The elements of inductive logic: Designed Mainly for the Use of Students in the Universities

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INDUCTIVE LOGIC

FOWLER

ZanOon
MACMILLAN AND CO.

PUBLISHERS TO THE UNIVERSITY OF

€lva;tr^an ^r«ss S^nes

THE ELEMENTS

OF

INDUCTIVE LOGIC

DESIGNED MAINLY
FOR THE USE OF STUDENTS IN THE UNIVERSITIES

BY

THOMAS FOWLER, M.A.

Fellow and Tutor of Lincoln College, Oxford

©xforlr

AT THE CLARENDON PRESS
MDCCCLXX

\_All rights reserved'\

PREFACE.

THE object of the following work is to serve as an
introduction to that branch of scientific method which
is known as Induction. It is designed mainly for the
use of those who have not time or opportunity to con-
sult larger works, or who require some preliminary
knowledge before they can profitably enter upon the
study of them.

To the works of Mr. Mill, Dr. Whewell, and Sir John
Herschel, the Author must, once for all, express his obH-
gations. * He has, however,' if he may be allowed to
repeat the language already employed in the Preface
to his Manual of Deductive Logic, * endeavoiured, on all
disputed points, to reason out his own conclusions, feel-
ing assured that no manual, however elementary, can be
of real service to the student, imless it express what may
be called the " reasoned opinions " of its author.'

The analysis of Induction presents far more difficulties
than that of Deduction, and requires to be illustrated

VI PREFACE,

by far more numerous and more intricate examples.
But, on the other hand, it is more interesting both to
the teacher and to the student; and, being a compara-
tively recent study, is less hampered by conventionalities
of treatment. Since the time of Bacon, it has always,
with ""more or less of success, claimed a place in liberal
education, and many, to whom the technical terms and
subtle distinctions of the older logic are justly repulsive,
have experienced a peculiar delight in attempting to
discover and test the grounds on which the results of
modem science mainly rest.

The study of Deductive Logic can be of little service
unless it be supplemented by, at least, some knowledge
of the principles of Induction, which supplies its pre-
misses. Many of the objections directed against the
study of Logic are due to the narrow conceptions which
are entertained of its province, and might be easily met
by showing that the study, when we include both its
parts, has a much wider range than is popularly assigned
to it.

Though the present work is mainly intended for stu-
dents in the Universities, it is hoped that it will be found
to present some interest* for the general reader, and that
it may be useful to students of medicine and the physical

PREFACE, Vii

sciences, as well as to some of the more advanced scholars
in our Public Schools.

The number of scientific examples adduced throughout
the work renders it necessary, perhaps, that the Author
should state emphatically that the work is intended as an
introduction, not to science, but to scientific method. Its
object is not to give a r^sum^ of the sciences, physical
or social, a task to which the Author would be wholly
incompetent, but to show the grounds on which our
scientific knowledge rests, the methods by which it has
been built up, and the defects from which it must be
free. Notwithstanding its frequent incursions into the
domain of science, the purport of the work must be
regarded as strictly logical.

The examples have, as a rule, been selected from the
physical rather than the social sciences, as being usually
less open to dispute, and lying within a smaller compass.
Wherever it has been possible, they have been given in
the exact words of the author from whom they are taken.

Some of the more complicated cases of inductive rea-
soning, such as those which have to deal with Progres-
sive Causes or Intermixture of Effects, have, if alluded
to at all, been only briefly noticed. Any detailed exami-
nation of these more intricate questions seeovt^ \xi \sr.

Vlll PREFACE.

without the scope of the treatise. The student who has
leisure to pursue the subject will find ample information
in the pages of Mr. Mill's Logic,

It only remains for the Author to express his grateful
acknowledgments to those who have assisted him in the
execution of the work. These are, in the first place, due
to Dr. Liddell, Dean of Christ Church, through whose
hands the sheets have passed, and who, in addition to
revising the proofs, has, from time to time, offered many
most valuable suggestions. They are due also, in no
small degree, to Sir John Herschel and Professor Bar-
tholomew Price, who most kindly undertook to revise
the scientific examples; to Professors Rolleston and
Clifton, who have frequently allowed the Author to con-
sult them on questions connected with the subjects of
their respective chairs, and to the Rev. G. W. Kitchin,
the Organising Secretary of the Clarendon Press Series.
The Author must, however, be regarded as alone re-
sponsible for any errors which may occur either in the
theoretical portion of the work or in the examples.

Lincoln Collbob,
Oct, 30, 1869.

CONTENTS.

CHAP. PAGE

I. The Nature of Inductire Inference 3

II. Processes subsidiary to Induction ...... 33

§ I . Observation and Experiment . . .33

•- § 2. Classification, Nomenclature, and Terminology . 45

(l) Classification 45

(3) Nomenclature 81

^ (3) Terminology 84

§ 3. Hypotbens 89

III. The Inductive Methods 116

Method of Agreement lao

Method of Difference . » 138

Double Method of Agreement . . . . .150

Method of Residues 163

Method of Concomitant Variations . . . • 1 73

rV. Imperfect Inductions 205

Inductio per Simplicem Enumerationem . . . 205

Argument from Analogy 209

Imperfect applications of the Inductive Methods . .220

X CONTENTS.

CHAP. PAGE

V. The Relation of Induction to Deduction, and Verification . 224

VI. The Fallacies incident to Induction 237

A. Fallacies incident to the subsidiary processes . . '237

I. Fallacy of Non-observation, consisting in neglect either

(i) of some of the instances . . . •237
or (2) of some of the circumstances attendant on a

given instance 250

n. Fallacy of Mal-observation 254

m. Errors incidental to the operations of Classification,

Nomenclature, Terminology, and Hypothesis . 259

B. Fallacies incident to the Inductive process itself, or Fallacies

of Generalisation 259

IV. Error originating in the employment of the Inductio
per Simplicem Enumerationem (including the illegiti-
mate use of the Argument from Authority) . .260
V. Errors common to the emplo3rment of the various In-
ductive Methods 274

(i) Mistaking a for the cause of b, when the

real cause is c 276

(2) Mistaking a for the sole cause, when a and

c are the joint causes, either as
(a) both contributing to the toted effect . 281
or (jS) being both essential to tiie production of

any effect whatever .... 285

(3) Mistaking joint effects for cause and effect . 290

CONTENTS, XI

PAGE

(4) Mistaking the remote cause for the proximate

cause, or the reverse 294

(5) Neglecting to take into account the mutual action

(mutuality) of cause and effect . . . 298

(6) Inversion of cause and effect . . . • 301
VI. False analogy (including the illegitimate use of the

Argument from Antiquity, and of the Argument
from Final Causes) 304

Index 331

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dvoXvrcKoiff Xeyofiev' ^ flip yap di iiraycDy^Sy ff de crvXkoyuTfi^.
*H fiev drf cTraycoy^ ^PX$ ^*""* ***^ ''O'' iKo^t^Xov, 6 dc avWoyia-fibs
€K Tap Ka$6Kov, Ela\p &pa ap\cLi i^ hv 6 avXXoyurfihs, ^v ovk
loTi (rvXXoyi(rfi6s' eiraycoy^ &pa,

Aristotle's Nicomacbean Etbtcs^ vi. 3 (3).

Quamvis ad scientiain quamlibet via unica pateat, qua nempe a
notionibus ad minus nota et a manifestis ad obscuriorum notitiam
progredimur, atque universalia nobis praecipu^ nota sint (ab univer-
salibus enim ad particularia ratiocinando oritur scientia), ipsa tamen
universalium in intellectu comprehensio a singulariuni in sensibus
nostris perceptione exsurgit.

Preface to Harvey's Treatise De Generatione Animalium.

ELEMENTS

OF

INDUCTIVE LOGIC.

B

*#* The notes appended to the Chapters (as dis-
tinguished from the foot-notes) are designed to inform
the student of any divergences from the ordinary mode
of treatment, or to afford him information on disputed
questions which it appeared inconvenient to notice in
the text. They may be omitted on the first reading.

CHAPTER I.
On the Nature of Inductive Inference.

TWO bodies of unequal weight (say a guinea and
a feather) are placed at the same height under the ex-
hausted receiver of an air-pump. When released, they
are observed to reach the bottom of the vessel at the
same instant of time, or, in other words, to fall in equal
times. From this fact, it is inferred that a repetition of
the experiment either with these two bodies or with any
other bodies would be attended with the same result, and
that, if it were not for the resistance of the atmosphere
and other impeding circumstances, all bodies, whatever
their weight, would fall through equal vertical spaces in
equal times. Now, that these two bodies in this par-
ticular experiment fall to the bottom of the receiver in
equal times is merely a fact of observation, but that they
would do so if we repeated the experiment, or that the
next two bodies we selected, or any bodies, or all bodies,
would do so, is an inference, and is an inference of that
particular character which is called an Inductive Inference
or an Induction ^.

^ The student must throughout bear in mind the ambiguous use of
the words Induction, Inference, &c., as signifying both the rutdt and

B a

4 NATURE OF

What assumptions underlie this inference, and on what
grounds does it rest ?

My object in placing the two bodies under the receiver
was obviously to answer a question which I had pre-
viously addressed to myself: viz. whether, when subject
to the action of gravity^ only, they would fall in equal
or in unequal times. By exhausting the air in the re-
ceiver, I am able to tsolafe the phenomenon^ and thus, by
removing all circumstances affecting the bodies, except
the action of gravity, to watch the effect of this cause
operating alone. But in trying this experiment, in iso-
lating the phenomenon, and asking what will be the effect
of the action of gravity operating alone, I am evidently
assuming that the effect, whatever it may be, will be
entirely due to the cause or causes which are then and
there in action; in other words, I am assuming that
nothing can happen without a cause, that no change can
take place without being preceded or attended by circum-
stances which, if we were fully acquainted with them,
would fully account for that change. This assumption
(which may be called the Law of Universal Causation)
is universally admitted by mankind, or at least by the

the process by which the result is arrived at. See Deductive Logic,
Preface, and Part III. ch. i. note I.

^ When I employ the expression * action of gravity ' or ' force of
gravity/ I must not be understood as adopting any particular theory on
the nature of the phenomenon which we call * gravitation.' I use these
terms simply because they are short and recognised phrases for expressing
the fact that all terrestrial bodies, when left entirely free, fall in the
direction of the earth's centre.

INDUCTIVE INFERENCE. 5

reflecting portion of mankind, though the grounds on
which it is admitted have been variously stated; some
justifying it by an appeal to the continuous and uncon-
tradicted experience not only of the individual himself
but of the human race, others by an appeal to ' the neces-
sities of thought.

Thus far, however, we have only ascertained that the
fact of these two particular bodies, in this particular
instance, falling to the ground in equal times is due to
the action of gravity, unimpeded by any other circum-
stances. But why should I infer that they, if the experi-
ment were repeated, or any other two bodies, if exposed
to the same circumstances, would behave in the same
way ? It is not enough to feel assured that nothing can
happen without a cause, and that the only cause operating
in this particular instance is the action of gravity ; I must
also feel assured that the same cause will ' invariably be
followed by the same effect, or, to speak more accurately,
that the same cause or combination of causes, will, if
unimpeded by the action of any other cause or combina-
tion of causes, be invariably followed by the same effect
or combination of effects, or, to state the same proposi-
tion in somewhat different language, that, whenever the
same antecedents, and none others, are introduced, the
same consequents will invariably follow. This assiunp-

* The expression * will * is used for the sake of convenience. The
argument, however, is not simply from the present to the future, but
from cases within the range of our experience to all cases, past, present,
or future, without that range. See p. a 6, note 19.

6 NATURE OF

tion (or law) is, like the former, universally admitted by
ipankind, or the reflecting portion of mankind, though
the grounds on which it is admitted have been variously
stated, some, as in the case of the former law, referring it
to experience, others to certain necessities of thought
arising from the original constitution of the human mind.
This law may be called /he Law of the Uniformity of
Nature^,

The argument, then, in the case which we have selected
as our instance, may be represented as follows : —

I observe that these two bodies (though of un-
equal weight) reach the bottom of the receiver
at the same moment.
This fact must be due to some cause or com-
bination of causes (Law of Universal Causation).
The only cause operating in this instance is the
action of gravity.
.-. The fact that these two bodies reach the bottom of
the receiver at the same moment is due to the
action of gravity, operating alone.
But, whenever the same cause or combination of
causes is in operation, and that only, the same
eflfect will invariably follow (Law of Uniformity of
Nature).

* It is, perhaps, necessary thus early to warn the student that the
converse of the Law of the Uniformity of Nature does not hold true.
Though the same cause, that is, the same antecedent or combination of
antecedents, is never followed by different effects, the same effect may
be due to different causes. We can, thus, always argue from the cause
to the effect, but we cannot always argue from the effect to the cause.

INDUCTIVE INFERENCE, J

.'. Whenever these two bodies, or any other two or
more bodies (even though of unequal weight), are
subject to the action of gravity only, they will
reach the bottom of the receiver at the same
moment^ or, in other words, will fall in equal
times.
From the above example, and from what has already
been said in distinguishing Induction from Deduction in
the Manual of Deductive Logic ^ it will be seen that In-
duction may be defined as the legitimate inference of the
unknown from the known, that is, of propositions appli-
cable to cases hitherto unobserved and unexamined from
propositions which are known to be true of the cases
observed and examined. Thus, from the proposition
that a guinea and a feather, if placed under the exhausted
receiver of an air-pump, will fall in equal times, may be
inferred inductively the proposition that a shilling, a
penny, and a straw will, if exposed to the same circum-
stances, also fall in equal times. But, as we can only
draw this inference on grounds which are equally ap-
plicable to all bodies whatsoever, when exposed to the
same circumstances, and as we might make the same
assertion of any two or more bodies, and consequently of
all bodies, it will be seen that Induction is not only an
inference of the unknown from the known ; but, in virtue
of that fact, of the general from the particular. In every
inductive argument, in fact, it is implied that wherever or
whenever the same circiunstances are repeated, the same
effects will follow. Induction may, therefore, also be

8 NATURE OF

defined as the legitimate inference of the general from the
particular y or (in order to include those cases where
general propositions are themselves employed a3 the
starting-point of an inductive argument, of which
nimierous instances will occur as we proceed) of the more
general from the less general.

In trying the experiment which has furnished our
instance in this chapter, we have been attempting to
find an answer to the question, 'Do bodies, when
subject to the action of gravity only, fall through
equal vertical spaces in equal or in unequal times?*
The experiment may be regarded as an attempt to
decide between two rival theories (or hypotheses^ as they
are usually called), one being that bodies fall quicker in
proportion to their weights, the other that the weight of
the body, when the resistance of the atmosphere is re-
moved, makes no difference to the time of falling. The
experiment is decisive in favour of the latter hypothesis,
which is thus entitled to rank as a valid induction. Our
inductions are often, as in this case, the result of an
attempt to decide between rival hypotheses, or a reply
to the question whether some particular hypothesis be
true or not, the hypothesis or hypotheses suggesting the
particular experiment to be tried. Sometimes, however,
we have no assistance of this kind, and we try experi-
ments simply * to see what will come of them.' Thus,
if a chemist discovers a new element, he will proceed to
try a variety of experiments in order to determine the

INDUCTIVE INFERENCE. 9

proportions in which it will combine with other elements,
as well as to discover the various properties of such
combinations. Supposing the experiments to have been
properly conducted, the inductions at which he arrives
will be perfectly valid, though he may have formed no
previous theories as to the results of his researches. Oc-
casionally, too, an induction will not be the result of any
definite course of investigation, but will be obtruded on
our notice, as in the following instance, adduced by Sir
John Herschel, to show that * after much labour in vain,
and groping in the dark, accident or casual observation
will present a case which strikes us at once with a full
insight into a subject.' * The laws of crystallography
were obscure, and its causes still more so, till Hauy for-
tunately dropped a beautiful crystal of calcareous spar
on a stone pavement, and broke it. In piecing together
the fragments, he observed their facets not to correspond
with those of the crystal in its entire state, but to belong

to another form ; and following out the hint

thus casually obtruded on his notice, he discovered the
beautiful laws of the cleavage, and the primitive forms
of minerals^.'

Thus, we perceive that our inductions are sometimes
preceded by hypotheses, at other times not. In most
cases, probably, we have formed some theory (or hypo-
thesis) as to the character of a phenomenon before we
enter upon, or, at least, before we complete, its inves-
tigation. Such theories (or hypotheses) are often of the

' Herschel's Discourse on the Study of Natural Philosophy , § 191.

lO NATURE OF

Utmost service in directing the course which our experi-
ments and observations shall take. Frequently, also, it is
impossible to perform any experiment, or to institute any
series of observations, which shall be decisive of the
question before us. In this case, unless we altogether
suspend our judgment, we must rest content with an
unproved theory, and it becomes of prime importance to
determine to what conditions such a theory (or hypo-
thesis) must conform in order to entitle it to rank as a
probable or possible solution of our difficulties. A sub-
sequent section will be specially devoted to these ques-
tions, but meanwhile it seemed desirable at once to direct
the attention of the student to the distinction between
hypothesis and induction. He must bear in mind that,
though the formation of hypotheses is frequently an im-
portant step in the inductive process, a hypothesis must
be carefully distinguished from a valid induction. With-
out at present attempting any formal definition of a
hypothesis, it may be distinguished from an induction
(that is, a valid, complete, or perfect induction) as a mere
supposition or assumption from an ascertained truth.

*4.* The word 'cause' is commonly used in a very
vague and indefinite sense. Of the various antecedents
whose presence or absence is essential to the event,
it is usual to single out one as the Cause, and either to
overlook the others, or to speak of them as * conditions.'
Strictly speaking, however, the Cause consists in the pre-
sence of all those antecedents, the withdrawal of any of

INDUCTIVE INFERENCE. II

which, and in the absence of all those antecedents, the
introduction of any of which, might frustrate the event.
Thus, to take the homely instance of lighting a fire. The
application of the lighted match is what would ordinarily
be called the cause of the combustion. But there are
other conditions equally necessary, as, for instance,
amongst the positive conditions, the presence of fuel and
of atmospheric air, and, amongst the negative conditions,
the absence of such a quantity of moisture as would pre-
vent the fuel from igniting. In assigning the cause of a
phenomenon, it is seldom that the negative conditions are
mentioned. It is generally imderstood that we assign a
cause, subject to the qualification *no counteracting
cause intervening.' Amongst the positive conditions, we
usually select that which, being last introduced, completes
the assemblage of conditions, and stands in closest prox-
imity to the effect. Thus, in our example, the combus-
tion is said to be due to the application of the match,
and, when a man, who has previously been in a bad state
of health, is attacked by a fever, we speak of the fever as
the cause of his death. These, however, as observed by
Mr. Mill, are by no means invariable rules. * It must not
be supposed that in the emplojnnent of the term this or
any other rule is always adhered to. Nothing can better
show the absence of any scientific ground for the dis-
tinction between the cause of a phenomenon and its con-
ditions, than the capricious manner in which we select
from among the conditions that which we choose to
denominate the cause. However numerous the con-

12 NATURE OF

ditions may be, there is hardly any of them which may
not, according to the pmpose of our immediate dis-
com'se, obtain that nominal pre-eminence/ Thus, if
a plot of dry heath is ignited by a spark from a railway-
engine, we may, in conmion parlance, attribute the fire
either to the spark, or to the dryness of the heath, or to the
ill construction of the engine ; the first of these assigned
causes being the proximate event, the second one of the
other positive conditions, the last a negative condition.
What, when employing popular language, we dignify
with the name of Cause is that condition which happens
to be most prominent in our minds at the time. It is,
perhaps, superfluous to add that, when aiming at scien-
tific accuracy, we ought to enumerate all the conditions,
or, at least, all the positive conditions, on which a phe-
nomenon depends, unless we have a right to presume
that there is no likelihood of their being overlooked by
those whom we address ®.

In the science of Medicine, the cause which completes
the assemblage of conditions is often distinguished as the
exciting cause, the other causes being cdHHtdipre-disposing,
Thus, the peculiarities of constitution, age, sex, occupa-
tion, &c., which render a person more than ordinarily
liable to any particular disorder, would be called the pre-
disposing causes; the contagion (by which the body is
brought into ^contact with some specific poison), a sud-
den chill, bodily fatigue, mental depression, or any cir-

' The subject of this paragraph is treated with great ability in Mr.
MiU's Logic, Bk. III. ch. v. § 3.

INDUCTIVE INFERENCE. 13

cumstance, on the supervention of which the disease is
immediately consequent, would be called the exciting
cause''. The pre-disposing causes of Asiatic Cholera,
for instance, are enumerated in Dr. Guy's Edition of Dr.
Hooper's * Vade Mecum,' as * debility ; impaired health ;
intemperance ; impure air ; low and damp situations ; the
summer and autumn seasons : the exciting causes as con-
tagion; a peculiar poison diffused through the atmosphere.'
The importance of attending to this distinction in histori-
cal and political investigations is forcibly stated and illus-
trated by Sir G. C. Lewis, in his Methods of Observation
and Reasoning in Politics, vol. i. ch. ix. p. 333, &c.

Note I ^. — Mr. Mill {Logic, vol. ii. ch. iii.) maintains
that all inference (by which he means inductive inference)
is from particulars to particulars. Dr. Whewell, on the
other hand, holds that all inductive inference is from the
particular to the general. {Philosophy of Discovery,
ch. xxii. § 1-14.) Though I prefer Dr. Whewell's mode
of statement (which is that ordinarily employed) and have
adopted it in the text, I cannot recognise the importance
of the difference which he believes to exist between
himself and Mr. Mill. To say that what I find to be
true of this case will be true of the next which resembles

' See Dr. Watson's Lectures on Pbysic, Lecture VI.

^ The student, unless he have some previous acquaintance with the
subjects discussed in them, is recommended to omit these notes on the
first reading.

14 NATURE OF

it in certain assignable respects, \diatever that case may
be, or that what I found to be true of that case must
be true of this (the instance being taken indifFerently),
because this resembles that in certain assignable respects,
is virtually to say that it is true of any and every case
which presents these points of resemblance. What is
true of any case, taken indifferently, must be true • of all,
* The burnt child dreads the fire/ Why ? because it once
suffered pain, from burning its finger. Now, it appears
to me indifferent whether we represent the child as
having in its mind the proposition ' That object causes
pain,' or the proposition * That object will cause me pain
now, if I approach too near to it.' But, as the former
(the general) inference seems to be undoubtedly implied
in the latter (the particular), I prefer adhering to the
common, and, as I think, the more intelligible account of
induction. Mr. Mill is hardly consistent in his language.
He himself, in one place, speaks of Induction as * generali-
sation from experience,' and, in another, as ' the inference
of a more general from less general propositions.'

Though agreeing with Dr. Whewell in his main
position, I must express my entire dissent from the
distinction which, throughout this discussion, he attempts
to draw between our reasonings in the ordinary affairs
of life, and Induction as employed in scientific research.
However various may be the conditions of their applica-
tion, I cannot but regard the mental processes as iden-
tical, on whatever classes of objects they may be exercised.
We may meet with insurmountable difficulties in the

INDUCTIVE INFERENCE. 1 5

attempt to apply Induction to some obscure question
of Physiology, and we may employ it with ease and
success a hundred times a day in avoiding pain or se-
curing ease, but I believe the mental process to be
essentially the same in both cases.

JVo/e 2L — Since the time of Hume, the nature of our
conception of Cause has formed one of the principal
topics of philosophical controversy. Previously to his
time, it appears to have been taken for granted by the
great majority of modem philosophers of all schools* (if
we except those who, like Malebranche, believed God
to be the only efficient cause in the universe, and so-
called acts of causation to be only the occasions of the
Divine interference^^), that the idea of causation neces-
sarily implies the idea of power or necessary connection ;
necessary connection^ that is to say, between the cause and
efiect, or power in the cause to produce the effect. Even
Locke, who effected a revolution in modem philosophy,
left this idea of Power unassailed, though he attempted
to account for its formation. 'The mind,' says he^^,

• Dugald Stewart (in his Pbilosopby of the Human Mindj Notes
G and MM) has certainly succeeded in showing that Hume's views on
the nature of Cause were anticipated by casual remarks of several other
writers ; but it still remains true that Hirnie was the first philosopher
who definitely attacked the prevalent philosophical theory.

^® Still, even according to these philosophers, every act of causation
implied an act of power, only that the power was exerted not by the
so-called cause, but by the Deity himself. It will be noticed that I
speak only of modem philosophers. Into the difficult question of the
notions of causation entertained by ancient writers I do not enter.

^ Locke's Essay t vol. ii. ch. xxi. § i.

1 6 NATURE OF

' being every day informed, by the senses, of the
alteration of those simple ideas it observes in things
without; and taking notice how one comes to an end,
and ceases to be, and another begins to exist, which
was not before; reflecting also on what passes within
itself, and observing a constant change of its ideas,
sometimes by the impression of outward objects on the
senses, and sometimes by the determination of its own
choice; and concluding from what it has so constantly
observed to have been, that the like changes will for the
future be made, in the same things, by like agents, and
by the like ways, considers in one thing the possibility of
having any of its simple ideas changed, and in another
the possibility of making that change ; and so comes by
that idea which we call Power. Thus we say, fire has
a power to melt gold, i.e. to destroy the consistency of
its insensible parts, and consequently its hardness, and
make it fluid ; and gold has a power to be melted : that
the sun has a power to blanch wax, and wax a power to
be blanched by the sun, whereby the yellowness is de-
stroyed, and whiteness made to exist in its room. In
which, and the like cases, the power we consider, is in
reference to the change of perceivable ideas. For we
cannot observe any alteration to be made in, or operation
upon anything, but by the observable change of its
sensible ideas ; nor conceive any alteration to be made,
but by conceiving a change of some of its ideas.' He
then proceeds to include our idea of Power amongst
our Simple Ideas. Hume contested the validity of this

INDUCTIVE INFERENCE. 17

idea by an appeal to experience. Whence do we obtain
this notion of necessary connection between two events ?
Do we observe any such connection in the events which
take place in the external world, or in the relation between
volition and the motion of the organs of the body, or in
the act of the will by which it summons up, dwells on,
or dismisses ideas ? ' We have sought in vain for an
idea of power or necessary connection, in all the soiuces
from which we could suppose it to be derived. It ap-
pears, that, in single instances of the operation of bodies,
we never can, by our utmost scrutiny, discover anything but
one event following another ; without being able to com-
prehend any force or power, by which the cause operates,
or any connection between it and its supposed effect.
The same difficulty occurs in contemplating the opera-
tions of mind on body ; where we observe the motion of
the latter to follow upon t!ie volition of the former ; but
are not able to observe or conceive the tie, which binds
together the motion and volition, or the energy by which
the mind produces this effect. The authority of the will
over its own faculties and ideas is not a whit more com-
prehensible : so that, upon the whole, there appears not,
throughout all nature, any one instance of connection,
which is conceivable by us. All events seem entirely
loose and separate. One event follows another ; but we
never can observe any tie between them. They seem
conjoined, but never connected. And as we can have no
idea of anything, which never appeared to our outward
sense or inward sentiment, the necessary conclusion seems

l8 NATURE OF

to be, that we have no idea of connection or power at all,
and that these words are absolutely without any meaning,
when employed either in philosophical reasonings, or
common life^^/ Does Hume then deny th^/acf of causa-
tion] namely, that, when we have been accustomed to
observe one event invariably followed by another, we may
confidently expect, other circumstances remaining the
same, that it will continue to be followed by it in the
future, and that, if we perceive a change in any phe-
nomenon, we may be confident that some other event has
preceded that change? Certainly not. There is, in
Hume's writings, absolutely no foundation for the viru-
lence with which he is attacked by Reid*'. What he

^* Hume's Essays, Essay on the Idea of Necessary Causation.

*^ The following may serve as a specimen of Reid's diatribes against
Hume. * Of all the paradoxes this author has advanced, there is not
one more shocking to the human undtestanding than this, That things
may begin to exist without a cause. This would put an end to all
speculation, as well as to all the business of life. The employment
of speculative men, since the beginning of the world, has been to
investigate the causes of things. What pity is it, they never thought
of putting the previous question, Whether things have a cause or not ?
This question has at last been started ; and what is there so ridiculous
as not to be maintained by some philosopher?' — Active Powers^ Essay I.
ch. iv. Sir W. Hamilton and Dr. Mansel take a far juster view of Hume's
position. Even Sir W. Hamilton, however, in commenting on Reid's
statement, says, * This * (namely. That things may begin to exist without
a cause) * is not Hume's assertion ; but that, on the psychological doc-
trine generally admitted, we have no valid assurance that they may not.*
The latter is, certainly, not Hume's assertion. It is true that he bases
the notion of causation on experience, but then he regards experience
as the sole source of all our knowledge. Sir William Hamilton's note
requires only to be compared with the following passage from the

INDUCTIVE INFERENCE. 19

called in question was not the invariableness of the fact
of causation, but the grounds of the prevalent notions
attached to the word Cause. Whether his speculations
on this subject be well or ill-founded, he certainly did
not deny the correctness of the principles on which men
act in ordinary life or which guide them in scientific
research.

There is another objection to the statements contained
in Hume's Essay which is better founded than the fore-
jB^oing. If the term ' cause ' be .convertible with the term
* invariable antecedent,' it has been justly objected by
Reid^* that we might speak of day as the cause of night,
and of night as the cause of day. That there are loose
expressions in the Essay, in which the cause seems to
be confounded with the invariable antecedent or the
sum of the invariable antecedents, cannot be denied.
Such is the following : * Suitably to this experience,
therefore, we may define a cause to be an object,
followed by another, and when all the objects, similar
to the first, are followed by objects similar to the second.'
But then the sentence proceeds : ' Or, in other words,
where y if the first object had not heen^ the second never had
existed^ Now this alternative definition is not open to
Reid's objection, and a simpler and less questionable

Essay : * But when one particular species of event has always, in all
instances, been conjo ned with another, we make no longer any scruple
of foretelling one upon the appearance of the other, and of employing
that reasoning, which can alone assure us of any matter of fact or
existence.'
" Active Powers^ Essay IV. ch. iii.

C 2

20 NATURE OF

definition of cause has probably never been proposed.
Slightly modified, it would run thus : ' Cause and Effect
are two events, or sets of events, which are so related,
that, if the first had not been, the second had never existed/
The first author of eminence who adopted Hume's
view of the nature of Cause was Dr. Thomas Brown ;
singularly enough, however, so far from assuming with
Hume that its origin was to be found in experience, he
regarded it as instinctive. The notion of 'Power' he
supposed was simply a gratuitous hypothesis, needlessly
interpolated between the antecedent, which we call the
Cause, and the consequent, which we call the Effect.
* We are eager to supply, by a littie guess-work of
fancy, the parts unobserved, and suppose deficiencies
in our observation where there may truly have been
none ; till at length, by this habitual process, every
phenomenon becomes, to our imagination, the sign of
something intermediate as its cause, the discovery of
which is to be an explanation of the phenomenon. The
mere succession of one event to another appears, to us,
very difiicult to be conceived, because it wants that inter-
vening something, which we have learned to consider as
a cause : but there seems to be no longer any mystery,
if we can only suppose something intervening between
them, and can thus succeed in doubling the diflficulty,
which we flatter ourselves with having removed; since,
by the insertion of another link, we must now have two
sequences of events instead of one simple sequence^*.'

^^ Brown's Lectures on the Pbilosopby of the Human Mind, Lecture
IX. Cf. Lecture IL

INDUCTIVE INFERENCE. 21

Hume's position is also accepted by James Mill in his
Analysts of the Phenomena of the Human Mind, and by
John Stuart Mill in his System of Logic.

Hume's antagonists have generally (with Kant) com-
bated his arguments by denying the assumption on which
they are based, namely, that the origin of our conception
of Cause is to be sought in experience. Hume, it will be
recollected, challenges those who maintain the hypothesis
of * power ' or * necessary connection ' to show how we
can have become acquainted with it. Does it come from
our experience of the external world, or from our experi-
ence of the control of our will over our own acts or our own
thoughts ? The answer of the Kantian School would be
that it does not come from experience at all, that it is one
of those fundamental conceptions which are native to the
human mind, not given by experience but evoked by it.
Others, like Reid and Stewart, to whom we may add
M. Maine de Biran, surrender the notion of power as
applied to causation in the external world, while they
maintain it as applied to our own actions, which are the
results of will. We are conscious, they say, of power in
ourselves, though we perceive only succession in the ex-
ternal world. Dr. Mansel, following Cousin, adopts a
third view, and maintains that the notion of ' Power ' is
given only in the control of the mind over its own opera-
tions. ' The intuition of Power is not immediately given
in the action of matter upon matter ; nor yet can it be
g^ven in the action of matter upon mind, nor in that of
mind upon matter ; for to this day we are utterly ignorant

Z2 NATURE OF

how matter and mind operate upon each other. We
know not how the material refractions of the eye are
connected with the mental sensation of seeing, nor how
the determination of the will operates in bringing about
the motion of the muscles. We can investigate severally
the phenomena of matter and of mind, as we can examine
severally the constitution of the earth, and the architecture
of the heavens : we seek the boundary line of their junc-
tion, as the child chases the horizon, only to discover that
it flies as we pursue it. There is thus no alternative, but
either to abandon the inquiry after an immediate intuition
of power, or to seek for it in mind as determining its awn
modifications ; — a course open to those who admit ah
immediate consciousness of self, and to them only. My
first and only presentation of power or causality is thus to
be found in my consciousness of myself as willing ^^'

The relation subsisting between an act of will and the
motion of the limbs, or between a physical antecedent and
its consequent, he regards as beyond our knowledge.
*Our clearest notion of efl&ciency is that of a relation
between two objects, similar to that which exists between
ourselves and our volitions. But what relation can exist
between the heat of fire and the melting of wax, similar
to that between a conscious mind and its self-determina-
tions ? Or, if there is nothing precisely similar, can there
be anything in any degree analogous? We cannot say
that there is, or, if there is, how far the analogy extends,
and how and where it fails. We can form no positive

" Prolegomena Logica, pp. 138, 139.

