§ 6. Another natural prejudice, of most extensive prevalence, and which

had a great share in producing the errors fallen into by the ancients in

their physical inquiries, was this: That the differences in nature must

correspond to our received distinctions; that effects which we are

accustomed, in popular language, to call by different names, and arrange

in different classes, must be of different natures, and have different

causes. This prejudice, so evidently of the same origin with those

already treated of, marks more especially the earliest stage of science,

when it has not yet broken loose from the trammels of every-day

phraseology. The extraordinary prevalence of the fallacy among the Greek

philosophers may be accounted for by their generally knowing no other

language than their own; from which it was a consequence that their

ideas followed the accidental or arbitrary combinations of that

language, more completely than can happen among the moderns to any but

illiterate persons. They had great difficulty in distinguishing between

things which their language confounded, or in putting mentally together

things which it distinguished; and could hardly combine the objects in

nature, into any classes but those which were made for them by the

popular phrases of their own country: or at least could not help

fancying those classes to be natural, and all others arbitrary and

artificial. Accordingly, scientific investigation among the Greek

schools of speculation and their followers in the middle ages, was

little more than a mere sifting and analysing of the notions attached to

common language. They thought that by determining the meaning of words,

they could become acquainted with facts. "They took for granted," says

Dr. Whewell,[12] "that philosophy must result from the relations of

those notions which are involved in the common use of language, and they

proceeded to seek it by studying such notions." In his next chapter, Dr.

Whewell has so well illustrated and exemplified this error, that I shall

take the liberty of quoting him at some length.

"The propensity to seek for principles in the common usages of language

may be discerned at a very early period. Thus we have an example of it

in a saying which is reported of Thales, the founder of Greek

philosophy. When he was asked, 'What is the _greatest_ thing?' he

replied '_Place_; for all other things are _in_ the world, but the world

is _in_ it.' In Aristotle we have the consummation of this mode of

speculation. The usual point from which he starts in his inquiries is,

that _we say_ thus or thus in common language. Thus, when he has to

discuss the question whether there be, in any part of the universe, a

void, or space in which there is nothing, he inquires first in how many

senses we say that one thing is _in_ another. He enumerates many of

these; we say the part is in the whole, as the finger is _in_ the hand;

again we say, the species is in the genus, as man is included _in_

animal; again, the government of Greece is _in_ the king; and various

other senses are described and exemplified, but of all these _the most

proper_ is when we say a thing is _in_ a vessel, and generally _in

place_. He next examines what _place_ is, and comes to this conclusion,

that 'if about a body there be another body including it, it is in

place, and if not, not.' A body moves when it changes its place; but he

adds, that if water be in a vessel, the vessel being at rest, the parts

of the water may still move, for they are included by each other; so

that while the whole does not change its place, the parts may change

their place in a circular order. Proceeding then to the question of a

_void_, he as usual examines the different senses in which the term is

used, and adopts as the most proper, _place without matter_: with no

useful result.

"Again, in a question concerning mechanical action, he says, 'When a man

moves a stone by pushing it with a stick, _we say_ both that the man

moves the stone, and that the stick moves the stone, but the latter

_more properly_.'

"Again, we find the Greek philosophers applying themselves to extract

their dogmas from the most general and abstract notions which they could

detect; for example, from the conception of the Universe as One or as

Many things. They tried to determine how far we may, or must, combine

with these conceptions that of a whole, of parts, of number, of limits,

of place, of beginning or end, of full or void, of rest, or motion, of

cause and effect, and the like. The analysis of such conceptions with

such a view, occupies, for instance, almost the whole of Aristotle's

Treatise on the Heavens."

The following paragraph merits particular attention:--"Another mode of

reasoning, very widely applied in these attempts, was the _doctrine of

contrarieties_, in which it was assumed, that adjectives or substances

which are in common language, or in some abstract mode of conception,

opposed to each other, must point at some fundamental antithesis in

nature, which it is important to study. Thus Aristotle says that the

Pythagoreans, from the contrasts which number suggests, collected ten

principles--Limited and Unlimited, Odd and Even, One and Many, Right and

Left, Male and Female, Rest and Motion, Straight and Curved, Light and

Darkness, Good and Evil, Square and Oblong.... Aristotle himself deduced

the doctrine of four elements and other dogmas by oppositions of the

same kind."

Of the manner in which, from premises obtained in this way, the ancients

attempted to deduce laws of nature, an example is given in the same work

a few pages further on. "Aristotle decides that there is no void, on

such arguments as this. In a void there could be no difference of up and

down; for as in nothing there are no differences, so there are none in a

privation or negation; but a void is merely a privation or negation of

matter; therefore, in a void, bodies could not move up and down, which

it is in their nature to do. It is easily seen" (Dr. Whewell very justly

adds) "that such a mode of reasoning elevates the familiar forms of

language, and the intellectual connexions of terms, to a supremacy over

facts; making truth depend upon whether terms are or are not privative,

and whether we say that bodies fall _naturally_."

The propensity to assume that the same relations obtain between objects

themselves, which obtain between our ideas of them, is here seen in the

extreme stage of its development. For the mode of philosophizing,

exemplified in the foregoing instances, assumes no less than that the

proper way of arriving at knowledge of nature, is to study nature itself

subjectively; to apply our observation and analysis not to the facts,

but to the common notions entertained of the facts.

Many other equally striking examples may be given of the tendency to

assume that things which for the convenience of common life are placed

in different classes, must differ in every respect. Of this nature was

the universal and deeply-rooted prejudice of antiquity and the middle

ages, that celestial and terrestrial phenomena must be essentially

different, and could in no manner or degree depend on the same laws. Of

the same kind, also, was the prejudice against which Bacon contended,

that nothing produced by nature could be successfully imitated by man:

"Calorem solis et ignis toto genere differre; ne scilicet homines

putent se per opera ignis, aliquid simile iis quæ in Natura fiunt,

educere et formare posse:" and again, "Compositionem tantum opus

Hominis, Mistionem vero opus solius Naturæ esse: ne scilicet homines

sperent aliquam ex arte Corporum naturalium generationem aut

transformationem."[13] The grand distinction in the ancient scientific

speculations, between natural and violent motions, though not without a

plausible foundation in the appearances themselves, was doubtless

greatly recommended to adoption by its conformity to this prejudice.

§ 7. From the fundamental error of the scientific inquirers of

antiquity, we pass, by a natural association, to a scarcely less

fundamental one of their great rival and successor, Bacon. It has

excited the surprise of philosophers that the detailed system of

inductive logic, which this extraordinary man laboured to construct, has

been turned to so little direct use by subsequent inquirers, having

neither continued, except in a few of its generalities, to be recognised

as a theory, nor having conducted in practice to any great scientific

results. But this, though not unfrequently remarked, has scarcely

received any plausible explanation; and some, indeed, have preferred to

assert that all rules of induction are useless, rather than suppose that

Bacon's rules are grounded on an insufficient analysis of the inductive

process. Such, however, will be seen to be the fact, as soon as it is

considered, that Bacon entirely overlooked Plurality of Causes. All his

rules tacitly imply the assumption, so contrary to all we now know of

nature, that a phenomenon cannot have more than one cause.

When he is inquiring into what he terms the _forma calidi aut frigidi_,

_gravis aut levis_, _sicci aut humidi_, and the like, he never for an

instant doubts that there is some one thing, some invariable condition

or set of conditions, which is present in all cases of heat, or cold, or

whatever other phenomenon he is considering; the only difficulty being

to find what it is; which accordingly he tries to do by a process of

elimination, rejecting or excluding, by negative instances, whatever is

not the _forma_ or cause, in order to arrive at what is. But, that this

_forma_ or cause is _one_ thing, and that it is the same in all hot

objects, he has no more doubt of, than another person has that there is

always some cause _or other_. In the present state of knowledge it could

not be necessary, even if we had not already treated so fully of the

question, to point out how widely this supposition is at variance with

the truth. It is particularly unfortunate for Bacon that, falling into

this error, he should have fixed almost exclusively upon a class of

inquiries in which it was especially fatal; namely, inquiries into the

causes of the sensible qualities of objects. For his assumption,

groundless in every case, is false in a peculiar degree with respect to

those sensible qualities. In regard to scarcely any of them has it been

found possible to trace any unity of cause, any set of conditions

invariably accompanying the quality. The conjunctions of such qualities

with one another constitute the variety of Kinds, in which, as already

remarked, it has not been found possible to trace any law. Bacon was

seeking for what did not exist. The phenomenon of which he sought for

the one cause has oftenest no cause at all, and when it has, depends (as

far as hitherto ascertained) on an unassignable variety of distinct

causes.

And on this rock every one must split, who represents to himself as the

first and fundamental problem of science to ascertain what is the cause

of a given effect, rather than what are the effects of a given cause. It

was shown, in an early stage of our inquiry into the nature of

Induction,[14] how much more ample are the resources which science

commands for the latter than for the former inquiry, since it is upon

the latter only that we can throw any direct light by means of

experiment; the power of artificially producing an effect, implying a

previous knowledge of at least one of its causes. If we discover the

causes of effects, it is generally by having previously discovered the

effects of causes: the greatest skill in devising crucial instances for

the former purpose may only end, as Bacon's physical inquiries did, in

no result at all. Was it that his eagerness to acquire the power of

producing for man's benefit effects of practical importance to human

life, rendering him impatient of pursuing that end by a circuitous

route, made even him, the champion of experiment, prefer the direct

mode, though one of mere observation, to the indirect, in which alone

experiment was possible? Or had even Bacon not entirely cleared his mind

from the notion of the ancients, that "rerum cognoscere _causas_" was

the sole object of philosophy, and that to inquire into the _effects_ of

things belonged to servile and mechanical arts?

It is worth remarking that, while the only efficient mode of cultivating

speculative science was missed from an undue contempt of manual

operations, the false speculative views thus engendered gave in their

turn a false direction to such practical and mechanical aims as were

suffered to exist. The assumption universal among the ancients and in

the middle ages, that there were _principles_ of heat and cold, dryness

and moisture, &c., led directly to a belief in alchemy; in a

transmutation of substances, a change from one Kind into another. Why

should it not be possible to make gold? Each of the characteristic

properties of gold has its _forma_, its essence, its set of conditions,

which if we could discover, and learn how to realize, we could

superinduce that particular property upon any other substance, upon

wood, or iron, or lime, or clay. If, then, we could effect this with

respect to every one of the essential properties of the precious metal,

we should have converted the other substance into gold. Nor did this, if

once the premises were granted, appear to transcend the real powers of

mankind. For daily experience showed that almost every one of the

distinctive sensible properties of any object, its consistence, its

colour, its taste, its smell, its shape, admitted of being totally

changed by fire, or water, or some other chemical agent. The _formæ_ of

all those qualities seeming, therefore, to be within human power either

to produce or to annihilate, not only did the transmutation of

substances appear abstractedly possible, but the employment of the

power, at our choice, for practical ends, seemed by no means

hopeless.[15]

A prejudice, universal in the ancient world, and from which Bacon was so

far from being free, that it pervaded and vitiated the whole practical

part of his system of logic, may with good reason be ranked high in the

order of Fallacies of which we are now treating.

§ 8. There remains one _à priori_ fallacy or natural prejudice, the most

deeply-rooted, perhaps, of all which we have enumerated: one which not

only reigned supreme in the ancient world, but still possesses almost

undisputed dominion over many of the most cultivated minds; and some of

the most remarkable of the numerous instances by which I shall think it

necessary to exemplify it, will be taken from recent thinkers. This is,

that the conditions of a phenomenon must, or at least probably will,

resemble the phenomenon itself.

