenature or qualities) both the PlatonicIdeas, and also theSubstantial FormsandSecond Substancesof the Aristotelians, even though the latter did see the distinction between things differing bothspecieandnumero, and those differingnumeroonly. And thence, too, sprang Berkeley's proof of the existence of a Universal Mind from the supposed need of such a Being to harbour, in the interval, the idea, which, one and the same (really, only twosimilarideas), a man's mind has entertained at two distinct times. The difficulty inAchilles and the Tortoisearises from the use ofinfinity, or,for ever, in the premisses,to signify a finite time which is infinitely divisible, and, in the conclusion, to signify an infinite time. Thus, again, 'right' is used to express, both what others have no right to stop a man from doing, and also what it is not against his own duty to do; both what people are entitled to expect from, and also what they may enforce from others. The Fallacy of Composition and Division, i.e. the use of the same term in a syllogism, at one time in a collective, at another in a distributive sense, is one of the Fallacies of Ambiguous Terms. Examples of it are the arguments, thatgreat men(collectively) could be dispensed with, because the place of any particular great man might have been supplied (i.e., in fact, by some other great man); and, that a high prize in a lottery may be reasonably expected (bya certain individual, viz. oneself), because a high prize is commonly gained (by some one or other).
2. In Petitio Principii, the premisses are not even verbally sufficient for the conclusion, since one premiss is either clearly the same as the conclusion, or actually proved from it, or not susceptible of any other proof. Men commonly fall into it, through believing that the premisswasverified, though they have forgotten how. But the variety, termed Reasoning in a Circle, implies a conscious attempt to prove two propositions reciprocally from each other. This formal proof is not often attempted, except under the pressure of controversy; but, from mistaking mutual coherency for truth, propositions, which cannot be proved except from each other, are oftenadmitted, when expressed in different language, without other proof. Frequently a proposition ispresented in abstract terms as a proof of the same in concrete, as, in Molière's parody, 'L'opium endormit parcequ'il a une vertu soporifique.' So, some qualities of a thing selected arbitrarily are termed its nature or essence, and then reasoned from as though not able to be counteracted by any of the rest. 'Question-begging appellatives,' particularly, are cases of Petitio Principii, e.g. the styling any reform aninnovation, which it really is, only thatinnovationconveys, besides its dictionary meaning, a covert sense of something extreme. Thus, in Cicero's De Finibus, 'Cupiditas,' which usually implies vice, is used to express certain desires the moral character of which is the point in question. Again, the infinite divisibility of matter was assumed by the argument which was used to prove it, viz. that the least portion of matter must have both an upper and an under surface (which, as every other Fallacy of Confusion, when cleared up, appears as a fallacy of a different sort, under shelter of which, as indeed in ratiocinative fallacies generally, the mere verbal juggle at first escapes detection). Such, again, was Euler's argument, thatminusmultiplied byminusgivesplus,becauseit could not give the same asminusmultiplied byplus, which givesminus. So, some ethical writers begin by assuming, that certain general sentiments are thenaturalsentiments of mankind, and thence argue that any which differ are morbid andunnatural. Thus, lastly, Hobbes and Rousseau rested the existence of government and law on a supposed social compact, and not on men's perception of the interests of society, which, however, could be the only ground for their abiding by such compact if a fact.
3. In Ignoratio Elenchi, or, the Fallacy of Irrelevant Conclusion, the error lies not either in mistaking the import of the premisses, or in forgetting what they are, but in mistaking what is the conclusion to be proved. Sometimes, a particular is substituted for the universal as the proposition needing proof, and sometimes, a proposition with different terms. Under this fallacy come the cases, not only of proving what was not denied, but of disproving what was not asserted; e.g. the argument used against Malthus (whose own position was, that population increases onlyin so far as not kept downby prudence, or by poverty and disease), that, at times, population has been nearly stationary; or again, that, in some country or other, population and comfort are increasing together, Malthus himself having asserted that this might be so, if capital has increased. Similarly, even Reid, Stewart, and Brown (not merely Dr. Johnson) urged that Berkeley ought, if consistent, to have run his head against a post, as though the non-recognition of an occultcauseof sensations implies disbelief in anyfixed order among them.