INDUCTIVE INFERENCE, 2^

conception of a power of thistkind : we can only say, that
it is something different from the only power of which we
are intuitively conscious. But, on the other hand, we are
not warranted in denying the existence of anything of
the kind ; for denial is as much an act of positive thought
as affirmation, and a negative idea furnishes no data for
one or the other ^^.'

It would, however, be beside my purpose to enter into
a detailed account of the history of this controversy.
On account, however, of its historical importance, it
seemed essential to notice it, and to point out that, what-
ever theory may be adopted as to the nature of Cause,
and however great our inability to conceive how one
event is followed by another, there is, at least, sufficient
definiteness in the conception to entitle it to be accepted
as the basis of scientific reasoning. Whether we acknow-
ledge that one event has invariably the power of producing
another, or whether we content ourselves with asserting
that it is invariably followed by that other, it is, in either
case, the element of invartableness which makes the
connection or conjunction, whichever we may call it, a
fitting object of scientific research. But remove the
element of invariableness, and suppose, if it be sup-
posable, that the same antecedent or set of antecedents
is sometimes followed by one consequent, and sometimes
by another, and sometimes by none at all ; in that case
science would be impossible.

The student who wishes to obtain further information

" Prolegomena Logica^ p. 140.

24 NATURE OF

on this controversy (a controversy, however, which pos-
sesses a historical rather than a practical or scientific
interest), is referred to Hume's Essay on the Idea of
Necessary Connection; Dugald Stewart's Dissertation, Part
II. sect. 8; Mill's Logic, Book III. ch. v; Sir W. HamU-
ton's Lectures on Metaphysics, Lectures XXXIX, XL;
Hansel's Prolegomena Logica, ch. v; Mill on Hamilton,
ch. xvi ; Lewes' History of Philosophy, Articles on Hume
and Kant. I refer only to books likely to be within the
student's reach. In quoting or referring to Hume, I
have employed only his Essays, Many writers persist in
making references to his Treatise of Human Nature, a
work which he himself repudiated, as containing an im-
mature expression of his opinions. In the Advertisement
to his Essays, he desires that ' the following Pieces may
alone be regarded as containing the author's philosophical
sentiments and principles.'

Note 3. — That a cause is ; that every

event has a cause; that the same cause is always at-
tended with the same effect ; are obviously three distinct
propositions, and still there are few writers who, in their
treatment of the question of Causation, have not more
or less confounded them. The first proposition (if
completed) would be the Definition of Cause, the pre-
dicate, of course, depending on the view adopted with
reference to the question discussed in the previous note.
The second is a statement of the Law of Universal Causa-
tion, the third of the Law of the Uniformity of Nature.

It will be observed that in the text of this chapter I

INDUCTIVE INFERENCE. 25

have said of each of these laws that it 'is universally
admitted by mankind, or, at least, by the reflecting portion
of mankind/ The latter clause must be regarded as
emphatic, and suggests, I think, a sufficient answer
to those authors who call in question their universal
reception. Mr. Lewes, speaking of the Law of Universal
Causation, says, * All believe irresistibly in particular acts
of causation. Few believe in universal causation; and
those few not till after considerable reflections^.' He then
proceeds to adduce the case of a student of chemistry,
who could not be convinced of the truth of the Law,
but 'looked upon the argument as an unwarrantable
assumption/ Now I venture to think that this incapacity
was due to the terms of the proposition not being made
sufficiently intelligible to him. I question whether any
man of average powers of understanding could be found
who would maintain the contradictory of either of these
Laws; who would assert, that is to say, that an event
might happen without anything to account for it, or that
a repetition of exactly the same circumstances might be
followed by a different effect. That a considerable
amount of intelligence is necessary in ordef to understand
the general terms in which the propositions are stated,
is undeniable, but, when once understood, I presume that
the propositions cannot fail to be acquiesced in. Like
all other propositions, however, of wide import, they
may be both understood and acquiesced in, without being
fully realized. It is the full and constant realization of

" Lewes' History of Philosophy t Article on Kant.

26 NATURE OF

these Laws, at all times and under all circumstances,
which mainly distinguishes the man of scientific from the
man of unscientific habits of thought. The unscientific
man either does not think of inquiring into the causes
of the phenomena around him, or notes with little pre-
cision the circumstances which he is investigating. The
scientific man, on the other hand, insists on invariably
referring the phenomena in which he is interested to
their several causes, and is satisfied with nothing but the
most rigorous inquiry into the relation between these
causes and their effects.

But, it may be asked, if the Laws of Universal Causa-
tion and of the Uniformity of Nature are, on reflection,
thus universally received, by what mental process do
men assure themselves of their truth ? Of the origin of
these, as of kindred beliefs, two different explanations
are offered by rival schools of psychologists. According
to one school, the human mind is so constituted that it
cannot but accept them; they are fundamental beliefs
which exist in the mind prior to all experience, though
it is experience which occasions, us to realise our pos-
session of them. We have never learnt them ; we have
simply discovered that we possess them. Thus Reid,
speaking of our conviction that the future will resemble
the past^® (what we have called the Law of the Uniformity

" This, however, is a very inadequate statement of the Law of the Uni-
formity of Nature. * It has been well pointed out,* says Mr. Mill, * that
Time, in its modifications of past, present, and future, has no concern either
with the belief itself, or with the grounds of it. We believe that fire will

INDUCTIVE INFERENCE. %*]

of Nature), says, 'The wise Author of our nature hath
implanted in human minds an original principle by which
we believe and expect the continuance of the course of
nature, and the continuance of those connections which
we have observed in times past. It is by this general
principle of our nature, that, when two things have been
found connected in time past, the appearance of the one
produces the belief of the other *^.' And Dr. Whewell,
speaking of the Law of Universal Causation, says, ' We
assert that "Every event must have a cause:" and this
proposition we know to be true, not only probably, and
generally, and as far as we can see : but we cannot
suppose it to be false in any single instance. We are
as certain of it as of the truths of arithmetic or geometry.
We cannot doubt that it must apply to all events past
and future, in every part of the universe, just as truly
as to those occurrences which we have ourselves observed.
What causes produce what effects ; — ^what is the cause
of any particular event ; — what will be the effect of any
peculiar process ; — these are points on which experience

burn to-morrow, because it burned to day and yesterday ; but we believe,
on precisely the same grounds, that it burned before we were bom, and
that it burns this very day in Cochin-China. It is not from the past to
the future, as past and future, that we infer, but from the known to the
unknown ; from facts observed to facts unobserved ; from what we have
perceived, or been directly conscious of, to what has not come within our
experience. In this last predicament is the whole region of the future ;
but also the vastly greater portion of the present and of the past* —
Mill's Logic^ Bk. III. ch. iii.

^ Reid's Inquiry into the Humttn Mind on the Principles of Common
Sense, chap. vi. sect. 24.

7,S NATURE OF

may enlighten us. Observation and experience may be
requisite, to enable us to judge respecting such matters.
But that every event has some cause, Experience cannot
prove any more than she can disprove. She can add
nothing to the evidence of the truth, however often she
may exemplify it. This doctrine, then, cannot have been
acquired by her teaching ^^.'

The opposite school of psychologists (of which Mr.
Mill and Mr. Alexander Bain may be taken as the modern
representatives) maintains that there is nothing in these
and kindred beliefs which compels us to distinguish them
generically from other truths, but that, like all other truths,
they are the results of Experience. From our earliest
years, we have been so constantly accustomed to observe
one change preceded by another change, and the same
antecedents followed by the same consequents, as well as
to find our own experience in these respects corroborated
by that of others, that, on reflection, we all acquiesce, and
cannot but acquiesce, in the statements which generalize
these facts. This, it is held, is a sufficient explanation of
that universality and necessity, which, by the advocates of
the intuitional theory, described in the last paragraph, are
supposed to discriminate the ' fundamental beliefs of the
human mind' or *the principles of common sense,' as
they are called by these authors, from all other truths.
The beliefs have acquired the character of universality
and necessity, not because they have sprung from any
other source than our ordinary beliefs, but because of the

^ Whewell's History of Scientific Ideas, Bk. III. ch. ii. § i.

INDUCTIVE INFERENCE. 29

constancy and variety of the experience from which they
are gained. * In fact, our whole lives/ says James Mill,
* are but a series of changes, that is, of antecedents and
consequents. The conjunction, therefore, is incessant;
and, of course, the union of the ideas perfectly insepa-
rable. We can no more have the idea of an event with-
out having the ideas of its antecedents and its conse-
quents, than we can have the idea and not have it at the
same time ^,* But here . occurs a difficulty. If the Laws
of Universal Causation and of the Uniformity of Nature
are inferred from particular facts of causation, are gene-
ralisations from experience, or, in other words, inductions,
how is it that they are made the grounds of all other
inductions? Is not this to argue in a circle? The
answer to this difficulty is that the Laws in question are
the result of* an imiform and constant experience, co-
extensive not with the life of the single individual who
employs them, but with the entire history of the human
race; that, consequently, when we adduce them as the
grounds on which our other inductions rest, we are per-
forming the perfectly legitimate process of resolving
narrower into wider cases of experience. The argument,
in short, is this: the inference from this narrow field of
observation (the particular induction which we happen to

^ James 'M\\V% Analysis of the Phenomena of the Human Mind^ ch. xi.
The position maintained by James Mill is that these beliefs owe their
universality to the fact of their being inseparably associated with all our
other cognitions. This is only another mode of stating the theory which
derives them from experience.

3© NATURE OF

be making) must be allowed to be trae, unless we are
prepared to deny one or other of the much wider gene-
ralisations which constitute the Laws of Universal Causa-
tion and of the Uniformity of Nature. To recur to the
instance adopted in the text, the proposition that bodies,
subject to the action of gravity only, fall in equal times,
can be called in question only on peril of doubting one
or other of the laws ; thus, the doubt which might attach
to it is shifted to two other propositions which no one
would think of questioning. Or, to state the same posi-
tion in a slightly different form, this particular instance is
shown to be a member of an infinitely long series, the
other members of which have been examined and ap-
proved; as, therefore, it differs in no essential respect
from them, it claims to be admitted also. There is, in-
deed, throughout this argument one assumption ; as the
rival theory assumed the trustworthiness of what it styled
our * fundamental beliefs,' so this assumes the validity of
experience. But, unless we make one or other of these
assumptions, we must be prepared to maintain that know-
ledge is altogether impossible ^^.

There is a third theory of the origin of universal beliefs

^ It should be noticed that Dr. Mansel, while agreeing in the main, as
he usually does, with the intuitional school in respect to the origin of
our belief in the Law of Universal Causation, refers to experience the
origin of our belief in the Uniformity of Nature. * The belief in the
uniformity of nature is not a necessary truth, however constantly guar-
anteed by our actual experience.* Mansel's Metaphysics^ Chapter on
Necessary Truths. Cf. Prolegomena Logical ch. v. Dr. Mansel's treat-
ment of these questions is, in many respects, peculiar to himself.

INDUCTIVE INFERENCE. 3 1

which combines, with certain modii&cations, both the
others. It would admit that all beliefs alike are ultimately
derived from experience, and still it would freely adopt
the language that there are some beliefs which are * native
to the human mind/ The word 'experience,' as or-
dinarily employed by psychologists, includes not only the
experience of the individual, but the recorded experience
of mankind. On the theory, however, of which we are
now speaking, it has a still more extended meaning ; it
includes experience, or, to speak more strictly, a peculiar
facility for forming certain experiences, transmitted by
hereditary descent from generation to generation. While
some ideas occur only to particular individuals, at par-
ticular times, there are others which, from the frequency
and constancy with which they are obtruded upon men's
minds at all times and under all circumstances, become,
after an accumulated experience of many generations,
connatural, as it were, to the human mind. We assume
them, often unconsciously, in our special perceptions, and
when the propositions, which embody them, are pro-
pounded to us, we find it impossible, on reflection, to
doubt their truth. It is by personal experience of ex-
ternal objects and their relations that each man recognises
them, but the tendency to recognise them is transmitted,
like the physical or mental peculiarities of race, from
preceding generations, and is anterior to any special ex-
perience whatever on the part of the individual. This
theory, to which much of modem speculation appears to

32 NATURE OF INDUCTIVE INFERENCE.

be converging, is advocated with great ability in the works
of Mr. Herbert Spencer ^.

The student who wishes for further information on the
questions discussed in this Note is referred to Dugald
Stewart's Philosophy of the Human Mind^ Part II. ch. v.
§ 2 ^" (' Of that Permanence or Stability in the order of
Nature which is presupposed in our Reasonings concerning
Contingent Truths'); Reid's Intellectual Powers, Essay VI.
ch. vi ; Reid's Active Powers, Essay I. ch. iv ; Hamilton's
Supplementary Dissertations to Reid's Works, Note A, § 3,
Note Q; Hamilton's Lectures on Metaphysics, Lectures
XXXIX, XL ; James Mill's Analysis of the Phenomena
of the Human Mind, ch. xi ; Mill's Logic, Book III.
ch. iii-v, xxi ; Mansel's Prolegomena Logica, ch. v ; Man-
sel's Metaphysics, Section on Necessary Truths ; Mill on
Hamilton, ch. xvi ; Lewes' History of Philosophy, Article
on Kant; Bain's Moral and Mental Science, Book II.
ch. vi, with Appendix B ; Herbert Spencer's Principles of
Psychology, Part IV. The student, in employing these
references, must be careful to distinguish between what
relates to the Law of Universal Causation (sometimes
called the Principle of Causality) and the Law of the
Uniformity of Nature. The two Laws, as already noticed,
are not always distinguished with sufl&cient care.

^ Sec especially his work on the Principles of Pyscbologyj Part IV.
^ In Sir W. Hamilton's edition of Stewart's Works, the corresponding
reference, is Part II. Subdivision I. ch. ii. section 4, subsection 2.

CHAPTER II.
Of Processes subsidiary to Induction.

OF the various mental processes subsidiary to In-
duction proper, it will be sufficient for our purpose to
discuss Observation and Experiment, Classification (in-
cluding Nomenclature and Terminolog}'), and Hypo-
thesis.

§1. Of Observation and Experiment,

These words are now so familiar, that they hardly
require any explanation. To observe is to watch with
attention phenomena as they occur, to experiment (or, to
adopt more ordinary language, to perform an experiment^
is, not only to observe, but also to place the phenomena
under peculiarly favourable circumstances, as a pre-
liminary to observation. Thus, every experiment im-
plies an observation, but it also implies something more.
Jn an experiment, I arrange or create the circumstances
imder which I wish to make my observation. Thus, if
two bodies are falling to the ground, and I attend to the
phenomenon, I am said to observe it, but, if I place the
bodies imder the exhausted receiver of an air-pump, or
cause them to be dropped under any special circum-
stances whatever, I may be said not only to make an

D

34 PROCESSES SUBSIDIARY TO INDUCTION.

observation, but also to perform an experiment. Bacon
has not inaptly compared experiment with the torture of
witnesses ^. Mr. Mill distinguishes between the two pro-
cesses, by saying that in observation we Jind our instance
in nature, in experiment we Tnake it, by an artificial ar-
rangement of circumstances. *When, as in astronomy,
we endeavour to ascertain causes by simply watching
their effects, we observe ; when, as in our laboratories, we
interfere arbitrarily with the causes or circumstances of
a phenomenon, w^ are said to experiment^*

As Observation often involves little or no conscious
effort, while Experiment always implies an, artificial
arrangement of circumstances, it might be expected that
the general employment of the former for scientific pur-
poses would long precede that of the latter. And this
supposition is confirmed by the History of Science.
Though it is false to afl&rm that Experiment was never
employed by the Greeks', its general neglect was cer-
tainly one cause of the little progress made by them in
the physical sciences.

^ * Quemadmodum enim in civilibus ingenium cujusque, et occultus
animi affectuumque sensus, melius elicitur, cum quis in perturbation«
ponitur, quam alias : simili modo, et occulta naturae magis se produrit
per vexationes artium, quam cum cursu suo meant.' Nov. Org., Bk. I.
Aph. xcviii.

^ Thomson and Tait's Natural Pbiloscpby, vol. i. § 369.

* For a refutation of this popular misconception, see Mr. Lewes* work
on AristotUy ch. vi. Mr Lewes, however, seems to me not sufficiently to
recognise the slight extent to which Experiment was employed in ancient
as compared with modem times.

OBSERVATION AND EXPERIMENT. 35

In the attempt to ascertain the effect of a given cause,
there can be no question of the general superiority of
Experiment over Observation. To be able to vary the
circumstances as we choose, to produce the phenomenon
under investigation in the precise degree which is most
convenient to us, and as frequently as we wish to com-
bine it with other phenomena or to isolate it altogether,
are such obvious advantages that it is not necessary to
insist upon them. Without the aid of artificial experi-
ment, it would have been impossible, for instance, to
ascertain the laws of falling bodies. To disprove the old
theory that bodies fall in times inversely proportional to
their weights, it was necessary to try the experiment ; to
be able to afiirm with certainty that all bodies, if moving
in a non-resisting medium, would fall to the earth through
equal vertical spaces in equal times, it was essential to
possess the means of removing altogether the resisting
medium by some such contrivance as that of the air-
pump. In some of the sciences, such as Chemistry, the
Sciences of Heat, Light, and Electricity, it is next
to impossible, at least in their inductive stage, to ad-
vance a single step without the aid of Experiment. No
amoimt of mere Observation would ever have enabled
us to detect the chemical elements of which various
bodies are composed, or to ascertain the effects of these
elements in their pure state. Even when Observation
alone reveals to us a fact of nature. Experiment is often
necessary in order to give precision to our knowledge.
That the metals are fusible, and that some are fusible at

D 2

36 PROCESSES SUBSIDIARY TO INDUCTION,

a lower temperature than others, is a fact which we can
conceive to have been obtruded upon man's observation,
but the precise temperatiu-e at which each metal begins
to change the solid for the liquid condition could be
learnt only by artificial experiment

But, though, in ascertaining the effect of a given cause.
Experiment is a far more potent instrument than Ob-
servation, the latter process is also available, and is
frequently of the greatest service. Thus, the Science of
Medicine equally avails itself,, for this purpose, both of
observations and experiments. The scientific physician
will not only fry the effects of different medicaments,
different modes of diet, and the like, but he will also
watch the effects on the organic system of various occu-
pations, habits, and pursuits. In some cases even, as
in all astronomical and many physiological phenomena,
the only means open to us of ascertaining the effect of
a given cause is Observation. If we wish to ascertain
the various phenomena attendant on a shower of meteors,
or a total eclipse of the sun, we must wait till the shower
of meteors occurs or the total eclipse takes place. If
we wish to learn the effects of the lesion of a particular
part of the nervous system, we must generally wait till
an instance offers itself; there are many experiments too
dangerous and too costly to be made, at least in the case
of man.

While, however, both Observation and Experiment are
available in ascertaining the effects of a given cause,
in the reverse process of ascertaining the cause of a

OBSERVATION AND EXPERIMENT. 37

given effect, Observation alone is open to us. *We
can take a cause/ says Mr. Mill, *and try what it will
produce; but we cannot take an effect, and try' [that
is, experimentally], * what it will be produced by. We
can only watch till we see it produced, or are enabled
to produce it by accident.' In those cases, consequently,
in which effects alone are patent to us, and the causes
are concealed from our view, we are compelled to have
recourse to Observation. A new disease makes its ap-
pearance : the mode of its action, and the conditions
favourable or unfavourable to its diffusion, can only be
learned by a careful observation and comparison of
cases.

It will readily be seen that those Sciences which de-
pend wholly or mainly on Observation are, as inductive
sciences, at a great disadvantage compared with those
in which it is possible largely to employ Experiment.
Where we wish to ascertain the effect of a given cause,
and we cannot make the instances for ourselves, the
want of appropriate and definite instances will often
completely baffle us. And, though the cause of a given
effect can only be learned by Observation, this is gene-
rally an enquiry of extreme difficulty, requiring to be
supplemented by experiment, or the actual production
of the given effect by the supposed cause, before we can
be certain that it has been conducted with the required
accuracy. Thus, mere observation of the electrical phe-
nomena which we witness in the heavens could never
have given us the Science of Electricity. The experiments

38 PROCESSES SUBSIDIARY TO INDUCTION.

which we may conduct in an hour are often worth a
century spent in observations.

In the Science of Astronomy this defect is more than
compensated for by the extreme simplicity of the phe-
nomena, the heavenly bodies being regarded by us, not
in themselves, but only in their mutual relations. Hence,
we are, at a comparatively early stage, enabled to apply
the Deductive Method, and to solve the problems of
Astronomy by mathematical calculations. But in the

very complex Science of Physiology this resource is not

*

open to us, and hence the backwardness of those de-
partments of physiological science in which direct ex-
periment is not available. Any animal or vegetable
organism is so complex, the data are so numerous, and
bear to each other so many different relations, that,
hitherto, it has been found impracticable to subject
physiology, at least in its details, to a deductive treat-
ment. In social and political speculations, the want of
experiment is, to some extent, supplied by statistics. A
social or political experiment is generally as impracticable
as an experiment in physiology, and the danger with
which it is attended is often incomparably greater. But
the number of observations open to us in these enquiries
(as, for instance, in respect to crime, education, trade,
taxation, &c.) is often very large, and, by carefully
comparing and systematising them, we may frequently
detect some relation between two circumstances which
enables us, with great probability, to infer that one has
something to do with the production of the other. We

OBSERVATION AND EXPERIMENT. 39

are here, however, trenching on the province of those
chapters which treat more peculiarly of inductive inference.

The following Rules may be laid down for the right
conduct of Observations and Experiments : —

Rule I. They must be precise. It is often of the
utmost importance to notice the exact time at which
an event occurs, the length of its duration, the position
of an object in space, its relation to surrounding objects,
and the like. We are all acquainted with the prime im-
portance of precision of detail in legal evidence ; it is no
less indispensable in scientific research. For the purpose
of enabling us to attain this object, various instruments
and methods have been invented. As instances of these
may be given, amongst instruments, the telescope, the
microscope, the thermometer, the barometer, measures
of various kinds, the balance, the dial, the clock, the
watch, the chronometer, the vernier, the goniometer, the
galvanometer, the thermo-electric pile ; amongst methods,
the decimal system of notation, fractions both vulgar
and decimal, the divisions of time, the various con-
trivances for the measurement of space, the method of
double-weighing, the method of least squares, the per-
sonal equation in astronomical observations. To these
instances might be added numerous others, but these
will be sufficient to show the great aid derived by what
may be called the natural methods of observation from
artificial contrivances. The Thermometer and the Method
of Double- Weighing furnish such striking exemplifica-
tions of the assistance thus derived, that, though they

40 PROCESSES SUBSIDIARY TO INDUCTION.

are probably familiar to most of our readers, it may be
desirable to explain them, one as an example of an
instmment, the other of a method.

The Thermometer (it is not necessary here to describe
the different kinds of thermometers) is a contrivance for
determining the degree of temperature, irrespective of
the mode in which it aflfects individual organisms. As
our sensibility varies considerably imder diflferent circum-
stances, so that what at one time affects us with the
sensation of hot will at another affect us with that of
cold, the sense of touch cannot be depended upon for
giving us accurate measurements of temperature. But
the fact that an augmentation of temperature, with cer-
tain rare exceptions (to be noticed hereafter), expands
the bodies subject to its influence furnishes us with such
a means of measurement. We take a substance which
notably exemplifies the power of heat in expansion, such
as mercury, alcohol, or, where it is necessary to ensure
great precision, atmospheric air carefully prepared, and,
by confining it within a tube, and marking off a scale
of measurements along the side, we are enabled, by
noting the degree of expansion of the substance in the
tube, to estimate, at least approximately, the exact degree
of temperature in the atmosphere or any other body, the
conditions of which we are investigating.

The method of Double- Weighing is peculiarly simple
and ingenious. It is a contrivance for remedying any
possible defects in the construction of the Balance. The
body to be weighed and the standard weight are sue-

OBSERVATION AND EXPERIMENT. 41

r

cessively placed in the same scale, and balanced by a
third body, so that there can be no question of their
exactly balancing each other, whatever may be the imper-
fections of the balance in which they are weighed.

It frequently happens, however, that a single observa-
tion may greatly mislead us. I may be in a district at
one time, and find the air very temperate and agreeable ;
the next time I come, it may be peculiarly hot, or chill,
or. moist. I may see a man, at the first shot, hit his
mark ; but at the subsequent shots, he may fire very wide
of it. Hence the importance, whenever there is any
liability to error, of taking an average of observations.
If a sufficient number of observations be taken, there is
every probability that an error in one direction will be
compensated by an error in the other, and that an ave-
rage, derived from all the observations, will approximate
much more nearly to the truth than any single observa-
tion is likely to do. Thus, if I wish to ascertain the true
character of the climate at any particular place, the obser-
vations I consult must extend over a considerable number
of years ; if I wish to estimate truly the skill of the marks-
man, I must watch, not a single shot, but many successive
ones. The average, it is true, is liable to error, but any
single observation is much more so. There is hardly
any department of science, depending upon observation,
in which, if it be our object to obtain precision, this
method is not indispensable *.

* The student who may wish for further information in connection
with Rule I. is referred to Dr. Whewell's Novum Organon Renovatum,

42 PROCESSES SUBSIDIARY TO INDUCTION.

Rule II. But, though it is necessary to be precise in
our observations and experiments, it is also important,
in order to avoid distraction and waste of time, to attend
only to the material circumstances of the case we are in-
vestigating. A physician, for instance, in prescribing for
his patient, would not now think it necessary to take an
observation of the planets, nor would a chemist, in gather-
ing herbs for his decoctions, think it of any consequence
to notice the phase of the moon. A caution should, how-
ever, be added. Before neglecting any circumstance in
our observations, it is of the utmost importance to have
ascertained beyond doubt that it is not material to the
subject of our enquiries*. To neglect this caution would
be a violation of the first Rule.

Rule III. The circumstances under which an observa-
tion or experiment is made should, except in the very
simplest cases, be varied as much as possible. A phy-
sician, in studying the character of a disease, will note its

Bk. III. ch. ii., and Herschel's Discourse on the Study of Natural Pbi*
losopbyt § 387-9. On the importance of taking an average of obser-
vations, see Herschel's Discourse^ § 226-30.

^ The neophyte in science requires to be reminded that observations
which might at first be supposed to be immaterial are often afterwards found
to be amongst the circumstances most material to the enquiry. * Could
anything' (says Dr. Rolleston, in his Address before the Medical Asso-
ciation in 1868) * have seemed at first sight to be more impertinent,
more otiosely curious and trifling, than to enquire during an epidemic of
cholera what was the nature of the subsoil in the area it was ravaging,
to what depth it was porous, and at what level the water was, and had
been previously, standing in it ? Yet, as I think. Von Pcttenkofer has
at last fought out and won his battle on these points.'

OBSERVATION AND EXPERIMENT. 43

effects on persons of different ages, constitutions, habits
of life, and the like. An astronomical observer will not be
content with a single observation of a newly-discovered
comet, but will note the phenomena which attend it at va-
rious stages in its passage through the heavens. A chemist
will combine a newly-discovered element with the various
other elements, and will try upon it the effect of heat,
pressure, &c. It is, of course, implied that some discretion
will be employed in the application of this Rule, and that
the variation of circumstances will not be carried beyond
the point at which there is some probability of its adding
to our knowledge.

Rule IV. The phenomenon under investigation should
if possible be isolated from all other phenomena, or, at
least, from all those which are likely to interfere with our
study of it. In studying the eflfects of the action of
gravity upon bodies, it was necessary- to exhaust the
atmosphere and to withdraw the support, and, by thus
insulating the phenomenon, to enable us to perceive how
bodies behave when subject to the action of gravity only.
A physician, in trying the effects of a new drug, will, at
first at least, administer it alone, and not in combination
with other drugs which might augment or counteract its
influence on the system *.

A beautiful instance of the isolation of a phenomenon

* By observing the third of these rules we usually prepare our instances
for the application of what will hereafter be explained as the Method of
Agreement, and by observing the fourth for the application of what will
hereafter be explained as the Method of Difference.

44 PROCESSES SUBSIDIARY TO INDUCTION.

is afforded whenever there occurs a total eclipse of the
sun. As, on these occasions, the moon, by a curious
coincidence, exactly covers, or rather more than covers,
the sun's surface, and thus intercepts all light from it, we
are able to see, what we see on no other occasion, cer-
tain rose-coloured protuberances, projecting, as it were,
from the dark edge of the moon, but really belonging to
the sun. The real nature of these *red flames* was long
a matter of dispute, but it seems now to be conclusively
settled that they are portions of an atmosphere of incan-
descent hydrogen in which the sun is enveloped, and
which shoots out in these flames to a distance estimated
at not less than forty or fifty thousand miles. Had it not
been for the insulation of the phenomenon thus produced
for us by the intervention of the moon, we should have
been ignorant of their existence. Here, to use a bold
metaphor, we might say that Nature herself performs an
experiment for us^.

When it is impossible entirely to isolate a phenomenon,
it is sometimes possible so far to diminish the action of
the concomitant circumstances as to be able accurately
or approximately to calculate the effect, if they were alto-
gether absent. Thus, we can never altogether remove
the influence of friction on a moving body, but we can

■^ A method has recently been devised by which these protuberances
may be observed at any time when the sun is shining. Till quite re-
cently, however, a total eclipse of the sun afforded the only occasion for
observing them, and, if it had not been for the attention thus drawn to
them, they would probably never have been discovered.

CLASSIFICATION. 45

SO far diminish it as to be able to say what the effect
would be were no such influence at work. We cannot
altogether eliminate the influence of extraneous circum-
stances on a patient subject to medical regime, but, by
due care, we may minimise the excitement, fatigue, ennui,
or other unfavourable conditions which might interfere
with our treatment.

The circumstances under which we perform our experi-
ments being more in our own power than those under
which we conduct our observations, it is obvious that
the foregoing rules, and especially the third and fourth,
can be more easily observed in experiments than in
observations.

§ 2. On Classification^ Nomenclature, and Terminology,

(i) Of Classification.

A classification, in the widest sense of the term, is a
division, or a series of divisions and subdivisions ^. The
process of classifying our own thoughts or feelings, or
the actions of ourselves or others, or the external objects
which surround us, is one of the most constant occupa-
tions of the mind. Thus, we are perpetually dividing
outward objects into those which are useful or those
which are useless or noxious to us ; those which are useful
into such as are within and such as are beyond our power
to attain ; those which are useful and which it is within our

' See Deductive Logic, Part II. ch. viii.

46 PROCESSES SUBSIDFARY TO INDUCTION.

power to attain into such as are to be sought at once,
and those the effort to appropriate which may be more
advantageously postponed,— -each of these divisions ad-
mitting of ahnost infinite subdivision. In fact, as has
frequently been remarked, every attribution of a general
name implies an act of division or classification.
When we speak of a horse, we are dividing all objects
into those which are horses and those which are not.
When we speak of a bay horse, we are superadding to
this division the subdivision of horses into bay horses and
those of any other colour.

But the process of Classification of which we are about
to treat, though the same in kind with that which we
employ in the affairs of ordinary life, is of a much more
complex and systematic character. The great difference
is that, whereas in the affairs of ordinary life we generally
classify objects with reference to some one principle, that
principle varying according to the particular purpose we
happen to have in view (thus we classify horses according
to their colour, their breed, their strength, &c., each classi-
fication being suggested by some distinct purpose), a
scientific classification must take account of all the points
of difference which are in any way likely to facilitate
the scientific investigation of the group. The purport of
the science being defined, the classification must be based,
not on one or two characters, selected arbitrarily, but on
the entire assemblage of characters which the science in-
vestigates. Thus, if Botany be defined as the science
which investigates the organisation (including under that

CLA SSIFICA TION. 4 7

. term the form, structure, and functions) of plants, a bota-
nical classification, in order to be strictly scientific, must
not omit to take into account any part of that organisa-
tion. But it is evident that such a requirement would
produce endless confusion, unless we could discover some
mode of subordinating the characters, so as to make the
more important points of diflference the basis of the higher
divisions in the series. Hence we see already that a
scientific classification must be guided by at least two
principles, a review of all the characters or distinguishing
marks, so far as they are known and so far as they fall
within the scope of the science, and a subordination of
these characters one to another. To these principles
others will subsequently be added.

Before proceeding to the attempt to ascertain induc-
tively facts of co-existence or causation amongst a vast
mass of phenomena, it is often highly important, if not
essential, to arrange these phenomena in groups, as well
as to determine the order in which these groups them-
selves shall be arranged. Hence the importance of laying
down correct rules for Classification in a System of
Inductive Logic. It is exclusively as subsidiary to In-
duction that we shall here consider the subject of Classi-
fication.