Conformably to what we have before remarked to be of frequent

occurrence, this fallacy might without much impropriety have been placed

in a different class, among Fallacies of Generalization: for experience

does afford a certain degree of countenance to the assumption. The cause

does, in very many cases, resemble its effect; like produces like. Many

phenomena have a direct tendency to perpetuate their own existence, or

to give rise to other phenomena similar to themselves. Not to mention

forms actually moulded on one another, as impressions on wax and the

like, in which the closest resemblance between the effect and its cause

is the very law of the phenomenon; all motion tends to continue itself,

with its own velocity, and in its own original direction; and the motion

of one body tends to set others in motion, which is indeed the most

common of the modes in which the motions of bodies originate. We need

scarcely refer to contagion, fermentation, and the like; or to the

production of effects by the growth or expansion of a germ or rudiment

resembling on a smaller scale the completed phenomenon, as in the growth

of a plant or animal from an embryo, that embryo itself deriving its

origin from another plant or animal of the same kind. Again, the

thoughts, or reminiscences, which are effects of our past sensations,

resemble those sensations; feelings produce similar feelings by way of

sympathy; acts produce similar acts by involuntary or voluntary

imitation. With so many appearances in its favour, no wonder if a

presumption naturally grew up, that causes must _necessarily_ resemble

their effects, and that like could _only_ be produced by like.

This principle of fallacy has usually presided over the fantastical

attempts to influence the course of nature by conjectural means, the

choice of which was not directed by previous observation and experiment.

The guess almost always fixed upon some means which possessed features

of real or apparent resemblance to the end in view. If a charm was

wanted, as by Ovid's Medea, to prolong life, all long-lived animals, or

what were esteemed such, were collected and brewed into a broth:--

... nec defuit illic

Squamea Cinyphii tenuis membrana chelydri

Vivacisque jecur cervi: quibus insuper addit

Ora caputque novem cornicis sæcula passæ.

A similar notion was embodied in the celebrated medical theory called

the "Doctrine of Signatures," "which is no less," says Dr. Paris,[16]

"than a belief that every natural substance which possesses any

medicinal virtue indicates by an obvious and well-marked external

character the disease for which it is a remedy, or the object for which

it should be employed." This outward character was generally some

feature of resemblance, real or fantastical, either to the effect it

was supposed to produce, or to the phenomenon over which its power was

thought to be exercised. "Thus the lungs of a fox must be a specific for

asthma, because that animal is remarkable for its strong powers of

respiration. Turmeric has a brilliant yellow colour, which indicates

that it has the power of curing the jaundice; for the same reason,

poppies must relieve diseases of the head; Agaricus those of the

bladder; _Cassia fistula_ the affections of the intestines, and

Aristolochia the disorders of the uterus: the polished surface and stony

hardness which so eminently characterize the seeds of the Lithospermum

officinale (common gromwell) were deemed a certain indication of their

efficacy in calculous and gravelly disorders; for a similar reason, the

roots of the Saxifraga granulata (white saxifrage) gained reputation in

the cure of the same disease; and the Euphrasia (eye-bright) acquired

fame, as an application in complaints of the eye, because it exhibits a

black spot in its corolla resembling the pupil. The blood-stone, the

Heliotropium of the ancients, from the occasional small specks or points

of a blood-red colour exhibited on its green surface, is even at this

very day employed in many parts of England and Scotland, to stop a

bleeding from the nose; and nettle tea continues a popular remedy for

the cure of _Urticaria_. It is also asserted that some substances bear

the _signatures_ of the humours, as the petals of the red rose that of

the blood, and the roots of rhubarb and the flowers of saffron that of

the bile."

The early speculations respecting the chemical composition of bodies

were rendered abortive by no circumstance more, than by their invariably

taking for granted that the properties of the elements must resemble

those of the compounds which were formed from them.

To descend to more modern instances; it was long thought, and was

stoutly maintained by the Cartesians and even by Leibnitz against the

Newtonian system, (nor did Newton himself, as we have seen, contest the

assumption, but eluded it by an arbitrary hypothesis), that nothing (of

a physical nature at least) could account for motion, except previous

motion; the impulse or impact of some other body. It was very long

before the scientific world could prevail upon itself to admit

attraction and repulsion (_i. e._ spontaneous tendencies of particles to

approach or recede from one another) as ultimate laws, no more requiring

to be accounted for than impulse itself, if indeed the latter were not,

in truth, resolvable into the former. From the same source arose the

innumerable hypotheses devised to explain those classes of motions which

appeared more mysterious than others because there was no obvious mode

of attributing them to impulse, as for example the voluntary motions of

the human body. Such were the interminable systems of vibrations

propagated along the nerves, or animal spirits rushing up and down

between the muscles and the brain; which, if the facts could have been

proved, would have been an important addition to our knowledge of

physiological laws; but the mere invention, or arbitrary supposition of

them, could not unless by the strongest delusion be supposed to render

the phenomena of animal life more comprehensible, or less mysterious.

Nothing, however, seemed satisfactory, but to make out that motion was

caused by motion; by something like itself. If it was not one kind of

motion, it must be another. In like manner it was supposed that the

physical qualities of objects must arise from some similar quality, or

perhaps only some quality bearing the same name, in the particles or

atoms of which the objects were composed; that a sharp taste, for

example, must arise from sharp particles. And reversing the inference,

the effects produced by a phenomenon must, it was supposed, resemble in

their physical attributes the phenomenon itself. The influences of the

planets were supposed to be analogous to their visible peculiarities:

Mars, being of a red colour, portended fire and slaughter; and the like.

Passing from physics to metaphysics, we may notice among the most

remarkable fruits of this _à priori_ fallacy, two closely analogous

theories, employed in ancient and modern times to bridge over the chasm

between the world of mind and that of matter: the _species sensibiles_

of the Epicureans, and the modern doctrine of perception by means of

ideas. These theories are indeed, probably, indebted for their existence

not solely to the fallacy in question, but to that fallacy combined

with another natural prejudice already adverted to, that a thing cannot

act where it is not. In both doctrines it is assumed that the phenomenon

which takes place _in us_ when we see or touch an object, and which we

regard as an effect of that object, or rather as its presence to our

organs, must of necessity resemble very closely the outward object

itself. To fulfil this condition, the Epicureans supposed that objects

were constantly projecting in all directions impalpable images of

themselves, which entered at the eyes and penetrated to the mind; while

modern metaphysicians, though they rejected this hypothesis, agreed in

deeming it necessary to suppose that not the thing itself, but a mental

image or representation of it, was the direct object of perception. Dr.

Reid had to employ a world of argument and illustration to familiarize

people with the truth, that the sensations or impressions on our minds

need not necessarily be copies of, or bear any resemblance to, the

causes which produce them; in opposition to the natural prejudice which

led people to assimilate the action of bodies upon our senses, and

through them upon our minds, to the transfer of a given form from one

object to another by actual moulding. The works of Dr. Reid are even now

the most effectual course of study for detaching the mind from the

prejudice of which this was an example. And the value of the service

which he thus rendered to popular philosophy, is not much diminished

although we may hold, with Brown, that he went too far in imputing the

"ideal theory" as an actual tenet, to the generality of the philosophers

who preceded him, and especially to Locke and Hume: for if they did not

themselves consciously fall into the error, unquestionably they often

led their readers into it.

The prejudice, that the conditions of a phenomenon must resemble the

phenomenon, is occasionally exaggerated, at least verbally, into a still

more palpable absurdity; the conditions of the thing are spoken of as if

they _were_ the very thing itself. In Bacon's model-inquiry, which

occupies so great a space in the _Novum Organum_, the _inquisitio in

formam calidi_, the conclusion which he favours is that heat is a kind

of motion; meaning of course not the feeling of heat, but the

conditions of the feeling; meaning, therefore, only that wherever there

is heat, there must first be a particular kind of motion; but he makes

no distinction in his language between these two ideas, expressing

himself as if heat, and the conditions of heat, were one and the same

thing. So Darwin, in the beginning of his _Zoonomia_, says, "The word

_idea_ has various meanings in the writers of metaphysic: it is here

used simply for those notions of external things which our organs of

sense bring us acquainted with originally," (thus far the proposition,

though vague, is unexceptionable in meaning,) "and is defined a

contraction, a motion, or configuration, of the fibres which constitute

the immediate organ of sense." Our _notions_, a configuration of the

fibres! What kind of logician must he be who thinks that a phenomenon is

_defined_ to _be_ the condition on which he supposes it to depend?

Accordingly he says soon after, not that our ideas are caused by, or

consequent on, certain organic phenomena, but "our ideas _are_ animal

motions of the organs of sense." And this confusion runs through the

four volumes of the _Zoonomia_; the reader never knows whether the

writer is speaking of the effect, or of its supposed cause; of the idea,

a state of mental consciousness, or of the state of the nerves and brain

which he considers it to presuppose.

I have given a variety of instances in which the natural prejudice, that

causes and their effects must resemble one another, has operated in

practice so as to give rise to serious errors. I shall now go further,

and produce from writings even of the present or very recent times,

instances in which this prejudice is laid down as an established

principle. M. Victor Cousin, in the last of his celebrated lectures on

Locke, enunciates the maxim in the following unqualified terms. "Tout ce

qui est vrai de l'effet est vrai de la cause." A doctrine to which,

unless in some peculiar and technical meaning of the words cause and

effect, it is not to be imagined that any person would literally adhere:

but he who could so write must be far enough from seeing, that the very

reverse might be the fact; that there is nothing impossible in the

supposition that no one property which is true of the effect might be

true of the cause. Without going quite so far in point of expression,

Coleridge, in his _Biographia Literaria_,[17] affirms as an "evident

truth," that "the law of causality holds only between homogeneous

things, _i. e._ things having some common property," and therefore

"cannot extend from one world into another, its opposite:" hence, as

mind and matter have no common property, mind cannot act upon matter,

nor matter upon mind. What is this but the _à priori_ fallacy of which

we are speaking? The doctrine, like many others of Coleridge, is taken

from Spinoza, in the first book of whose _Ethica (De Deo)_ it stands as

the Third Proposition, "Quæ res nihil commune inter se habent, earum una

alterius causa esse non potest," and is there proved from two so-called

axioms, equally gratuitous with itself: but Spinoza, ever systematically

consistent, pursued the doctrine to its inevitable consequence, the

materiality of God.

The same conception of impossibility led the ingenious and subtle mind

of Leibnitz to his celebrated doctrine of a pre-established harmony. He,

too, thought that mind could not act upon matter, nor matter upon mind,

and that the two, therefore, must have been arranged by their Maker like

two clocks, which, though unconnected with one another, strike

simultaneously, and always point to the same hour. Malebranche's equally

famous theory of Occasional Causes was another form of the same

conception: instead of supposing the clocks originally arranged to

strike together, he held that when the one strikes, God interposes, and

makes the other strike in correspondence with it.

Descartes, in like manner, whose works are a rich mine of almost every

description of _à priori_ fallacy, says that the Efficient Cause must at

least have all the perfections of the effect, and for this singular

reason: "Si enim ponamus aliquid in ideâ reperiri quod non fuerit in

ejus causâ, hoc igitur habet a nihilo;" of which it is scarcely a parody

to say, that if there be pepper in the soup there must be pepper in the

cook who made it, since otherwise the pepper would be without a cause. A

similar fallacy is committed by Cicero in his second book _De Finibus_,

where, speaking in his own person against the Epicureans, he charges

them with inconsistency in saying that the pleasures of the mind had

their origin from those of the body, and yet that the former were more

valuable, as if the effect could surpass the cause. "Animi voluptas

oritur propter voluptatem corporis, et major est animi voluptas quam

corporis? ita fit ut gratulator lætior sit quam is cui gratulatur." Even

that, surely, is not an impossibility: a person's good fortune has often

given more pleasure to others than it gave to the person himself.