A scientific Classification, regarded as subsidiary to
Induction employed for scientific purposes, may be de-
fined as A Series of Divisions, so arranged as best to

facilitate the complete and separate study of the several
groups which are the result of the divisions, as well as of

48 PROCESSES SUBSIDIARY TO INDUCTION.

the entire subject under investigation. * The general pro-
blem of classification/ says Mr. Mill^ *in reference to
these [namely, scientific] purposes, may be stated as
follows : To provide that things shall be thought of in
such groups, and those groups in such an order, as will
best conduce to the remembrance and to the ascertain-
ment of their laws/

The sciences of Botany and Zoology are rightly re-
garded as furnishing the best examples of Scientific Clas-
sification. The excellence of the classifications which
they present may be referred to two reasons. The first
is the extraordinary multiplicity of the different kinds
of animals and plants which are found on the surface of
the globe: this has, from the earliest times, exercised
man's ingenuity in the attempt to name them and reduce
them to order. The second reason may be found in the
imperfection of these sciences in their present condition :
the difl&culty, amounting almost to impossibility, of dis-
covering laws of succession, or, in other words, relations
of cause and effect, in the animal and vegetable kingdoms
has naturally led scientific enquirers to concentrate their
attention on the far easier task of describing and ar-
ranging the objects themselves. Mineralogy, though its
classifications are less systematic and complete, is also,
in the present state of the science, mainly occupied in
attempting the work of classification.

The best means, perhaps, of making the student ac-
quainted with the nature of scientific classification is to

» MiU's Logic, Bk. IV. ch. vii. § i.

CLA SSIFICA TION. 49

compare the method of natural classification (which aims
at being strictly scientific) with that of artificial classifica-
tion (which, so far as it is artificial, is not scientific), giving
illustrations from the sciences of Botany and Zoology.
An examination of the natural system will enable us to
lay down certain rules for scientific classification, and we
shall conclude with such remarks as may seem necessary in
order to preserve the student from erroneous impressions.
A natural system of Classification aims at classifying
objects according to the whole of their resemblances and
differences, so far as these are recognised by the science
in whose service the classification is made. But amongst
these resemblances and differences some are found to be
invariably attended by a number of others, and conse-
quently these, as the more important^ are selected as the
characters by which to discriminate the higher divisions
of the series, the less important characters being, through-
out the whole series, subordinated to the more important.
This successive subordination of characters and the con-
sequent coincidence of the groups formed by our classi-
fications with what appear to be the great divisions of
nature are the peculiarities which mainly distinguish a
natural system. An artificial system, on the other hand,
is one which selects arbitrarily some point of difference
amongst the objects to be classified, and then, so far as
possible, makes this or similar points the basis of its
classifications. No system, however, as we shall see pre-
sently, is purely artificial. Though of little use, except
as a preliminary effort, for the purposes of science, an

E

50 PROCESSES SUBSIDIARY TO INDUCTION.

artificial system possesses one great advantage. As it
bases its divisions, where possible, on some one property,
and that generally something which at once strikes the
eye (one of the earliest of the modern attempts to classify
plants took for its basis the form of the corolla), it is
peculiarly easy of application, and can be much more
readily learnt than a natural system. It thus often serves
the purposes of a key, by which we may easily discover
the place of a group in a natural system. We now pro-
ceed to offer illustrations.

In Botany, the most celebrated artificial system is that
known as the Linnaean, though Linnaeus also did much
towards the establishment of a natural system. In this
system, which was a great advance on preceding artificial
systems, the main basis of classification is the number of
stamens and pistils which are to be found in the flowering
plant. This character is, however, to some extent
modified by other considerations, such as the relative
lengths of the stamens, the shape of the fruit, &c. ; so far
as these modifications are admitted, the Linnaean system
approaches to a natural system. The annexed Tables
(extracted from Balfour's Manual of Botany^^) will give
the student some idea of the manner in which the Classes
(higher divisions) and the Orders (divisions intermediate
between the Classes and Genera) are constituted accord-
ing to the Linnaean system. It should be premised that
the stamens are the male organs, and the pistils the
female organs of a plant.

^' §§7J6. 7'7-

CLASSIFICATION. 51

Tabxtlar View of the Classes of the Linnjean System.

A. Flowers present, or evident Stamens and Pistils (Phanerogamia).
I. Stamens and Pistil in every flower.
I. Stamens Free,

a. Stamens of equal length, or not differing in certain propor-
tions ;
in number I Class I. Monandria.

— 2 II. Diandria.

— 3 III. Triandria.

— 4 IV. Tetrandria.

— 5 .. • • • V. Pentandria.

— 6 VL Hezandria.

— 7 VII. Heptandria.

— 8 VIII. Octandria.

— 9 IX. Enneandria.

— lo X. Decandria.

— 12-19 XI. Dodecandria.

— 20 J inserted on Calyx — XII. Icosandria.
or more J on Receptacle XIII. Polyandria.

b. Stamens of different lengths ;

two long and two short XIV. Didynamia.

four long and two short XV. Tetradynamia.

2. Stamens united ;

by Filaments in one bundle XVI. Monadelphia.

in two bundles XVII. Diadelphia.

in more than two bundles XVIII. Polyadelphia.

by Anthers (Compound flowers) XIX. Syngenesia.

with Pistil on a Colunm XX. Gynandria.

II. Stamens and Pistil in different flowers ;

on the same Plant XXI. Monoecia.

on different Plants XXII. DIcecia.

III. Stamens and Pistil in the same or in

different flowers on the same or on ^ XXIII. Polygamia.

different plants

B. Flowers absent, or Stamens and Pistils not
evident

}

I XXrV. Cryptogamia.

E 2

^2 PROCESSES SUBSIDIARY TO INDUCTION.

The Classes are sub-divided into Orders, as will be
seen from the next Table, on a less uniform plan than
that on which they themselves were constituted.

Tabular View of the Orders of the Linnjean System.

Class. I.

II.

III.

IV.

V.

VI.

VII.

VIII.

IX.

X.

XL

XII.

XIII.

Monogynia ^^ i Free Style.

Digynia 2 Free Styles.

Trigynia 3 —

Tetragynia 4 —

Pentagynia 5 —

Hexagynia 6 —

Heptagynia 7 — ^

Octogynia 8 —

Enneagynia 9 —

Decagynia 10 —

Dodecagynia 1 2-19 —

Polygynia 20 and upwards.

( Gymnospermia Fruit formed by four Achsenia.

XIV. < Angiospermia Fruit, a two-celled Capsule with

( many seeds.

yy f Siliculosa Fruit, a Silicula.

* \ Siliquosa Fruit, a Siliqua.

XVI.
XVII. ^Triandria, Decandria, &c. (number of Stamens), as in Classes.

^•1
XVIII. J

Polygamia ^qualis. . . . Florets all hermaphrodite.

Superflua. . . . Florets of the disk hermaphrodite,

those of the ray pistilliferous and
fertile.

Frustranea . . Florets of the disk hermaphrodite,

XIX. -l those of the ray neuter.

Necessaria. . . Florets of the disk staminiferous,

those of the ray pistilliferous.

Segregata . . . Each floret having a separate in-
volucre.

Monogamia Anthers united, flowers compound.

^* It must not be supposed tliat all the Orders, Monogynia, &c., exist
in each of the first thirteen Classes. When an Order is absent, the next
Order which is present takes its place in the numerical arrangement.
Thus, if the Order Trigynia be absent, and the next Order which is pre-
sent be Tetragynia, as in Class IV, this latter will rank as the third
Order.

XX.

XXI.
XXII.

XXIII.

XXIV. ^

CLASSIFICATION. 53

Monandria, Diandria, &c. (number of Stamens), as in the

Classes.

' Monoecia Hermaphrodite, staminiferous, and

pistiliferous flowers on the same
plant.

Dicecia on two plants.

Tricecia on three plants.

Filices Ferns.

Musci Mosses.

Hepaticse Liverworts.

Lichenes Lichens.

Algx Sea-weeds.

Fungi Mushrooms.

* Even as an artificial method/ says Professor Balfour ^^,
* this system has many imperfections. If plants are not in
full flower, with all the stamens and styles perfect, it is
impossible to determine their class and order. In many
instances, the different flowers on the same plant vary as
regards the number of the stamens. Again, if carried
out rigidly, it would separate in many instances the
species of the same genus ; but as Linnaeus did not wish
to break up his genera, which were founded on natural
aflMties, he adopted an artifice by which he kept all the
species of a genus together. Thus, if in a genus nearly
all the species had both stamens and pistils in every
flower, while one or two were monoecious or dioecious,
he put the name of the latter in italics, in the classes and
orders to which they belonged according to his method,
and referred the student to the proper genus for the
description.'

The species of the Linnaean system coincide with those

" Balfcur*8 Manual of Botany, § 718.

54 PROCESSES SUBSIDIARY TO INDUCTION.

of the natural system. The same is mostly the case with
the genera, or next higher divisions. The Linnaean
system is, therefore, far from being purely artificial. In
fact, when we come to the lower groups of vegetables
(genera and species), we are compelled to discriminate
them one from another by a multiplicity of characters, so
that a purely artificial system of botany would be im-
possible.

The framers of natural systems of botany, instead of
selecting some one character, such as the number of
stamens and pistils, as the basis of the higher divisions, at-
tempt to discover a number of characters, any one of which,
if employed as the instrument of division, would give the
same results as any of the others. This coincidence of
divisions founded on various characters is a proof that we
have reached some real distinction in nature. The main
division of plants into cellular and vascular, or acoty-
ledonous and cotyledonous, and the sub-division of vas-
cular or cotyledonous plants into monocotyledonous and
dicotyledonous, furnish remarkable instances of such
a coincidence, and may consequently be regarded as cor-
responding with grand divisions in nature itself.

*In taking a survey of the Vegetable Kingdom, some
plants are found to be composed of cells only, and are
called Cellular ; while others consist of cells and vessels,
especially spiral vessels, and are denominated Vascular,
If the embryo is examined, it is found in some cases to
have cotyledons or seed-lobes, in other cases to want
them; and thus some plants are cotyledonous^ others

CLA SSIFICA TION. 55

dcoiyUdonous ; the former being divisible into monocotyle-
donous, having one cotyledon, and dicotyledonous, having
two [or more] cotyledons. The radicle, or young root
of acotyledons, is helerorhizal, that of monocotyledons is
endorhizalf that of dicotyledons, exorhizal. When the
stems are taken into consideration, it is seen that marked
differences occur here also, acotyledons being acrogenous,
monocotyledons endogenous, and dicotyledons exogenous.
The venation of leaves, parallel, reticulated, or forked,
establishes the same great natural divisions ; and similar
results are obtained from a consideration of the flowers,
monocotyledons and dicotyledons being phanerogamous ,
and acotyledons crypiogamous!

* Thus, the following grand natural divisions are arrived
at: —

I. Cellular. ..Acotyledonous. Heterorhizal. Acrogenous. i ^^TP^O"

I gamous.

( Monocotyledonous. Endorhizal. Endogenous. )Phanero-

' (Dicotyledonous. Exorhizal. Exogenous. ) gamous .

Having established these Primary Divisions of the
vegetable kingdom, the botanist, guiding himself as far as
possible by the same principles as those on which the
primary divisions were formed, proceeds to divide and
sub-divide till at last he arrives at species, which are
generally defined to be collections of individuals so nearly
resembling each other that they may be supposed to be
descended from a common stock. Thus, the Class
* Dicotyledones or Exogenae ' is sub-divided into four sub-

" Balfour's Manual of Botany, §§ 723, 724.

^6 PROCESSES SUBSIDIARY TO INDUCTION.

classes, one of which is the * Thalamiflorae/ characterised
as having * calyx and corolla present, petals distinct and
inserted into the thalamus or receptacle, stamens hy-
pogynous/ This sub-class is divided into a number of
orders (sixty in Professor Balfour's Manual)^ one of which
is Hypericaceae, the Tutsan or St. John's-wort family,
thus described: —

' Sepals 4-5, separate or united, persistent, usually with glandular dots,
unequal ; aestivation imbricated. Petals 4-5, oblique, often with black
dots, aestivation contorted. Stamens hypogynous, indefinite in number ;
generally polyadelphous, very rarely 10, and monadelphous or distinct ;
filaments filiform ; anthers bilocular, with longitudinal dehiscence ; car-
pels 2-5, united round a central or basal placenta ; styles the same num-
ber as the carpels, usually separate ; stigmas capitate or simple. Fruit
either fleshy or capsular, multilocular, and multivalvular, rarely unilocu-
lar. Seeds usually indefinite in number, minute, anatropal, usually ex-
albuminous; embryo usually straight. — Herbaceous plants, shrubs or
trees, with exstipulate entire leaves, which are usually opposite and
dotted. Flowers often yellow.'

In this order th^re are fifteen known genera, one of
which is the Hypericum, which is thus described in
Irvine's Handbook 0/ British Plants : —

* H3rpericum, St. John*s-wort. Herbaceous plants or shrubs, with
opposite, simple, entire leaves, which are usually furnished with pellucid
dots (reservoirs of essential oil). Sepals five, free or united at the base,
ovate, slightly unequal, permanent. Petals as many as the sepals,
obtuse, spreading. Stamens indefinite, combined at the base into three
or five sets, with small roundish anthers. Ovary with three-five cells
or carpels and as many styles, with simple stigmas. Fruit capsular,
rarely baccate, three-five-celled, with numerous seeds.*

This genus is divided into sub-genera or sections, one
of which is thus described :

CLA SSIFICA TION. 5 J

* Steins herbaceous. Stamens in three parcels (triadelphous). Styles
three. Capsule three-celled, three-valved.*

This sub-genus or section is again divided into sub-
sections, one of which is characterized as having * stems
round, sepals with ciliary glands/ This sub-section con-
tains amongst its species the well-known Hypericum
Pulchrum, * Elegant St. John's-wort,' thus described :

* Stems erect, bent at the base, round, glabrous, simple or branching.
Leaves ovate, clasping, coriaceous, smooth, with numerous translucent
dots. Flowers in opposite panicled cymes. Sepals obovate, roundisb,
with a point, ciliated, with nearly sessile glands. Petals oblong, ribbed,
with black sessile glands ^*.*

The first peculiarity which strikes us in these descrip-
tions is the large number of characters which is employed
in constituting even the higher divisions of the series.
Instead of describing merely the number and distribution
of the stamens, as in the Linnaean system, we have, even in
the description of the Order, a reference to almost every
part of the plant. We next notice the much greater
definiteness which the characters assume, as we descend
lower in the series. Thus, to take the sepals as an in-
stance, the description of the sub-class simply informs
us of the presence of a calyx, while each successive divi-
sion (except the sub-genus) gives us more and more
definite information as to the number, position, form, &c.
of the sepals which constitute the calyx. Again, we
observe that, in the lower divisions, the stem, leaves,
sepals, and petals are the characters which are brought

" See Irvine's Handbook of British Plants, under Order CIII.

58 PROCESSES SUBSIDIARY TO INDUCTION.

into greatest prominence, whereas the stamens and the
various parts of the pistil (the carpels, styles, and stigmas),
which are employed in the higher divisions, disappear
from the lower, as no longer affording grounds of differ-
ence. Now the stamens and pistil, inasmuch as any
peculiarity in them is generally accompanied by a larger
number of peculiarities in other parts of the plant, are
usually of far more importance than the corolla (petals)
and calyx (sepals), and therefore it is reasonable to suppose
that the grounds of difference furnished by them would
be likely to be exhausted in the higher divisions. At the
same time we see that, in the instance we have taken, the
sepals and petals furnish grounds of difference at a very
early stage of the classification, and consequently that
even the less important characters are often used co-
ordinately with others to determine the higher divisions.

In Zoology, the advantage of a natural over an artificial
classification is more readily recognised than in Botany,
the structure and functions of animals being more fa-
miliar and apparent than those of plants. A division of
animals, for instance, which adopted the number of limbs
as its sole distinguishing character, and thus brought
together, as quadrupeds ^ the ox and the frog, would be so
absurd on the face of it, as to be rejected at once. * No
arrangement of animals,' says Dr. Whewell ^®, ' which, in
a large number of instances, violated strong and clear
natural aflSnities, would be tolerated because it answered

'* History of the Inductive Sciences^ Bk. XVI. ch. vii.

CLA SSIFICA TION. 59

the purpose of enabling us easily to find the name and
place of the animal in the artificial system. Every system
of Zoological arrangement may be supposed to aspire
to be a natural system.' He then proceeds to give an
instance of an attempt to constitute an artificial classifica-
tion in the ichthyological branch of Zoology. *Bloch,
whose ichthyological labours have been mentioned, fol-
lowed in his great work the method of Linnaeus/ (who
devoted much of his attention to the classification of
animals as well as of plants.) * But towards the end of
his life he had prepared a general system, founded upon
one single numerical principle — the number of fins ; just
as the sexual system of Linnaeus is founded upon the
number of stamina : and he made his sub-divisions ac-
cording to the position of the ventral and pectoral fins ;
the same character which Linnaeus had employed for his
primary division. He could not have done better, says
Cuvier, if his object had been to turn into ridicule all
artificial methods, and to show to what absurd combina-
tions they may lead.'

*By the natural meihodl says M. Milne Edwards^®
(whose remarks on Zoological Classifications and the
Primary Divisions and Classes of the Animal Kingdom
are well worthy of the attention of all students of induc-
tive logic), ' the divisions and subdivisions of the animal

*• See Milne Edwards' Zoologie (in the Cours elementaire (Tbistoire
naturelle), septifeme edition, §§ 364, 365. There is an English transla-
tion of this work by Dr. R. Knox. I have followed it, except in a few
places where it docs not accurately represent the original.

6o PROCESSES SUBSIDIARY TO INDUCTION.

kingdom are founded on the whole of the characters fur-
nished by each animal, arranged according to their degree
of respective importance; thus, in knowing the place
which the animal occupies, we also know the more re-
markable traits of its organisation, and the manner in
which its principal functions are exercised.

* The rules to be observed in arriving at a natural clas-
sification of the animal kingdom are of extreme simplicity,
but often there is much diflSculty in the application. They
may be reduced to two, for the object of the zoologist in
establishing such a classification is, —

' I St. To arrange animals in natural series, according
to the degree of their respective affinities, — that is to say,
to distribute them in such a manner that those species
which most nearly resemble each other may occupy the
nearest places, while the distance of two species from
each other may, in some sort, be the measure of their
non-resemblance.

' 2nd. To divide and subdivide this series according
to the principle of subordination of characters, — that is
to say, by reason of the importance of the differences
which these animals present between them.'

The Primary Divisions of the animal kingdom, ac-
cording to the natural system, are four, there being four
types of structure and of nervous organisation, to which
animal life conforms.

* These four principal forms may be understood by a
reference to four well-known animals — the dog, the cray-
fish or lobster, the snail, the asterias or sea-star.

CLASSIFICATION. 6 1

*In order that the zoological classification might be a
faithful representation of the more or less important
modifications introduced into the structure of animals, it
was necessary to distribute these beings into four prin-
cipal groups or divisions; and this is, in fact, what
Cuvier did.

* The animal kingdom is divided into vertebrate animals,
articulated or annulated animals, molluscs, and zoophytes.

* The fundamental differences distinguishing these four
primary divisions depend chiefly on the mode of arrange-
ment of the different parts of the body and on the con-
formation of the nervous system. It is easy to under-
stand the importance of these two dominant characters :
to feel and to move is the especial character of animal
life, and these two functions belong to the nervous system.
It might readily, then, be anticipated that the mode of
conformation of this system would exert a powerful
influence over the nature of animals, and would furnish
characters of primary importance in classification.

* The general disposition or mode of reimion of the
'different parts of the body exercises an equally impor-
tant influence, as modifying the localisation of the func-
tions and the division of the physiological result ^'^!

Vertebrate animals are thus described :

' The verlehrate animals resemble man in the more important points
of their structure ; almost all the parts of their bodies are in pairs, and
disposed symmetrically on the two sides of a medial longitudinal plane ;
their nervous system is highly developed, and is composed of nerves and

" Mihie Edwards, §§ 372, 373.

62 PROCESSES SUBSIDIARY TO INDUCTION.

-ganglionic and of a brain and spinal marrow. To these we may add,
that the principal muscles are attached to an internal skeleton, composed
of separate pieces, connected together, and disposed so as to protect the
more important organs, and to form the passive instruments of loco-
motion ; that the more important part of this skeleton forms a sheath
for the brain and spinal marrow, and results from the reunion of annular
portions, called vertebrae ; that the apparatus for the circulation is very
complete, and that the heart offers at least two distinct reservoirs ; that
the blood is red; that the limbs are almost always four in number,
and never more ; finally, that there exist distinct organs lodged in the
head for sight, hearing, smell, and taste '*/

The Primary Division (embranchement) 'Vertebrate
Animals ' is sub-divided into the five classes, Mammals,
Birds, Reptiles, Batrachia, Fishes, of which Mammals
are thus described :

' Organs of lactation. Hot blood. Circulation complete, and heart
with four cavities. Pulmonary respiration siipple. Lobes of the cere*
helium reunited by an annular protuberance. Lower jaw articulated
directly with the cranium. The body generally covered with hairs.
Viviparous.*

* There exist considerable differences amongst the
mammalia, and these modifications of structure serve
as the basis for the division of the class into groups^
of an inferior rank, called orders. Most of these groups
are so distinct as to admit of no doubt in respect
of their limits : they constitute, in fact, natural divisions ;
but in others the line of demarcation is by no means so
distinct. Thus a mammal may have points of resemblance
so close to two groups as to render it almost indifferent
to which it be referred. To some naturalists, differences

" Milne Edwards, § 374.

CLASSIFICATION. 63

appear important which are disregarded by others, and
hence a want of agreement on the subject of classification
has always prevailed.

* The method followed here is nearly the same as that
proposed by Cuvier. It rests mainly on the differences
mammals show in respect of their extremities and teeth,
differences which always imply a crowd of others in
habits, structm-e, and even intelligence.

' Keeping in view the ensemble of these characters, the
class mammalia may be divided into two groups, — the
monodelphic and didelphic.

* The monodelphic or monodelphian are the more nu-
merous, and are distinguished chiefly by their mode of
development. At birth they are already provided with all
their organs, and before birth they derive their nomish-
ment from the mother by means of a placenta. Their
brain is more perfect than the didelphian, by the presence
of a corpus callosum uniting the two cerebral hemispheres.
Finally, the walls of the abdomen have no osseous sup-
ports attached to the margins of the pelvis, as we find
in the second great class of mammals. The mammals
thus organised have been subdivided into two groups, —
namely, ordinary mammals and pisciform mammals,

*The ordinary mammals are organised principally to
live on solid ground; the skin is provided with hairs.
These animals are further subdivided into ten orders : the
bimana, quadrumana, cheiroptera, insectivora, rodentia,
edentata, camivora, amphibia, pachydermata, and rumi-
nantia. The first eight of these orders have flexible

64 PROCESSES SUBSIDIARY TO INDUCTION.

fingers and toes, with nails covering only the dorsal aspect
of the toe or finger, and comparatively small ; hence they
have been called unguiculata ; the last two, — namely, the
pachydermata and ruminantia, have the extremity of the
finger and toe entirely enclosed in a hoof; they are thus
called ungulaia,

' The order bimana includes only man : in him alone
the arms are destined for prehension, the limbs for pro-,
gression and support in the erect attitude. Thus, his
natural position on the soil is unmistakeably vertical. The
teeth are of three kinds, and have their edges on the same
plane ; they are frugivorous : finally, the brain is more per-
fect, more highly developed, than in any other animal ^'.'

Here the Order is coextensive with the Species, but
usually the Order is divided into Genera, and each Genus
into Species. Thus, the Order *Carnivora' is divided
into the Genera * cat,' * hygena,' ' dog,' * bear,' &c. Again,
the Genus * dog' comprises the dog properly so called, the
wolf, and the fox. The genus * cat ' comprises not only
the cat properly so called, but the tiger, lion, panther, &c.

It may be as well to add an account of the characters
which distinguish respectively the Order ' Carnivora,' the
Genus * Felis,' and the Species * Leo,' in order to serve
as an example or illustration of the manner in which these
several degrees in the scale of Classification are usually
described : —

* The order of camivora is composed of ordinary unguiculated mam-
mals ; the form of their dentition is complete, but they have no opposing

^* Milne Edwards, § 409-412.

CLASSIFICATION. 65

thumb. According to the mode of life of these animals, their intestinal
canal is short ; their jaws and their muscles strong, in order to seize and
devour their prey ; their head from this circumstance seems large. The
jaws are short, thus favouring their strength, and the form of the tem-
poral-maxillary articulation proves that the teeth are made for tearing
and cutting, not for grinding or masticating. The canine teeth are
large, long, and very powerful ; the incisors, six in number in each jaw,
small ; the molars, sometimes adapted merely for cutting, in others sur-
mounted with rounded tubercles, presenting no conical points, arranged
as in the insectivora. One of these molar teeth is usually much longer
and more cutting than the others, and has therefore been called the car-
nivorous molar tooth ; behind these (on each side) are one or two molars,
almost flat, and between the carnivorous molar and the canine a variable
number of false molars. The food of the animal, whether exclusively
composed of flesh or mixed with other matters, may be judged of by the
varying proportions of these cutting or tuberculated molars.

* Animals of this order have generally the toes armed with claws
adapted to hold and to tear their prey ; usually also they have no collar-
bones.'

The following are the characteristics of the genus
*Felis/ and of the species * Leo :' —

* Their jaws are short, and are acted on by muscles of extraordinary
strength ; their retractile nails, concealed between the toes in a state of
repose by means of elastic ligaments, are never blunted. Their toes are
five in number on the anterior limbs, and four on those behind. Their
hearing is exceedingly fine, and the best developed of all their senses.
They see well by day and night, but they are not farsighted ; in some
the pupil is elongated vertically, in others it is round. They make great
use of the organ of smell ; they consult it before eating, and often when
anything disturbs them. Their tongue is covered with homy and very
rough points. Their coat is in general soft and fine, and the surface
of the body very sensible to the touch ; their whiskers especially seem
to be instruments of great sensibility. Though of prodigious vigour,
they generally do not attack animals openly, but employ cunning and
artifice. They never push their prey to flight, but watching by the
margins of rivers and pools in covert, they spring at once on their victim.

F

66 PROCESSES SUBSIDIARY TO INDUCTION.

* At the head of this genus stands the Hon, measuring frequently
twelve feet in length, or over six feet to the setting on of the tail ; about
three feet in height, and characterised by the square head, the tuft of
hair terminating the tail, and in the male by the mane which flows from
the head and neck ^.'

The process by which the Zoologist constitutes the
Primary Divisions of animal life, and then descends from
these to the Species, is distinguished by the same pecu-
liarities as those which we remarked in reviewing the
natural classifications of the Botanist. In one step or
other of the classification almost every known charac-
teristic of a species will be found. As we descend the
series, the characters gain in definiteness and, as a rule,
lose in importance. Moreover, even in the higher divi-
sions of the series, numerous characters are used, and
those not always of great apparent importance. Thus,
that *the body is generally covered with hairs' is one
of the characters of Mammalia.

The student will now be in a position to understand
the rules which may be laid down for the right conduct
of a Natural Classification.

I. Not only the lower, but the higher groups of the
series should be so constituted as to differ from one
another by a multitude of characters. It is only when,
as is the case in the primary divisions of Botany and
Zoology, we arrive at the same divisions from a variety
of different considerations, that we can feel assured that
our groups really correspond with distinctions in Nature.

» Milne Edwards, § 414.

CLASSIFICATION. 67

It is this coincidence^ in the higher groups of the series,
of divisions formed on different principles, that distin-
guishes a Natural from an Artificial Classification.

II. The more important characters should be selected
for the purpose of determining the higher groups. This
is called the principle of the subordination of characters.
But how are we to determine the relative importance
of characters? *We must consider as the most im-
portant attributes,' says Mr. Mill^^, 'those which contribute
most, either by themselves or by their effects, to render
the things like one another, and unlike other things;
which give to the class composed of them the most
marked individuality; which fill, as it were, the largest
space in their existence, and would most impress the
attention of a spectator who knew all their properties but
was not specially interested in any/ This is perfectly
true, but it seems to be hardly sufficiently definite. The
following criteria may be proposed for the purpose of
discriminating between the more and the less important
properties of natural objects, (i.) A character which is
found to furnish an invariable index to the possession
of certain other characters is of more importance than
a character which fiunishes no such index. Thus, the
internal structure of an animal is of more importance than
its size, and the mode of fructification of a plant than
the colour of its flowers. (2.) Amongst such characters,
a character is regarded as of more or less importance,

» Mill's Logic, Bk. IV. ch. vii. § 2.
F 2

68 PROCESSES SUBSIDIARY TO INDUCTION.

according as it accompanies a greater or smaller number
of other differences. Thus, in the classification of ani-
mals, the characters from which the classes imguiculata
and ungulata are so called are of more importance than
the form of the teeth, which is used in distinguishing the
orders. For the same reason, the mode of growth of
flowering plants (which leads to the distinction of en-
dogenous and exogenous plants) is of far more im-
portance, as a character, than the number of stamens
or pistils. Hence, in constituting the higher divisions
of a series we must look for those characters which are
accompanied by the largest number of differences.

III. The classification should be gradual, proceeding
by a series of divisions and subdivisions. When the
group to be classified consists of an enormous number
of species, as in the case of animals and plants, the
necessity of observing this rule is obvious. To descend
at once from the Primary Divisions to, say. Genera and
Species, would render the Classification comparatively
worthless. The object of a classification being to bring
together those groups which resemble each other and
to separate those groups which differ from each other,
we must take account of degrees of resemblance and
difference, so that, as a rule, the number of gradations
will increase with the number of groups to be classified.
Both in Botany and Zoology, the grand divisions which
seem now to be universally recognised are Primary
Divisions, or Sub-Kingdoms (embranchements), Classes,
Orders, Genera, and Species. Between these various

CLA SSIFICA TJON. 6g

Other divisions are interpolated, according to the seeming
requirements of each particular system, and often accord-
ing to the views of each individual author. Moreover,
below Species are often reckoned Varieties, and even
Varieties are sometimes subdivided, this being especially
the case when animals have become domesticated or
plants cultivated. Taking as an instance the Anthyllis
Vulneraria (Common Lady's Finger), the divisions and
subdivisions of a natural classification may be illustrated
thus 22 :—

I. Primary Division .... Cotyledones.

i^II. Class ...... Dicotyledones.

Subclass Calyciilorae.

III. Order Leguminosae.

Suborder Papilionaceae.

Tribe Loteae.

Subtribe ..... Genisteae.

IV. Genus Anthyllis.

Subgenus or Section . . . Vulneraria.

V. Species Vulneraria.

Variety Dillenii.

Race ...... Floribus coccineis.

Variation Foliis hirsutissimis.

In very extensive groups, other divisions may be inter-
polated ; thus a subgenus or section is often divided into
a subsection. On the other hand, many of these divisions
often disappear; if a genus consist of only a small
number of species, and there be no very striking points
of difference amongst them, we may descend at once,

^ Balfour's Manual of Botany, § 725.

70 PROCESSES SUBSIDIARY TO INDUCTION.

without any intermediate divisions, from the Genus to
its various Species. Sometimes, even, an order may
contain only a single genus, or a genus a single species,
in which case the two may be regarded as coextensive.
In the case of Man, we saw that we descend at once from
the Order to the varieties, the order Bimana being coex-
tensive with the genus and species Homo, so that here
three even of the grand divisions are coincident.

IV. The groups should be so arranged, that those
which have the closest affinities may be brought nearest
to each other, while the distance of one group from
another may be taken as a measure of its dissimil^ty
from it. The observation of this rule would result in
what Mr. Mill calls 'the arrangement of the natural
groups into a natural series.' For the purposes of sub-
sequent induction, it is plain that it is of the utmost
importance not widely to dissever groups which present
many phenomena in common, or which we even suspect
may do so. The object aimed at by this rule is, to a
great extent, attained by the observation of the Subor-
dination of Characters (Rule 2), according to which, the
higher the place of the division in the series, the more
important is the collection of characters which serves for
its basis. If Rule 2 were duly observed, it would be
impossible for any two widely dissimilar groups to be
brought into juxtaposition in the lower divisions of the
series. Thus, the ox and the frog, the primrose and the
mushroom, would in any natural system be at consider-
able distances from each other. But it is not sufficient

CLA SSIFICA TION. 7 1

to observe the rule of the Subordination of Characters.
The arrangement of the cognate groups in each division
should be such that at the head of the series may come
those groups which are most like the groups of the
preceding division, while at the bottom of the series may
come those groups which are most like the groups of
the subsequent division. Thus, suppose that we have
Orders A, B, C, of which B resembles A more than C
does, and that A is subdivided into the genera a d' d"
y b" € ; B into the genera ni m" nop' p" ; C into the
genera :xf od' ^^y\y\ z; (of which the genera represented
by the earlier letters of the alphabet are more akin to
each other than those represented by the later, and
conversely) ; in our arrangement we ought to place c in
juxtaposition with m' m'\ and / p" in juxtaposition with
:xf od\ the remaining groups being arranged, as above,
on the same principle. If such an arrangement could
be effected, it is plain that those groups which pre-
sented in the greatest intensity the principal phenomena
of the class of objects under investigation would come
first in the series, and that those which presented them
in the least intensity would come last. In Zoology, for
instance, those groups would come first which presented
in the greatest intensity the principal phenomena of
animal life, and in Botany those which presented in the
greatest intensity the phenomena of vegetable life. It
is, of course, seldom, in the arrangement of natural
objects, that we are able to draw up an exact table of
precedency amongst the groups of any division, but we

7a PROCESSES SUBSIDIARY TO INDUCTION.

are often able to say that this or that group or collection
of groups {a or o^ d' d") should rank first in the series,
or that it should rank before some other group or collec-
tion of groups. Thus, no zoologist would hesitate to
assign to man (the Order Bimana) the highest place in
any classification of Mammalia, while he would place next
the Order Quadrumana, and in this Order he would select
apes, and, amongst apes, the anthropoid apes, to be
brought into closest juxtaposition with man.

This rule is obviously of most diflficult application. It
points out an ideal to be aimed at,* but one which is never
likely to be perfectly realised. So many are the pro-
perties to be taken into consideration in every natural
object, that it is often impossible to say that this object
is, on the whole, more like another than that. The
groups of the higher divisions may often, those of the
lower may sometimes, be tabulated in some order of
precedency ; but there remains a large majority of cases
to which the Rule is inapplicable, or in which, at least, it
has not yet been successfully applied. This is especially
the case in Botany, where, though, in respect of com-
plexity of structure and perfection of organism, Vascular
plants may be ranked above Cellular, and Dicotyledons
above Monocotyledons, there are but few cases among
the subdivisions, especially of Monocotyledons and
Dicotyledons, where any order of precedency can be
established. But, even if the rule were of universal
application, and if we were perfectly acquainted with all
the properties of bodies and their relative value, it would

CLA SSIFICA TION. 7 3

not follow that we could establish what Dr. Whewell, in
his opposition to this doctrine of Classification by Series,
calls * a mere linear progression in nature/ There might
still be' many Orders, Genera, or Species, which, to use
a familiar expression, we should be obliged to bracket,
* It would surely be possible,' says Mr. Mill ^^, ' to arrange
^places (for example) in the order of their distance from
the North Pole, though there would be not merely a
plurality, but a whole circle of places at every single
gradation in the scale.'

Remark I. A natural classification is supposed to be com-
plete, when it has descended as low as species, — a species
being regarded as a group consisting of individuals, all of
which have descended from a common stock. Or, if the
process be reversed, and the classification be an ascend-
ing instead of a descending one, species are regarded as
the starting-point of the naturalist, and it is supposed that
the problem before him is to group them under higher
divisions. But a species may, as we have seen, be divided
into varieties, sub-varieties, &c. Now, in what consists the
difference between the relation of a variety to a species
and the relation of a species to a genus ? To this ques-
tion a very large section of naturalists now maintain that
no satisfactory answer can be given. If it be said that
varieties of the same species may be developed in the
course of time, but that species themselves must be
regarded as distinct, it may be asked on what grounds

« Bk. IV. ch. viii. § i. Note.

74 PROCESSES SUBSIDIARY TO INDUCTION.

this supposition rests. Diflferent varieties of the same
species are certainly more like each other than diflferent
species of the same genus, just as species of the same
genus have more resemblance than genera of the same
order, or members of any lower division than members of
any higher division ; but, given a larger amount of time,
is there more diflftculty in supposing a common stock for
the diflferent species of a genus than for the diflferent
varieties of a species? This is the question originated
with so much ability by Mr. Darwin in his work on the
Origin of Species, His own solution of the question is
well known. * It will be seen,' he says ^, * that I look at
the term species, as one arbitrarily given for the sake of
convenience to a set of individuals closely resembling
each other, and that it does not essentially diflfer from the
term variety, which is given to less distinct and more
fluctuating forms. The term variety, again, in com-
parison with mere individual diflferences, is also applied
arbitrarily, and for mere convenience' sake/ It does not
fall within our province to discuss the question of the
'Origin of Species,' but it is desirable that the student
should be aware that the practice of naturalists in stopping
at species, as if they were the 'infimae species ' of the old
logicians below which divisions need not proceed, is far
from being universally accepted.

Remark 2. As our knowledge of the external world
becomes enlarged, the number of natural groups, recog-

^ Darwin's Origin of Species, ch. ii.

CLASSIFICA TION. 75

. nised by the classificatory sciences, is being continually
increased. Botanists and zoologists (especially the former)
are constantly discovering or recognising new varieties,
frequently new species, and occasionally, even, new
genera and orders. * The known species of plants,' says
Dr. Whewell^^ 'were 10,000 at the time of Linnaeus,
and are now [a. d. 1858] probably 60,000.' The
increase in the number of recognised varieties, sub-
varieties, &c., is even still more rapid. One common
effect of these constant discoveries and recognitions is to
bridge over what previously appeared to be gaps in
nature, thus illustrating the fact that there are but few
breaks in natural phenomena, that there pervades nature
a Law of Continuity, according to which a group seldom
occurs to which some other group may not be found very
closely allied. So complete, sometimes, is this continuity,
that it becomes very difficult to distinguish the groups by
any fixed characters. Two species (say) are discri-
minated, and then a third group is found which partakes
of the character of each of the others. This is con-
stituted a new species, and then a fourth group is found
intermediate between this and the first, and so on. * It
has been shown,' says Dr. Carpenter, as quoted by
Mr. Grove ^, *that a very wide range of variation exists
among Orbitolites, not merely as regards external form,
but also as to plan of developement ; and not merely as

» History ofSeierUifie Ideas, Bk. VIII. ch. ii. § 6.
^ Essay on Continuity, printed at the end of tiie Fifth Edition of
The Correlation of Physical Forces, pp. 326, 327.

j6 PROCESSES SUBSIDIARY TO INDUCTION,

to the shape and aspect of the entire organism, but also
with respect to the size and configuration of its com-
ponent parts. It would have been easy, by selecting
only the most divergent types from amongst the whole
series of specimens which I have examined, to prefer an
apparently substantial claim on behalf of these to be
accounted as so many distinct species. But after having
classified the specimens which could be arranged around
these types, a large proportion would yet have remained,
either presenting chalracters intermediate between those of
two or more of them, or actually combining those cha-
racters in different parts of their fabric; thus showing
that no lines of demarcation can be drawn across any
part of the series that shall definitely separate it into any
number of groups, each characterised by features entirely
peculiar to itself.' We certainly find in nature a per-
sistency of type, which is the result of the laws of here-
ditary transmission; if there were no such persistency,
the attempt to group natural objects would be fruitless
and absurd. But, at the same time, when we have
established groups, we constantly find that there are
individual members diverging more or less from the
ordinary type, and forming intermediate links between
proximate classes. To adopt and alter a metaphor em-
ployed by Dr. Whewell, natural classes may be regarded
as the forests of neighbouring hills, the hills being seldom
separated by well-defined valleys, and the valleys being
frequently interspersed with straggling trees or clumps.
Remark 3. It sometimes happens that one of the

CLA S Sine A TION. J 7

characters by which classes or groups are distinguished
from each other is to be found, not invariably, but only
usually or occasionally in the members of the group.
Thus, in the description of the Order Rosaceae, we find
that * the seeds are erect or inverted, usually exalbuminous
Flowers sometimes imisexual/ Such in-
definite descriptions would be entirely out of place in an
artificial classification, but in a natural classification, where
the entire assemblage of the characters must be taken
into consideration, a character, though not found in-
variably, or even though found but seldom, may still be
valuable in distinguishing a group.

Remark 4. The most important characters are not
always those by which a group is most easily recognised.
For the purpose of recognition, some external and pro-
minent character or set of characters is generally best
adapted. Thus, if we wished to determine whether a
plant were monocotyledonous or dicotyledonous, our
easiest course would be to examine the stem ; if the stem
were endogenous, we should know that the plant was
a monocotyledon, if exogenous, that the plant was a
dicotyledon. A single character is often sufiicient to
determine the place of a plant or animal in a series,
because we already know that the possession of this
character is a sign of the possession of the various other
characters which are enumerated in the description of the
natural class. The method of determining, by means of
one or a few characters, the place of a natural object in a
classification, is often called Diagnosis or Characteristick.

78 PROCESSES SUBSIDIARY TO INDUCTION. .

* The Characteristick/ says Dr. Whewell ^, * is an Arti-
ficial Key to a Natural System. As being Artificial, it
takes as few characters as possible ; as being Natural, its
characters are not selected by any general or prescribed
rule, but follow the natural affinities/ *The genera
Lamium and Galeopsis (Dead Nettle and Hemp Nettle)
are each formed into a separate group in virtue of their
general resemblances and differences, and not because
the former has one tooth on each side of the lower lip,
and the latter a notch in its upper lip, though they are
distinguished by these marks/

Note, — Dr. Whewell maintains that natural classes are
determined, not by definition, that is, by an enumeration
of characters, but by type, that is, by resemblance, more
or less complete, to some one member of the class, round
which the others are grouped. Thus, according to this
theory, the Class Mammalia would be determined, not by
an enumeration of characters, but by resemblance, more
or less complete, to some typical specimen, say Dog ; the
genus Dog would be determined not by an enumeration
of the characters which are common to the dog, wolf, and
fox (the species comprised in the genus), but by approxi-
mation to the type-species dog ; similarly, the Order Ro-
sacese would be determined not by an enumeration of
characters, common to a large number of genera, but by
the resemblance, more or less complete, of these genera

^ History of Scientific Ideas, Bk. VIII. ch. ii. § 7.

CLASSIFICATION. 79

to the type-genus Rosa. Dr. Whewell's view will be un-
derstood from the following extract : —

*In a Natural Group the class is steadily

fixed, though not precisely limited; it is given, though
not circumscribed ; it is determined, not by a boundary
line without, but by a central point within ; not by what
it strictiy excludes, but by what it eminently includes ; by
an example, not by a precept; in short, instead of
Definition we have a Type for our director.

'A Type is an example of any class, for instance, a
species of a genus, which is considered as eminently pos-
sessing the characters of the class. All the species which
have a greater afiinity with this Type-species than with
any others, form the genus, and are ranged about it,
deviating from it in various directions and different de-
grees. Thus a genus may consist of several species,
which approach very near the type, and of which the
claim to a place with it is obvious ; while there may be
other i^ecies which straggle further from this central
knot, and which yet are clearly more connected with it
than with any other. And even if there should be some
species of which the place is dubious, and which appear
to be equally bound by two generic types, it is easily seen
that this would not destroy the reality of the generic
groups, any more than the scattered trees of the inter-
vening plain prevent our speaking intelligibly of the distinct
forests of two separate hills.

*The Type-species of every genus, the Type-genus
of every family, is, then, one which possesses all the

8o PROCESSES SUBSIDIARY TO INDUCTION.

characters and properties of the genus in a marked and
prominent manner. The Type of the Rose family has
alternate stipulate leaves, wants the albumen, has the
ovules not erect, has the stigmata simple, and besides
these features, which distinguish it from the exceptions
or varieties of its class, it has the features which make it
prominent in its class. It is one of those which possess
clearly several leading attributes; and thus, though we
cannot say of any one genus that it mmi be the Type of
the family, or of any one species that it must be the Type
of the genus, we are still not wholly to seek : the Type
must be connected by many afl&nities with most of the
others of its group; it must be near the centre of the
crowd, and not one of the stragglers ^J

There is much force in what Dr. Whewell here says,
but his main position appears to me to be incorrect.
May not the various steps in the process of Classification
be described as follows? We, first, observe a general
resemblance amongst a variety of groups. Prompted by
the observation of this resemblance, we determine to con-
stitute the groups into a distinct class. But it is not

^* History of Scientific Ideas, Bk. VIII. ch. ii. § 3. art. lo. Mr. Mill
{Logic, Bk. IV. ch. vii. § 3, 4) examines Dr. Whewell's views at consider-
able length. He appears to me, in this examination, to insist too em-
phatically on what he calls * distinctions of kind,' and to assert, without
sufhcient warrant, that * the species of Plants are not only real kinds, but
are probably, all of them, real lowest kinds, Infimae Species, which if we
were to subdivide into sub-classes, the subdivision would necessarily be
founded on definite distinctions, not pointing (apart from what may be
known of their causes or effects) to any difference beyond themselves.'

NOMENCLATURE. 8 1

sufficient simply to enumerate the groups which the class
contains ; it is incumbent upon us to state the principle
on which the classification was mjide. This statement
consists in an enumeration of those characters which are
common to all the members of the newly-constituted
class, and which, at the same time, distinguish them from
the members of other classes, with the addition, in some
cases, of certain characters which belong to most, or,
even, to a few only, of the members of the class. Thus,
the class is determined (or ^ given* to use Dr. WhewelFs
expression) by an enmneration of characters. But, when
the class is once familiar to us, the repetition of the class-
name suggests, not the characters, but some typical
specimen of the class, some one group which stands out
prominently as possessing the characters by which the
class was determined, and it is by reference to this central
specimen, as it were, that we fix the position of the other
groups and adjudicate on the claims of any newly-dis-
covered group to take its place by the side of the others.
Thus, the t3T)e-species, type-genus, or typical order, may
be of the greatest service as a convenient embodiment of
the characters, but the characters must be enumerated,
and the class determined, before we can select our typical
example.

(2) Op Nomenclature.

Nomenclature is intimately connected with Classifica-
tion. The groups, whether natural or artificial, into which
objects are distributed, could neither be recollected by

o

82 PROCESSES SUBSIDIARY TO INDUCTION.

ourselves nor communicated to others, unless they were
fixed by the imposition of names. A Nomenclature is
a collection of such names, applied to the members of
the various divisions and subdivisions which constitute
a classification. The number of natural groups, however,
is so enormously large, that it would be next to im-
possible to devise, and, if possible to devise, it would
be impossible to remember, distinct names for each
group. Thus, the known species of plants, for instance,
amount to upwards of 60,000, and, if we took into
account varieties, sub-varieties, &c., the number of groups
would be represented by many multiples of this sum.
Some artifice, therefore, is necessary by which a com-
paratively small number of names may be made to dis-
tinguish a large number of groups. Botany and Chemistry
furnish admirable examples of the employment of such
an artifice, and some knowledge of the principles which
guide the imposition of names in those two sciences
(a knowledge which may be easily acquired) would
probably be of more service to the student than anything
which he might learn from a body of rules for Nomen-
clature in general.

In Botany, the higher groups (including genera) have dis-
tinct names. Thus, we have Dicotyledones, Rosaceae, Rosa,
&c. But, when we arrive at the species, these are known
by the generic name with the addition of some distinctive
attribute. Thus, the genus Geranium is represented in
the British Isles by thirteen species, called respectively
Geranium phaeum, G. nodosum, G. sylvaticum, G. pratense,

NOMENCLATURE. 83

G. sanguineum, G. pyrenaicum, . G. pusillum, G. dis-
sectum, G. columbinum, G. rotundifolium, G. molle, G.
lucidum, G. robertianum. The specific names are se-
lected from various considerations ; sometimes in honour
of an individual (as Equisetum Mackaii, Rosa Wilsoni),
sometimes from the country or the district in which the
plant abounds, sometimes from the soil which is most
favourable to it, sometimes from some peculiarity in the
plant itself. So arbitrary and fanciful sometimes are these
names, that Linnaeus (as we are told by Dr. Whewell^)
* gave the name of Bauhinia to a plant with leaves in
pairs, because the Bauhins were a pair of brothers, that
of Banisteria to a climbing plant, in honour of Banister,
who travelled among mountains.' It is plain that a name
which describes some peculiarity in the plant itself is
of most service to the learner ; but any name, easily re-
membered, serves the main purpose of a nomenclature,
which is to distinguish one group from another. Varieties,
sub-varieties, &c., are distinguished from each other on
the same principle as species. Thus, as we have seen,
of the species Anthyllis Vulneraria there is a variety
Dillenii, and of the variety Anthyllis Vulneraria Dillenii
there is a * race' Floribus coccineis, and of the race there
is a * variation' Foliis hirsutissimis. The nomenclature
of Zoology is now generally constructed on the same
principle as that of Botany. In some systems of Miner-
alogy, three names are employed, nam^y, those of the

» JKs/oiy of Scientific Ideas, Bk. VIII. ch. ii. § 6.

O 2

84 PROCESSES SUBSIDIARY TO INDUCTION.

Order, Genus, and Species, as for instance, Rhombohe-
dral Calc Haloide.

The nomenclature of Chemistry, or, at least, of In-
organic Chemistry, which, in some respects, furnishes
an interesting example of a scientific nomenclature, is
constructed on the principle of making the prefixes and
affixes of the words employed significant of the nature
of the substances for which they stand. Thus, we
have the afiixes ide^ ic, otis, ate, ite, &c., and the pre-
fixes mono, di, tri, sesqui\ &c., each having a special sig-
nificance, though not always, unfortunately, an unam-
biguous one.

It would transcend the limits of this work to give an
account, sufficiently clear and precise, of the Nomenclature
of Inorganic Chemistry (which, moreover, is at present
in a transitional state), but the student who is anxious
to gain some idea of the principles on which it is con-
structed, can refer to Watts' Dictionary of Chemistry,
vol. iv. Art. Nomenclature.

(3) Of Terminology.

A Nomenclature of a Science is, as we have seen, a
collection of names of groups. A Terminology is a col-
lection of the names (or terms) which distinguish either
the properties or the parts of the individual objects which
the science re(?bgnises. Thus, when we speak of the
genus *Rosa,' we are employing the nomenclature of
Botany; but, when we say that the individuals of the

TERMINOLOGY. 85

genus * Rosa ' have ' their corolla imbricated before flower-
ing, their styles with lateral insertion, their carpels nu-
merous,' &c., we are employing not the nomenclature,
but the terminology, of the science. In Botany we have
an almost perfect example of a complete and judiciously
constructed terminology.

* The formation of an exact and extensive descriptive
language for botany,' says Dr. WhewelP^, *has been
executed with a degree of skill and felicity, which, before
it was attained, could hardly have been dreamt of as
attainable. Every part of a plant has been named ; and
the form of every part, even the most minute, has had
a large assemblage of descriptive terms appropriated to it,
by means of which the botanist can convey and receive
knowledge of form and structure, as exacdy as if each
minute part were presented to him vastly magnified. This
acquisition was part of the Linnaean Reform. "Toume-
fort," says Decandolle, "appears to have been the first
who really perceived the utility of fixing the sense of terms
in such a way as always to employ the same word in the
same sense, and always to express the same idea by the
same word ; but it was Linnaeus who relfly created and
fixed this botanical language, and this is his fairest claim
to glory, for by this fixation of language he has shed
clearness and precision over all parts of the science."

* It is not necessary here to give any detailed account
of the terms of botany. The fundamental ones have
been gradually introduced, as the parts of plants were

* History of Scientific Ideas, Bk. VIII. ch. ii. § 2.

86 PROCESSES SUBSIDIARY TO INDUCTION.

more carefully and minutely examined. Thus the flower
was successively distinguished into the calyx, the corolla,
the stamens, and the pistils : the sections of the corolla
were termed petals by Columna ; those of the calyx were
called sepals by Necker. Sometimes terms of greater
generality were devised; 2& perianth to include the calyx
and corolla, whether one or both of these were present ;
pericarp for the part inclosing the grain, of whatever kind
it be, fruit, nut, pod, &c. And it may easily be imagined
that descriptive terms may, by definition and combination,
become very numerous and distinct. Thus leaves may
be called pinnatifid, pinnatipartite, pinnaiisect, pinnatilobate,
palmatifid, palmatipartite, &c., and each of these words
designates different combinations of the modes and extent
of the divisions of the leaf with the divisions of its outline.
In some cases arbitrary numerical relations are introduced
into the definition : thus a leaf is called bilobate when it
is divided into two parts by a notch ; but if the notch go
to the middle of its length, it is bifid; if it go near the
base of the leaf, it is bipartite ; if to the base, it is bisect.
Thus, too, a pod of a cruciferous plant is a siliqua if it be
four times as Iftig as it is broad, but if it be shorter than
this it is a silicula. Such terms being established, the
form of the very complex leaf or frond of a fern is exactly
conveyed by the following phrase : " fronds rigid pinnate,
pinnae recurved subunilateral pinnatifid, the segments
linear undivided or bifid spinuloso-serrate." '

A Terminology, we have said, comprises the terms
appropriated to express, not only the parts of objects, but

TERMINOLOGY, 87

also their properties. Thus, in the foregoing example,
the words * sepals,' 'petals/ &c., express parts of the
plant, the words * pinnatifid,' * bilobate,' &c., which are
applied to the shape of the leaves, express properties.
A complete terminology must be so constructed as to
express every shade of diflference in all those properties
which are recognised in a scientific treatment of the object.
Thus, if colour be regarded as of importance in the de-
scription of a plant, mineral, &c., it is essential that there
shall be some appropriate term by which to describe every
shade of colour. But there are few terms which, from
their mere signification, can call up any precise idea in
the mind. Hence it is necessary to fix by convention the
precise meaning of every technical term employed in
science. Again, to appropriate the words of Dr. Whewell,
* The meaning of technical terms can be fixed in the first
instance only by convention, and can be made intelligible
only by presenting to the senses that which the terms are
to signify. The knowledge of a colour by its name can
only be taught through the eye. No description can con-
vey to a hearer what we mean by apple-green or French
grey. It might, perhaps, be supposed that, in the first
example, the term apple, referring to so familiar an object,
sufficiently suggests the colour intended. But it may
easily be seen that this is not true; for apples are of
many different hues of green, and it is only by a conven-
tional selection that we can appropriate the term to one
special shade. When this appropriation is once made,
the term refers to the sensation, and not to the parts of

88 PROCESSES SUBSIDIARY TO INDUCTION.

this term ; for these enter into the compound merely as
a help to the memory, whether the suggestion be a natural
connection as in "apple-green," or a casual one as in
" French grey." In order to derive due advantage from
technical terms of this kind, they must be associated im-
mediately with the perception to which they belong ; and
not connected with it through the vague usages of common
language. The memory must retain the sensation ; and
the technical word must be understood as directly as- the
most familiar word, and more distinctly. When we find
such terms as tin-white or pinchbeck-brown, the metallic
colour so denoted ought to start up in our memory with-
out delay or search '^' When we have fixed, by conven-
tion, the meaning of a term, it must invariably be em-
ployed in this sense, and in no other. The least vague-
ness or inconsistency in the use of terms may interpose
a fatal obstacle in the way, not only of the learners, but
even of the promoters of a science. The progress of the
Mechanical Sciences and of what are commonly called
Physics was long retarded by the vague and unintelligent
use of such words as ' heavy,' * light,' * hot,' * cold,' * moist,'
' dry,' &c. Even still such words as * force,' ' fluid,'
* attraction,' * ether,' &c., are often employed without
sufficient precision.

A Terminology, as remarked by Dr. Whewell '*, is in-
dispensably requisite in giving fixity to a Nomenclature.
Thus, in Botany, * the recognition of the kinds of plants

'* History of Scientific Ideas^ Bk. VIII. ch. ii. § 2.
•^ Novum Organon RenovcUunif Bk. IV. Aphorism ii.

HYPOTHESIS. 89

must depend upon the exact comparison of their resem-
blances and diflferences; and to become a part of per-
manent science, this comparison must be recorded in
words/

Dr. Whewell devotes the last Book of his Novum Or-
ganon Renovatum to a series of aphorisms on the * Lan-
guage of Science,' including both Nomenclature and
Terminology. These aphorisms afford one of the best
examples of Dr. Whewell's style and mode of treatment,
and will well repay the attention of the student who is
desirous of acquainting himself further with the methods
of the Classificatory Sciences. Mr. Mill has some chapters
{LogtCy Bk. IV. ch. iii-vi) on * Naming ' and the * Requisites
of a Philosophical Language,' and, in addition to the pas-
sage already referred to. Dr. Whewell treats these subjects
in his History of Scientific Ideas, Bk. I. ch. ii ; Bk. VIIL
ch. ii. §§ 2 and 6 ; Bk. VIIL ch. iii. art. 5.

§ 3. On Hypothesis.

When the mind has before it a number of observed
facts, it is almost irresistibly driven to frame for itself
some theory as to the mode of their co-existence or
succession. It is from this irresistible impulse to refer to
some law the various phenomena around us that all
science as well as all scientific error has sprung. In all
the more important branches of inquiry, true theories
have usually been preceded by a number of false ones,
and it has not tmfrequently occurred that the false theories

90 PROCESSES SUBSIDIARY TO INDUCTION.

have been mainly instrumental in conducting to the true.
Thus, the elliptical theory of planetary motion was pre-
ceded by the circular theory, with its various modifica-
tions, and thfe undulatory theory of light by the emission
theory. Rather than rest satisfied with a number of un-
connected facts, men have often imagined the most
absurd relations between phenomena, such as that a
comet was the harbinger of war, or that the future could
be foretold by birds. These theories, assumptions, or
suppositions, when employed in scientific inquiry, are
called hypotheses, and have already been alluded to
(Chapter I. Appended Note 6). The word * hypothesis,*
as commonly employed, is exclusive of propositions which
rest upon absolute proof, whether inductive or deductive,
and is generally used in contradistinction to them. Thus,
we speak of a science being only in a hypothetical stage,
or of a hypothesis being converted into an induction or
being brought deductively under some general law already
ascertained to be true. On the other hand, we should
hardly dignify with the name of 'hypothesis' a supposition
which, at least in the eyes of its framer, did not possess
some amount of plausibility. A hypothesis ^' may be de-
scribed as a supposition made without evidence or without
sufficient evidence, in order that we may deduce from it
conclusions agreeing with actual facts. If these conclusions
are correctly deduced, and really agree with the facts, a
presumption arises that the hypothesis is true. More-

^ The following sentences, to the end of the paragraph, are slightly
altered from Mr. Mill's Logic, Bk. III. ch. xiv. § 4.

HYPOTHESIS. 91

over, if the hypothesis relates to the cause, or mode of
production of a phenomenon, it will serve, if admitted,
to explain such facts as are found capable of being de-
duced from it And this explanation is the purpose of
many, if not most, hypotheses. Explanation, in the
scientific sense, means the reduction of a series of facts
which occur uniformly but are not connected by any
known law of causation into a series which is so con-
nected, or the reduction of complex laws of causation
into simpler laws. If no such laws of causation are
known to exist, we may suppose or imagine a law that
would fulfil the requirement ; and this supposed law would
be a hypothesis.

A hypothesis may be serviceable in many ways. In
the first place, it may afford a solution, more or less
probable, of a problem which is incapable of any definite
solution, or which, at least, has not yet been definitely
solved. Thus, many of the advocates of the Darwinian
hypothesis maintain that it is the most probable solution
of an insoluble problem. Secondly, what was at first
started as a hypothesis may ultimately be established by
positive proof, as has been the case with the elliptical
theory of planetary motion, and, as many suppose, with
the undulatory theory of light. Thirdly, even though
a hypothesis may ultimately be discovered to be false, it
may be of great service in pointing the way to a truer
theory. Thus, as already remarked, the circular theory of
planetary motion, and the supplementary theory of epi-
cycles and eccentrics, imdoubtedly contributed to the for-

92 PROCESSES SUBSIDIARY TO INDUCTION.

mation of the hypothesis which was eventually proved to
be trae. Kepler himself tried no less than nineteen dif-
ferent hypotheses, before he hit upon the right one, and
his ultimate success was, no doubt, in no slight degree
due to his unsuccessful eflforts. There is hardly any
branch of science in which it might not be affirmed
that, without a number of false guesses, true theories
could never have been attained. Lastly, a hypothesis,
whether true or false, if it be applicable to all the
known facts, serves as a means of binding those facts
together, of colligating them, to use a technical phrase,
and thus, by presenting them under one point of
view, plainly marks off the phenomena to be explained.
A theory, Uke the Phlogistic theory in Chemistry, or
the theory of epicycles and eccentrics (which, by being
sufficiently extended, might have been made to include
all the phenomena of planetary motion), may thus have
been of the greatest service in the history of science,
simply by keeping before mens minds the precise phe-
nomena which demanded an explanation.

The formation of hypotheses is obviously the work of
the imaginative faculty, a faculty of hardly less importance
in science than in art. To lay down rules for the ex-
ercise of this faculty has hitherto been found futile. The
object of Inductive Logic is rather to restrain the ex-
uberant, than to excite the sluggish, imagination. The
latter office is best fulfilled by recounting the great
achievements of science, and thus arousing the ambition
and kindling the enthusiasm of her votaries. The former

RTPOTHESIS. 93

(which is no less necessary) may be promoted by de-
termining the conditions to which a hypothesis must con- .
form, in order that it may rank as a provisional explana-
tion of facts, and before it is entitled to demand the
honom's of a rigorous inductive examination. These
conditions may be reduced to three : —

I. The hypothesis must not be known or suspected to
be untrue. It would be absurd, for instance, in the pre-
sent state of knowledge, to propose design or compact
as the cause of the divergencies of the various dialects of
a language, or to suppose the heavenly bodies to move in
perfect circles. So simple a rule as this may appear to
be superfluous, but it seems necessary to include it in the
conditions to which a hypothesis must conform, as, other-
wise, a perverted ingenuity might succeed in framing
numberless hypotheses which violated none of the pre-
liminary conditions.

II. The hypothesis must be of such a character as to
admit of verification or disproof, or at least of being
rendered more or less probable, by subsequent investiga-
tions ^. Unless this restriction were placed on the for-
mation of hypotheses, there would be no limit to the

'* It may occur to the student that we have not provided for the case
where a supposition is already supported by a certain amount of probable
evidence, but where it is not likely to be rendered more or less probable
by further investigation. But such a supposition, though it would be an
imperfect induction or deduction, could hardly be called a hypothesis, a
term which seems always to imply something provisional, something
which, on further inquiry, may be either confirmed or weakened,
rendered more or less probable than it now is.

94 PROCESSES SUBSIDIARY TO INDUCTION.

wildness of conjecture in which theorists might indulge*
. It might, for instance, be maintained that falling bodies
are dragged to the earth by the action of invisible spirits,
and, wild as such a theory would be, there is nothing
positively to disprove it. Granted that, like many other
products of imagination, such a theory might possibly
be true, it would still fall without the scope of science.
The aim of science is proof, present or prospective, and
consequently what neither admits of proof, nor, so far
as we can foresee, is ever likely to admit of it, or even
approximate to it, is no fitting object of scientific in-
quiry. As affording a caution against the unrestrained
exercise of the imagination in matters of science, it may
be useful to adduce a few instances of suppositions or
hypotheses, which were probably considered as perfectly
satisfactory by those who proposed them or amongst
whom they were prevalent, which would now be regarded
by all competent authorities as absurd, and which still do
not admit of being distinctly disproved.

It was once very generally held that the position
of the planets with reference to the earth at any par-
ticular moment determines not only the course of human
events at that time, but the subsequent life of each
person bom under the 'conjuncture.' Such an absurd
theory is now probably held by no single person of sound
understanding; but, so complicated is the web both of
society and of individual life, and so easy would it be
to explain 'apparent exceptions' by having recourse to
* counteracting causes,' that, if any ingenious person were

HYPOTHESIS. 95

to maintain and defend this theory, it would probably
be impossible to disprove it. Palmistry affords another
instance of the same kind. The interlacing of the lines
on the palms of the hands is said to indicate a man's
* fortmies.' Such a notion is too absurd to be discussed ;
but, if maintained, how could it be disproved ? It might
always be said that the general theory of palmistry was
true, though there might be some error in the particular
rules by which the 'fortune'- in question was foretold**.
The early history of Geology is full of hypotheses of
this kind. The following examples of theories, which
no scientific man would now entertain, but which hardly
admit of disproof, are extracted from LyelFs Principles
of Geology ^ .• —

* Andrea Mattioll, an eminent botanist, the illustrator of
Dioscorides, embraced the notion of Agricola, a skilful German

^ The superstitions connected with dreams afford a similar instance :
* The ancients were convinced that dreams were usually supernatural.
If the dream was verified, this was plainly a prophecy. If the event was
the exact opposite of what the dream foreshadowed, the latter was still
Supernatural, for it was a recognised principle that dreams should some-
times be interpreted by contraries. If the dream bore no relation to
subsequent events unless it were transformed into a fantastic allegory,
it was still supernatural, for allegory was one of the most ordinary forms
of revelation. If no ingenuity of interpretation could find a prophetic
meaning in a dream, its supernatural character was even then not
necessarily destroyed, for Homer said there was a special portal through
which deceptive visions passed into the mind, and the Fathers declared
that it was one of the occupations of the daemons to perplex and be-
wilder us with unmeaning dreams.' — Lecky's History of European
Morals, vol. i. p. 385.