Descartes, with no less readiness, applies the same principle the

converse way, and infers the nature of the effects from the assumption

that they must, in this or that property or in all their properties,

resemble their cause. To this class belong his speculations, and those

of so many others after him, tending to infer the order of the universe,

not from observation, but by _à priori_ reasoning from supposed

qualities of the Godhead. This sort of inference was probably never

carried to a greater length than it was in one particular instance by

Descartes, when, as a proof of one of his physical principles, that the

quantity of motion in the universe is invariable, he had recourse to the

immutability of the Divine Nature. Reasoning of a very similar character

is however nearly as common now as it was in his time, and does duty

largely as a means of fencing off disagreeable conclusions. Writers have

not yet ceased to oppose the theory of divine benevolence to the

evidence of physical facts, to the principle of population for example.

And people seem in general to think that they have used a very powerful

argument, when they have said, that to suppose some proposition true,

would be a reflection on the goodness or wisdom of the Deity. Put into

the simplest possible terms, their argument is, "If it had depended on

me, I would not have made the proposition true, therefore it is not

true." Put into other words it stands thus: "God is perfect, therefore

(what I think) perfection must obtain in nature." But since in reality

every one feels that nature is very far from perfect, the doctrine is

never applied consistently. It furnishes an argument which (like many

others of a similar character) people like to appeal to when it makes

for their own side. Nobody is convinced by it, but each appears to think

that it puts religion on his side of the question, and that it is a

useful weapon of offence for wounding an adversary.

Although several other varieties of _à priori_ fallacy might probably be

added to those here specified, these are all against which it seems

necessary to give any special caution. Our object is to open, without

attempting or affecting to exhaust, the subject. Having illustrated,

therefore, this first class of Fallacies at sufficient length, I shall

proceed to the second.

CHAPTER IV.

FALLACIES OF OBSERVATION.

§ 1. From the fallacies which are properly Prejudices, or presumptions

antecedent to, and superseding, proof, we pass to those which lie in the

incorrect performance of the proving process. And as Proof, in its

widest extent, embraces one or more, or all, of three processes,

Observation, Generalization, and Deduction; we shall consider in their

order the errors capable of being committed in these three operations.

And first, of the first mentioned.

A fallacy of misobservation may be either negative or positive; either

Non-observation or Mal-observation. It is non-observation, when all the

error consists in overlooking, or neglecting, facts or particulars which

ought to have been observed. It is mal-observation, when something is

not simply unseen, but seen wrong; when the fact or phenomenon, instead

of being recognised for what it is in reality, is mistaken for something

else.

§ 2. Non-observation may either take place by overlooking instances, or

by overlooking some of the circumstances of a given instance. If we were

to conclude that a fortune-teller was a true prophet, from not adverting

to the cases in which his predictions had been falsified by the event,

this would be non-observation of instances; but if we overlooked or

remained ignorant of the fact that in cases where the predictions had

been fulfilled, he had been in collusion with some one who had given him

the information on which they were grounded, this would be

non-observation of circumstances.

The former case, in so far as the act of induction from insufficient

evidence is concerned, does not fall under this second class of

Fallacies, but under the third, Fallacies of Generalization. In every

such case, however, there are two defects or errors instead of one:

there is the error of treating the insufficient evidence as if it were

sufficient, which is a Fallacy of the third class; and there is the

insufficiency itself; the not having better evidence; which, when such

evidence, or in other words, when other instances, were to be had, is

Non-observation: and the erroneous inference, so far as it is to be

attributed to this cause, is a Fallacy of the second class.

It belongs not to our purpose to treat of non-observation as arising

from casual inattention, from general slovenliness of mental habits,

want of due practice in the use of the observing faculties, or

insufficient interest in the subject. The question pertinent to logic

is--Granting the want of complete competency in the observer, on what

points is that insufficiency on his part likely to lead him wrong? or

rather, what sorts of instances, or of circumstances in any given

instance, are most likely to escape the notice of observers generally;

of mankind at large.

§ 3. First, then, it is evident that when the instances on one side of a

question are more likely to be remembered and recorded than those on the

other; especially if there be any strong motive to preserve the memory

of the first, but not of the latter; these last are likely to be

overlooked, and escape the observation of the mass of mankind. This is

the recognised explanation of the credit given, in spite of reason and

evidence, to many classes of impostors: to quack doctors, and

fortune-tellers in all ages; to the "cunning man" of modern times and

the oracles of old. Few have considered the extent to which this fallacy

operates in practice, even in the teeth of the most palpable negative

evidence. A striking example of it is the faith which the uneducated

portion of the agricultural classes, in this and other countries,

continue to repose in the prophecies as to weather supplied by almanac

makers: though every season affords to them numerous cases of

completely erroneous prediction; but as every season also furnishes some

cases in which the prediction is fulfilled, this is enough to keep up

the credit of the prophet, with people who do not reflect on the number

of instances requisite for what we have called, in our inductive

terminology, the Elimination of Chance; since a certain number of casual

coincidences not only may but will happen, between any two unconnected

events.

Coleridge, in one of the essays in the _Friend_, has illustrated the

matter we are now considering, in discussing the origin of a proverb,

"which, differently worded, is to be found in all the languages of

Europe," viz. "Fortune favours fools." He ascribes it partly to the

"tendency to exaggerate all effects that seem disproportionate to their

visible cause, and all circumstances that are in any way strongly

contrasted with our notions of the persons under them." Omitting some

explanations which would refer the error to mal-observation, or to the

other species of non-observation (that of circumstances), I take up the

quotation farther on. "Unforeseen coincidences may have greatly helped a

man, yet if they have done for him only what possibly from his own

abilities he might have effected for himself, his good luck will excite

less attention, and the instances be less remembered. That clever men

should attain their objects seems natural, and we neglect the

circumstances that perhaps produced that success of themselves, without

the intervention of skill or foresight; but we dwell on the fact and

remember it, as something strange, when the same happens to a weak or

ignorant man. So too, though the latter should fail in his undertakings

from concurrences that might have happened to the wisest man, yet his

failure being no more than might have been expected and accounted for

from his folly, it lays no hold on our attention, but fleets away among

the other undistinguished waves in which the stream of ordinary life

murmurs by us, and is forgotten. Had it been as true as it was

notoriously false, that those all-embracing discoveries, which have shed

a dawn of _science_ on the _art_ of chemistry, and give no obscure

promise of some one great constitutive law, in the light of which dwell

dominion and the power of prophecy; if these discoveries, instead of

having been, as they really were, preconcerted by meditation, and

evolved out of his own intellect, had occurred by a set of lucky

_accidents_ to the illustrious father and founder of philosophic

alchemy; if they had presented themselves to Professor Davy exclusively

in consequence of his _luck_ in possessing a particular galvanic

battery; if this battery, as far as Davy was concerned, had itself been

an _accident_, and not (as in point of fact it was) desired and obtained

by him for the purpose of ensuring the testimony of experience to his

principles, and in order to bind down material nature under the

inquisition of reason, and force from her, as by torture, unequivocal

answers to _prepared_ and _preconceived_ questions,--yet still they

would not have been talked of or described as instances of _luck_, but

as the natural results of his admitted genius and known skill. But

should an accident have disclosed similar discoveries to a mechanic at

Birmingham or Sheffield, and if the man should grow rich in consequence,

and partly by the envy of his neighbours and partly with good reason, be

considered by them as a man _below par_ in the general powers of his

understanding; then, 'O what a lucky fellow! Well, Fortune _does_ favour

fools--that's for certain!--It is always so!' And forthwith the

exclaimer relates half a dozen similar instances. Thus accumulating the

one sort of facts and never collecting the other, we do, as poets in

their diction, and quacks of all denominations do in their reasoning,

put a part for the whole."

This passage very happily sets forth the manner in which, under the

loose mode of induction which proceeds _per enumerati onem simplicem_,

not seeking for instances of such a kind as to be decisive of the

question, but generalizing from any which occur, or rather which are

remembered, opinions grow up with the apparent sanction of experience,

which have no foundation in the laws of nature at all. "Itaque recte

respondit ille," (we may say with Bacon,[18]) "qui cum suspensa tabula

in templo ei monstraretur eorum, qui vota solverant, quod naufragii

periculo elapsi sint, atque interrogando premeretur, anne tum quidem

Deorum numen agnosceret, quæsivit denuo, _At ubi sunt illi depicti qui

post vota nuncupata perierunt?_ Eadem ratio est fere omnis

superstitionis, ut in Astrologicis, in Somniis, Ominibus, Nemesibus, et

hujusmodi; in quibus, homines delectati hujusmodi vanitatibus, advertunt

eventus, ubi implentur; ast ubi fallunt, licet multo frequentius, tamen

negligunt, et prætereunt." And he proceeds to say, that independently of

the love of the marvellous, or any other bias in the inclinations, there

is a natural tendency in the intellect itself to this kind of fallacy;

since the mind is more moved by affirmative instances, though negative

ones are of most use in philosophy; "Is tamen humano intellectui error

est proprius et perpetuus, ut magis moveatur et excitetur Affirmativis

quam Negativis; cum rite et ordine æquum se utrique præbere debeat; quin

contra, in omni Axiomate vero constituendo, major vis est instantiæ

negativæ."

But the greatest of all causes of non-observation is a preconceived

opinion. This it is which, in all ages, has made the whole race of

mankind, and every separate section of it, for the most part unobservant

of all facts, however abundant, even when passing under their own eyes,

which are contradictory to any first appearance, or any received tenet.

It is worth while to recal occasionally to the oblivious memory of

mankind some of the striking instances in which opinions that the

simplest experiment would have shown to be erroneous, continued to be

entertained because nobody ever thought of trying that experiment. One

of the most remarkable of these was exhibited in the Copernican

controversy. The opponents of Copernicus argued that the earth did not

move, because if it did, a stone let fall from the top of a high tower

would not reach the ground at the foot of the tower, but at a little

distance from it, in a contrary direction to the earth's course; in the

same manner (said they) as, if a ball is let drop from the mast-head

while the ship is in full sail, it does not fall exactly at the foot of

the mast, but nearer to the stern of the vessel. The Copernicans would

have silenced these objectors at once if they had _tried_ dropping a

ball from the mast-head, since they would have found that it does fall

exactly at the foot, as the theory requires: but no; they admitted the

spurious fact, and struggled vainly to make out a difference between the

two cases. "The ball was no _part_ of the ship--and the motion forward

was not _natural_, either to the ship or to the ball. The stone, on the

other hand, let fall from the top of the tower, was a _part_ of the

earth; and therefore, the diurnal and annular revolutions which were

_natural_ to the earth, were also _natural_ to the stone: the stone

would, therefore, retain the same motion with the tower, and strike the

ground precisely at the bottom of it."[19]

Other examples, scarcely less striking, are recorded by Dr. Whewell,[20]

where imaginary laws of nature have continued to be received as real,

merely because no person had steadily looked at facts which almost every

one had the opportunity of observing. "A vague and loose mode of looking

at facts very easily observable, left men for a long time under the

belief that a body ten times as heavy as another falls ten times as

fast; that objects immersed in water are always magnified, without

regard to the form of the surface; that the magnet exerts an

irresistible force; that crystal is always found associated with ice;

and the like. These and many others are examples how blind and careless

man can be even in observation of the plainest and commonest

appearances; and they show us that the mere faculties of perception,

although constantly exercised upon innumerable objects, may long fail in

leading to any exact knowledge."

If even on physical facts, and these of the most obvious character, the

observing faculties of mankind can be to this degree the passive slaves

of their preconceived impressions, we need not be surprised that this

should be so lamentably true as all experience attests it to be, on

things more nearly connected with their stronger feelings--on moral,

social, and religious subjects. The information which an ordinary

traveller brings back from a foreign country, as the result of the

evidence of his senses, is almost always such as exactly confirms the

opinions with which he set out. He has had eyes and ears for such things

only as he expected to see. Men read the sacred books of their religion,

and pass unobserved therein, multitudes of things utterly

irreconcileable with even their own notions of moral excellence. With

the same authorities before them, different historians, alike innocent

of intentional misrepresentation, see only what is favourable to

Protestants or Catholics, royalists or republicans, Charles I. or

Cromwell; while others, having set out with the preconception that

extremes must be in the wrong, are incapable of seeing truth and justice

when these are wholly on one side.