* Lyeirs Principles of Geology, ch. iii.

g6 PROCESSES SUBSIDIARY TO INDUCTION.

miner, that a certain "materia pinguis," or "fatty matter,'*
set into fermentation by heat, gave birth to fossil organic
shapes. Yet Mattioli had come to the conclusion, from his
own observations, that porous bodies, such as bones and shells,
might be converted into stone, as being permeable to what
he termed the " lapidifying juice." In like manner, Falloppio
of Padua conceived that petrified shells were generated by
fermentation in the spots where they are found, or that they
had in some cases acquired their form from " the tumultuous
movements of terrestrial exhalations." Although celebrated
as a professor of anatomy, he taught that certain tusks of
elephants, dug up in his time in Apulia, were mere earthy
concretions ; and, consistently with these principles, he even
went so far as to consider it probable, that the vases of Monte
Testaceo at Rome were natural impressions stamped in the
soil. In the same spirit, Mercati, who published, in 1574,
faithful figures of the fossil shells preserved by Pope Sixtus V.
in the Museum of the Vatican, expressed an opinion that they
were mere stones, which had assumed their peculiar con-
figuration from the influence of the heavenly bodies: and
Olivi of Cremona, who described the fossil remains of a rich
museum at Verona, was satisfied with considering them as
mere "sports of nature." Some of the fanciful notions of
those times were deemed less unreasonable, as being some-
what in harmony with the Aristotelian theory of spontaneous
generation, then taught in all the schools. For men who had
been taught in early youth, that a large proportion of living
animals and plants was formed from the fortuitous concourse
of atoms, or had sprung from the corruption of organic matter,
might easily persuade themselves, that organic shapes, often
imperfectly preserved in the interior of solid rocks, owed their
existence to causes equally obscure and mysterious.*

* As to the nature of petrified shells, Quirini conceived that
as earthy particles united in the sea to form the shells of mol-
lusca, the same crystallizing process might be effected on the

HYPOTHESIS. 97

land ; and that, in the latter case^ the germs of the animals
might have been disseminated through the substance of the
rocks, and afterwards developed by virtue of humidity.
Visionary as was this doctrine, it gained many proselytes even
amongst the more sober reasoners of Italy and Germany ; for
it conceded that the position of fossil bodies could not be
accounted for by the diluvial theory.*

It has been maintained by theologians, more ardent
than discreet, that all fossils were the creations of the
Devil, whose object was either to mimic the Almighty
or to tempt mankind to disbelieve the Mosaic account
of the creation. Such theories admit of no refutation;
every argument, grounded on the resemblance of fossil
remains to living organisms, shows only more distinctly,
to those who have once embraced the idea, the success
of the supposed agent as a mimic or as an impostor.

Other instances of hypotheses which violate this rule are
afforded by the Vortices of Descartes and the Crystalline
Spheres of the ancient astronomers, both of which were
imagined for the purpose of accounting for the pheno-
mena of planetary motion. Both of these hypotheses
have been subsequently disproved by the free passage of
comets through the spaces supposed to be occupied,
according to the one theory, by the Vortices, according
to the other, by the soUd Crystalline Spheres. But at
the time they were first started, there was no reasonable
ground for supposing that, if untrue, they could be dis-
proved, and, what is more important, there was no
possibiUty of proving them or even rendering them
more probable ; they were simply freaks of imagination,

H

98 PROCESSES SUBSIDIARY TO INDUCTION.

incapable of proof and, to all appearance, of disproof.
Another theory more absurd even than that of the solid
crystalline spheres, but which has not, like that, been
positively disproved, is the curious hypothesis by which
Lodovico delle Colombe endeavoured to reconcile the
Aristotelian doctrine that the moon was a perfect body
with the recent discoveries of Galileo, who, by the aid
of his telescope, had found that its surface was full of
hollows, and was consequently charged by his enemies
with taking a fiendish delight in distorting the fairest
works of nature ; the apparently hollow parts, suggested
Lodovico, were filled with a pure transparent crystal, and
so both the astronomer and the Stagirite were right.

It will be observed that we regard hypotheses as ad-
missible, even though they are not likely ever to be
positively proved or disproved, provided that the accumu-
lation of further evidence is likely to render them more
or less probable. Between such theories and the theories
just exemplified, which are neither supported nor likely
to be supported by any evidence whatever, there is the
widest difference, and, while the one have no place in
Science, the other, we conceive, have a legitimate claim
to further consideration. The ideal of Science, it is true,
is proof; but, while it can never recognise mere freaks
of fancy, it is often compelled to rest content with pro-
babilities. Instances of the hypotheses which we have
in view are the Darwinian hypothesis and the Meteoric
theory of the repair of Solar Heat, to be noticed pre-
sently.

HYPOTHESIS. 99

III. The hypothesis must be applicable to the descrip-
tion or explanation of all the observed phenomena, and,
if it assign a cause, must assign a cause fully adequate
to have produced them. A hypothesis, which does not
satisfy this requirement, may be at once rejected. Thus,
when the circular theory of planetary motion was found
inapplicable to describe several of the phenomena, it
was rightly abandoned, and the theory of epicycles and
eccentrics, which, though erroneous, was fully adequate
to explain all the known phenomena, was substituted for
it. One of the most familiar instances of an inadequate
hypothesis is the theory started by Voltaire, there is little
doubt in irony, that the marine shells found on the tops
of moimtains are Eastern species, dropped from the hats
of pilgrims, as they returned from the Holy Land. Such
a theory would obviously be inadequate to accoimt (i) for
the numbers of the shells, (2) for the fact that they are
found imbedded in the rocks, (3) for their existence far
away from the tracks of pilgrims, to say nothing of the
fact that many of these shells bear no resemblance to
recent Eastern species, while none resemble them exactly.
The contrast between an adequate and an inadequate
hypothesis is well illustrated by two of the rival hypo-
theses by which it is attempted to account for the genera-
tion and the maintenance of solar heat. These are
respectively the Meteoric Theory and the Theory of
Chemical Combustion. In speaking of the former theory.
Professor Tyndall says*'^ :—

^ Heat a Mode of Motion, §§ 689-693.

H 2

lOO PROCESSES SUBSIDIARY TO INDUCTION.

* I have already alluded to another theory, which, however
bold it may at first sight appear, deserves our serious atten-
tion — the Meteoric Theory of the Sun. Kepler's celebrated
statement that " there are more comets in the heavens than
fish in the ocean," implies that a small portion only of the
total number of comets belonging to our system are seen
from the earth. But besides comets, and planets, and moons,
a numerous class of bodies belong to our system which, from
their smallness, might be regarded as cosmical atoms. Like
the planets and the comets, these smaller asteroids obey the
law of gravity, and revolve in elliptic orbits round the sun.
It is they which, when they come within the earth's atmo-
sphere, and are fired by friction, appear to us as meteors and
falling stars.

* On a bright night, twenty minutes rarely pass at any part
of the earth's surface, without the appearance of at least one
meteor. Twice a year (on the 12th of August and 14th of
November) they appear in enormous numbers. During nine
hours in Boston, when they were described as falling as thick
as snowflakes, 240,000 meteors were observed. The number
falling in a year might, perhaps, be estimated at hundreds or
thousands of millions, and even these would constitute but
a small portion of the total crowd of asteroids that circulate
round the sun. From the phenomena of light and heat, and
by direct observations on Encke's comet, we learn that the
universe is filled by a resisting medium, through the friction
of which all the masses of our system are drawn gradually
towards the sun. And though the larger planets show, in
historic times, no diminution of their periods of revolution,
it may be otherwise with the smaller bodies. In the time
required for the mean distance of the earth to alter a single
yard, a small asteroid may have approached thousands of miles
nearer to the sun.

' Following up these reflections, we should be led to the
conclusion, that while an immeasurable stream of ponderable

HYPOTHESIS. lOI

meteoric matter moves unceasingly towards the sun, it must
augment in density as it approaches its centre of convergence.
And here the conjecture naturally rises, whether that vast
nebulous mass, the Zodiacal Light, which embraces the sun,
may not be a crowd of meteors. It is at least proved that
this luminous phenomenon arises from matter which circulates
in obedience to planetary laws ; hence, the entire mass of the
zodiacal light must be constantly approaching, and incessantly
raining its substance down upon the sun.

* It is easy to calculate both the maximum and the minimum
velocity, imparted by the sun's attraction to an asteroid circu-
lating round him. The maximum is generated when the body
approaches the sun from an infinite distance; the entire pull
of the sun being then exerted upon it. The minimum is that
velocity which would barely enable the body to revolve round
the sun close to his surface. The final velocity of the former,
just before striking the sun, would be 390 miles a second, that
of the latter 276 miles a second. The asteroid, on striking
the sun, with the former velocity, would develope more than
9000 times the heat generated by the combustion of an equal
asteroid of solid coal; while the shock, in the latter case,
would generate heat equal to that of the combustion of up-
wards of 4000 such asteroids. It matters not, therefore,
whether the substances falling into the sun be combustible or
not ; their being combustible would not add sensibly to the
tremendous heat produced by their mechanical collision.

' Here, then, we have an agency competent to restore his
lost energy to the sun, and to maintain a temperature at his
surface which transcends all terrestrial combustion. In the
fall of asteroids we find the means of producing the solar light
and heat. It may be contended that this showering down of
matter necessitates the growth of the sun ; it does so ; but
the quantity necessary to maintain the observed calorific
emission for 4000 years, would defeat the scrutiny of our best
instruments. If the earth struck the sun, it would utterly

I03 PROCESSES SUBSIDIARY TO INDUCTION.

vanish from perception ; but the heat developed by its shock
would cover the expenditure of a century.'

Of the other theory, Professor Tyndall says'^ : —

* Sir William Thomson adduces the following forcible
considerations to show the inadequacy of chemical com-
bination to produce the sun's heat. "Let us consider," he
says, "how much chemical action would be required to
produce the same effects. . . . Taking the former estimate,
2781 thermal units ^ Centigrade (each 1390 foot pounds)
or 3,869,000 foot pounds, which is equivalent to 7000 horse-
power, as the rate per second of emission of energy from
every square foot of the sun's surface, we find that more
than 0.42 of a pound of coal per second, 1500 lbs. per hour,
would be required to produce heat at the same rate. Now
if all the fires of the whole Baltic fleet (this was written in
1854) were heaped up and kept in full combustion over one
or two square yards of surface, and if the surface of a globe
all round had every square yard so occupied, where could
a sufficient supply of air come from to sustain the com-
bustion? Yet such is the condition we must suppose the
sun to be in, according to the hypothesis now under con-
sideration. ... If the products of combustion were gaseous,
they would, in rising, check the necessary supplies of fresh
air; if they were solid and liquid (as they might be if the
fuel were metallic), they would interfere with the suj^ly of
elements from below. In either, or in both ways, the fire
would be choked, and I think it may be safely affirmed that
no such fire could keep alight for more than a few minutes,

*® Heat a Mode of Motion^ § 700.

^ The thermal unit is the quantity of heat necessary to raise the
temperature of a pound of water one degree. If the degree be centi-
grade, this is equivalent to the heat generated by a pound weight falling
from a height of 1390 feet against the earth. The term foot-pound
expresses the energy requisite to lift one pound to the height of a foot.

HYPOTHESIS. 103

by any conceivable adaptation of air and fuel. If the sun
be a burning mass it must be more analogous to burning
gunpowder than to a fire burning in air; and it is quite
conceivable that a solid mass, containing within itself all the
elements required for combustion, provided the products of
combustion are permanently gaseous, could bum oflf at its
surface all round, and actually emit heat as copiously as the
sun. Thus, an enormous globe of gun-cotton might, if at
first cold, and once set on fire round its surface, get to a
permanent rate of burning, in which any internal part would
become heated sufficiently to ignite, only when nearly ap-
proached by the burning surface. It is highly probable
indeed that such a body might for a time be as large as the
sun and give out luminous heat as copiously, to be freely
radiated into space, without suflfering more absorption from
its atmosphere of transparent gaseous products than the light
of the sun actually does experience from the dense atmo-
sphere through which it passes. Let us therefore consider
at what rate such a body, giving out heat so copiously, would
burn away ; the heat of combustion could probably not be so
much as 4000 thermal units per pound of matter burned, the
greatest thermal equivalent of chemical action yet ascertained
falling considerably short of this. But 2781 thermal units
(as found above) are emitted per second from each square
foot of the sun; hence there would be a loss of about 0.7
of a pound of matter per square foot per second ... or
a layer half a foot thick in a minute, or 55 miles thick in
a year. At the same rate continued, a mass as large as the
sun is at present would burn away in 8000 years. If the sun
has been burning at that rate in past time he must have been
of double diameter, of quadruple heating power, and of eight-
fold mass only 8000 years ago. We may therefore quite
safely conclude that the sun does not get its heat by chemical
action . . . and we must therefore look to the meteoric theory
for fuel.*

I04 PROCESSES SUBSIDIARY TO INDUCTION.

A hypothesis which fulfils these three conditions is a
legitimate hypothesis, though it must conform to still more
rigorous requirements before it can be accepted as a
complete Induction, or even be regarded as possessing
any great amount of probability. Thus, the Meteoric
Theory, though it is not yet proved, and perhaps never
may be proved, to be the true explanation of the pheno-
menon of solar heat, is perfectly tenable as a hypothesis.
For, to state the conditions in the reverse order to that
in which they have been enumerated above, the impact
of a large number of meteors on a dense body, such as
the sun probably is, would be competent or adequate to
produce the given effect ; the theory in question is likely,
if not to be proved or disproved, at least to be rendered
more or less probable by the progress of astronomical
science ; lastly, we do not know, nor have we any reason
to suppose, that the hypothesis is an untrue explanation
of the facts. But, though legitimate as a hypothesis,
before we could accept the Meteoric Theory as a Valid
or Complete Induction, we should require to know not
only that there is a large number of meteors circulating
round the sun, that these meteors have a tendency to fall
into the central body, and that, i/thty fall or had fallen
in sufficient quantities, they would be competent or would
have been competent to produce the present amount of
solar heat, but also that they do, as a matter of fact, fall
in sufficient quantities to account for the phenomenon,
or, at least, that nothing else but the showering down of
asteroids and meteors could account for it.

HYPOTHESIS. 105

It was by availing himself of the latter mode of proof
that Newton demonstrated the existence in the sun of a
central force attracting the planets towards it. Assuming
Kepler's hypothesis (then sufficiently verified by obser-
vation to be universally accepted as a true statement
of the facts), that equal areas are described by the
radii vectores of the planets in equal times, Newton
showed that this fact could be due to only one cause,
namely, the deflection of the planets from their recti-
linear course by a force acting in the direction of the
sun's centre. The existence of the central force was,
at first, started by him as a hypothesis. * He then proved
that,' on the supposition of the existence of such a force,
'the planet will describe, as we know by Kepler's first
law that it does describe, equal areas in equal times ; and,
lastly, he proved that if the force acted in any other di-
rection whatever, the planet would not describe equal
areas in equal times. It being thus shown that no other
hypothesis would accord with the facts, the assumption
was proved; the hypothesis became an inductive truth.
Not only did Newton ascertain by this hypothetical pro-
cess the direction of the deflecting force ; he proceeded
in exactly the same manner to ascertain the law of varia-
tion of the quantity of that force. He assumed that the
force varied inversely as the square of the distance;
showed that from this assumption the remaining two of
Kepler's laws might be deduced; and finally, that any
other law of variation would give results inconsistent with
those laws, and inconsistent, therefore, with the real

lo6 PROCESSES SUBSIDIARY TO INDUCTION.

motions of the planets, of which Kepler's laws were
known to be a correct expression *^/

It will be noticed that the course of demonstration pur-
sued in this instance is the following : (i) we have certain
observed facts ; (2) these observed facts are generalised
in what are called Kepler's Laws; (3) we have the
assimiption of the central force ; (4) it is shown that the
central force will account for Kepler's Laws, and there-
fore, of course, for the particular facts of observation on
which those Laws were founded; (5) it is shown (and
this is what properly constitutes the demonstration)
that this assumption is the only one which will account
for the Laws or the particular facts expressed by them ;
(6) it is inferred inductively, by means of the Method
of Difference (to be hereafter described), that the as-
sumption of the central force, as it will account for, and
is the only supposition which will account for, the ob-
served facts, must be accepted as true ; (7) Kepler's
Laws (which had hitherto been accepted as correct
statements of observed facts, though they had not yet
been explained by reference to any cause competent
to account for them) are now proved deductively from
what we have ascertained to be the Valid Induction of
the Central Force.

A Hypothesis can only be converted into a Valid
Induction*^ by the application of one or other of the

*" Mill's Logic, Bk. III. ch. xiv. § 4.

" Though a hypothesis is usually contrasted with a Valid or Com-
plete Induction, it must not be forgotten that we have admitted, as

HYPOTHESIS, 107

Inductive Methods (to be described in the next Chapter),
or, if we insist on strict accurdcy of proof, of such of
them as furnish absolutely certain conclusions.

Note I. — According to the view here taken, which
agrees with that of Mr. Mill, a hypothesis cannot claim
to be regarded as an established truth, till it has con-
formed to the requirements of one or other of the
inductive methods, or has been shown to admit of
being deduced from some previously established In-
duction. Thus, when Newton proves the existence of
a central force, deflecting the planets from the recti-
lineal course which they would otherwise describe and
making them describe curves round the sun, by show-
ing that no other supposition would account for the fact
that their radii vectores describe equal areas in equal times,
he is, as Mr. Mill says, employing the Method of Difference.
The demonstration ' affords the two instances, ABC,
a be, and 'B C, he, A represents central force ; ABC,
the planets plus a central force ; B C, the planets as they
would be without a central force. The planets with a
central force give a (areas proportional to the times) ; the

legitimate, hypotheses which are never likely to rest on more than pro-
bable evidence. These can, of course, receive accessions of proof only
by the same means as those by which we establish Imperfect Inductions.
It should also be remembered that the truth of a hypothesis may be
demonstrated by deductive as well as by inductive methods.

Io8 PROCESSES SUBSIDIARY TO INDUCTION.

planets without a central force give 3 r (a set of motions)
without a, or with something else instead of a. This is
the Method of Difference in all its strictness. It is true,
the two instances which the method requires are obtained
in this case, not by experiment, but by a prior deduction.
But that is of no consequence. It is immaterial what is
the nature of the evidence from which we derive the as-
surance that ABC will produce adc^ and B C only dc ;
it is enough that we have that assurance. In the present
case, a process of reasoning furnished Newton with the
very instances, which, if the nature of the case had ad-
mitted of it, he would have sought by experiment *^'

Dr. Whewell, who does not acknowledge the utility of
Mr. Mill's methods, appears to regard the inductive pro-
cess as consisting simply in the framing of successive
hypotheses, the comparison of these hypotheses with the
ascertained facts of nature, and the introduction into
them of such modifications as that comparison may
render necessary. The first requisite in a hypothesis,
according to Dr. Whewell, is that it shall explain all
the observed facts. But its probability, he urges, will
be considerably enhanced, if, in addition to explaining
observed facts, it enables us to predict the future.
' Thus the hypotheses which we accept ought to explain
phenomena which we have observed. But they ought
to do more than this : our hypotheses ought to foretel
phenomena which have not yet been observed; at least

*» MUl's Logic, Bk. III. ch. xiv. § 4.

HYPOTHESIS. 109

all phenomena of the same kind as those which the
hypothesis was invented to explain. For our assent to
the hypothesis implies that it is held to be true of all
particular instances. That these cases belong to past or
to future times, that they have or have not already oc-
curred, makes no difference in the applicability of the
rule to them. Because the rule prevails, it includes all
cases ; and will determine them all, if we can only cal-
culate its real consequences. Hence it will predict the
results of new combinations, as well as explain the ap-
pearances which have occurred in old ones. And that
it does this with certainty and correctness, is one mode
in which the hypothesis is to be verified as right and
useful *'.'

Curiously enough, the first hypothesis which Dr.
Whewell cites as having fulfilled both these conditions,
is also one which eventually proved to be false. *For
example, the Epicyclical Theory of the heavens was
confirmed by its predicting truly eclipses of the sun
and moon, configurations of the planets, and other
celestial phenomena; and by its leading to the con-
struction of Tables by which the places of the heavenly
bodies were given at every moment of time. The truth
and accuracy of these predictions were a proof that the
hypothesis was valuable, and, at least to a great extent,
true; although, as was afterwards found, it involved a
false representation of the structure of the heavens.' A

^ Novum Organon Renovatumt Bk. II. cb. v. art. 10.

no PROCESSES SUBSIDIARY TO INDUCTION.

theory may thus not only enable us to explain known
facts, but even to predict the future, and still be untrae.
Notwithstanding, however, the infelicitous character of the
example, Dr. Whewell attaches the greatest importance
to the fulfilment of this condition by a hypothesis. * Men
cannot help believing that the laws laid down by dis-
coverers must be in a great measure identical with the
real laws of nature, when the discoverers thus determine
effects beforehand in the same manner in which nature
herself determines them when the occasion occurs. Those
who can do this, must, to a considerable extent, have
detected nature's secret ; — ^must have fixed upon the con-
ditions to which she attends, and must have seized the
rules by which she applies them. Such a coincidence of
untried facts with speculative assertions cannot be the
work of chance, but implies some large portion of truth
in the principles on which the reasoning is founded. To
trace order and law in that which has been observed, may
be considered as interpreting what nature has written
down for us, and will commonly prove that we under-
stand her alphabet. But to predict what has not been
observed, is to attempt ourselves to use the legislative
phrases of nature; and when she responds plainly and
precisely to that which we thus utter, we cannot but sup-
pose that we have in a great measure made ourselves
masters of the meaning and structure of her language.
The prediction of results, even of the same kind as those
which have been observed, in new cases, is a proof of real
success in our inductive processes.'

HYPOTHESIS. Ill

But what appears to Dr. Whewell to establish the truth
of a hypothesis beyond all question is what he calls a
Consilience of Inductions. ' We have here spoken of the
prediction of facts of the same kind as those from which
our rule was collected. But the evidence in favour of our
induction is of a much higher and more forcible character
when it enables us to explain and determine cases of
a kind different from those which were contemplated in
the formation of our hypothesis. The instances in which
this has occurred, indeed, impress us with a conviction
that the truth of our hypothesis is certain. No accident
could give rise to such an extraordinary coincidence. No
false supposition could, after being adjusted to one class
of phenomena, exactly represent a different class, where
the agreement was unforeseen and uncontemplated. That
rules springing from remote and unconnected quarters
should thus leap to the same point, can only arise from
that being the point where truth resides.

* Accordingly the cases in which inductions from classes
of facts altogether different have thus jumped together,
belong only to the best established theories which the
history of science contains. And as I shall have occasion
to refer to this peculiar feature in their evidence, I will
take the liberty of describing it by a particular phrase;
and will term it the Consilience of Inductions,

'It is exemplified principally in some of the greatest
discoveries. Thus it was found by Newton that the
doctrine of the Attraction of the Sun varying according
to the Inverse Square of the distance, which explained

112 PROCESSES SUBSIDIARY TO INDUCTION.

Kepler's Third Law, of the proportionality of the cubes
of the distances to the squares of the periodic times of
the planets, explained also his First and Second Laws,
of the elliptical motion of each planet ; although no con-
nection of these laws had been visible before. Again, it
appeared that the force of Universal Gravitation, which
had been inferred from the Perturbations of the moon
and planets by the sun and by each other, also accounted
for the fact, apparently altogether dissimilar and remote,
of the Precession of the equinoxes. Here was a most
striking and surprising coincidence, which gave to the
theory a stamp of truth beyond the power of ingenuity to
counterfeit **/

It is undeniable that a theory which thus appears to
afford an explanation of different classes of facts strikes
the imagination with considerable force, and that its very
simplicity furnishes primd facie evidence of its truth.
But what is required before a hypothesis can be placed
beyond suspicion is formal proof, and that, it appears
to me, is furnished by Mr. Mill's 'methods,' and not
by Dr. WhewelFs requisitions of explanation, prediction,
and consilience of inductions. For the questions at issue
between Mr. Mill and Dr. Whewell, see WhewelFs
Novum Organon Renovatum (where his views are stated
in their latest and most matured form), Bk. II. ch. v.
§ 3, and Mill's Logic, Bk. III. ch. xiv. § 6.

** Novum Organon Renovatum^ Bk. II. ch. v. art. 1 1 .

HYPOTHESIS. 113

Noie 2. — In attempting to determine the conditions to
which a legitimate hypothesis must conform, I have avoided
the employment of the expressions vera causa and adcB'
quata causa. In the first place, a hypothesis may simply
attempt to find a general expression for a number of
isolated facts without referring them to any cause, as was
the case with the various hypotheses respecting the shape
of the planetary orbits, and hence to speak as if a
hypothesis always assigned a cause is an undue limitation
of the meaning of the word. But to the expression vera
causa there is a more special exception. Its meaning is
ambiguous. Is it the actual cause which produces a pheno-
menon, or a cause which we know to be actually existent,
or a cause analogous to an existent cause ? The student
will find a criticism of this expression (first employed by
Newton) in Dr. WhewelFs Philosophy of Discovery, ch. xviii.
§ 5, &c. The expression cannot have been used in the first,
which is its most obvious, sense, for, as Dr. Whewell says,
* although it is the philosopher's aim to discover such
causes, he would be little aided in his search of truth, by
being told that it is truth which he is to seek.' But in the
second of the two remaining senses, the requirement, as
would now be generally acknowledged, is too stringent,
and, if it had been invariably observed, would have pre-
vented us from reaping some of the greatest discoveries
in science, while in the last it is so vague as to be of no
practical service. It has been attempted to aflix other
meanings to the phrase; but there can be little doubt
that Newton, having in mind the Vortices of Descartes,

114 PROCESSES SUBSIDIARY TO INDUCTION,

intended to protest against the introduction of causes of
whose existence we have no direct knowledge, and con-
sequently laid down a rule, which the subsequent history
of science has shown to be needlessly stringent.

Note 3. — We sometimes find the expression a * gratuitous
hypothesis/ By this is meant the assumption of an
unknown cause, when the phenomenon is capable of
being explained by the operation of known causes, or
the introduction of an^ extraneous (though it may be
known) cause, when the phenomenon is capable of being
accounted for by the causes already known to be in
operation. Of the latter case we should have instances,
where a man is supposed to have acted at the suggestion
of another, though his own motives would supply a
sufficient explanation of his conduct, or where a man
is supposed to have been poisoned though he was already
known to have been suffering from a fatal disease. Of
the former case we should have instances in the crystalline
spheres of the- ancient astronomers and in the masses
of crystal which were supposed by Lodovico delle Colombe
to fill up the cavities of the moon (there being no in-
stances known to us of the existence of crystal in these
huge masses, and the phenomena being capable of
explanation without making the supposition); in the
caloric (which was supposed to be a distinct substance)
of the early writers on heat, and in the * electrical fluid'
of the early electricians. In all these instances, under

HYPOTHESIS. 115

whichever of the two cases they may fall, the objection
to the hypothesis is that it seems ' not to be needed/

I have said nothing of * gratuitous hypotheses ' in the
text, as a h}'pothesis, though it may appear to be gra-
tuitous, may still be legitimate, and may even ultimately
turn out to be true.

c*gg<-e5-<

1 2

CHAPTER III.
On the Inductive Methods.

INDUCTION has been defined to be a legitimate
inference from the known to the imknown. But the
unknown must not be entirely imknown. It must be
known to agree in certain circumstances with the known,
and it is in virtue of this agreement that the inference is
made. Now, how are we to ascertain what are the com-
mon circumstances which justify the inductive infer-
ence. X and Y may both agree in exhibiting the circum-
stances ay 3, r, but it will not follow because X exhibits
the quality niy that therefore this quality will also neces-
sarily be found in Y. Nor even, if twenty, thirty, a
hundred, or a thousand cases could be adduced in which
the circumstances a^ h, c were found to be accompanied
by the circumstance m, would it follow necessarily (it
might not even follow probably) that the next case in
which we detected the circumstances a^bjC would also
exhibit the quality m. We might pass through a field
containing thousands of blue hyacinths, but this would
not justify us in expecting that the next time we saw a

INDUCTIVE METHODS. II7

hyacinth, it would be a blue one. This form of induction
(Indudio per Simplicem Enumerationem) may have no
value whatever. In most cases, the condemnation passed
on it by Bacon ^ is perfectly just: 'Inductio quae pro-
cedit per enumerationem simplicem, res puerilis est, et
precario concludit, et periculo exponitur ab instantia con-
tradictoria, et plenimque secundum pauciora quam par
est, et ex his tantummodo quae praesto sunt, pronunciat.'
But if we have reason to think that any instances to the
contrary, if there were such, would be known to us, the
argument may possess considerable value, and if, as in
the case of the Laws of Causation and of the Uniformity
of Nature, we feel certain, from a wide and various ex-
perience, that there are no cases to the contrary, no
stronger argument (to us individually) can be adduced.
It is rarely, however, that an Inductio per Simplicem
Enumerationem can afford us this certainty ^. Our trust-
worthy inductions are, in nearly all cases, the result of
our detecting some fact of causation among the observed
phenomena. We find, for instance, that, amongst the
observed phenomena «, 3, r, d of X, a is the cause of r,
and, consequently, if we observe the phenomenon a in Y,
we infer that, if there are no counteracting circumstances,
Y will possess the quality c as well ; or, if we observe

* Novum Organunit Bk. I. aph. cv.

^ It must be remembered that a complete enumeration of instances,
when we know the enumeration to be complete, inasmuch as it leaves
no room for an inference from the known to the unknown, does not
furnish an inductive but a deductive argument. See Elements 0/ De-
ductive Logic, Part III. ch. i. appended Note a.

Il8 INDUCTIVE METHODS.

the phenomenon c in Y, we infer that it is not unlikely '
that a may be present as well. The problem of Indue-
tion, therefore, resolves itself (except in the few very rare
cases in which we may legitimately employ Inductio per
Simplicem Enumerationem) into the problem of detecting
facts of Causation. Certain rules for this purpose have
been laid down by Mr. Mill, called by him the Experi-
mental Methods, but which we shall distinguish as the
Inductive Methods.

Before proceeding to state and explain these Rules or
Methods, it may be useful to make some preliminary
remarks on the nature of the causal relations which may
subsist among phenomena.

(i) The same cause, unless there are counteracting
circumstances, that is, other causes which prevent it from
acting or which modify its action, is invariably followed
by the same effect.

(2) As already shown (Chapter I. pp. 10-12), several
causes may have co-operated in producing any given
effect In this case, it is not unusual to speak of the
' combination of causes ' or the * sum of the causes.'

(3) The same effect may be due to several distinct
causes, or combinations of causes, being due sometimes
to one and sometimes to another, and, hence, though we
may always argue from a particular cause to its effect, we
cannot always argue from an effect to any particular

^ We say * not unlikely/ for c might be due to some other cause as
well as a, and, therefore, the presence of c does not enable us to infer
with certainty the presence of a, as that of a does the presence of c.

INDUCTIVE METHODS. II9

cause, Thus, ignition may be due, not only to the concen-
tration of the rays of. solar heat, but also to friction,
electricity, &c.

(4) It frequently happens that between the original
cause and the ultimate effect there intervene a number
of intermediate causes. Thus, suppose we make an
experiment by which motion is converted into heat, heat
into electricity, and electricity into chemical affinity ; we
might, roughly speaking, say that motion had been
the cause of the chemical afl&nity, or chemical affinity
the effect of the motion, but, speaking strictly, we ought
to enumerate the intervening causes.

(5) Sometimes a number of effects appear to be pro-
duced simultaneously by the same cause. Thus, it would
appear that there are many cases in which, if one of the
agents, motion, heat, light, electricity, magnetism, and
chemical action, is excited, the rest are simultaneously
developed*. These simultaneous effects, whether we
conceive that they are really or only apparently simul-
taneous, would be called joint or common effects of. the
cause. The expression * joint effects ' is also employed
for the effects produced by the same cause on different
bodies, or different portions of the same body. Thus, if
a blow bruises my forehead, and at the same time gives
me a headache, the bruise and the headache would be
called joint effects of the blow. These joint effects may
be, as it were, in different degrees of descent from the
same cause. Thus, if the headache incapacitates me for

* See Grove's Correlation of Physical Forces, Concluding Remarks.

lao INDUCTIVE METHODS.

work, my incapacity for work and the bruise on my fore-
head would be joint effects, but in different degrees of
descent from the original cause.

Any phenomena which are cpnnected, either as cause
and effect, and that either immediately or remotely, or as
joint effects, and that either in the same or in different
degrees of descent from the same cause, may be spoken
of as being causally connected^ or as being related to one
another through ^m&facl of causation.

We now proceed to the statement of the Inductive
Methods.

METHOD OF AGREEMENT.
CANON ^,

If two or more instances of the phenomenon under investi-
gation have only one circumstance in common^ the circum-
stance in which alone all the instances agree may he regarded,
with more or less of probability , as the cause (or effect) of the
given phenomenon^ or, at least, as connected with it through
some fact of causation.

Wherever the phenomenon a is found, we observe that
b is found, either invariably or frequently ^, in conjunction

' The statement of the Canons is taken, with some modifications,
from Mr. Mill's Logic. The authorities for the various examples, when
these are not of a familiar character, are cited at the foot of the page.

' We add * or frequently,* as it is not necessary that the conjunction
shall be invariable. The student need not, however, at present trouble
himself with the distinction, which will be fully explained below. See
pp.128, 135-137-

METHOIi OF AGREEMENT, 121

with it. This fact leads us to suspect that there is some
causal connection between them. On what grounds,
and under what circumstances, are we justified in drawing
such an inference ? And what is the particular character
of the inference which we are justified in drawing?
The answer to these questions involves many difiiculties,
of which we shall now attempt to offer a solution.

When antecedents and consequents are discriminated
in this discussion, antecedents will be represented by
Roman capitals, A, B, C, &c., and consequents by Greek
characters, a, ft y, &c. When circumstances are not
distinguished as antecedents and consequents, we shall
employ the small Roman letters, a, b, c, &c.