The influence of a preconceived theory is well exemplified in the

superstitions of barbarians respecting the virtues of medicaments and

charms. The negroes, among whom coral, as of old among ourselves, is

worn as an amulet, affirm, according to Dr. Paris,[21] that its colour

"is always affected by the state of health of the wearer, it becoming

paler in disease." On a matter open to universal observation, a general

proposition which has not the smallest vestige of truth is received as a

result of experience; the preconceived opinion preventing, it would

seem, any observation whatever on the subject.

§ 4. For illustration of the first species of non-observation, that of

Instances, what has now been stated may suffice. But there may also be

non-observation of some material circumstances, in instances which have

not been altogether overlooked--nay, which may be the very instances on

which the whole superstructure of a theory has been founded. As, in the

cases hitherto examined, a general proposition was too rashly adopted,

on the evidence of particulars, true indeed, but insufficient to support

it; so in the cases to which we now turn, the particulars themselves

have been imperfectly observed, and the singular propositions on which

the generalization is grounded, or some at least of those singular

propositions, are false.

Such, for instance, was one of the mistakes committed in the celebrated

phlogistic theory; a doctrine which accounted for combustion by the

extrication of a substance called phlogiston, supposed to be contained

in all combustible matter. The hypothesis accorded tolerably well with

superficial appearances: the ascent of flame naturally suggests the

escape of a substance; and the visible residuum of ashes, in bulk and

weight, generally falls extremely short of the combustible material. The

error was, non-observation of an important portion of the actual

residue, namely, the gaseous products of combustion. When these were at

last noticed and brought into account, it appeared to be an universal

law, that all substances gain instead of losing weight by undergoing

combustion; and, after the usual attempt to accommodate the old theory

to the new fact by means of an arbitrary hypothesis (that phlogiston had

the quality of positive levity instead of gravity), chemists were

conducted to the true explanation, namely, that instead of a substance

separated, there was on the contrary a substance absorbed.

Many of the absurd practices which have been deemed to possess medicinal

efficacy, have been indebted for their reputation to non-observance of

some accompanying circumstance which was the real agent in the cures

ascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby:

"Whenever any wound had been inflicted, this powder was applied to the

weapon that had inflicted it, which was, moreover, covered with

ointment, and dressed two or three times a day. The wound itself, in the

meantime, was directed to be brought together, and carefully bound up

with clean linen rags, but _above all, to be let alone_ for seven days,

at the end of which period the bandages were removed, when the wound was

generally found perfectly united. The triumph of the cure was decreed to

the mysterious agency of the sympathetic powder which had been so

assiduously applied to the weapon, whereas it is hardly necessary to

observe that the promptness of the cure depended on the total exclusion

of air from the wound, and upon the sanative operations of nature not

having received any disturbance from the officious interference of art.

The result, beyond all doubt, furnished the first hint which led

surgeons to the improved practice of healing wounds by what is

technically called the _first intention_."[22] "In all records," adds

Dr. Paris, "of extraordinary cures performed by mysterious agents, there

is a great desire to conceal the remedies and other curative means which

were simultaneously administered with them; thus Oribasius commends in

high terms a necklace of Pæony root for the cure of epilepsy; but we

learn that he always took care to accompany its use with copious

evacuations, although he assigns to them no share of credit in the cure.

In later times we have a good specimen of this species of deception,

presented to us in a work on Scrofula by Mr. Morley, written, as we are

informed, for the sole purpose of restoring the much injured character

and use of the Vervain; in which the author directs the root of this

plant to be tied with a yard of white satin riband around the neck,

where it is to remain until the patient is cured; but mark--during this

interval he calls to his aid the most active medicines in the materia

medica."[23]

In other cases the cures really produced by rest, regimen, and

amusement, have been ascribed to the medicinal, or occasionally to the

supernatural, means which were put in requisition. "The celebrated John

Wesley, while he commemorates the triumph of sulphur and supplication

over his bodily infirmity, forgets to appreciate the resuscitating

influence of four months' repose from his apostolic labours; and such is

the disposition of the human mind to place confidence in the operation

of mysterious agents, that we find him more disposed to attribute his

cure to a brown paper plaister of egg and brimstone, than to Dr.

Fothergill's salutary prescription of country air, rest, asses' milk,

and horse exercise."[24]

In the following example, the circumstance overlooked was of a somewhat

different character. "When the yellow fever raged in America, the

practitioners trusted exclusively to the copious use of mercury; at

first this plan was deemed so universally efficacious, that, in the

enthusiasm of the moment, it was triumphantly proclaimed that death

never took place after the mercury had evinced its effect upon the

system: all this was very true, but it furnished no proof of the

efficacy of that metal, since the disease in its aggravated form was so

rapid in its career, that it swept away its victims long before the

system could be brought under mercurial influence, while in its milder

shape it passed off equally well without any assistance from art."[25]

In these examples the circumstance overlooked was cognizable by the

senses. In other cases, it is one the knowledge of which could only be

arrived at by reasoning; but the fallacy may still be classed under the

head to which, for want of a more appropriate name, we have given the

appellation Fallacies of Non-observation. It is not the nature of the

faculties which ought to have been employed, but the non-employment of

them, which constitutes this Natural Order of Fallacies. Wherever the

error is negative, not positive; wherever it consists especially in

_overlooking_, in being ignorant or unmindful of some fact which, if

known and attended to, would have made a difference in the conclusion

arrived at; the error is properly placed in the Class which we are

considering. In this Class, there is not, as in all other fallacies

there is, a positive mis-estimate of evidence actually had. The

conclusion would be just, if the portion which is seen of the case were

the whole of it; but there is another portion overlooked, which vitiates

the result.

For instance, there is a remarkable doctrine which has occasionally

found a vent in the public speeches of unwise legislators, but which

only in one instance that I am aware of has received the sanction of a

philosophical writer, namely M. Cousin, who, in his preface to the

_Gorgias_ of Plato, contending that punishment must have some other and

higher justification than the prevention of crime, makes use of this

argument--that if punishment were only for the sake of example, it would

be indifferent whether we punished the innocent or the guilty, since the

punishment, considered as an example, is equally efficacious in either

case. Now we must, in order to go along with this reasoning, suppose,

that the person who feels himself under temptation, observing somebody

punished, concludes himself to be in danger of being punished likewise,

and is terrified accordingly. But it is forgotten that if the person

punished is supposed to be innocent, or even if there be any doubt of

his guilt, the spectator will reflect that his own danger, whatever it

may be, is not contingent on his guiltiness, but threatens him equally

if he remains innocent, and how therefore is he deterred from guilt by

the apprehension of such punishment? M. Cousin supposes that people will

be dissuaded from guilt by whatever renders the condition of the guilty

more perilous, forgetting that the condition of the innocent (also one

of the elements in the calculation) is, in the case supposed, made

perilous in precisely an equal degree. This is a fallacy of overlooking;

or of non-observation, within the intent of our classification.

Fallacies of this description are the great stumbling-block to correct

thinking in political economy. The economical workings of society afford

numerous cases in which the effects of a cause consist of two sets of

phenomena: the one immediate, concentrated, obvious to all eyes, and

passing, in common apprehension, for the whole effect; the other widely

diffused, or lying deeper under the surface, and which is exactly

contrary to the former. Take, for instance, the common notion so

plausible at the first glance, of the encouragement given to industry by

lavish expenditure. A, who spends his whole income, and even his

capital, in expensive living, is supposed to give great employment to

labour. B, who lives on a small portion, and invests the remainder in

the funds, is thought to give little or no employment. For everybody

sees the gains which are made by A's tradesmen, servants, and others,

while his money is spending. B's savings, on the contrary, pass into the

hands of the person whose stock he purchased, who with it pays a debt he

owed to some banker, who lends it again to some merchant or

manufacturer; and the capital being laid out in hiring spinners and

weavers, or carriers and the crews of merchant vessels, not only gives

immediate employment to at least as much industry as A employs during

the whole of his career, but coming back with increase by the sale of

the goods which have been manufactured or imported, forms a fund for the

employment of the same and perhaps a greater quantity of labour in

perpetuity. But the observer does not see, and therefore does not

consider, what becomes of B's money; he does see what is done with A's:

he observes the amount of industry which A's profusion feeds; he

observes not the far greater quantity which it prevents from being fed;

and thence the prejudice, universal to the time of Adam Smith, that

prodigality encourages industry, and parsimony is a discouragement to

it.

The common argument against free trade was a fallacy of the same nature.

The purchaser of British silk encourages British industry; the purchaser

of Lyons silk encourages only French; the former conduct is patriotic,

the latter ought to be interdicted by law. The circumstance is

overlooked, that the purchaser of any foreign commodity necessarily

causes, directly or indirectly, the export of an equivalent value of

some article of home production (beyond what would otherwise be

exported), either to the same foreign country or to some other; which

fact, though from the complication of the circumstances it cannot always

be verified by specific observation, no observation can possibly be

brought to contradict, while the evidence of reasoning on which it rests

is irrefragable. The fallacy is, therefore, the same as in the preceding

case, that of seeing a part only of the phenomena, and imagining that

part to be the whole: and may be ranked among Fallacies of

Non-observation.

§ 5. To complete the examination of the second of our five classes, we

have now to speak of Mal-observation; in which the error does not lie in

the fact that something is unseen, but that something seen is seen

wrong.

Perception being infallible evidence of whatever is really perceived,

the error now under consideration can be committed no otherwise than by

mistaking for conception what is in fact inference. We have formerly

shown how intimately the two are blended in almost everything which is

called observation, and still more in every Description.[26] What is

actually on any occasion perceived by our senses being so minute in

amount, and generally so unimportant a portion of the state of facts

which we wish to ascertain or to communicate; it would be absurd to say

that either in our observations, or in conveying their result to others,

we ought not to mingle inference with fact; all that can be said is,

that when we do so we ought to be aware of what we are doing, and to

know what part of the assertion rests on consciousness, and is therefore

indisputable, what part on inference, and is therefore questionable.

One of the most celebrated examples of an universal error produced by

mistaking an inference for the direct evidence of the senses, was the

resistance made, on the ground of common sense, to the Copernican

system. People fancied they _saw_ the sun rise and set, the stars

revolve in circles round the pole. We now know that they saw no such

thing; what they really saw was a set of appearances, equally

reconcileable with the theory they held and with a totally different

one. It seems strange that such an instance as this, of the testimony of

the senses pleaded with the most entire conviction in favour of

something which was a mere inference of the judgment, and, as it turned

out, a false inference, should not have opened the eyes of the bigots of

common sense, and inspired them with a more modest distrust of the

competency of mere ignorance to judge the conclusions of cultivated

thought.

In proportion to any person's deficiency of knowledge and mental

cultivation, is generally his inability to discriminate between his

inferences and the perceptions on which they were grounded. Many a

marvellous tale, many a scandalous anecdote, owes its origin to this

incapacity. The narrator relates, not what he saw or heard, but the

impression which he derived from what he saw or heard, and of which

perhaps the greater part consisted of inference, though the whole is

related not as inference but as matter-of-fact. The difficulty of

inducing witnesses to restrain within any moderate limits the

intermixture of their inferences with the narrative of their

perceptions, is well known to experienced cross-examiners; and still

more is this the case when ignorant persons attempt to describe any

natural phenomenon. "The simplest narrative," says Dugald Stewart,[27]

"of the most illiterate observer involves more or less of hypothesis;

nay, in general, it will be found that, in proportion to his ignorance,

the greater is the number of conjectural principles involved in his

statements. A village apothecary (and, if possible, in a still greater

degree, an experienced nurse) is seldom able to describe the plainest

case, without employing a phraseology of which every word is a theory:

whereas a simple and genuine specification of the phenomena which mark a

particular disease; a specification unsophisticated by fancy, or by

preconceived opinions, may be regarded as unequivocal evidence of a mind

trained by long and successful study to the most difficult of all arts,

that of the faithful _interpretation_ of nature."

The universality of the confusion between perceptions and the inferences

drawn from them, and the rarity of the power to discriminate the one

from the other, ceases to surprise us when we consider that in the far

greater number of instances the actual perceptions of our senses are of

no importance or interest to us except as marks from which we infer

something beyond them. It is not the colour and superficial extension

perceived by the eye that are important to us, but the object, of which

those visible appearances testify the presence; and where the sensation

itself is indifferent, as it generally is, we have no motive to attend

particularly to it, but acquire a habit of passing it over without

distinct consciousness, and going on at once to the inference. So that

to know what the sensation actually was, is a study in itself, to which

painters, for example, have to train themselves by special and

long-continued discipline and application. In things further removed

from the dominion of the outward senses, no one who has not great

experience in psychological analysis is competent to break this intense

association; and when such analytic habits do not exist in the requisite

degree, it is hardly possible to mention any of the habitual judgments

of mankind on subjects of a high degree of abstraction, from the being

of a God and the immortality of the soul down to the multiplication

table, which are not, or have not been, considered as matter of direct

intuition. So strong is the tendency to ascribe an intuitive character

to judgments which are mere inferences, and often false ones. No one can

doubt that many a deluded visionary has actually believed that he was

directly inspired from Heaven, and that the Almighty had conversed with

him face to face; which yet was only, on his part, a conclusion drawn

from appearances to his senses, or feelings in his internal

consciousness, which afforded no warrant for any such belief. A caution,

therefore, against this class of errors, is not only needful but

indispensable; though to determine whether, on any of the great

questions of metaphysics, such errors are actually committed, belongs

not to this place, but, as I have so often said, to a different science.

CHAPTER V.

FALLACIES OF GENERALIZATION.

§ 1. The class of Fallacies of which we are now to speak, is the most

extensive of all; embracing a greater number and variety of unfounded

inferences than any of the other classes, and which it is even more

difficult to reduce to sub-classes or species. If the attempt made in

the preceding books to define the principles of well-grounded

generalization has been successful, all generalizations not conformable

to those principles might, in a certain sense, be brought under the

present class: when however the rules are known and kept in view, but a

casual lapse committed in the application of them, this is a blunder,

not a fallacy. To entitle an error of generalization to the latter

epithet, it must be committed on principle; there must lie in it some

erroneous general conception of the inductive process; the legitimate

mode of drawing conclusions from observation and experiment must be

fundamentally misconceived.

Without attempting anything so chimerical as an exhaustive

classification of all the misconceptions which can exist on the subject,

let us content ourselves with noting, among the cautions which might be

suggested, a few of the most useful and needful.

§ 2. In the first place, there are certain kinds of generalization

which, if the principles already laid down be correct, _must_ be

groundless: experience cannot afford the necessary conditions for

establishing them by a correct induction. Such, for instance, are all

inferences from the order of nature existing on the earth, or in the

solar system, to that which may exist in remote parts of the universe;

where the phenomena, for aught we know, may be entirely different, or

may succeed one another according to different laws, or even according

to no fixed law at all. Such, again, in matters dependent on causation,

are all universal negatives, all propositions that assert impossibility.

The non-existence of any given phenomenon, however uniformly experience

may as yet have testified to the fact, proves at most that no cause,

adequate to its production, has yet manifested itself; but that no such

causes exist in nature can only be inferred if we are so foolish as to

suppose that we know all the forces in nature. The supposition would at

least be premature while our acquaintance with some even of those which

we do know is so extremely recent. And however much our knowledge of

nature may hereafter be extended, it is not easy to see how that

knowledge could ever be complete, or how, if it were, we could ever be

assured of its being so.

The only laws of nature which afford sufficient warrant for attributing

impossibility (even with reference to the existing order of nature, and

to our own region of the universe), are first, those of number and

extension, which are paramount to the laws of the succession of

phenomena, and not exposed to the agency of counteracting causes; and

secondly, the universal law of causality itself. That no variation in

any effect or consequent will take place while the whole of the

antecedents remain the same, may be affirmed with full assurance. But,

that the addition of some new antecedent might not entirely alter and

subvert the accustomed consequent, or that antecedents competent to do

this do not exist in nature, we are in no case empowered positively to

conclude.

§ 3. It is next to be remarked that all generalizations which profess,

like the theories of Thales, Democritus, and others of the early Greek

speculators, to resolve all things into some one element, or like many

modern theories, to resolve phenomena radically different into the same,

are necessarily false. By radically different phenomena I mean

impressions on our senses which differ in quality, and not merely in

degree. On this subject what appeared necessary was said in the chapter

on the Limits to the Explanation of Laws of Nature; but as the fallacy

is even in our own times a common one, I shall touch on it somewhat

further in this place.

When we say that the force which retains the planets in their orbits is

resolved into gravity, or that the force which makes substances combine

chemically is resolved into electricity, we assert in the one case what

is, and in the other case what might, and probably will ultimately, be a

legitimate result of induction. In both these cases, motion is resolved

into motion. The assertion is, that a case of motion, which was supposed

to be special, and to follow a distinct law of its own, conforms to and

is included in the general law which regulates another class of motions.

But, from these and similar generalizations, countenance and currency

have been given to attempts to resolve, not motion into motion, but heat

into motion, light into motion, sensation itself into motion; states of

consciousness into states of the nervous system, as in the ruder forms

of the materialist philosophy; vital phenomena into mechanical or

chemical processes, as in some schools of physiology.

Now I am far from pretending that it may not be capable of proof, or

that it will not be an important addition to our knowledge if proved,

that certain motions in the particles of bodies are among the

_conditions_ of the production of heat or light; that certain assignable

physical modifications of the nerves may be the _conditions_ not only of

our sensations or emotions, but even of our thoughts; that certain

mechanical and chemical conditions may, in the order of nature, be

sufficient to determine to action the physiological laws of life. All I

insist upon, in common with every thinker who entertains any clear idea

of the logic of science, is, that it shall not be supposed that by

proving these things one step would be made towards a real explanation

of heat, light, or sensation; or that the generic peculiarity of those

phenomena can be in the least degree evaded by any such discoveries,

however well established. Let it be shown, for instance, that the most

complex series of physical causes and effects succeed one another in the

eye and in the brain to produce a sensation of colour; rays falling on

the eye, refracted, converging, crossing one another, making an inverted

image on the retina, and after this a motion--let it be a vibration, or

a rush of nervous fluid, or whatever else you are pleased to suppose,

along the optic nerve--a propagation of this motion to the brain itself,

and as many more different motions as you choose; still, at the end of

these motions, there is something which is not motion, there is a

feeling or sensation of colour. Whatever number of motions we may be

able to interpolate, and whether they be real or imaginary, we shall

still find, at the end of the series, a motion antecedent and a colour

consequent. The mode in which any one of the motions produces the next,

might possibly be susceptible of explanation by some general law of

motion; but the mode in which the last motion produces the sensation of

colour, cannot be explained by any law of motion; it is the law of

colour: which is, and must always remain, a peculiar thing. Where our

consciousness recognises between two phenomena an inherent distinction;

where we are sensible of a difference which is not merely of degree, and

feel that no adding one of the phenomena to itself would produce the

other; any theory which attempts to bring either under the laws of the

other must be false; though a theory which merely treats the one as a

cause or condition of the other, may possibly be true.

§ 4. Among the remaining forms of erroneous generalization, several of

those most worthy of and most requiring notice have fallen under our

examination in former places, where, in investigating the rules of

correct induction, we have had occasion to advert to the distinction

between it and some common mode of the incorrect. In this number is what

I have formerly called the natural Induction of uninquiring minds, the

Induction of the ancients, which proceeds _per enumerationem

simplicem_: "This, that, and the other A are B, I cannot think of any A

which is not B, therefore every A is B." As a final condemnation of this

rude and slovenly mode of generalization, I will quote Bacon's emphatic

denunciation of it; the most important part, as I have more than once

ventured to assert, of the permanent service rendered by him to

philosophy. "Inductio quæ procedit per enumerationem simplicem, res

puerilis est, et precario concludit" (concludes only _by your leave_, or

provisionally,) "et periculo exponitur ab instantiâ contradictoriâ, et

plerumque secundum pauciora quam par est, et _ex his tantummodo quæ

præsto sunt pronunciat_. At Inductio quæ ad inventionem et

demonstrationem Scientiarum et Artium erit utilis, Naturam separare

debet, per rejectiones et exclusiones debitas; ac deinde post negativas

tot quot sufficiunt, super affirmativas concludere."

I have already said that the mode of Simple Enumeration is still the

common and received method of Induction in whatever relates to man and

society. Of this a very few instances, more by way of memento than of

instruction, may suffice. What, for example, is to be thought of all the

"common-sense" maxims for which the following may serve as the universal

formula, "Whatsoever has never been, will never be." As for example:

negroes have never been as civilized as whites sometimes are, therefore

it is impossible they should be so. Women, as a class, are supposed not

to have hitherto been equal in intellect to men, therefore they are

necessarily inferior. Society cannot prosper without this or the other

institution; _e.g._ in Aristotle's time, without slavery; in later

times, without an established priesthood, without artificial

distinctions of rank, &c. One poor person in a thousand, educated, while

the nine hundred and ninety-nine remain uneducated, has usually aimed at

raising himself out of his class, therefore education makes people

dissatisfied with the condition of a labourer. Bookish men, taken from

speculative pursuits and set to work on something they know nothing

about, have generally been found or thought to do it ill; therefore

philosophers are unfit for business, &c. &c. All these are inductions by

simple enumeration. Reasons having some reference to the canons of

scientific investigation have been attempted to be given, however

unsuccessfully, for some of these propositions; but to the multitude of

those who parrot them, the _enumeratio simplex, ex his tantummodo quæ

præsto sunt pronuncians_, is the sole evidence. Their fallacy consists

in this, that they are inductions without elimination: there has been no

real comparison of instances, nor even ascertainment of the material

facts in any given instance. There is also the further error, of

forgetting that such generalizations, even if well established, could

not be ultimate truths, but must be results of laws much more

elementary; and therefore, until deduced from such, could at most be

admitted as empirical laws, holding good within the limits of space and

time by which the particular observations that suggested the

generalization were bounded.

This error, of placing more empirical laws, and laws in which there is

no direct evidence of causation, on the same footing of certainty as

laws of cause and effect, an error which is at the root of perhaps the

greater number of bad inductions, is exemplified only in its grossest

form in the kind of generalizations to which we have now referred.

These, indeed, do not possess even the degree of evidence which pertains

to a well-ascertained empirical law; but admit of refutation on the

empirical ground itself, without ascending to causal laws. A little

reflection, indeed, will show that mere negations can only form the

ground of the lowest and least valuable kind of empirical law. A

phenomenon has never been noticed; this only proves that the conditions

of that phenomenon have not yet occurred in experience, but does not

prove that they may not occur hereafter. There is a better kind of

empirical law than this, namely, when a phenomenon which is observed

presents within the limits of observation a series of gradations, in

which a regularity, or something like a mathematical law, is

perceptible: from which, therefore, something may be rationally presumed

as to those terms of the series which are beyond the limits of

observation. But in negation there are no gradations, and no series: the

generalizations, therefore, which deny the possibility of any given

condition of man and society merely because it has never yet been

witnessed, cannot possess this higher degree of validity even as

empirical laws. What is more, the minuter examination which that higher

order of empirical laws presupposes, being applied to the subject-matter

of these, not only does not confirm but actually refutes them. For in

reality the past history of Man and Society, instead of exhibiting them

as immovable, unchangeable, incapable of ever presenting new phenomena,

shows them on the contrary to be, in many most important particulars,

not only changeable, but actually undergoing a progressive change. The

empirical law, therefore, best expressive, in most cases, of the genuine

result of observation, would be, not that such and such a phenomenon

will continue unchanged, but that it will continue to change in some

particular manner.