Now, suppose that we have A B followed by o 0, and
A C by a y ; it might, at first sight, appear that A must be
the cause of a, or, if we were attempting to ascertain the
effect of a given cause (which, however, is a much rarer
application of this method), that a must be the effect
of A. And there is much plausibility in this supposition,
for whatever can, in any given instance, be excluded,
or, to use the technical term, eliminated without pre-
judice to a phenomenon, cannot have any influence
on it in the way of causation, nor can an effect which
disappears be due to a cause which continues to
operate. Thus, if we were attempting to find the
cause of a given effect a, it might be argued that B
cannot be its cause, for it is absent in one of the cases
where a is present, and similarly of C ; but that a must be
due to some cause; and, consequently, is due to A, the only

122 INDUCTIVE METHODS.

antecedent remaining. Or, if we were attempting to find
the effect of a given cause A, it might be argued that fi
cannot be its effect, for it is absent in one of the cases
where A is present, and similarly of y; but that, as a has
been permanently present, A must be its cause. If it
were not for the fact that the same event may be due to
a great number of distinct causes (as is exemplified in the
familiar cases of motion, death, disease, &c.), this reason-
ing would be perfectly just. Now it will be observed that,
when B was removed, it was replaced by C. It is, there-
fore, conceivable that a may have been due to B in the
first instance, and to C in the second, it being, of course,
in each case, only a portion of the effect, the remaining
portions being respectively /S, y, and A having been
throughout inoperative. This consideration, it is plain,
vitiates the reasoning, whether we are attempting to dis-
cover the effect of a given cause or the cause of a given
effect. Thus, suppose that there are two distinct drugs,
either of which is potent to remove a given disease, and
that, in administering each of them, we mix it with some
perfectly inert substance, which is the same in each
case ; if the principles of the above reasoning were cor-
rect, and we were justified in neglecting to take account
of what may be called the Plurality of Causes, we should
be at liberty to argue (if we were seeking the cause of a
given effect) that the restoration of the patients to health
was, in each case, due to the inert substance, or (if we
were seeking the effect of a given cause) that the inert
substance was the cause of their restoration to health.

METHOD OF AGREEMENT. 1 23

But, if the Method of Agreement is open to so serious
an objection, it may be asked on what grounds is it
recognised as an Inductive Method? The answer is
that, by the multiplication and variation of instances, the
possible error due to the Plurality of Causes may be
rendered less and less probable, till, at last, for all
practical purposes, it may be regarded as having dis-
appeared. Thus, if to the instances AB, ajS; AC, ay;
we can add A D, ad; A E, ae, &c. &c. ; it is plain that we
may, at each step, be very considerably diminishing the
possibility of an error in our reasoning, and, after a certain
number of instances, may be justified in feeling morally
certain that we have avoided it. It is not likely that,
in a number of instances, each agreeing in some one
circumstance (besides the phenomenon which is being
investigated) but differing as widely as possible in all
other circumstances, the same event should in each case,
or in a majority of cases, or in even a great number of
cases, be due to different causes. The chance of an inert
substance being successively mixed with two potent
drugs, and of the effects which are really due to them
being erroneously ascribed to it, is, in the present state
of medical science, but a very slight one; but the pro-
bability is obviously considerably diminished, if instead
of two such errors we suppose three, instead of three
we suppose four, and so on.

For the sake of simplicity, we have assumed groups
of two antecedents and two consequents (A B, ajS ; A C,
ay ; &c. &c.), but it is extremely seldom that we find in

124 INDUCTIVE METHODS.

nature combinations so simple. We have usually a vast
mass of antecedents and a vast mass of consequents
(or, to state the same proposition in more scientific
language, a vast mass of antecedents all, or most of them,
contributing to a complex efiect), and hence it often
becomes a matter of extreme difficulty to discover a
collection of instances which, presenting the phenomenon
in question, agree in only one other circumstance or even
in a small number of other circumstances. The dif-
ficulty, therefore, of rigidly satisfying the requirements
of the Method must be added to what Mr. Mill calls its
characteristic imperfection^ namely, the imcertainty attach-
ing to its conclusions from the consideration of the
Plurality of Causes.

But there is still a third difficulty incident to the
Method of Agreement, which, however, is, in a majority
of cases, of a theoretical rather than a practical nature.
If we insisted literally on the fulfilment of the condition
that the instances presenting the given phenomenon
should have only one other circumstance in conunon,
it would be simply impossible to find such instances.
All instances must agree in a number of circumstances
which are immaterial to the point under investigation.
Thus, if we are enquiring into the properties of a group
of external objects, they will all agree in the fact that they
are subject to the action of gravity, and probably also
in the facts that they are surrounded by atmospheric air
and exposed to the light of the sun; but, if these facts
do not affect the subject of our enquiry, we piay pass

METHOD OF AGREEMENT. 12^

them over as if they had no existence. When, therefore,
we employ the expression *only one circumstance in
common,' we must be understood to mean 'only one
material circumstance,' and to exclude all circumstances
which a wide experience or previous inductions have
shown to be immaterial to the question before us. It
need hardly be added that, in forming this judgment
as to the material or immaterial character of the circum-
stances, the greatest caution is often required.

But, suppose we have ascertained (when enquiring
into the cause of a given effect) that the instances agree
in only one antecedent (or rather one material ante-
cedent), namely A, and that we have so multiplied and
varied the instances as to have satisfied ourselves that
we have excluded the possibility of a Plurality of
Causes, are we justified in drawing the inference that
A is the cause of a? We are so justified, for a must
be due to something which went before it, and, as it
has been shown that it is not due to any of the other
antecedents, it must be due to A. Similarly, if our
object be to enquire into the effect of a given cause A,
we are justified, if we discover a consequent a, of which
we can assure ourselves that it is not due to any of the
other antecedents, in regarding it as the effect of A.

Hitherto, we have supposed the antecedents and con-
sequents to be discriminated. But, suppose that we have
a number of phenomena abcde, adefg, &c., in which
we cannot discriminate them, how will the conclusions
of the Method of Agreement be affected? There will,

126 INDUCTIVE METHODS.

as in the former cases, obviously be the difficulties arising
from Plurality of Causes and the complexity of the
phenomena. Supposing, however, these to be overcome,
and two circumstances only, a and b, to have been ascer-
tained to be common to all the instances, what conclusion
shall we be justified in drawing with reference to the
connection between a and b ? It is only reasonable
to suppose that they must be causally connected in
some way, else their connection would be a mere
casual coincidence; a supposition which we assume to
have been excluded by the number and variety of the
instances examined. But they need not necessarily stand
to each other in the relation of cause and effect, for they
may be common effects (in the same, or in different
degrees of descent) of some cause which has itself ceased
to operate. In social and physiological phenomena this
is frequently the case. A disease will leave effects behind
it which will continue to co-exist for years after the
disease has passed away, and which, though not standing
to each other in the relation of cause and effect, are thus
causally connected. The social condition of any old
country is, to a great extent, an aggregate of such effects,
the original cause or causes of which have long ceased
to have any existence.

It should be noticed that the Method of Agreement
is mainly, though not exclusively, a Method of Observa-
tion rather than of Experiment, and that it is applied far
more frequently to enquire into the causes of given effects
than into the effects of given causes. The reason of this

METHOD OF AGREEMENT. 1 27

peculiarity is that in trying an experiment, pr in enquiring
into the effect of a given cause, we are generally able
to employ one of the other Methods, which, as will be
seen, are not exposed to the same diflSculties as the
Method of Agreement.

It should also be noticed that where, after a careful
elimination and an examination of a sufficiently large
number of instances, we have, instead of two, some three,
four, or more circumstances common to all the instances,
we may, with much probability, regard them all, unless
we know or suspect any of them to be immaterial cir-
cumstances, as being causally connected. If the common
circumstances be a, b, c, d, this is all that we can infer.
But, if they be A, B, C, a, we may infer that the cause
of a is certainly either A or B or C, or some two of them
acting jointly, or all acting together, while those common
antecedents, which do not either constitute or contribute
to the cause, probably stand in some causal relation to
it, and consequently to its effect a. Similar conclusions
may be drawn, if the common circumstances left after
elimination be A, a, ft y. Thus, for instance, a, jS, y
might all be joint effects of A, or a might be its im-
mediate effect, and ft y effects of a, and so on.

It is perhaps not superfluous to remind the student
that, in the application of this Method, he should be
peculiarly careful not to overlook any instance in which
the given phenomenon is unaccompanied by the other
circumstance. Such an instance should at once lead him
to suspect that some third common circumstance, which

128 INDUCTIVE METHODS.

may be the trae cause (or effect) of the given phenomenon,
has escaped his attention, but it does not necessarily vitiate
his conclusion. If the given phenomenon be the conse-
quent, and this other circumstance the antecedent, such
an instance may only point to some other and independent
cause of the phenomenon in addition to the cause he sup-
poses himself to have ascertained. If, on the other hand,
the given phenomenon be the antecedent, and this other
circumstance the consequent, such an instance may only
point to a counteracting cause which, in this exceptional
case, frustrates the supposed effect. The only condition
essential to an application of the Method of Agreement is
that the cases on which the inference is founded shall
present only two circumstances in common. It is not
necessary that these circumstances should invariably be
found in conjunction, provided that in the cases where
they are found in conjunction no other common cir-
cumstance can be detected. We shall recur to this sub-
ject below '.

In the statement of the Canon, we have thought it
desirable to introduce the expression * with more or less
of probability/ in order to show that, under no circum-
stances, does an inference drawn in accordance with the
Method of Agreement attain to absolute and formal cer-
tainty, though, as we have seen, it may attain to moral
certainty.

As familiar examples of the employment of the Method
of Agreement, the following may be adduced : —

' See pp. I35~I37-

METHOD OF AGREEMENT. 1^9

A particular kind of food, whatever else I may eat
or drink, and however various my general state of health,
the temperature of the air, the climate in which I am
living, and my divers other surroundings, invariably makes
me ill; I am justified in regarding it as the probable
cause of my illness, and avoid it accordingly. This
example furnishes a good illustration both of the diflSculties
and of the possible cogency of the Method of Agreement
What made me ill may have been some different viand
on each of two, three, or four occasions, but it is very
unlikely, if the number of occasions on which the in-
ference is based be considerable, that it has been a dif-
ferent viand on each of them.

I find that a certain plant always grows luxuriantly
on a particular kind of soil; if my experience of the
places, where the soil is to be found, be sufiicientiy
large, I am justified in concluding that the soil possesses
certain chemical constituents which are peculiarly favour-
able to the production of the plant.

Trade is observed to be in a languishing condition
wherever there exist certain restrictions, such as high
duties, difficulties thrown in the way of landing or loco-
motion, &c. ; if it could be ascertained that these countries
agreed in no other respect which could influence the
condition of trade, except in being subject to these
restrictions, it might be inferred that the commercial
depression was due to the restrictions as a cause.

In all these cases, it will be seen that the great diffi-
culty consists in ascertaining that the supposed cause is

K

130 INDUCTIVE METHODS.

the only drcomstance, or the only material drcnmstance,
which, in addition to the phenomenon itself, the \'arious
instances possess in conmion.

We now append a few instances of a less familiar cha-
racter : —

The occurrence of Aurora Borealis has, under meteo-
rological conditions of very different character, been in-
variably found to be accompanied by considerable mag-
netic disturbances. It is rightly inferred that there is
some causal connection between magnetic disturbance
and the occurrence of the Aurora Borealis.

It has been obser\'ed uniformly, and under a \'ariety
of circumstances, that, wherever an indiscriminate sys-
tem of almsgiving has pre\*ailed, the population has,
sooner or later, become indolent and pauperised.
This may be noticed especially in the neighbourhood
of large monasteries, in parishes where large sums of
money are distributed in the shape of ' ddes,' in places
which are the residence of rich and charitable but
injudicious persons, and the like. The reason is not
(Mfikult to discover. The unfortunate recipients of the
charity are left without the ordinary motives to exertion,
and consequendy, when the abnormal supply ceases, or
becomes loo small for the wants of an increased popula-
tion, being without self-reliance or any special skill, they
have no resource but beggary.

After a variety of experiments on substances of the
most different kinds, and under the most different cir-
cumstances, it has been found that, as a body passes

METHOD OF AGREEMENT. I3I

from one degree of temperature to another, it invariably
undergoes a change of Volume, though that change may
not always be in the same direction, it being, in the great
majority of cases, in the direction of expansion, but,
occasionally, in that of contraction. Hence it has been
inferred that change of volume is an invariable effect
of change of temperature. It has been supposed by
some writers on physics that we may go further than
this, and state that augmentation of temperature is invari-
ably followed by augmentation of volume, and diminution
of temperature by diminution of volume, the exceptions
of water® as well as of bismuth and of the casting-metals
generally (which suddenly expand at the moment of
solidification) being explained as anomalies due to some
interfering cause. We are, however, at present so little
acquainted with the intimate constitution of bodies, that
it might be rash to state the proposition in this form,
and, stated as above, it is open to no exception*.

^ Water follows the general rule, and continues to contract in bulk
as its temperature is lowered, till it reaches about 39° Fahrenheit or 4°
Centigrade, when it begins to expand and continues to do so till after its
conversion into ice, so that a given weight of water at the temperature
(say) of 37°, or when frozen, occupies more space than it occupied at
(say) the temperature of 40°. This anomaly is somewhat boldly ex-
plained by Mr. Grove as due to the setting in of the process of crystalli-
zation, which he supposes to begin at 39°, and to interfere with the
ordinary law of contraction and expansion. (See Grove's Correlation of
Physical Forces, fifth ed. p. 58, &c.)

^ I adduce this as an example of the Method of Agreement rather
than of the Method of Concomitant Variations, because the argument,
as here stated, rests rather upon the variation of circumstances and the

K 2

l^Z INDUCTIVE METHODS.

The following example, which also illustrates the
caution necessary to be observed in framing a general
proposition, is extracted from Sir John Herschel's Dt's-
course on the Study of Natural Philosophy '^^ : —

* A great number of transparent substances, when exposed
in a certain particular manner, to a beam of light which has
been prepared by undergoing certain reflexions or refractions
(and has thereby acquired peculiar properties, and is said
to be "polarized**), exhibit very vivid and beautiful colours,
disposed in streaks, bands, &c. of great regularity, which seem
to arise within the substance, and which, from a certain
regular succession observed in their appearance, are called
"periodical colours." Among the substances which exhibit
these periodical colours occur a great variety of transparent
solids, but no fluids and no opaque solids. Here, then, there

great diversity of bodies in which the law is found to hold good, than
upon the relation between the various degrees of expansion or contrac-
tion and the various degrees of temperature in the same body. Had
the stress been laid upon the latter consideration, the argument would
undoubtedly have been an instance of the Method of Concomitant
Variations.

It frequently happens, in fact, that two or more Methods are com-
bined in the same proof. In the present instance, as will be seen below,
the argument as applied to each particular kind of body (mercury, for
instance) is an argument based on the Method of Concomitant Varia-
tions ; but when we proceed to extend the experiment to other bodies,
and then argue from the variety of the bodies examined that a body, in
passing from one degree of temperature to another, invariably undergoes
a change of volume, it appears to me that we are no longer employing
the Method of Concomitant Variations but the Method of Agreement.
It must be borne in mind that the object of our enquiry is not strictly
the effects of heat (for the total effects of heat, inasmuch as we cannot
wholly exhaust any body of its heat, must be unknown to us), but the
effects of a change of temperature. ^^ § 90.

METHOD OF AGREEMENT. 1 33

seems to.be sufficient community of nature to enable us to
use a general term, and to state the proposition as a law,
viz. transparent solids exhibit periodical colours by exposure
to polarized light. However, this, though true of many, does
not apply to all transparent solids, and therefore we cannot
state it as a general truth or law of nature in this form;
although the reverse proposition, that all solids which exhibit
such colours in such circumstances are transparent, would
be correct and general. It becomes necessary, then, to make
a list of those to which it does apply ; and thus a great
number of substances of all kinds become grouped together,
in a class linked by this common property. If we examine
the individuals of this group, we find among them the utmost
variety of colour, texture, weight, hardness, form, and com-
position; so that, in these respects, we seem to have fallen
upon an assemblage of contraries. But when we come to
examine them closely in all their properties, we find they have
all one point of agreement, in the property of double re-
fraction, and therefore we may describe them all truly as
doubly refracting substances. We may, therefore, state the fact
in the form, " Doubly refracting substances exhibit periodical
colours by exposure to polarized light;" and in this form
it is found, on further examination, to be true, not only for
those particular instances which we had in view when we
first propounded it, but in all cases which have since occurred
on further enquiry, without a single exception; so that the
proposition is general, and entitled to be regarded as a law
of nature.'

The experiments by which Dr. Wells ^* established his

" Dr. Wells* Memoir on Ae Theory of Dew^ which had become very
scarce, was reprinted by Longmans and Co. in 1866. It is very brief,
and well deserves to be carefully read by every student of scientific
method. Sir John Herschel (Natural Philosophy, § 168) speaks of the
speculation as * one of the most beautiful spedmen^* \w& casL cai2^\.^ \scisi^

134 INDUCTIVE METHODS.

Theory of Dew afford a remarkable example of the
Method of Agreement. By employing various objects
of different material under a variety of circumstances,
he showed that, whatever the texture of the object, the
state of the atmosphere, &c., it is an invariable condition
of the deposition of dew that the object on which it is
deposited shall be colder than the surrounding atmo-
sphere, the greater coldness of the object being itself
produced by the radiation of heat from its surface. This,
to quote the words of Sir John Herschel, is the case not
only with ' nocturnal dew,' but with ' the analogous phe-
nomena ' of * the moisture which bedews a cold metal or
stone when we breathe upon it ; that which appears on
a glass of water fresh from the well in hot weather ; that
which appears on the inside of windows when sudden
rain or hail chills the external air ; that which runs down
our walls when, after a long frost, a warm moist thaw
comes on.'

It is by the Method of Agreement that we discover the
symptoms of a disease, the signs of a political revolution,
national characteristics, the collocation of parts in an
animal or vegetable organism, the order of superposition
among geological strata, grammatical rules, and the like.

The first division of Bacon's insianticB solttarice coin-
cides with the cases contemplated in the Method of
Agreement, as the second coincides with the cases con-

*of inductive experimental enquiry lying within a moderate compass.*
Mr. Mill also employs it as one of his Miscellaneous Examples in
ch. ix.

METHOD OF AGREEMENT. 1 35

templated in the Method of Difference. The example of
the first is so remarkable both in itself, and as an antici-
pation of Newton's Speculations on Colour, that we may
adduce it as an additional instance of the Method of
Agreement : —

'Exempli gratia: si fiat inquisitio de natura colon's,
instanitcB solttartce sunt prismata, gemmae crystallinae, quae
reddunt colores, non solum in se, sed exterius supra
parietem. Item rores, &c. Istae enim nil habent com-
mune cum coloribus fixis in floribus, gemmis coloratis,
metallis, lignis, &c. praeter ipsum colorem. Unde facile
colligitur, quod color nil aliud sit quam modificatio ima-
ginis lucis immissae et receptae: in priore genere, per
gradus diversos incidentiae ; in posteriore, per texturas et
schematismos varios corporis. Istae autem tnstanttce sunt
soh'tartcB quatenus ad similitudinem*^'

In attempting to ascertain the cause of a given effect,
a, it may happen that we find a particular antecedent,
A, frequently, but not invariably, accompanying it. If,
in those cases which present both a and A, no other
common circumstance can be detected, we may infer
that A is probably a cause of a. We say * a cause,' for
the fact that a may be present without A is a proof that
A is not the only cause. Our meaning will be plain from
the following example : —

We compare instances in which bodies are known to
assume a crystalline structure, but which have no other
point of agreement ; in the great majority of instances,

" Novum Organum, Bk. II. aph. xxii.

136 INDUCTIVE METHODS.

though not in all, we find that these bodies have assumed
their crystalline structure during the process of solidifica-
tion from a fluid state, either gaseous or liquid, and,
so far as we can ascertain, these cases have no other
circumstance in common. From this it may be reason-
ably inferred that the passage from a fluid to a solid
state is a cause, though not the only cause, of crystal-
lization^'.

Again, when A is frequently, though not invariably,
followed by a, and there is, so far as we can ascertain,
no other common antecedent, we are justified in sus-
pecting that A is a cause of a, and that, in the cases
where a does not occur, the operation of A is counteracted
by some other cause. If, for example, a certain occupa-
tion or mode of living is found to be usually, though not
invariably, attended by a particular form of disease, we
seem to be justified in regarding this occupation or
mode of living as a cause of the disease, and in ex-
plaining the few cases in which the disease does not
occur as due to exceptional and counteracting circum-
stances.

Similarly, when a and b are found in frequent, though

^ This example is adopted, with considerable modifications, from one
which occurs in Mr. Mill's Logic^ Bk. III. ch viii. §1. I am indebted
to Sir John Herschel for pointing cut to me that Mr. Mill's example
(which I htd originally adopted as it stood) is too broadly stated. * The
solidification of a substance from a liquid [it should be fluid] state'
is not *an invariable,' but only an usual * antecedent of its crystallization.'
The reader will find several exceptions noticed in Watts* Dictionary of
Cbemistry, art. Crystallization.

METHOD OF AGREEMENT. 1 37

not invariable, conjunction", and, in the cases where they
are found together, there occurs, so far as we can ascertain,
no other common circumstance, we are justified in suspect-
ing that there exists some causal connection between them.
The student who is acquainted with the science of
Medicine, will find a good illustration of the extreme
diflficulty attending the application of the Method of
Agreement, as well as of the Joint Method of Agreement
and Difference (to be noticed presently), in the disputes
which still occur as to the cause of the mental disease
which is known as Atactic Aphasia, that is, the condition
in which, with reference to certain sounds, the patient has
lost the power of co-ordinating the muscles of speech.
The French physiologist, M. Broca, laid down the posi-

'^ The invariable conjunction of two phenomena, when the presence
of the one implies the presence of the other, and the absence of the one
the absence of the other, is a case falling under the Double Method of
Agreement, to be explained presently; but those cases in which we
simply know that a given phenomenon is invariably preceded or in-
variably followed by another fall under the Method of Agreement just
discussed. If a given phenomenon is, so far as we know, invariably
preceded by another, this fact justifies us in suspecting (though it does
not prove) that the antecedent is not only a cause, but the only cause,
of the given phenomenon. Such a conclusion can only be proved (even
approximately) by the Double Method of Agreement, to be explained
presently. It is not, however, as already pointed out, in the invariableness
of the antecedence, but in the fact that the instances examined present, so
far as we can ascertain, only two phenomena in common, that the cogency
of the Method of Agreement consists. But of this fact invariableness of
antecedence (or of consequence) furnishes one of the strongest proofs,
inasmuch as it implies a very wide variation of circumstances, and hence
the stress laid upon it in some of the examples adduced above«

138 INDUCTIVE METHODS.

tion that this disease is invariably due to a lesion of the
third frontal convolution of the left hemisphere of the
brain, the disease being invariably attended by the specific
lesion, and the lesion never occurring without the disease.
His followers maintain that the instances are decisive in
favour of this theory, while the apparent exceptions admit
of a satisfactory explanation ; his opponents, on the
other hand, assert that there are well-established cases
both of atactic aphasia without the specific lesion, and
of the lesion without aphasia^**.

METHOD OF DIFFERENCE.
CANON.

If an instance in which the phenomenon under investi-
gation occurs^ and an instance in which it does not occur,
have every circumstance in common save one, that one oc^
curring only in the former ; the circumstance in which
alone the two instances differ, is the effect, or catise, or a
necessary part of the cause, of the phenomenon.

The circumstances a, b, c are found in conjunction
with d, e, f, and the omission or disappearance of the cir-

^* See a paper by Dr. William Ogle in the St. George* s Hospital Reports^
vol. ii. ; a Pamphlet by Dr. Frederic Bateman of Norwich, published by
J. E. Adlard, Bartholomew Close, London, 1 868 ; Dr. Reynolds' System
of Medicine, vol ii. pp. 442-444; and various reports of discussions
published in the Lancet and other medical journals. I have to thank
my friends, Professors Acland and Rolleston, for their kindness in sup-
plying me with information on this interesting subject, and regret that
my space prevents me from pursuing it at greater length.

METHOD OF DIFFERENCE. I39

cumstance a is found to be attended by the disappearance
of the circumstance d. It is inferred that a and d are
so connected that one is cause (or a necessary part of
the cause) and the other effect. If, moreover, it can
be ascertained that a is the antecedent and d the con-
sequent, or that, though there are instances in which d
occurs without a, there are no instances in which a occurs
without d, we may proceed to infer (in the latter case, on
the ground that a phenomenon may have more than one
cause, but that a cause, unless counteracted by some other
cause, must be attended by its effect) that a is the cause,
and d the eflfect. Similarly, if the circumstances a, b, c
are found in conjunction with d, e, f, and the introduction
of the circumstance x into the former set of phenomena
is found to be attended by the appearance of the cir-
cumstance y in the latter set of phenomena (so that they
may be represented respectively as a, b, c, x ; d, e, f, y),
it may be inferred that x and y are related as cause
and eflfect, or, if x be the antecedent and y the con-
sequent, or the appearance of x be invariably attended
by the appearance of y while the appearance of y is
not invariably attended by the appearance of x, that x
is the cause and y the eflfect. The reasons on which
the Canon rests are obvious. All other circumstances
remaining the same, if the introduction or omission of
any circumstance be followed by a change in the remain-
ing circumstances, that change must be due to such
introduction or omission, as an eflfect to a cause; or,
if two new circumstances enter simulta\ve.o\js»Vj ^ ^^rs&^<^xiX

140 INDUCTIVE METHODS.

producing any other change in the phenomenon, these
two circumstances (except on the improbable suppo-
sition that they are two causes exactly counteracting each
other) must be related as cause and eflfect, though we
may be unable to say which of the two is cause and
which eflfect. * The Method of Agreement/ says Mr.
Mill, * stands on the ground that whatever can be eli-
minated, is not connected with the phenomenon by any
law. The Method of Diflference has for its foundation
that whatever can not be eliminated, is connected with
the phenomenon by a law/ In the Method of Diflfer-
ence, the instances agree in everything, except in the
possession of two circumstances which are present in
the one instance and absent in the other. In the Method
of Agreement, the various instances compared (for here
we generally require more than two instances) agree in
nothing, except in the possession of two circumstances
which are common to all the instances. ,One Method
is called the Method of Agreement, because we compare
various instances to see in what they agree ; the other
is called the Method of Diflference, because we compare
an instance in which the phenomenon occurs with
another in which it does not occur, in order to see in
what they diflfer.

Instances of the Method of Diflference are not far
to seek. A piece of paper is thrown into a stove; we
have no hesitation in regarding its apparent consumption
as the eflfect of the heat of the fire, for we feel assured
that the sudden increase of temperature is the only new

METHOD OF DIFFERENCE. I41

circumstance to which the piece of paper is exposed, and
that, therefore, any change in the condition of the paper
must be due to that cause. A bullet is fired from a gun;
or a dose of prussic acid is administered, and an animal
instantly falls down dead. There is no hesitation in
ascribing the death to the gun-shot woimd or the dose
of poison. Nor is this confidence the effect of any
special experience, for, if it were the first time that we
had seen a gun fired or a dose of poison administered,
we should have no hesitation in ascribing the altered
condition of the animal to this novel cause; we should
know that there was only one new circumstance operating
upon it, and, consequently, that any change in its con-
dition must be due to that one circimistance. In all these
instances, there is the introduction of a new antecedent,
X, to which the new consequent, y, must be due. But,
if the omission of one circumstance be attended by the
omission of another, we may argue with equal confidence.
I withdraw my hand from this book which is resting
upon it, and the book instantly falls to the ground ; there
is no hesitation in referring the altered position of the
book to the withdrawal of my support A man is de-
prived of food, and he dies ; we have no hesitation in
ascribing the disappearance of the phenomenon we call
life to the withdrawal of the means by which it is main-
tained. In these instances, we have certain antecedents,
followed by certain consequents, and, observing the simul-
taneous or successive disappearance of A and a, we have
no hesitation in connecting the two as cause and effect.

14a INDUCTIVE METHODS.

All crucial instances (instantiae" crucis, as they are
called by Bacon) are applications of the Method of Dif-
ference. A crucial instance is some observation or ex-
periment which enables us at once to decide between two
or more rival hj^otheses. It will be familiar to every one
in the form of the chemical test, as where we apply an
acid for the purpose of determining the character of
a metal, or a metal for the purpose of detecting latent
poison. According to the metaphor, there are two or
more ways before us, and the observation or experiment
acts as a ' guide-post ' (crux) in determining us which to
take. The following beautiful example of a Crucial
Instance is borrowed from Sir John Herschel ^'^,

^^ * Inter praerogativas instantianim ponemus loco decimo quarto in-
stantias crucis; translato vocabulo a crucibuSj qux, erectae in biviis, indicant
et signant vianim separationes. Has etiam instarUias decisorias, et judi-
dales, et in casibus nonnullis instantias oraculi, et mandati, appellare con-
suevimus. Earum ratio talis est. Cum in inquisitione naturse alicujus,
intellectus ponitur tanquam in aequilibrio, ut incertus sit, utri naturanim
e duabus, vel quandoque pluribus, causa naturae inquisitae attribui aut
assignari debeat, propter complurium naturanim concursum frequentem
et ordinarium; instantice crucis ostendunt consortium unius ex naturis
(quoad naturam inquisitam) fidum et indissolubile, alterius autem varium
et separabile ; unde terminatur quaestio, et recipitur natura ilia prior pro
causa, missa altera et repudiata. Itaque hujusmodi instantise sunt max-
imae lucis, et quasi magnae auctoritatis ; ita ut curriculum interpretationis
quandoque in illas desinat, et per illas perficiatur. Interdum autem
instantice crucis illae occurrunt et inveniuntur inter jampridem notatas ;
at ut plurimum novae sunt, et de industria atque ex composito quaesitae
et applicatae, et diligentla sedula et acri tandem erutae.' — Novum Orga-
num, Bk. II. aph. xxxvi.

1^ Discourse on the Study of Natural Pbilosopby, > 218.

METHOD OF DIFFERENCE. I43

* A curious example is given by M. Fresnel, as decisive,
in his mind, of the question between the two great opinions
on the nature of light, which, since the time of Newton
and Huyghens, have divided philosophers ; ' — that is be-
tween what is called * the emission theory,' according to
which light consists of actual particles emitted from lumi-
nous bodies, and what is called * the undulatory theory,'
according to which light consists in the vibrations of an
elastic medium pervading all space.

*When two very clean glasses are laid one on the other,
if they be not perfectly flat, but one or both in an almost im-
perceptible degree convex or prominent, beautiful and vivid
colours will be seen between them ; and if these be viewed
through a red glass, their appearance will be that of alternate
dark and bright stripes. These stripes are formed betfween
the two surfaces in apparent contact, as any one may satisfy
himself by using, instead of a flat plate of glass for the upper
one, a triangular-shaped piece, called a prism, like a three-
cornered stick, and looking through the inclined side of it
next the eye, by which arrangement the reflection of light
from the upper surface is prevented from intermixing with
that from the surfaces in contact. Now, the coloured stripes
thus produced are explicable on both theories, and are ap-
pealed to by both as strong confirmatory facts ; but there is
a difference in one circumstance according as one or the other
theory is employed to explain them. In the case of the
Huyghenian doctrine, the intervals between the bright stripes
ought to appear absolutely blacky in the other, half bright,
when so viewed through a prism. This curious case of dif-
ference was tried as soon as the opposing consequences of
the two theories were noted by M. Fresnel, and the re-
sult is stated by him to be decisive in favour of tj^a^ ^2c>si5sr^

144 INDUCTIVE METHODS,

which makes light to consist in the vibrations of an elastic
medium".'

The following is an example of a similar kind. It had
been determined, from theoretical considerations, that, on
the assumption of the undulatory theory, the velocity of light
must be less in the more highly refracting medium, while,
according to the emission theory, it ought to be greater.
When M. Foucault had invented his apparatus for deter-
mining the velocity of light, it became possible to submit
the question to direct experiment ; and it was established
by M. Fizeau that the velocity of light is less in water (the
more highly refracting medium) than in air, in the inverse
proportion of the refractive indices. The result is, there-
fore, decisive in favour of the undulatory, or at least,
against the emission theory ^^

There is no science, perhaps, in which the Method
of Difference is so extensively used as the science of
Chemistry, and that because chemistry is emphatically a
science of experiment. Almost any chemical experiment
will serve as an instance of the Method of Difference. Mix,
for example, chloride of mercury with iodide of potassium,

^* Mr. Mill {Logic, Bk. III. ch. xiv. § 6) maintains that it does not
follow from this experiment that * the phenomena of light are results of
the laws of elastic fluids, but at most that they are governed by laws
partially identical with these.* But though the experiment may not be
decisive as in favour of the Undulatory Theory, it is undoubtedly de-
cisive as against the Emission Theory. It may be necessary to add that
the term * fluids* would now be repudiated by those who hold the
Undulatory Theory.

" See Lloyd's Wave Theory of Light, Art. 37 ; Ganot*s Physics,
English translation, third edition, Art. 436.

METHOD OF DIFFEREN'CE. I45

and the result will be a colourless liquid at the top of

the vessel with a brilliant red precipitate at the bottom.

There can be no hesitation in ascribing this result to the

mixture of the two liquids ; and two similar experiments

will enable us to determine that the chlorine has been set

free from the mercury and united with the potassium,

which itself has been set free from the iodine with which

it was previously imited, while the iodine has united with

the mercury, the former producing chloride of potassium

(dissolved in the colourless liquid), the latter iodide of

mercury (the red precipitate).