Accordingly, while almost all generalizations relating to Man and

Society, antecedent to the last fifty years, have erred in the gross way

which we have attempted to characterize, namely, by implicitly assuming

that human nature and society will for ever revolve in the same orbit,

and exhibit essentially the same phenomena; which is also the vulgar

error of the ostentatiously practical, the votaries of so-called common

sense, in our day, especially in Great Britain; the more thinking minds

of the present age, having applied a more minute analysis to the past

records of our race, have for the most part adopted a contrary opinion,

that the human species is in a state of necessary progression, and that

from the terms of the series which are past we may infer positively

those which are yet to come. Of this doctrine, considered as a

philosophical tenet, we shall have occasion to speak more fully in the

concluding Book. If not, in all its forms, free from error, it is at

least free from the gross and stupid error which we previously

exemplified. But, in all except the most eminently philosophical minds,

it is infected with precisely the same _kind_ of fallacy as that is. For

we must remember that even this other and better generalization, the

progressive change in the condition of the human species, is, after all,

but an empirical law: to which, too, it is not difficult to point out

exceedingly large exceptions; and even if these could be got rid of,

either by disputing the facts or by explaining and limiting the theory,

the general objection remains valid against the supposed law, as

applicable to any other than what, in our third book, were termed

Adjacent Cases. For not only is it no ultimate, but not even a causal

law. Changes do indeed take place in human affairs, but every one of

those changes depends on determinate causes; the "progressiveness of the

species" is not a cause, but a summary expression for the general result

of all the causes. So soon as, by a quite different sort of induction,

it shall be ascertained what causes have produced these successive

changes, from the beginning of history, in so far as they have really

taken place, and by what causes of a contrary tendency they have been

occasionally checked or entirely counteracted, we may then be prepared

to predict the future with reasonable foresight; we may be in possession

of the real _law_ of the future; and may be able to declare on what

circumstances the continuance of the same onward movement will

eventually depend. But this it is the error of many of the more advanced

thinkers, in the present age, to overlook; and to imagine that the

empirical law collected from a mere comparison of the condition of our

species at different past times, is a real law, is _the_ law of its

changes, not only past but also to come. The truth is, that the causes

on which the phenomena of the moral world depend, are in every age, and

almost in every country, combined in some different proportion; so that

it is scarcely to be expected that the general result of them all should

conform very closely, in its details at least, to any uniformly

progressive series. And all generalizations which affirm that mankind

have a tendency to grow better or worse, richer or poorer, more

cultivated or more barbarous, that population increases faster than

subsistence, or subsistence than population, that inequality of fortune

has a tendency to increase or to break down, and the like, propositions

of considerable value as empirical laws within certain (but generally

rather narrow) limits, are in reality true or false according to times

and circumstances.

What we have said of empirical generalizations from times past to times

still to come, holds equally true of similar generalizations from

present times to times past; when persons whose acquaintance with moral

and social facts is confined to their own age, take the men and the

things of that age for the type of men and things in general, and apply

without scruple to the interpretation of the events of history, the

empirical laws which represent sufficiently for daily guidance the

common phenomena of human nature at that time and in that particular

state of society. If examples are wanted, almost every historical work,

until a very recent period, abounded in them. The same may be said of

those who generalize empirically from the people of their own country to

the people of other countries, as if human beings felt, judged, and

acted, everywhere in the same manner.

§ 5. In the foregoing instances, the distinction is confounded between

empirical laws, which express merely the customary order of the

succession of effects, and the laws of causation on which the effects

depend. There may, however, be incorrect generalization when this

mistake is not committed; when the investigation takes its proper

direction, that of causes, and the result erroneously obtained purports

to be a really causal law.

The most vulgar form of this fallacy is that which is commonly called

_post hoc, ergo propter hoc_, or, _cum hoc, ergo propter hoc_. As when

it was inferred that England owed her industrial pre-eminence to her

restrictions on commerce: as when the old school of financiers, and some

speculative writers, maintained that the national debt was one of the

causes of national prosperity: as when the excellence of the Church, of

the Houses of Lords and Commons, of the procedure of the law courts,

&c., were inferred from the mere fact that the country had prospered

under them. In such cases as these, if it can be rendered probable by

other evidence that the supposed causes have some tendency to produce

the effect ascribed to them, the fact of its having been produced,

though only in one instance, is of some value as a verification by

specific experience: but in itself it goes scarcely any way at all

towards establishing such a tendency, since, admitting the effect, a

hundred other antecedents could show an equally strong title of _that_

kind to be considered as the cause.

In these examples we see bad generalization _à posteriori_, or

empiricism properly so called: causation inferred from casual

conjunction, without either due elimination, or any presumption arising

from known properties of the supposed agent. But bad generalization _à

priori_ is fully as common: which is properly called false theory;

conclusions drawn, by way of deduction, from properties of some one

agent which is known or supposed to be present, all other coexisting

agents being overlooked. As the former is the error of sheer ignorance,

so the latter is especially that of semi-instructed minds; and is mainly

committed in attempting to explain complicated phenomena by a simpler

theory than their nature admits of. As when one school of physicians

sought for the universal principle of all disease in "lentor and morbid

viscidity of the blood," and imputing most bodily derangements to

mechanical obstructions, thought to cure them by mechanical

remedies;[28] while another, the chemical school, "acknowledged no

source of disease but the presence of some hostile acid or alkali, or

some deranged condition in the chemical composition of the fluid or

solid parts," and conceived, therefore, that "all remedies must act by

producing chemical changes in the body. We find Tournefort busily

engaged in testing every vegetable juice, in order to discover in it

some traces of an acid or alkaline ingredient, which might confer upon

it medicinal activity. The fatal errors into which such an hypothesis

was liable to betray the practitioner, received an awful illustration in

the history of the memorable fever that raged at Leyden in the year

1699, and which consigned two-thirds of the population of that city to

an untimely grave; an event which in a great measure depended upon the

Professor Sylvius de la Boe, who having just embraced the chemical

doctrines of Van Helmont, assigned the origin of the distemper to a

prevailing acid, and declared that its cure could alone [only] be

effected by the copious administration of absorbent and testaceous

medicines."[29]

These aberrations in medical theory have their exact parallels in

politics. All the doctrines which ascribe absolute goodness to

particular forms of government, particular social arrangements, and even

to particular modes of education, without reference to the state of

civilization and the various distinguishing characters of the society

for which they are intended, are open to the same objection--that of

assuming one class of influencing circumstances to be the paramount

rulers of phenomena which depend in an equal or greater degree on many

others. But on these considerations it is the less necessary that we

should now dwell, as they will occupy our attention more largely in the

concluding Book.

§ 6. The last of the modes of erroneous generalization to which I shall

advert, is that to which we may give the name of False Analogies. This

Fallacy stands distinguished from those already treated of by the

peculiarity, that it does not even simulate a complete and conclusive

induction, but consists in the misapplication of an argument which is at

best only admissible as an inconclusive presumption, where real proof is

unattainable.

An argument from analogy, is an inference that what is true in a certain

case, is true in a case known to be somewhat similar, but not known to

be exactly parallel, that is, to be similar in all the material

circumstances. An object has the property B: another object is not known

to have that property, but resembles the first in a property A, not

known to be connected with B; and the conclusion to which the analogy

points, is that this object has the property B also. As, for example,

that the planets are inhabited, because the earth is so. The planets

resemble the earth in describing elliptical orbits round the sun, in

being attracted by it and by one another, in being nearly spherical,

revolving on their axes, &c.; but it is not known that any of these

properties, or all of them together, are the conditions on which the

possession of inhabitants is dependent, or are marks of those

conditions. Nevertheless, so long as we do not know what the conditions

are, they _may_ be connected by some law of nature with those common

properties; and to the extent of that possibility the planets are more

likely to be inhabited, than if they did not resemble the earth at all.

This non-assignable and generally small increase of probability, beyond

what would otherwise exist, is all the evidence which a conclusion can

derive from analogy. For if we have the slightest reason to suppose any

real connexion between the two properties A and B, the argument is no

longer one of analogy. If it had been ascertained (I purposely put an

absurd supposition) that there was a connexion by causation between the

fact of revolving on an axis and the existence of animated beings, or if

there were any reasonable ground for even suspecting such a connexion, a

probability would arise of the existence of inhabitants in the planets,

which might be of any degree of strength, up to a complete induction;

but we should then infer the fact from the ascertained or presumed law

of causation, and not from the analogy of the earth.

The name analogy, however, is sometimes employed by extension to denote

those arguments of an inductive character but not amounting to a real

induction, which are employed to strengthen the argument drawn from a

simple resemblance. Though A, the property common to the two cases,

cannot be shown to be the cause or effect of B, the analogical reasoner

will endeavour to show that there is some less close degree of connexion

between them; that A is one of a set of conditions from which, when all

united, B would result; or is an occasional effect of some cause which

has been known also to produce B; and the like. Any of which things, if

shown, would render the existence of B by so much more probable, than if

there had not been even that amount of known connexion between B and A.

Now an error or fallacy of analogy may occur in two ways. Sometimes it

consists in employing an argument of either of the above kinds with

correctness indeed, but overrating its probative force. This very common

aberration is sometimes supposed to be particularly incident to persons

distinguished for their imagination; but in reality it is the

characteristic intellectual vice of those whose imaginations are barren,

either from want of exercise, natural defect, or the narrowness of their

range of ideas. To such minds objects present themselves clothed in but

few properties; and as, therefore, few analogies between one object and

another occur to them, they almost invariably overrate the degree of

importance of those few: while one whose fancy takes a wider range,

perceives and remembers so many analogies tending to conflicting

conclusions, that he is much less likely to lay undue stress on any of

them. We always find that those are the greatest slaves to metaphorical

language, who have but one set of metaphors.

But this is only one of the modes of error in the employment of

arguments of analogy. There is another, more properly deserving the name

of fallacy; namely, when resemblance in one point is inferred from

resemblance in another point, though there is not only no evidence to

connect the two circumstances by way of causation, but the evidence

tends positively to disconnect them. This is properly the Fallacy of

False Analogies.

As a first instance, we may cite that favourite argument in defence of

absolute power, drawn from the analogy of paternal government in a

family, which government, however much in need of control, is not and

cannot be controlled by the children themselves, while they remain

children. Paternal government, says the argument, works well; therefore,

despotic government in a state will work well. I wave, as not pertinent

in this place, all that could be said in qualification of the alleged

excellence of paternal government. However this might be, the argument

from the family to the state would not the less proceed on a false

analogy; implying that the beneficial working of parental government

depends, in the family, on the only point which it has in common with

political despotism, namely, irresponsibility. Whereas it depends, when

real, not on that but on two other circumstances of the case, the

affection of the parent for the children, and the superiority of the

parent in wisdom and experience; neither of which properties can be

reckoned on, or are at all likely to exist, between a political despot

and his subjects; and when either of these circumstances fails even in

the family, and the influence of the irresponsibility is allowed to work

uncorrected, the result is anything but good government. This,

therefore, is a false analogy.

Another example is the not uncommon _dictum_, that bodies politic have

youth, maturity, old age, and death, like bodies natural: that after a

certain duration of prosperity, they tend spontaneously to decay. This

also is a false analogy, because the decay of the vital powers in an

animated body can be distinctly traced to the natural progress of those

very changes of structure which, in their earlier stages, constitute its

growth to maturity: while in the body politic the progress of those

changes cannot, generally speaking, have any effect but the still

further continuance of growth: it is the stoppage of that progress, and

the commencement of retrogression, that alone would constitute decay.