The science of Heat (or, as Dr. Whewell proposes to

call it, Thermotics) also furnishes excellent examples of the

Method of Difference. The following instances are adapted

from Professor Tyndall's Ilea/ a Mode 0/ Motion^: —

* Here is a brass tube, four inches long, and of three-
quarters of an inch interior diameter. It is stopped at the
bottom, and screwed on to a whirling table, by means of
which the upright tube can be caused to rotate very rapidly.
These two pieces of oak are united by a hinge, in which are
two semicircular groves, intended to embrace the brass tube.
Thus the pieces of wood form a kind of tongs, the gentle
squeezing of which produces friction when the tube rotates.
I partially fill the tube with cold water, stop it with a cork
to prevent the splashing out of the liquid, and now put the
machine in motion. As the action continues, the temperature
of the water rises, and now the tube is too hot to be held in
the fingers. Continuing the action a little longer, the cork
is driven out with explosive violence, the steam which follows
it producing by its precipitation a small cloud in the atmo-
sphere.'

» Third Edition, ch. i. |§ ii^-16.

li

146 INDUCTIVE METHODS,

In this experiment it will be noticed that only one new
antecedent is introduced, namely the motion of the ma-
chine ; hence the increased temperature of the water and
the various effects which follow upon it are due to the
motion as a cause. The experiment, then, shows that
heat is generated by the action of mechanical force.

The converse of this proposition, namely that heat is
consumed in mechanical work, or, as it is often stated,
transmuted into mechanical energy, is proved by the two
next experiments.

*This strong vessel is filled at the present moment with
compressed air. It has lain here for some hours, so that the
temperature of the air within the vessel is now the same as
that of the air of the room without it. At the present mo-
ment this inner air is pressing against the sides of the vessel,
and if this cock be opened a portion of the air will rush
violently out. The word * rush,' however, but vaguely ex-
presses the true state of things ; the air which issues is driven
out by the air behind it ; this latter accomplishes the work of
urging forward the stream of air. And what will be the con-
dition of the working air during this process? It will be
chilled. The air executes work, and the only agent it can
call upon to perform the work is the heat to which the elastic
force with which it presses against the sides of the vessel is
entirely due. A portion of this heat will be consumed, and
a lowering of temperature will be the consequence. Observe
the experiment. I will turn the cock, and allow the current
of air from the vessel to strike against the face of the pile '*^.

^^ That is, the thermo-electric pile, a delicate instrument for indicating
very small degrees of heat. It is by means of this instrument that it
has recently been shown that we receive heat (though, of course, in in-
finitesimal quantities) from the moon's rays.

METHOD OF DIFFERENCE. 1 47

The magnetic needle instantly responds ; its red end is driven
towards me, thus declaring that the pile has been chilled by
the current of air.*

* Here moreover is a bottle of soda-water, slightly warmer
than the pile, as you see by the deflection it produces. Cut
the string which holds it, the cork is driven out by the elastic
force of the carbonic acid gas ; the gas performs work, in so
doing it consumes heat, and now the deflection produced by
the bottle is that of cold.'

The last experiment furnishes a good instance of the
extreme simplicity of the examples by which scientific
truths may often be illustrated.

The uncertainty which, as we have seen, always at-
taches to conclusions arrived at by the Method of Agree-
ment renders it desirable that they should, wherever it is
possible, be confirmed by an application of the Method
of Difference. A beautiful instance of such a confirma-
tion is adduced by Mr. Mill in the case of Crystallization.
The Method of Agreement has already led us to the con-
clusion that the solidification of a substance from a fluid
state is a very frequent antecedent of its crystallization,
and consequently, in all probability, one, at least, of its
causes. But the Method of Difference completes the
evidence, and enables us to state positively that it is
a cause.

* For in this case we are able, after detecting the antece-
dent A, to produce it artificially, and by finding that a follows
it, verify the result of our induction. The importance of
thus reversing the proof was never more strikingly manifested
than when, by keeping a phial of water ela.Ttg»^ 'wVCc^ ^^t^^^pos*

L 2

148 INDUCTIVE METHODS,

particles undisturbed for years, a chemist (I believe Dr. Wol-
laston) succeeded in obtaining crystals of quartz; and in
the equally interesting experiment in which Sir James Hall
produced artificial marble, by the cooling of its materials
from fusion under immense pressure: two admirable ex-
amples of the light which may be thrown upon the most
secret processes of nature by well- contrived interrogation
of her 22/

It will be noticed that the Method of Diflference is
specially adapted to the discovery of the effects of given
causes, whereas, where it is our object to discover the
cause of a given effect, we are generally compelled to
have recourse to the Method of Agreement. The Method
of Agreement is, in fact, mainly a Method of Observation,
whereas the Method of Difference is mainly a Method of
Experiment. We may indeed arrange the conditions of
an experiment so as to satisfy the requirements of the
Method of Agreement, and Nature may (as in the familiar
case of lightning) herself satisfy the requirements of the
Method of Difference, but, as a rule, it will be found that
arguments based on observations fall under the former,
and arguments based on experiments under the latter
Method. It is hardly necessary to add that, wherever we
have our choice between the two methods, we should
invariably select the Method of Difference.

^ Mill's Logic y 6k. III. ch. viii. §1. I have been obliged, in accordance
with what has been said on p. 136, to state, with considerable modifica-
tions, the conclusion in this instance as arrived at by the Method of
Agreement. The account of the application to it of the Method of
Difference has been stated in Mr. Mill's own words.

METHOD OF DIFFERENCE. 1 49

In the employment of the Method of Difference, the
greatest care should be taken to introduce only one new
antecedent, or at least only one new antecedent which
can influence the result. As the whole force of the
argument based on this Method depends on the assump-
tion that any change which takes place in the phenome-
non is due to the antecedent then and there introduced,
it is plain that we can place no reliance on our conclusion
unless we feel perfectly assured that no other antecedent
has intervened. If, for instance, it is our object to as-
certain the heat of the atmosphere, we must take the
greatest care that our thermometer is not affected by the
heat radiated from or conducted by other bodies. The
most curious examples of the disregard of this caution
may be found in the History of Medicine. Something
perfectiy inert has been administered to a patient in
combination with some powerful drug, some important
alterations in his diet, or some strict regime; then the
effects of the drug, diet, or regime have been unwittingly
ascribed to the inert substance. Had the ancients re-
cognised that instead of one cause acting on falling
bodies, as appeared to them to be the case, there were
really two, the action of gravity tending downwards and
the resistance of the atmosphere pressing upwards, they
could never have fallen into the gross mistake of sup-
posing that bodies fall in times inversely proportional to
their weights.

150 INDUCTIVE METHODS.

DOUBLE METHOD OF AGREEMENT.

CANON.

If two or more instances in which the phenomenon occurs
have only one other circumstance in common, while two or
more instances from which the phenomenon is absent have
nothing in common save the absence of that circumstance ;
the circumstance in which alone the two sets of instances
differ is the effect, or cause, or a necessary part of the cause,
of the phenomenon. Moreover {supposing the requirements
of the Method to he rigorously fulfilled), the circumstance
proved by the Method to be the came is the only cause of
the phenomenon.

The uncertainty attaching to the Method of Agreement
may, even where it is impossible to have recourse to the
Method of Difference, be, to some extent, remedied by
the employment of what is called by Mr. Mill the Joint
Method of Agreement and Difference, or the Indirect
Method of Diflference. This consists in a double employ-
ment of the Method of Agreement and a comparison of
the results thus obtained, the comparison assimilating it
to the Method of Difference. We, first of all, compare
cases in which the phenomenon occurs, and, so far as we
can ascertain, find them to agree in the possession of
only one other circumstance. But, though we may not
be justified in regarding this inference as certain, we may

DOUBLE METHOD OF AGREEMENT. 151

increase our assurance by proceeding to compare cases
in which the phenomenon does not occur. If these agree
in nothing but the non-possession of the circumstance
which the other cases agreed in possessing, we have a
set of negative instances agreeing in nothing but the
absence of the given phenomenon and the absence of
the aforesaid circumstance. The set of negative instances
may now be compared with the set of positive instances,
and we may argue thus : The positive instances agree in
nothing but the presence of the given phenomenon and
this other circumstance, and the negative instances agree
in nothing but the absence of the given phenomenon and
this other circumstance. Hence we may regard it as a
highly probable inference that they are connected together
as cause and effect. We say * highly probable,' for, as we
are not absolutely certain that the conditions of the Method
of Agreement have been satisfied in the case of the posi-
tive instances, so, from the extreme difficulty of proving a
negative, we must be still less certain that they have been
satisfied in the case of the negative instances. What (in
addition to another advantage, to be noticed presently) is
gained by the Method is a sort of double assurance, so far
as the assurance goes, -^the one set of instances agreed
in nothing but the presence of the two circumstances,
and if the other set of instances agreed in nothing but
the absence of the two circumstances, then we should
be able to infer, by the Method of Difference, that the
introduction of the given phenomenon (which we will
suppose to be the consequent) is always v^^t^^'sjs&asj^:^

15a INDUCTIVE METHODS.

by the introduction of the other circumstance (which
we will suppose to be the antecedent), and, vice versd,
that the removal of the given phenomenon is always
necessitated by the removal of the other circumstance,
or, in other words, that the given phenomenon is the
effect and the other circumstance the cause.

But this Method, supposing its conditions to be
rigorously satisfied, possesses one advantage peculiar to
itself. The Single Method of Agreement, as we have
seen, is always theoretically open to the objection arising
from Plurality of Causes, but this Method, if the set of
negative instances be perfect, is not only free from that
objection, but also sustains the conclusion that the in-
ferred cause is the only cause of the phenomenon in
question (or, in case we do not know which is ante-
cedent and which is consequent, that a and b are
so connected that one of them is the cause and the
only cause of the other). * In the joint method,' says
Mr. MilP^ *it is supposed not only that the instances
in which a is agree only in containing A, but also
that the instances in which a is not agree only in
not containing A. Now, if this be so, A must be not
only the cause of a, but the only possible cause : for
if there were another, as for example B, then in the
instances in which a is not, B must have been absent
as well as A, and it would not be true that these instances
agree only in not containing A.* It may be asked, then,

23 Mill's Logic, Bk, III. ch. x. § a.

DOUBLE METHOD OF AGREEMENT. 1 53

if the negative branch of the argument be so forcible,
why should we employ the positive branch? It is by
means of the positive branch that we are, as it were,
put on the track of the one other circumstance in which
the instances presenting the given phenomenon agree,
and by means of the negative branch that we prove the
accuracy of our conclusion. ' It is generally,' continues
Mr. Mill, * altogether impossible to work the Method of
Agreement by negative instances without positive ones :
it is so much more difficult to exhaust the field of ne-
gation than that of affirmation.'

It is plain that the conditions of the Joint Method can
only be rigorously fulfilled where there is an invariable
conjunction between two phenomena, so that the two are
(unless counteracting circiunstances intervene) always
present together and always absent together. For, if A
be the only cause of a, the effect a cannot be present
without the cause A, nor can the cause A be present
without being attended by the effect a. Hence, invariable .
conjunction may be regarded as a sign that the con-
ditions of this Method are fulfilled, and it is from the
observation of such an invariable conjunction that the
argument frequentiy proceeds. In such cases, the niunber
of instances, both positive and negative, which have been
observed, is supposed to be so great and of such variety
as to have excluded all other common circumstances
except the presence or absence of the two phenomena
in question.

The Joint Method of Agreement axvd "DSSi^T^-w:.^ V^^^

154 INDUCTIVE METHODS.

the Indirect Method of Diflference, or, as I should prefer
to call it, the Double Method of Agreement) is being
continually employed by us in the ordinary affairs of life.
If, when I take a particular kind of food, I find that
I invariably suffer from some particular form of illness,
whereas, when I leave it off, I cease to suffer, I entertain
a double assurance that the food is the cause of my
illness. I have observed that a certain plant is invariably
plentiful on a particular soil ; if, with a wide experience,
I fail to find it growing on any other soil, I feel con-
firmed in my belief that there is in this particular soil
some chemical constituent, or some peculiar combination
of chemical constituents, which is highly favourable, if
not essential, to the growth of the plant.

Dr. Wells' Ussay on the Theory of Dew presents an
'extremely instructive instance of the application of the
Double Method of Agreement : —

* It appears' (I am here quoting from Mr. Mill *) * that the
instances in which much dew is deposited, which are very
various, agree in this, and, so far as we are able to observe,
in this only, that they either radiate heat rapidly or conduct
it slowly : qualities between which there is no other circum-
stance of agreement, than that by virtue of either, the body
tends to lose heat from the surface more rapidly than it can
be restored from within. The instances, on the contrary,
in which no dew, or but a small quai^ity of it, is formed, and
which are also extremely various, agree (as far as we can
observe) in nothing except in not having this same property.
We seem, therefore, to have detected the characteristic dif-

2* MiU's Logic, Bk. III. ch. ix. § 3.

DOUBLE METHOD OF AGREEMENT. 1 55

ferenee between the substances on which dew is produced,
and those on which it is not produced. And thus have been
realized the requisitions of what we have termed the Indirect
Method of Difference, or the Joint Method of Agreement
and Difference.'

Several beautiful illustrations of the Joint Method of
Agreement and Difference may be found in the recent
discoveries made by means of Spectrum Analysis. We
shall select one which is peculiarly interesting on account
of its employment in the attempt to determine the con-
stitution of the Sim and some of the other heavenly
bodies.

A ray of light proceeding from incandescent hydrogen
is passed through a prism, and it is invariably found that
in the spectrum thus obtained there are two bright lines
occupying precisely the same position. Moreover, rays
of white Ught proceeding from various incandescent sub-
stances are passed through incandescent hydrogen, and
the emergent light is then broken up by a prism. In
the spectra thus obtained it is foimd that there are
invariably two dark (or, under certain circumstances,
bright^) lines occupying exactly the same positions in
the spectrum as the lines above mentioned. Hence it is

^ The darkness of the lines is due to the property possessed by incan-
descent media of absorbing rays of light of the same refrangibility as
those emitted by them. When the absorption exerted upon the trans-
mitted light is more than compensated by the luminosity of the hydro-
gen light, these lines, instead of being dark, appear bright, as is also
the case when the ray of light proceeds directly from incandescent
hydrogen itself.

156 INDUCTIVE METHODS.

inferred, by the Method of Agreement, that a ray of light,
whether i proceed directly from incandescent hydrogen
itself, or be transmitted through it from some other
incandescent, substance, will invariably produce these two
lines. But, if we try the same experiments with any
other element than incandescent hydrogen, although we
may obtain bright or dark lines, we never find these
lines occupying the same positions in the . spectrum as
the two lines in question.

Here, then, we have the negative instances of the
Double Method ; and it is inferred (subject, of course, to
the assumption that our k owledge of the negative in-
stances is sufficiently complete) that the presence in the
spectrum of these two lines is invariably due either to a
ray of light proceeding directly from incandescent hydro-
gen, or to a ray transmitted through it from some other
incandescent substance ; that is to say, that one or other
of these is the cause, and the only cause of the presence
in the spectrum of these two particular lines. When
these lines are bright, it is doubtful whether the rays
proceed directly from incandescent hydrogen or have
been transmitted through it, but, when they are dark,
the rays must have been transmitted. Wherever, there-
fore, two dark lines occupying these positions occur in
the spectrum we may infer (deductively) the passage
of the ray of light through a medium composed wholly
or partially of incandescent hydrogen. But we detect
such lines in the spectrum of the sun and several of
the stars, and hence (unless we suppose it possible or

DOUBLE METHOD OF AGREEMENT, l^J

not improbable that there is in the sun or other stars
some element agreeing in this respect with hydrogen,
but differing in others) we may conclude that the sun
and these other stars are surrounded with an atmo-
sphere of incandescent hydrogen^.

The following examples are selected from a subject of
a widely different character, the History of Language.
M. Auguste Brachet, in his Historical Grammar of the
French Tongue^, lays down that there are three sure tests
by which we can discriminate between popular words
derived from the Peasant Latin (lingua Latina rustica)
by a regular process, and Latin words of learned origin
imported into Modem French by scholars. These tests
are (i) the continuance of the tonic accent; (2) the sup-
pression of the short vowel ; (3) the loss of the middle
or medial consonant. It will be seen that it is by the
employment of the Double Method of Agreement that
M. Brachet arrives at these conclusions.

^ It must be understood that, in this example, I have not stated the
historical steps by which the discovery was arrived at, but simply
attempted to give a logical analysis of the arguments by which it would
now be established. It may be added that the lines in question are
known as C and F in the solar spectrum. It was the exact coincidence
of the bright lines in the hydrogen spectrum with the dark lines C and
F in the solar spectrum, which first led to the belief that hydrogen
enters into the constitution of the solar atmosphere. It is now, how-
ever, rendered possible, through an ingenious contrivance, to separate, as
it were, the solar atmosphere from the glowing body within it, and thus
to obtain these lines bright instead of dark. The student will find a brief
account of these discoveries in Professor Stokes* Address to the British
Association in 1869. ^ Mr. Kitchin's Ttwv,\V^\\o\v^^.'Xj'i«

158

INDUCTIVE METHODS.

* Look at such words (i.e. words of popular origin) carefully, and you
will see that the syllable accented in Latin continues to be so in French ;
or, in other words, that the accent remains where it was in Latin. This
continuance of the accent is a general and absolute law : all words be-
longing to popular and real French respect the Latin accent : all such
words as portique from pdrtious, or viatique from viaticum, which
break this law, will be found to be of learned origin, introduced into the
language at a later time by men who were ignorant of the laws which
nature had imposed on the transformation from Latin to French. We
may lay it down as an infallible law, that Tbe Latin accent continues in
French in all words of popular origin ; all words which violate this law
are of learned origin : thus —

LATIN.

POPULAR WORDS.

LEARNED WORDS.

Alt^mlne

aliin

alumine

Angelus

dnge

angelus

Bldsphemum

blame

blaspheme

Cdnoer

chancre

cancir

Odrnputimi

cdmpte

compUt

D^bittun

dette

debit

B^cima
....

dime

• • • •

decime, &c.

• • •

* We have seen that the tonic accent is a sure touchstone by which to
distinguish popular from learned words. There is another means, as
certain, by which to recognise the age and origin of words — the loss of
the short vowel. Every Latin word, as we have said, is made up of one
accented vowel, and others not accented — one tonic and others atonic.
The tonic always remains ; but of the atonies the short vowel^ which
immediately precedes the tonic vowels always disappears in French:
as in —

Bon(i)tdtem

San(i)t&teni

Pos(i)ttira

Clar(i)t&tem

Sep(tl)in^uia

Coin(i)t&tu8

Pop(u)16tus

bontd

santd

posture

clart4

semaine (O. Fr. sepmaine)

comte

peupld, &c.

' Words such as circuler, ciroiil&re, which break this law and keep

DOUBLE METHOD OF AGREEMENT.

159

the short vowel, are always of learned origin ; all words of popular origin
lose it, as cereler. This will be seen from the following examples : —

LATIN. POPXJLAR WORDS. LF.ARNED WORDS.

Ang(a)latiui

angU angule

Bla8ph(S)mdTe

blamer (0. Fr. blasmer) blaspbimer

Oap(i)tae

cbeptel capital

Car(l)tdtem

cberti cbarite

Ciro(u)16re

• • •

cercler circtder, &c.

* The third characteristic, serving to distinguish popular from learned
words, is the loss of the medial consoi^nt, i.e. of the consonant which
stands between two vowels, like the t in xnatiirus. We will at once
give the law of this change : — All Frencb words wbicb drop tbe medial
consonant are popular in origin^ wbile words of learned origin retain it.
Thus the Latin vooalis becomes, in popular French, voyelle, in learned
French vocale. There are innumerable examples of this : as —

LATIN.

Au(g)listii8

Advo(c)&tii8

Anti(p]i)6xLa

Cre(d)6ntia

Oomnium(o)&re

POPULAR WORDS.

aoUt

avoui

antienne

creance

communier

LEARNED WORDS.

auguste

avocat

antipbone

credence

communiquer, &c.'

The requisitions of the Double Method of Agree-
ment may be far from being rigorously fulfilled, and still
two phenomena may be so frequently present together
and so frequently absent together, that we may be justi-
fied in suspecting some causal connection between them.
Unless they were invariably absent together, as well as
invariably present, and unless they were the only cir-
cumstances which were invariably present and absent
together, we should not be justified in regarding one as
the cause, and the ortly cause, of the other ; but the mere
detection of the fact that they are frequently ^!:^^^\5&. •iscA.

l6o INDUCTIVE METHODS.

absent together may justify us in believing that there
is between them some causal connection. The precise
character of this causal connection may hereafter be
determined by one of the other inductive methods, or
by bringing the case under a previous deduction. The
following instances will serve as illustrations of what has
been here said.

Sir John Herschel conceives that he has detected a
connection between a full moon and a calm night : * The
only effect distinctly connected with its [the moon's]
position with regard to the sun, which can be reckoned
upon with any degree of certainty, is its tendency to clear
the sky of cloud, and to produce not only a serene but a
calm night, when so near the full as to appear round to
the eye — a tendency of which we have assured ourselves
by long-continued and registered observation.' The pre-
cise nature of the causal connection can here be deter-
mined: *The effect in question, so far as the clearance
of the sky is concerned, is traceable to a distinct physical
cause, the warmth radiated from its [the full moon's]
highly -heated surface; though why the effect should
not continue for several nights after the full, remains
problematic*^.'

In this example, there is not, of course, an invariable
connection between the clear night and the full moon;
for, in the determination of the weather, there are so
many and so various causes at work that they must
necessarily modify or counteract each other. The moon

^* HerscheVs Familiar Lectures on Scientific Subjects, pp. 146, 147.

DOUBLE METHOD OF AGREEMENT. l6l

might exercise considerable influence, might, as Sir John
Herschel says, have a tendency to produce a cahn night,
and still be overpowered by other influences. It is suflS-
cient, in order to lead us to suspect some causal connec-
tion between the two phenomena, that we should find a
calm night proportionably oftener, and oftener in a con-
siderable proportion, when there is a full moon than
when there is not Thus suppose that, after a long
series of observations of nights when there is a full
moon, we find the proportion of calm nights to nights
which cannot be called calm to be 5 to 2 (we are, of
course, taking an imaginary case), and the proportion
on ordinary nights to be 3 to 2, there can be little doubt
that the full moon is, in some way or other, connected
with the larger proportion of calm nights.

The employment of the Double Method of Agreement
may lead to the detection of facts of causation in many
instances of a similar kind. Thus, suppose that, in a
particular part of the country, a particular wind is found
to be proportionably oftener attended with rain than
other winds, we begin to suspect that there is some
causal connection between rain and this wind, so that,
when the wind blows, we may expect rain, at least with
more confidence than when other winds blow ; and, if the
proportion in which rain accompanies this wind be much
greater than that in which it accompanies other winds,
our expectation is proportionably strengthened, and we
have no hesitation in speaking of the quarter from which
the wind blows as * the rainy quarter/ In this casfc^^^

1 62 INDUCTIVE METHODS.

cause is, of course, to be sought in the character of the
tract over which the wind blows. Similarly, if, after
sufficiently long observation, we find the death-rate in
some particular place decidedly larger than in the sur-
rounding neighbourhood, we have no hesitation in ascrib-
ing the fact to some peculiarity either in the place or the
population, and we at once begin to consider whether
there is anything exceptional in the soil, the climate, the
habits or occupations of the people, and the like, which,
either alone or in conjunction with other circumstances,
would account for the phenomenon.

In all cases of this kind, we are, as it were, set on the
track of a cause by discovering that some phenomenon is
present in a proportionably greater number of instances
when some other phenomenon is present than when it is
absent. The cause itself may hereafter be detected either
by one of the other inductive methods, or by bringing the
case under a previous deduction. Thus, we know that
the surface of that part of the moon which we call ' full '
is highly heated, and that it is the tendency of warmth
radiated from a highly-heated surface to clear the atmo-
sphere. Hence the series of observed phenomena is
accounted for by being brought deductively under pre-
vious inductions.

METHOD OF RESIDUES. 1 63

METHOD OF RESIDUES.

CANON.

Subtract from any phenomenon such pari as is known
by previous inductions to be the effect of certain antecedents ^
and the residue of the phenomenon is the effect of the re-
maining antecedents.

If the antecedents are A, B, C, D, and the complex
phenomenon can be resolved into the consequents a, jS,
y, 5, €, of which y, 5, e are ascertained by previous
inductions to be due to C, D, then the remaining
consequents a, /3 must be referred to the remaining ante-
cedents A, B. Given that the total result is due to a
certain number of antecedents, and that part of the result
is due to a portion of those antecedents; the residue
of the result must necessarily be due to the remaining
antecedents. This rule appears so obvious as to be
hardly worth stating; it has, however, as will be seen
from the examples given below, been mainly instrumental
in leading to many of the most important discoveries of
modern times. ' It is by this process, in fact,' says Sir
John Herschel'^, 'that science, in its present advanced
state, is chiefly promoted. Most of the phenomena which
nature presents are very complicated ; and when the
effects of all known causes are estimated with exactness,
and subducted, the residual facts are constantly appearing

^ Discourse on the Study of Natural Pbilo&o^Vj, H '^'^-

ML 2

164 INDUCTIVE METHODS.

in the form of phenomena altogether new, and leading
to the most important conclusions/

There is one difficulty connected with this Method.
Subtraction being a deductive process, why is the Method
of Residues included among the inductive methods ?
The Method, it must be confessed, is strictly deductive,
but, as it is applied to the result of previous inductions
and generally suggests subsequent inductions, it may
vindicate its claim to discussion in this place. It is by
induction that we ascertain that y, 5, € are due to C, D ;
by the Method of Residues we determine that the re-
maining consequents a, /S must be due to the remaining
antecedents A, B ; we then generally proceed to decide
by one of the other inductive methods which of the
remaining consequents is due to which of the remaining
antecedents.

The following are instances of the employment of the
Method of Residues, and it will be noticed that the
science of astronomy is peculiarly rich in such ex-
amples : —

* The return of the comet predicted by Professor Encke,
a great many times in succession, and the general good agree-
ment of its calculated with its observed place during any one
of its periods of visibility, would lead us to say that its gravi-
tation towards the sun and planets is the sole and sufficient
cause of all the phenomena of its orbitual motion ; but when
the effect of this cause is strictly calculated and subducted
from the observed motion, there is found to remain behind
a residual phenomenon i which would never have been otherwise
ascertained to exist, which is a small anticipation of the time

METHOD OF RESIDUES. 165

of its reappearances or a diminution of its periodic time, which
cannot be accounted for by gravity, and whose cause is there-
fore to be inquired into. Such an anticipation would be
caused by the resistance of a medium disseminated through
the celestial regions; and as there are other good reasons
for believing this to be a vera causa, it has therefore been
ascribed to such a resistance^*.*

*The planet Jupiter is attended by four satellites which
revolve round it in orbits very nearly circular, and whose
dimensions, forms, and situations with respect to that of the
planet itself are now perfectly well known. The periodical
times of their respective revolutions are also ascertained with
extreme precision, and all the particulars of their motions
have been investigated with extraordinary care and persever-
ance. The three interior of them are so near the planet, and
the planes of their orbits so little inclined to that in which it
revolves round the sun, that they pass through its shadow,
and therefore undergo eclipse, at every revolution. These
eclipses have been assiduously observed ever since the dis-
covery of the satellites, and their times of occurrence regis-
tered. As they afford a means of determining the longitudes
of places, the prediction beforehand of the exact times of their
occurrence becomes an object of great importance : and it is
evident enough that, all the particulars of their motions being
known (as well as of that of the planet itself, and therefore of
the size and situation of its shadow), there would be no diffi-
culty in making such prediction (starting from the time of
some one observed eclipse of each as an epoch) ; provided always
each eclipse were seen at the identical moment fwhen it actually
happened. Moreover, on that supposition, the times recorded
of all the subsequent eclipses ought to agree with the times so

** Herschcrs Discourse on the Study of Natural Philosophy ^ § 159.
It will be noticed that Sir J. Herschel uses the expression ' vera causa ' in
the sense of * an actually existing fact.'

l66 INDUCTIVE METHODS,

predicted. This, however, proved not to be the case. The
observed times were sometimes earlier, sometimes later than
the predicted ; not, however, capriciously, but according to a
regular law of increase and decrease in the amount of dis-
cordance, the difference either way increasing to a maximum,
— then diminishing, vanishing, and passing over to a maxi-
mum the other way, and the total amount of fluctuation to
and fro being about i6™ 27". Soon after this discrepancy
between the predicted and observed times of eclipse was
noticed, it was suggested that such a disagreement would
necessarily arise if the transmission of light were not instan-
taneous. This suggestion was converted into a certainty by
Roemer, a Danish astronomer, who ascertained that they
always happened earlier than their calculated time when the
earth in the course of its annual revolution approached
nearest to Jupiter, and later when receding farthest : so that
in effect the extreme difference of the errors or total extent
of fluctuation — the 16™ 27" in question — is no other than the
time taken by light to travel over the diameter of the earth's
orbit, that being the extreme diflference of the distances of
the two planets at different points of their respective revolu-
tions. At present, in our ahnanacs a due allowance of time
for the transmission of light at this rate, assuming a uniform
velocity, is made in the calculation of these eclipses ; and the
discrepancy in question between the observed and predicted
times has ceased to exist ^®.*

The circumstances which led to the discovery of the
planet Neptune furnish, perhaps, the most striking in-
stance of the employment of the Method of Residues.
From the year 1804 it had been noticed that the orbit
of the planet Uranus was subject to an amount of per-

^ HerscheVs Familiar Lectures on Scientific Subjects^ p. 226, &c.

METHOD OF RESIDUES. 167

turbation which could not be accounted for from the
influence of the known planets.

* Of the various hypotheses formed to account for it
(the perturbation), during the progress of its development,
none seemed to have any degree of rational probability but
that of the existence of an exterior, and hitherto undiscovered,
planet, disturbing, according to the received laws of planetary
disturbance, the motion of Uranus by its attraction, or rather
superposing its disturbance on those produced by Jupiter and
Saturn, the only two of the old planets which exercise any
sensible disturbing action on that planet. Accordingly, this
was the explanation which naturally, and almost of necessity,
suggested itself to those conversant with the planetary per-
turbations who considered the subject with any degree of
attention. The idea, however, of setting out from the ob-
served anomalous deviations, and employing them as data
to ascertain the distance and situation of the unknown body,
or, in other words, to resolve the inverse problem of pertur-
bations, ^^ given the disturbances to find the orbit ^ and place in
that orbit of the disturbing planet^"* appears to have occurred
only to two mathematicians, Mr. Adams in England and
M. Leverrier in France, with suflScient distinctness and hope-
fulness of success to induce them to attempt its solution.
Both succeeded, and their solutions, arrived at with perfect
independence, and by each in entire ignorance of the other's
attempt, were found to agree in a surprising manner when
the nature and difficulty of the problem is considered ; the
calculations of M. Leverrier assigning for the heliocentric
longitude of the disturbing planet for the 23rd Sept. 1846,
326' o', and those of Mr. Adams (brought to the same date)
329° 19', differing only 3° 19'; the plane of its orbit deviating
very slightly, if at all, from that of the ecliptic.

* On the day above mentioned — a day for ever memorable
in the annals of astronomy — Dr. Galle, one of tha ^&\x^^\^\snk^

1 68 INDUCTIVE METHODS.

of the Royal Observatory at Berlin, received a letter from
M. Leverrier, announcing to him the result he had arrived
at, and requesting him to look for the disturbing planet in
or near the place assigned by his calculation. He did so, and
on that very night actually found it, A star of the eighth mag-
nitude was seen by him and by M. Encke in a situation
where no star was marked as existing in Dr. Bremiker's
chart, then recently published by the Berlin Academy. The
next night it was found to have moved from its place, and
was therefore assuredly a planet. Subsequent observations
and calculations have frilly demonstrated this planet, to which
the name of Neptune has been assigned, to be really that
body to whose disturbing attraction, according to the New-
tonian law of gravity, the observed anomalies in the motion
of Uranus were owing ^.'

Besides furnishing an instance of the Method of Residues,
the above example is also a happy illustration of the com-
bination of deduction with observation which has been
so eminently fertile in astronomical research.

* Almost all the greatest discoveries in astronomy have re-
sulted from the consideration of what we have elsewhere
termed residual phenomena, of a quantitative or numerical
kind, that is to say, of such portions of the numerical or
quantitative results of observation as remain outstanding and
unaccounted for after subducting and allowing for all that
would result from the strict application of known principles'^.

** Herschel's Outlines of Astronomy ^ Fourth Edition, §§ 767, 768.

^^ A very striking example of the employment of the Method of
Residues is to be found in the recent investigations by which Mr.
Huggins has shown that the slight deviation of the lines C and F in
the spectrum of Sirius is to be accounted for on the supposition that
the soiar system and that star are mutually receding from each other

METHOD OF RESIDUES. 1 69

It was thus that the grand discovery of the precession of the
equinoxes resulted as a residual phenomenon, fronfi the im-
perfect explanation of the return of the seasons by the return
of the sun to the same apparent place among the fixed stars.
Thus, also, aberration and nutation resulted as residual phe-
nomena from that portion of the changes of the apparent
places of the fixed stars which was left unaccounted for by
precession. And thus again the apparent proper motions of
the stars are the observed residues of their apparent move-
ments outstanding and unaccounted for by strict calculation
of the effects of precession, nutation, and aberration. The
nearest approach which human theories can make to per-
fection is to diminish this residue, this caput mortuum of
observation, as it may be considered, as much as practicable,
and, if possible, to reduce it to nothing, either by showing
that something has been neglected in our estimation of
known causes, or by reasoning upon it as a new fact, and on
the principle of the inductive philosophy ascending from the
effect to its cause or causes ^^.'