Bodies politic die, but it is of disease, or violent death: they have no

old age.

The following sentence from Hooker's _Ecclesiastical Polity_ is an

instance of a false analogy from physical bodies to what are called

bodies politic. "As there could be in natural bodies no motion of

anything unless there were some which moveth all things, and continueth

immovable: even so in politic societies there must be some unpunishable,

or else no man shall suffer punishment." There is a double fallacy here,

for not only the analogy, but the premise from which it is drawn, is

untenable. The notion that there must be something immovable which

moves all other things, is the old scholastic error of a _primum

mobile_.

The following instance I quote from Archbishop Whately's _Rhetoric_: "It

would be admitted that a great and permanent diminution in the quantity

of some useful commodity, such as corn, or coal, or iron, throughout the

world, would be a serious and lasting loss; and again, that if the

fields and coal mines yielded regularly double quantities, with the same

labour, we should be so much the richer; hence it might be inferred,

that if the quantity of gold and silver in the world were diminished

one-half, or were doubled, like results would follow; the utility of

these metals, for the purposes of coin, being very great. Now there are

many points of resemblance and many of difference, between the precious

metals on the one hand, and corn, coal, &c., on the other; but the

important circumstance to the supposed argument is, that the _utility_

of gold and silver (as coin, which is far the chief) _depends on their

value_, which is regulated by their scarcity; or rather, to speak

strictly, by the difficulty of obtaining them; whereas, if corn and coal

were ten times as abundant (_i.e._ more easily obtained), a bushel of

either would still be as useful as now. But if it were twice as easy to

procure gold as it is, a sovereign would be twice as large; if only half

as easy it would be of the size of a half-sovereign, and this (besides

the trifling circumstance of the cheapness or dearness of gold

ornaments) would be all the difference. The analogy, therefore, fails in

the point essential to the argument."

The same author notices, after Bishop Copleston, the case of False

Analogy which consists in inferring from the similarity in many respects

between the metropolis of a country and the heart of the animal body,

that the increased size of the metropolis is a disease.

Some of the false analogies on which systems of physics were confidently

grounded in the time of the Greek philosophers, are such as we now call

fanciful, not that the resemblances are not often real, but that it is

long since any one has been inclined to draw from them the inferences

which were then drawn. Such, for instance, are the curious speculations

of the Pythagoreans on the subject of numbers. Finding that the

distances of the planets bore or seemed to bear to one another a

proportion not varying much from that of the divisions of the monochord,

they inferred from it the existence of an inaudible music, that of the

spheres: as if the music of a harp had depended solely on the numerical

proportions, and not on the material, nor even on the existence of any

material, any strings at all. It has been similarly imagined that

certain combinations of numbers, which were found to prevail in some

natural phenomena, must run through the whole of nature: as that there

must be four elements, because there are four possible combinations of

hot and cold, wet and dry; that there must be seven planets, because

there were seven metals, and even because there were seven days of the

week. Kepler himself thought that there could be only six planets

because there were only five regular solids. With these we may class the

reasonings, so common in the speculations of the ancients, founded on a

supposed _perfection_ in nature: meaning by nature the customary order

of events as they take place of themselves without human interference.

This also is a rude guess at an analogy supposed to pervade all

phenomena, however dissimilar. Since what was thought to be perfection

appeared to obtain in some phenomena, it was inferred (in opposition to

the plainest evidence) to obtain in all. "We always suppose that which

is better to take place in nature, if it be possible," says Aristotle:

and the vaguest and most heterogeneous qualities being confounded

together under the notion of being _better_, there was no limit to the

wildness of the inferences. Thus, because the heavenly bodies were

"perfect," they must move in circles and uniformly. For "they" (the

Pythagoreans) "would not allow," says Geminus,[30] "of any such disorder

among divine and eternal things, as that they should sometimes move

quicker and sometimes slower, and sometimes stand still; for no one

would tolerate such anomaly in the movements even of a man, who was

decent and orderly. The occasions of life, however, are often reasons

for men going quicker or slower; but in the incorruptible nature of the

stars, it is not possible that any cause can be alleged of quickness or

slowness." It is seeking an argument of analogy very far, to suppose

that the stars must observe the rules of decorum in gait and carriage,

prescribed for themselves by the long-bearded philosophers satirized by

Lucian.

As late as the Copernican controversy it was urged as an argument in

favour of the true theory of the solar system, that it placed the fire,

the noblest element, in the centre of the universe. This was a remnant

of the notion that the order of nature must be perfect, and that

perfection consisted in conformity to rules of precedency in dignity,

either real or conventional. Again, reverting to numbers: certain

numbers were _perfect_, therefore those numbers must obtain in the great

phenomena of nature. Six was a perfect number, that is, equal to the sum

of all its factors; an additional reason why there must be exactly six

planets. The Pythagoreans, on the other hand, attributed perfection to

the number ten; but agreed in thinking that the perfect number must be

somehow realized in the heavens; and knowing only of nine heavenly

bodies, to make up the enumeration, they asserted "that there was an

_antichthon_ or counter-earth, on the other side of the sun, invisible

to us."[31] Even Huygens was persuaded that when the number of the

heavenly bodies had reached twelve, it could not admit of any further

increase. Creative power could not go beyond that sacred number.

Some curious instances of false analogy are to be found in the arguments

of the Stoics to prove the equality of all crimes, and the equal

wretchedness of all who had not realized their idea of perfect virtue.

Cicero, towards the end of his Fourth Book _De Finibus_, states some of

these as follows. "Ut, inquit, in fidibus plurimis, si nulla earum ita

contenta numeris sit, ut concentum servare possit, omnes æque incontentæ

sunt; sic peccata, quia discrepant, æque discrepant; paria sunt igitur."

To which Cicero himself aptly answers, "æque contingit omnibus fidibus,

ut incontentæ sint; illud non continuo, ut æque incontentæ." The Stoic

resumes: "Ut enim, inquit, gubernator æque peccat, si palcarum navem

evertit, et si auri; item æque peccat qui parentem, et qui servum,

injuriâ verberat;" assuming, that because the magnitude of the interest

at stake makes no difference in the mere defect of skill, it can make

none in the moral defect: a false analogy. Again, "Quis ignorat, si

plures ex alto emergere velint, propius fore eos quidem ad respirandum,

qui ad summam jam aquam appropinquant, sed nihilo magis respirare posse,

quam eos, qui sunt in profundo? Nihil ergo adjuvat procedere, et

progredi in virtute, quominus miserrimus sit, antequam ad eam

pervenerit, quoniam in aquâ nihil adjuvat: et quoniam catuli, qui jam

despecturi sunt, cæci æque, et ii qui modo nati; Platonem quoque necesse

est, quoniam nondum videbat sapientiam, æque cæcum animo, ac Phalarim

fuisse." Cicero, in his own person, combats these false analogies by

other analogies tending to an opposite conclusion. "Ista similia non

sunt, Cato.... Illa sunt similia; hebes acies est cuipiam oculorum:

corpore alius languescit: hi curatione adhibitâ levantur in dies: alter

valet plus quotidie: alter videt. Hi similes sunt omnibus, qui virtuti

student; levantur vitiis, levantur erroribus."

§ 7. In these and all other arguments drawn from remote analogies, and

from metaphors, which are cases of analogy, it is apparent (especially

when we consider the extreme facility of raising up contrary analogies

and conflicting metaphors) that so far from the metaphor or analogy

proving anything, the applicability of the metaphor is the very thing to

be made out. It has to be shown that in the two cases asserted to be

analogous, the same law is really operating; that between the known

resemblance and the inferred one there is some connexion by means of

causation. Cicero and Cato might have bandied opposite analogies for

ever; it rested with each of them to prove by just induction, or at

least to render probable, that the case resembled the one set of

analogous cases and not the other, in the circumstances on which the

disputed question really hinged. Metaphors, for the most part,

therefore, assume the proposition which they are brought to prove:

their use is, to aid the apprehension of it; to make clearly and vividly

comprehended what it is that the person who employs the metaphor is

proposing to make out; and sometimes also, by what media he proposes to

do so. For an apt metaphor, though it cannot prove, often suggests the

proof.

For instance, when D'Alembert (I believe) remarked that in certain

governments, only two creatures find their way to the highest places,

the eagle and the serpent; the metaphor not only conveys with great

vividness the assertion intended, but contributes towards substantiating

it, by suggesting, in a lively manner, the means by which the two

opposite characters thus typified effect their rise. When it is said

that a certain person misunderstands another because the lesser of two

objects cannot comprehend the greater, the application of what is true

in the literal sense of the word _comprehend_, to its metaphorical

sense, points to the fact which is the ground and justification of the

assertion, viz. that one mind cannot thoroughly understand another

unless it can contain it in itself, that is, unless it possesses all

that is contained in the other. When it is urged as an argument for

education, that if the soil is left uncultivated, weeds will spring up,

the metaphor, though no proof, but a statement of the thing to be

proved, states it in terms which, by suggesting a parallel case, put the

mind upon the track of the real proof. For, the reason why weeds grow in

an uncultivated soil, is that the seeds of worthless products exist

everywhere, and can germinate and grow in almost all circumstances,

while the reverse is the case with those which are valuable; and this

being equally true of mental products, this mode of conveying an

argument, independently of its rhetorical advantages, has a logical

value; since it not only suggests the grounds of the conclusion, but

points to another case in which those grounds have been found, or at

least deemed to be, sufficient.

On the other hand, when Bacon, who is equally conspicuous in the use and

abuse of figurative illustration, says that the stream of time has

brought down to us only the least valuable part of the writings of the

ancients, as a river carries froth and straws floating on its surface,

while more weighty objects sink to the bottom; this, even if the

assertion illustrated by it were true, would be no good illustration,

there being no parity of cause. The levity by which substances float on

a stream, and the levity which is synonymous with worthlessness, have

nothing in common except the name; and (to show how little value there

is in the metaphor) we need only change the word into _buoyancy_, to

turn the semblance of argument involved in Bacon's illustration against

himself.

A metaphor, then, is not to be considered as an argument, but as an

assertion that an argument exists; that a parity subsists between the

case from which the metaphor is drawn and that to which it is applied.

This parity may exist though the two cases be apparently very remote

from one another; the only resemblance existing between them may be a

resemblance of relations, an analogy in Ferguson's and Archbishop

Whately's sense: as in the preceding instance, in which an illustration

from agriculture was applied to mental cultivation.

§ 8. To terminate the subject of Fallacies of Generalization, it remains

to be said, that the most fertile source of them is bad classification:

bringing together in one group, and under one name, things which have no

common properties, or none but such as are too unimportant to allow

general propositions of any considerable value to be made respecting the

class. The misleading effect is greatest, when a word which in common

use expresses some definite fact, is extended by slight links of

connexion to cases in which that fact does not exist, but some other or

others, only slightly resembling it. Thus Bacon,[32] in speaking of the

_Idola_ or Fallacies arising from notions _temere et inæqualiter à rebus

abstractæ_, exemplifies them by the notion of Humidum or Wet, so

familiar in the physics of antiquity and of the middle ages. "Invenietur

verbum istud, Humidum, nihil aliud quam nota confusa diversarum

actionum, quæ nullam constantiam aut reductionem patiuntur. Significat

enim, et quod circa aliud corpus facile se circumfundit; et quod in se

est indeterminabile, nec consistere potest; et quod facile cedit

undique; et quod facile se dividit et dispergit; et quod facile se unit

et colligit; et quod facile fluit, et in motu ponitur; et quod alteri

corpori facile adhæret, idque madefacit; et quod facile reducitur in

liquidum, sive colliquatur, cum antea consisteret. Itaque quum ad hujus

nominis prædicationem et impositionem ventum sit; si alia accipias,

flamma humida est; si alia accipias, aer humidus non est; si alia,

pulvis minutus humidus est; si alia, vitrum humidum est: ut facile

appareat, istam notionem ex aquâ tantum, et communibus et vulgaribus

liquoribus, absque ullâ debitâ verificatione, temere abstractam esse."

Bacon himself is not exempt from a similar accusation when inquiring

into the nature of heat: where he occasionally proceeds like one who

seeking for the cause of hardness, after examining that quality in iron,

flint, and diamond, should expect to find that it is something which can

be traced also in hard water, a hard knot, and a hard heart.

The word [Greek: kinêsis] in the Greek philosophy, and the words

Generation and Corruption both then and long afterwards, denoted such a

multitude of heterogeneous phenomena, that any attempt at philosophizing

in which those words were used was almost as necessarily abortive as if

the word _hard_ had been taken to denote a class including all the

things mentioned above. [Greek: Kinêsis], for instance, which properly

signified motion, was taken to denote not only all motion but even all

change: [Greek: alloiôsis] being recognised as one of the modes of

[Greek: kinêsis]. The effect was, to connect with every form of [Greek:

alloiôsis] or change, ideas drawn from motion in the proper and literal

sense, and which had no real connexion with any other kind of [Greek:

kinêsis] than that. Aristotle and Plato laboured under a continual

embarrassment from this misuse of terms. But if we proceed further in

this direction we shall encroach upon the Fallacy of Ambiguity, which

belongs to a different class, the last in order of our classification,

Fallacies of Confusion.

CHAPTER VI.

FALLACIES OF RATIOCINATION.

§ 1. We have now, in our progress through the classes of Fallacies,

arrived at those to which, in the common books of logic, the appellation

is in general exclusively appropriated; those which have their seat in

the ratiocinative or deductive part of the investigation of truth. On

these fallacies it is the less necessary for us to insist at any length,

as they have been most satisfactorily treated in a work familiar to

almost all, in this country at least, who feel any interest in these

speculations, Archbishop Whately's _Logic_. Against the more obvious

forms of this class of fallacies, the rules of the syllogism are a

complete protection. Not (as we have so often said) that the

ratiocination cannot be good unless it be in the form of a syllogism;

but that, by showing it in that form, we are sure to discover if it be

bad, or at least if it contain any fallacy of this class.

§ 2. Among Fallacies of Ratiocination, we ought perhaps to include the

errors committed in processes which have the appearance only, not the

reality, of an inference from premises; the fallacies connected with the

conversion and æquipollency of propositions. I believe errors of this

description to be far more frequently committed than is generally

supposed, or than their extreme obviousness might seem to admit of. For

example, the simple conversion of an universal affirmative proposition,

All A are B, therefore all B are A, I take to be a very common form of

error: though committed, like many other fallacies, oftener in the

silence of thought than in express words, for it can scarcely be clearly

enunciated without being detected. And so with another form of fallacy,

not substantially different from the preceding: the erroneous

conversion of an hypothetical proposition. The proper converse of an

hypothetical proposition is this: If the consequent be false, the

antecedent is false; but this, If the consequent be true, the antecedent

is true, by no means holds good, but is an error corresponding to the

simple conversion of an universal affirmative. Yet hardly anything is

more common than for people, in their private thoughts, to draw this

inference. As when the conclusion is accepted, which it so often is, for

proof of the premises. That the premises cannot be true if the

conclusion is false, is the unexceptionable foundation of the legitimate

mode of reasoning called a _reductio ad absurdum_. But people

continually think and express themselves, as if they also believed that

the premises cannot be false if the conclusion is true. The truth, or

supposed truth, of the inferences which follow from a doctrine, often

enables it to find acceptance in spite of gross absurdities in it. How

many philosophical systems which had scarcely any intrinsic

recommendation, have been received by thoughtful men because they were

supposed to lend additional support to religion, morality, some

favourite view of politics, or some other cherished persuasion: not

merely because their wishes were thereby enlisted on its side, but

because its leading to what they deemed sound conclusions appeared to

them a strong presumption in favour of its truth: though the

presumption, when viewed in its true light, amounted only to the absence

of that particular evidence of falsehood, which would have resulted from

its leading by correct inference to something already known to be false.

Again, the very frequent error in conduct, of mistaking reverse of wrong

for right, is the practical form of a logical error with respect to the

Opposition of Propositions. It is committed for want of the habit of

distinguishing the _contrary_ of a proposition from the _contradictory_

of it, and of attending to the logical canon, that contrary

propositions, though they cannot both be true, may both be false. If the

error were to express itself in words, it would run distinctly counter

to this canon. It generally, however, does not so express itself, and

to compel it to do so is the most effectual method of detecting and

exposing it.

§ 3. Among Fallacies of Ratiocination are to be ranked in the first

place, all the cases of vicious syllogism laid down in the books. These

generally resolve themselves into having more than three terms to the

syllogism, either avowedly, or in the covert mode of an undistributed

middleterm, or an _illicit process_ of one of the two extremes. It is

not, indeed, very easy fully to convict an argument of falling under any

one of these vicious cases in particular; for the reason already more

than once referred to, that the premises are seldom formally set out: if

they were, the fallacy would impose upon nobody; and while they are not,

it is almost always to a certain degree optional in what manner the

suppressed link shall be filled up. The rules of the syllogism are rules

for compelling a person to be aware of the whole of what he must

undertake to defend if he persists in maintaining his conclusion. He has

it almost always in his power to make his syllogism good by introducing

a false premise; and hence it is scarcely ever possible decidedly to

affirm that any argument involves a bad syllogism: but this detracts

nothing from the value of the syllogistic rules, since it is by them

that a reasoner is compelled distinctly to make his election what

premises he is prepared to maintain. The election made, there is

generally so little difficulty in seeing whether the conclusion follows

from the premises set out, that we might without much logical

impropriety have merged this fourth class of fallacies in the fifth, or

Fallacies of Confusion.

§ 4. Perhaps, however, the commonest, and certainly the most dangerous

fallacies of this class, are those which do not lie in a single

syllogism, but slip in between one syllogism and another in a chain of

argument, and are committed by _changing the premises_. A proposition is

proved, or an acknowledged truth laid down, in the first part of an

argumentation, and in the second a further argument is founded not on

the same proposition, but on some other, resembling it sufficiently to

be mistaken for it. Instances of this fallacy will be found in almost

all the argumentative discourses of unprecise thinkers; and we need only

here advert to one of the obscurer forms of it, recognised by the

schoolmen as the fallacy _à dicto secundum quid ad dictum simpliciter_.

This is committed when, in the premises, a proposition is asserted with

a qualification, and the qualification lost sight of in the conclusion;

or oftener, when a limitation or condition, though not asserted, is

necessary to the truth of the proposition, but is forgotten when that

proposition comes to be employed as a premise. Many of the bad arguments

in vogue belong to this class of error. The premise is some admitted

truth, some common maxim, the reasons or evidence for which have been

forgotten, or are not thought of at the time, but if they had been

thought of would have shown the necessity of so limiting the premise

that it would no longer have supported the conclusion drawn from it.

Of this nature is the fallacy in what is called, by Adam Smith and

others, the Mercantile Theory in Political Economy. That theory sets out

from the common maxim, that whatever brings in money enriches; or that

every one is rich in proportion to the quantity of money he obtains.

From this it is concluded that the value of any branch of trade, or of

the trade of the country altogether, consists in the balance of money it

brings in; that any trade which carries more money out of the country

than it draws into it is a losing trade; that therefore money should be

attracted into the country and kept there, by prohibitions and bounties:

and a train of similar corollaries. All for want of reflecting that if

the riches of an individual are in proportion to the quantity of money

he can command, it is because that is the measure of his power of

purchasing money's worth; and is therefore subject to the proviso that

he is not debarred from employing his money in such purchases. The

premise, therefore, is only true _secundum quid_; but the theory assumes

it to be true absolutely, and infers that increase of money is increase

of riches, even when produced by means subversive of the condition under

which alone money can be riches.

A second instance is, the argument by which it used to be contended,

before the commutation of tithe, that tithes fell on the landlord, and

were a deduction from rent; because the rent of tithe-free land was

always higher than that of land of the same quality, and the same

advantages of situation, subject to tithe. Whether it be true or not

that a tithe falls on rent, a treatise on Logic is not the place to

examine; but it is certain that this is no proof of it. Whether the

proposition be true or false, tithe-free land must, by the necessity of

the case, pay a higher rent. For if tithes do not fall on rent, it must

be because they fall on the consumer; because they raise the price of

agricultural produce. But if the produce be raised in price, the farmer

of tithe-free as well as the farmer of tithed land gets the benefit. To

the latter the rise is but a compensation for the tithe he pays; to the

first, who pays none, it is clear gain, and therefore enables him, and

if there be freedom of competition forces him, to pay so much more rent

to his landlord. The question remains, to what class of fallacies this

belongs. The premise is, that the owner of tithed land receives less

rent than the owner of tithe-free land; the conclusion is, that

therefore he receives less than he himself would receive if tithe were

abolished. But the premise is only true conditionally; the owner of

tithed land receives less than what the owner of tithe-free land is

enabled to receive _when other lands are tithed_; while the conclusion

is applied to a state of circumstances in which that condition fails,

and in which, by consequence, the premise would not be true. The

fallacy, therefore, is _à dicto secundum quid ad dictum simpliciter_.

A third example is the opposition sometimes made to legitimate

interferences of government in the economical affairs of society,

grounded on a misapplication of the maxim, that an individual is a

better judge than the government, of what is for his own pecuniary

interest. This objection was urged to Mr. Wakefield's principle of

colonization; the concentration of the settlers, by fixing such a price

on unoccupied land as may preserve the most desirable proportion between

the quantity of land in culture, and the labouring population. Against

this it was argued, that if individuals found it for their advantage to

occupy extensive tracts of land, they, being better judges of their own

interest than the legislature (which can only proceed on general rules)

ought not to be restrained from doing so. But in this argument it was

forgotten that the fact of a person's taking a large tract of land is

evidence only that it is his interest to take as much as other people,

but not that it might not be for his interest to content himself with

less, if he could be assured that other people would do so too; an

assurance which nothing but a government regulation can give. If all

other people took much, and he only a little, he would reap none of the

advantages derived from the concentration of the population and the

consequent possibility of procuring labour for hire, but would have

placed himself, without equivalent, in a situation of voluntary

inferiority. The proposition, therefore, that the quantity of land which

people will take when left to themselves is that which is most for their

interest to take, is true only _secundum quid_: it is only their

interest while they have no guarantee for the conduct of one another.

But the arrangement disregards the limitation, and takes the proposition

for true _simpliciter_.

One of the conditions oftenest dropped, when what would otherwise be a

true proposition is employed as a premise for proving others, is the

condition of _time_. It is a principle of political economy that prices,

profits, wages, &c. "always find their level;" but this is often

interpreted as if it meant that they are always, or generally, _at_

their level; while the truth is, as Coleridge epigrammatically expresses

it, that they are always _finding_ their level, "which might be taken as

a paraphrase or ironical definition of a storm."

Under the same head of fallacy (_à dicto secundum quid ad dictum

simpliciter_) might be placed all the errors which are vulgarly called

misapplications of abstract truths: that is, where a principle, true (as

the common expression is) _in the abstract_, that is, all modifying

causes being supposed absent, is reasoned on as if it were true

absolutely, and no modifying circumstance could ever by possibility

exist. This very common form of error it is not requisite that we

should exemplify here, as it will be particularly treated of hereafter

in its application to the subjects on which it is most frequent and most

fatal, those of politics and society.[33]

CHAPTER VII.

FALLACIES OF CONFUSION.

§ 1. Under this fifth and last class it is convenient to arrange all

those fallacies, in which the source of error is not so much a false

estimate of the probative force of known evidence, as an indistinct,

indefinite, and fluctuating conception of what the evidence is.