*Many of the new elements of chemistry have been de-
tected in the investigation of residual phenomena. Thus,
Arfwedson discovered lithia by perceiving an excess of ^weight
in the sulphate produced from a small portion of what he
considered as magnesia present in a mineral he had analysed.
It is on this principle, too, that the small concentrated residues
of great operations in the arts are almost sure to be the lurk-
ing places of new chemical ingredients : witness iodine, brome,
selenium, and the new metals accompanying platina in the
experiments of Wollaston and Tennant. It was a happy

at the rate of 29*4 miles a second. A brief account of this speculation
may be found in Professor Stokes' Address before the British Association
in 1869.

^ Herschel's Outlines of Astronomy^ ^ B^6.

ft

170 INDUCTIVE METHODS.

thought of Glauber to examine what everybody else threw
away^.'

'The unforeseen effects of changes in legislation, or of
improvements in the useful arts, may often be discerned by
the Method of Residues. In comparing statistical accounts,
for example, or other registers of facts, for a series of years,
we perceive at a certain period an altered state of circum-
stances, which is unexplained by the ordinary course of
events, but which must have some cause. For this residuary
phenomenon^ we seek an explanation until it is furnished by the
incidental operation of some collateral cause. For example,
on comparing the accounts of live cattle and sheep annually
sold in Smithfield market for some years past, it appears that
there is a large increase in cattle, while the sheep are nearly
stationary. The consumption of meat in London may be
presumed to have increased, at least in proportion to the
increase of its population ; and there is no reason for sup-
posing that the consumption of beef has increased faster than
that of mutton. There is, therefore, a residuary pheno-
menon — viz. the stationary numbers of the sheep sold in
Smithfield — for which we have to find a cause. This cause is
the increased transport of dead meat to the metropolis, owing
to steam navigation and railways, and the greater convenience
of sending mutton than beef in a slaughtered state.

'Again : on comparing the consumption of wine with that of
spirits and beer in England during the last sixty years *, we
find that the former has remained stationary, while the latter
has undergone a great increase. The general causes, such as
increase of population and wealth, which have increased the

^ Herschel's Discourse on the Study of Natural Philosophy ^ § i6l.

'* This was written in 1852. Since that time, owing to the reduction
of the duties, the greater familiarity of Englishmen with foreign countries
and habits, and, perhaps, the taste for a more refined style of living,
the consumption of wine has enormously increased.

METHOD OF RESIDUES, 171

consumption of spirits and beer, have not increased the con-
sumption of wine. For this residuary phenomenon, a special
cause must be sought ; and it may be found principally in the
alteration of habits among the upper classes with respect to
drinking ^,'

We shall conclude our instances with what Sir John
Herschel truly calls *a very elegant example,' the diflfer-
ence between the observed and calculated velocities of
sound. We quote from Professor TyndalFs Lectures on
Sound : —

* I now come to one of the most delicate points in the
whole theory of sound. The velocity through air has been
determined by direct experiment ; but knowing the elasticity
and density of the air, it is possible without any experiment
at all to calculate the velocity with which a sound-wave is
transmitted through it. Sir Isaac Newton made this cal-
culation, and found the velocity at the freezing temperature
to be 916 feet a second. This is about one-sixth less than
actual observation had proved the velocity to be, and the
most curious suppositions were made to account for the dis-
crepancy. Newton himself threw out the conjecture that it
was only in passing from particle to particle of the air that
sound required time for its transmission; that it moved in-
stantaneously through the particles themsehfes. He then sup-
posed the line along which sound passes to be occupied by
air-particles for one-sixth of its extent, and thus he sought to
make good the missing velocity. The very art and ingenuity
of this assumption were sufficient to ensure its rejection ;
other theories were therefore advanced, but the great French
mathematician Laplace was the first to completely solve the

^ Sir George Comewall Lewis on the Methods of Observation and
Reasoning in Politics, vol. i. p. 356.

172 INDUCTIVE METHODS.

enigma. I shall now endeavour to make you thoroughly
acquainted with his solution.

* I hold in my hand a strong cylinder of glass, accurately
bored, and quite smooth within. Into this cylinder, which
is closed at the bottom, fits this air-tight piston. By push-
ing the piston down, I condense the air beneath it; and
when I do so heat is developed. Attaching a scrap of
amadou to the bottom of the piston, I can ignite it by the
heat generated by compression. Dipping a bit of cotton
wool into bisulphide of carbon, and attaching it to the piston,
when the latter is forced down, a flash of light, due to the
ignition of the bisulphide of carbon vapour, is observed within
the tube. It is thus proved that when air is compressed, heat
is generated. By another experiment, I can show you that
when air is rarefied, cold is developed. This brass box con-
tains a quantity of condensed air. I open the cock, and
permit the air to discharge itself against a suitable thermo-
meter ; the sinking of the instrument declares the chilling of
the air.

*A11 that you have heard regarding the transmission of a
sonorous pulse through air, is, I trust, still fresh in your
minds. As the pulse advances, it squeezes the particles of air
together, and two results follow from this compression of the
air. Firstly, its elasticity is augmented through the mere
augmentation of its density. Secondly, its elasticity is aug-
mented by the heat developed by compression. It was the
change of elasticity which resulted from a change of density
that Newton took into account, and he entirely overlooked
the augmentation of elasticity due to the second cause above
mentioned. Over and above, then, the elasticity involved in
Newton's calculation, we have an additional elasticity due to
changes of temperature produced by the sound itself. When
both are taken into account, the calculated and the observed
velocity agree perfectly '^.'

^ Lectures on Sounds ch. i.

METHOD OF CONCOMITANT VARIATIONS. 173

It is not necessary, for our purposes, to pursue the
quotation, but the student who wishes to see an example
of the extreme delicacy and caution with which it is
requisite to conduct physical researches, may with great
advantage read the remainder of the chapter.

METHOD OF CONCOMITANT VARIATIONS.

CANON.

Whatever phenomenon varies in any manner whenever
another phenomenon varies in some particular manner, is
either a cause or an effect of that phenomenon^ or is connected
with it through some fact of causation:

,37

This Method is really a peculiar application, or series
of applications, of the Method of Difference. It is em-
ployed in those cases where a phenomenon cannot be
made to disappear altogether, but where we have the
power of augmenting or diminishing its quantity, or at least
where Nature presents it in greater or smaller amounts.
Thus, suppose we drop a quantity of quicksilver into a
glass tube, we shall find that every sensible augmenta-
tion of the temperature of the surrounding atmosphere
is accompanied by a sensible augmentation of the volume
of the quicksilver in the tube, and, vice versd, that every
sensible diminution of the temperature is accompanied

^ On p. 176 will be found a tvdai \a >&a%C.^v.wv,

174 INDUCTIVE METHODS.

by a sensible diminution of the volume of the quicksilver.
Now each particular experiment is an application of the
Method of Difference, and, providing we have ascertained
that the conditions of that Method have been rigorously
satisfied, partakes of its cogency. That certain definite
augmentations of temperature will increase the volume of
quicksilver by, say, one-twentieth, one-thirtieth, or one-
fiftieth part, is an absolutely certain inference, supposing
due care to have been taken in the performance of the
experiments, and is simply a result of the Method of
DilBference. But, inasmuch as there are limits above and
below which we cannot try the experiment, or inter-
mediate points of temperature at which we do not find
it convenient to do so, the question arises whether we
are justified, in virtue of the experiments already tried, in
asserting that the volume of the quicksilver will invariably
expand or contract in proportion to the increasing
or diminishing temperature of the surrounding media.
We are justified in making such an assertion, and for
this reason. The cause which occasions the quicksilver
to expand or contract at two definite points must, if it
continue to act, and if it be counteracted by no other
cause, operate at all intermediate points ; and, similarly,
the cause which occasions it to expand or contract up
to a certain point must, on the same suppositions, go on
producing a like effect. This is implied in the very
notion of Causation. We arrive, then, at the conclusion
that the volume of the quicksilver is invariably de-
pendent on the temperature of the surrounding me-

METHOD OF CONCOMITANT VARIATIONS. 1 75

dhim ; in other words, that augmentation of temperature
is the cause of its expansion^.

It may be asked, Why not employ the Method of
Difference once and for all ? Because, ex hypothesis the
phenomenon is one which is only capable of augmenta-
tion or diminution, and cannot be made to vanish. We
may reduce to a minimum the resistance to motion, but
we cannot remove the resistance altogether. We may
more and more diminish the heat of a body, but we
cannot wholly deprive the body of its heat. Hence we
can apply the Method of Diflference to the several aug-
mentations and diminutions of the phenomenon, but we
cannot apply it to the phenomenon as a whole.

In the example given above, we know that augmenta-
tion of temperature and augmentation of volume are
related as cause and effect, because, in the experiments,
we can assure ourselves that they are the only two cir-
cumstances which vary in common; if we were not
certain of this fact, there might be some third circum-
stance which was the cause of both. Moreover, we know
that augmentation of temperature is the cause and aug-
mentation of volume the effect, because, in this case, the
former is the antecedent and the latter the consequent.
There is another class of cases where, though we are not
able to determine which of two circumstances is cause

^^ The student acquainted with the phraseology of Mathematics will
understand our meaning, when we say that the Method of Concomitant
Variations is really an integration of a (supposed) infinite number of
applications of the Method of Difference.

176 INDUCTIVE METHODS.

and which is effect, we may regard the relation as being;
one of cause and eflfect, inasmuch as we feel confident
that there is present no third circumstance varying pro-
portionately with the other two. But, if we cannot be
confident even of this fact, the two circumstances may,
for aught we know, both be effects of the same cause,
as, for instance, the loudness of a clap of thunder varies
with the intensity of a flash of lightning, though neither
is the cause of the other, both alike being effects of the
electrical condition of the atmosphere. Hence will be seen
the importance of the concluding words of the Canon, * or is
connected with it through some fact of causation.' The
first and second cases differ from the third in this, that
in both of them we suppose a rigorous fulfilment of the re-
quisitions of the Method of Difference as applied to those
individual observations or experiments on which the Method
of Concomitant Variations is founded. In the last case,
however, we suppose that there is some uncertainty as to
whether the requisitions of the Method of Difference have
been rigorously fulfilled or not. It will thus be seen that
the statement of the Canon, as given above, is adapted
to the weakest case. We may add to it the following
rider : —

I/we can assure ourselves that there is no third pheno-
menon varying concurrently with these two, we may affirm
that the one phenomenon is either a cause or an effect of
the other.

The Method of Concomitant Variations may be used
for two purposes, either to establish a causal connection,

METHOD OF CONCOMITANT tARlATIONS. JJJ

or to detennine the law according to which two pheno-
mena vary. Thus, it may either establish the fact that
any increase of temperature causes quicksilver to expand,
or it may determine the exact rate according to which
this expansion takes place, a determination which is, in
fact, eflfected by the ordinary thermometer. In the latter
case, the application of the Method is not confined to
those permanent natural agents, the influence of which
we cannot altogether remove ; it may come in as supple-
mentary to the Method of Difference. Thus it is by
the Method of Difference that we discover that certain
kinds of impurity in the atmosphere produce certain kinds
of disease, but, if we could ascertain the relation subsisting
between the amount of impurity in the atmosphere and
the amount of disease, it would be by an application of
the Method of Concomitant Variations.

In the latter class of enquiries, the attempt to determine
the nimierical relations according to wliich two pheno-
mena vary, the utmost caution is required as soon as
our inference outsteps the limits of our observations. In
the first place, there is always the possibility of the in-
tervention of some counteracting cause. In the case of
water, we found that, at 39°, instead of continuing to
contract as it becomes colder, it ceases at that point to
do so, and thenceforward begins to expand. * No coun-
teracting cause intervening' is, however, a qualification
with which we must understand all our inductions, by
whatever method they may have been arrived at. But
there is an element of uncertainty which is peculiar to

N

178 INDUCTIVE METHODS.

the Method of Concomitant Variations as applied to
determine the law or rate of variation between two
phenomena, especially when the range of our obser-
vations is confined within comparatively narrow limits.
' Any one/ says Mr. Mill^, * who has the slightest acquaint-
ance with mathematics, is aware that very different laws
of variation may produce numerical results which differ
but slightly from one another within narrow limits ; and
it is often only when the absolute amounts of variation
are considerable, that the difference between the results
given by one law and by another becomes appreciable.
When, therefore, such variations in the quantity of the
antecedents as we have the means of observing are small
in comparison with the total quantities, there is much
danger lest we should mistake the numerical law, and
be led to miscalculate the variations which would take
place beyond the limits; a miscalculation which would
vitiate any conclusion respecting the dependence of th^
effect upon the cause, that could be founded on those
variations. Examples are not wanting of such mis-
takes. " The formulae," says Sir John Herschel, " which
have been empirically deduced for the elasticity of
steam (till very recently), and those for the resistance
of fluids, and other similar subjects," when relied on
beyond the limits of the observations from which they
were deduced, " have almost invariably failed to support
the theoretical structures which have been erected on

» MiU's Logic, Bk. III. ch. viii. § 7.

METHOD OF CONCOMITANT VARIATIONS. 179

them."' This, however, it must be noticed, is an un-
certainty which does not vitiate the method, but simply
renders necessary the exercise of the utmost caution in
its application.

Perhaps no simpler instance of the Method of Con-
comitant Variations can be given than the experimental
proof of the First Law of Motion, which Law may be
stated thus : that all bodies in motion continue to move
in a straight line with uniform velocity until acted upon
by some new force.

' This assertion,' I am quoting from Mr. Mill*^, * is in
open opposition to first appearances; all terrestrial objects,
when in motion, gradually abate their velocity and at last
stop ; which accordingly the ancients, with their inductto per
enumerationem simplicem, imagined to be the law. Every
moving body, however, encounters various obstacles, as
friction, the resistance of the atmosphere, &c., which we
know by daily experience to be causes capable of destroying
motion. It was suggested that the whole of the retardation
might be owing to these causes. How was this enquired into ?
If the obstacles could have been entirely removed, the case
would have been amenable to the Method of Difference.
They could not be removed, they could only be diminished,
and the case, therefore, admitted only of the Method of
Concomitant Variations. This accordingly being employed,
it was found that every diminution of the obstacles diminished
the retardation of the motion : and inasmuch as in this case
(unlike the case of heat) the total quantities both of the
antecedent and of the consequent were known ; it was prac-
ticable to estimate, with an approach to accuracy, both the
amount of the retardation and the amount of the retarding

*• MiU's Logic, Bk. III. ch. viii. § 7,
N 2

l8o INDUCTIVE METHODS.

causes or resistances, and to judge how near they both were
to being exhausted ; and it appeared that the effect dwindled
as rapidly [as the cause], and at each step was as far on the road
towards annihilation as the cause was. The simple oscillation
of a weight suspended from a fixed point, and moved a little
out of the perpendicular, which in ordinary circumstances lasts
but a few minutes, was prolonged in Borda's experiments to
more than thirty hours, by diminishing as much as possible
the friction at the point of suspension, and by making the
body oscillate in a space exhausted as nearly as possible of
its air. There could therefore be no hesitation in assigning
the whole of the retardation of motion to the influence of the
obstacles: and since, after subducting this retardation from
the total phenomenon, the remainder was an uniform velocity,
the result was the proposition known as the first law of
motion.'

We have already employed as an illustration the fact
that a change in the temperature of a body is always
accompanied by a change in its volume. The following
extract places the same fact in a new light, and shows
that the nature of substance (whether solid, fluid, or aeri-
form) depends on, and, at considerable intervals, varies
with, the temperature to which it is exposed.

* The most striking and important of the effects of heat
consist, however, in the liquefaction of solid substances, and
the conversion of the liquids so produced into vapour. There
is no solid substance known which, by a sufficiently intense
heat, may not be melted, and finally dissipated in vapour ;
and this analogy is so extensive and cogent, that we cannot
but suppose that all those bodies which are liquid under
ordinary circumstances, owe their liquidity to heat, and would
freeze or become solid if their heat could be sufficiently

METHOD OF CONCOMITANT VARIATIONS. l8l

reduced. In many we see this to be the case in ordinary
winters ; for some, severe frosts are requisite ; others freeze
only with the most intense artificial colds; and some have
hitherto resisted all our endeavours; yet the number of
these last is few, and they will probably cease to be excep-
tions as our means of producing cold become enlarged.

*A similar analogy leads us to conclude that all aeriform
fluids are merely liquids kept in the state of vapour by heat.
Many of them have been actually condensed into the liquid
state by cold accompanied with violent pressure ; and as our
means of applying these causes of condensation have improved,
more and more refractory ones have successively yielded.
Hence we are fairly entitled to extend our conclusion to those
which we have not yet been able to succeed with ; and thus
we are led to regard it as a general fact, that the liquid and
aeriform or vaporous states are entirely dependent on /beat ;
that were it not for this cause, there would be nothing but
solids in nature ; and that, on the other hand, nothing but a
sufficient intensity of heat is requisite to destroy the cohesion
of every substance, and reduce all bodies, first to liquids, and
then into vapour".'

An interesting application of the Method of Concomi-
tant Variations is found in the arguments by which it is
estabhshed that refrigeration at night (when the sun's rays
are withdrawn) is, cceterts paribus, proportional to the
dryness of the atmosphere. Thus, in the British Isles,
where the atmosphere almost always contains a large
amount of aqueous vapour, the, difference between the
temperature at day and night is comparatively slight,
whereas, in countries far inland, where the atmosphere is

*^ Herschcl's Discourse on the Study of Natural Pbilosopby^ §§ 357,
358.

1 82 INDUCTIVE METHODS.

extremely dry, the variations of temperature are compara-
tively large. This phenomenon is due to the fact that
masses of aqueous vapour, though they intercept, also
radiate heat. Hence, while during the day they protect
us from the excessive heat of the sun, they intercept the
heat which is radiated from the earth's surface during
the night, and, at the same time, return to it some
portion of the heat they have absorbed during the day.

*A freedom of escape,* says Professor Tyndall*^, 'would
occur at the earth's surface generally, were the aqueous
vapour removed from the air above it, for the great body
of the atmosphere is a practical vacuum, as regards the
transmission of radiant heat. The withdrawal of the sun
from any region over which the atmosphere is dry, must
be followed by quick refrigeration. The moon would be
rendered entirely uninhabitable by beings like ourselves
through the operation of this single cause ; with a radiation,
uninterrupted by aqueous vapour, the difference between her
monthly maxima and minima must be enormous. The win-
ters of Thibet are almost unendurable, from the same cause.
Witness how the isothermal lines dip from the north into
Asia, in winter, as a proof of the low temperature of this
region. Humboldt has dwelt upon the "frigorific power" of
the central portions of this continent, and controverted the
idea that it was to be explained by reference to the elevation ;
there being vast expanses of country, not much above the sea-
level, with an exceedingly low temperature. But not 'knowing
the influence which we are now studying, Humboldt, I ima-
gine, omitted the most potent cause of the cold. The refri-
geration at night is extreme when the air is dry. The removal,
for a single summer night, of the aqueous vapour from the

^ Tyndall's Heat a Mode of Motion^ § 492.

METHOD OF CONCOMITANT VARIATIONS. 1 83

atmosphere which covers England, would be attended by the
destruction of every plant which a freezing temperature could
kill. In Sahara, where " the soil is fire and the wind is flame,"
the cold at night is often painful to bear. Ice has been formed
in this region at night. In Australia, also, the diurnal range
of temperature is very great, amounting, commonly, to be-
tween 40 and 50 degrees. In short, it may be safely predicted,
that wherever the air is dry^ the daily thermometric range will
be great. This, however, is quite different from saying that
where the air is clear y the thermometric range will be great.
Great clearness to light is perfectly compatible with great
opacity to heat ; the atmosphere may be charged with aqueous
vapour while a deep blue sky is overhead, and on such occa-
sions the terrestrial radiation would, notwithstanding the
" clearness," be intercepted.'

The science of Geology abounds in instances of the
employment of the Method of Concomitant Variations.
In fact, as the agents with which it is concerned, land and
water, subsidence and elevation, deposition and denuda-
tion, are constantly present and acting on the earth's
surface, and as it is impossible to cause the influence of any
one of them to vanish altogether, the geologist is compelled
in his explanations and arguments to avail himself mainly
of this method. The following extract from Lyell's Prin-
ciples of Geology furnishes a good illustration, and will be
peculiarly interesting to any one who has visited the
place. It is designed as an explanation of the alternate
subsidence and elevation of the famous temple of Jupiter
Serapis, at Pozzuoli, on the Bay of Naples.

< We can scarcely avoid the conclusion, as Mr. Babbage has
hinted, " that the action of heat is in some way or other the

184 INDUCTIVE METHODS.

cause of the phenomena of the change of level of the temple.
Its own hot spring, its immediate contiguity to the Solfatara,
its nearness to the Monte Nuovo, the hot spring at the baths
of Nero, on the opposite side of the Bay of Baiae ; the boiling
springs and ancient volcanos of Ischia on one side and Vesu-^
vius on the other, are the most prominent of a multitude of
facts which point to that conclusion." And when we reflect
on the dates of the principal oscillations of level, and the
volcanic history of the country before described, we seem to
discover a connection between each era of upheaval and a
local development of volcanic heat, and again between each
era of depression and the local quiescence or dormant condi-
tion of the subterranean igneous causes. Thus for example,
before the Christian era, when so many vents were in frequent
eruption in Ischia, and when Avemus and other points in the
Phlegraean Fields were celebrated for their volcanic aspect
and character, the ground on which the temple stood was
several feet above water. Vesuvius was then regarded as a
spent volcano ; but when, after the Christian era, the fires of
that mountain were rekindled, scarcely a single outburst was
ever witnessed in Ischia, or around the Bay of Baiae. Then
the temple was sinking. Vesuvius, at a subsequent period,
became nearly dormant for five centuries preceding the great
outbreak of 163 1, and in that interval the Solfatara was in
eruption a.d. 1198, Ischia in 1302, and Monte Nuovo was
formed in 1538. Then the foundations on which the temple
stood were rising again. Lastly, Vesuvius once more became
a most active vent, and has been so ever since, and during the
same lapse of time the area of the temple, so far as we know
anything of its history, has been subsiding.

* These phenomena would agree well with the hypothesis,
that when the subterranean heat is on the increase, and when
lava is forming without obtaining an easy vent, like that
afforded by a great habitual chimney, such as Vesuvius, the
incumbent surface is uplifted, but when the heated rocks

METHOD OF CONCOMITANT VARIATIONS. 1 85

below are cooling and contracting, and sheets of lava are
slowly consolidating and diminishing in volume, then the in-
cumbent land subsides*'.'

Laplace's Nebular Hypothesis, that stellar systems, like
our solar system, are formed from the gradual condensa-
tion of different nebular masses, is supported by an appeal
to this method. ' We see,' conceives Laplace, ' among these
nebulae' (which are diffused along the Milky Way), ' in-
stances of all degrees of condensation, from the most
loosely diffused fluid, to that separation and solidification
of parts by which suns and satellites and planets are
formed ; and thus we have before us instances of systems
in all their stages ; as in a forest we see trees in every
period of growth**.'

Physiology (so far as it is based on Anatomy, as dis-
tinct from direct experiment), for like reasons with
Geology, mainly employs the Method of Concomitant
Variations. It is very seldom, in this science, that we
obtain a phenomenon present in one set of instances and
entirely absent in another; but we frequently find a
phenomenon which, within certain limits, presents itself
in the most variable quantities. If, then, we find another

•

phenomenon varying as it varies, we may argue with

^ Lyell's Principlet of Geology, tenth edition, ch. xxx.

^ Whewell's iNTovMm CrganumRenovatum, Bk. III. ch. viii. sect. 2. § 9.
This example is adduced by Dr. Whewell as an instance of what he calls
the Method of Gradation, which, however, must not be confounded with
Mill's Method of Concomitant Variations. The example, so far as it
can be relied on, serves equally well as an instance of either.

1 86 INDUCTIVE METHODS.

tolerable confidence that they either stand to each other
in the relation of cause and effect, or are, at least, com-
mon effects of some unknown cause. Thus, it appears
to be established that, not only in different species, but
in different individuals of the same species, there is some
relation between the manifestations of intelligence and the
amount of cerebral development, understanding the latter
expression to include not only bulk of brain but also
complexity and depth of convolutions.

'With some apparent exceptions,' says Dr. Carpenter **,
a classical authority on most physiological questions, 'which
there would probably be no great difficulty in explaining
if we were in possession of all the requisite data, there is a
very close correspondence between the relative development
of the Cerebrum in the several tribes of Vertebrata and the
degree of Intelligence they respectively possess — using the
latter term as a comprehensive expression for that series of
mental actions which consists in the intentional adaptation
of means to ends, based on definite ideas as to the nature
of both.*

And again : —

* As we ascend the Mammalian series, we find the Cerebrum
becoming more and more elongated posteriorly by the de-
velopment of the middle lobes, and the intercerebral con-
missure becomes more complete ; but we must ascend as high
as the Camivora, before we find the least vestige of the
posterior lobes; and the rudiment which these possess is so
rapidly enlarged in the Quadrumana, that in some of that
group the posterior lobes are as fully developed in reference
to the Cerebrum as a whole, and as completely cover in the

i5

Carpenter's Principles of Human Pbystology, sixth edition. 1864.

METHOD OF CONCOMITANT VARIATIONS. 1 87

Cerebellum, as in the human subject. The attention which
has yet been given to this department of enquiry, has not
hitherto done more than confirm the statement already made,
with regard to the general correspondence between the de-
velopment of the Cerebrum and the manifestations of Intelli-
gence ; very decided evidence of which is furnished by the
great enlargement of the Cerebrum, and the corresponding
alteration in the form of the Cranium, which present them-
selves in those races of Dogs most distinguished for their
educability, when compared with those whose condition ap-
proximates most closely to what was probably their original
state of wildness.

* This general inference drawn from Comparative Anatomy,
is borne out by observation of the human species. When the
Cerebrum is fully developed, it offers innumerable diversities
of form and size among various individuals ; and there are
as many diversities of character. It may be doubted if two
individuals were ever exactly alike in this respect. That a
Cerebrum which is greatly under the average size is incapable
of performing its proper functions, and that the possessor
of it must necessarily be more or less idiotic, there can be
no reasonable doubt. On the other hand, that a large, well-
developed Cerebrum is found to exist in persons who have
.made themselves conspicuous in the world in virtue of their
intellectual achievements, may be stated as a proposition of
equal generality.'

Dr. Thurnam*^, taking the brain-weights of ten dis-
tinguished men, who died between the ages of fifty and
seventy, calculates the average weight of their brains
to have been 54*7 ounces. The average weight of the
brains of ordinary men, dying between the same ages,

*« On the Weight of the Brain^ by John Thuniam, M.D, l^^-s^&ss^x
J. £. Adlard. 1866.

1 88 INDUCTIVE METHODS.

is 47*1 ounces. This gives in favour of * cultivated and
intellectual man' an excess of 7*6 ounces, or 15 per
cent. Though, as a general rule, the connection between
intellectual and cerebral development appears to be sub-
stantiated, we must, however, be very cautious in draw-
ing any inferences as to particular cases. Megalo-
cephaly, or pathological enlargement of the brain, is a
' recognised disease, and is frequently attended with idiotcy.
In this class of cases, no doubt, if our means of investi-
gation were adequate, we should discover some peculiarity
either in the chemical composition or in the anatomical
structure of the brain which would enable us to explain
the exceptions in conformity with the rule.

It is, perhaps, needless to add that we are not justified
in drawing any further inference from these data, than
that the brain is the organ of intelligence, and that there
is some definite relation between the organ and its
functions.

Another interesting application of the Method of
Concomitant Variations may be found in one of the
arguments by which the distinction between Formed and
Germinal Material is established. Any piece of glandular
tissue, if examined under a microscope, will be found
to consist of two parts, one of which will take a tint
from carmine, the other not. The portion which takes
the tint is called Germinal, the portion which will not
take it is called Formed Material. The former is living
matter, capable of growth and germination; the latter
is dead matter, capable of no change but decay. Now,

METHOD OF CONCOMITANT VARIATIONS. 1 89

if this distinction between the two kinds of matter be
well founded, we may reasonably expect to find the ger-
minal matter developed in much larger proportions in the
younger than in the older specimens of animals and
plants, and in what may be called the more active than
in what may be called the more passive parts of animal
and vegetable organisms. And this is the case. In the
pith of rush, elder, &c. we find that, in the spring, there
are many portions of the cells which will take the carmine
tint ; in summer, few ; in autumn, none. In the
crystalline lens of the eyes of young animals the portions
which will take it preponderate, becoming proportionately
fewer as we examine the eyes of older specimens. In
the grey matter of the brain we find many parts which
will take the carmine tint, in the white matter but few.
In a grain of wheat, when formed, there is, in the peri-
sperm, no portion which will take it, in the white matter
but a- small portion, while in the embryo it is often
difl&cult to discover any part which does not take it.
These instances might be multiplied to any extent*^.

In physiological and medical researches, we must be
peculiarly careful to bear in mind that, though two pheno-
mena may vary proportionately, it by no means follows
that one is cause and the other effect They may both
be common effects of the same cause. Thus, though the
prevalence of cholera is said to be constantly attended

^ The student will find this subject fully treated in Dr. Lionel Beale's
Lectures on the Simple Tissue of tbe Human Body, and in, other works
of the same author.

190 INDUCTIVE METHODS.

by the appearance of certain low forms of organic life,
namely, fimgi or phytozoa, it by no means follows that
these fungi or phytozoa are the cause of cholera. Both
phenomena alike may be effects of certain conditions of
the atmosphere. Nothing but a direct experiment could
determine between these two theories.

The Method of Concomitant Variations, or, as it is
often called, when employed on subjects not strictly
physical, the Method of Comparison, is that which is
most frequently employed in the Science of Language.
It is found, for instance, that between two dissimilar words
employed at different epochs to express the same idea
may be interpolated a number of intermediate forms
employed at intermediate epochs, which make the transi-
tion from the one word to the other gradual and natural.
From this it is inferred that the word used at the later
epoch is derived from that used at the earlier epoch,
the lapse of time being regarded as the cause of the
divergence. * Thus, at first sight,' says M. Brachet*^,
'it is hard to see that dme is derived from anima; but
history, our guiding-line, shows us that in the thirteenth
century the word was written anniey in the eleventh aneme,
in the tenth animey which leads us straight to the Latin
anima* In this case there can be no doubt of the truth
of the conclusion.

Similarly, the loss of declension in the transition from

** M, Brachet's Historical Grammar of the French Tongue, Mr.
Kitchin's Translation, p. 42.

METHOD OF CONCOMITANT VARIATIONS. 191

the Latin language to the French is easily explained
when we take into account the following considera-
tions : —

* The tendency to simplify and reduce the number of cases
was early felt in the popular Latin : the cases expressed shades
of thought too delicate and subtle for the coarse mind of the
Barbarian. And so, being unable to handle the learned and
complicated machinery of the Latin declensions, he constructed
a system of his own, simplifying its springs, and reducing the
number of the effects at the price of frequently reproducing
the same form. Thus the Roman distinguished by means of
case-terminations the place where one is, from the place to
which one is going: "veniunt ad domum," "sunt in domo."
But the Barbarian, unable to grasp these finer shades, saw no
use in this distinction, and said, in either case alike, "sum
in domum," " venio ad domum."

'Thus, from the fifth centiuy downwards, long before
the first written records of the French language, popular
Latin reduced the number of cases to two: (i) the nominative
to mark the subject ; and (2) that case which occurred most
frequently in conversation, the accusative, to mark the object
or relation. From that time onwards the Latin declension
was reduced to this : — subject, muruj ; object, murum,

* The French language is the product of the slow develop-
ment of popular Latin; and French grammar, which was
originally nothing but a continuation of the Latin grammar,
inherited, and in fact possessed from its infancy, a completely
regular declension : subject, murs, murus ; object, mur^ murum:
and people said "ce murs est haut;" "j*ai construit un

mur"

* This declension in two cases forms the exact difference
between ancient and modern French. It disappeared in the
fourteenth century, not without leaving many traces in the
language, which look like so many insoluble exceptions^ but

1^2 INDUCTIVE METHODS.

find their explanation and historic justification in our know-
ledge of the Old French declension *^*

Here the conclusion is that French Grammar is derived
from Latin Grammar, and that the lapse of time is the
cause of the differences between them.

Again, nothing at first sight would appear more im-
probable than that the French word suz's and the Greek
word cifu are derived from the same root. But, when
we compare the Old French word sut\ the Latin sum,
the Old Latin esunij and the Old Greek form eV/Lit, the
connection of the two words and their ultimate derivation
from a common root becomes a certainty. Here the
divergence is accounted for not only by lapse of time,
but by the various influences operating upon people (like
the Latins and Greeks) occupying different tracts of
country, exposed to different circumstances, having the
organs of speech diflferentiy modified, and the like.

Amongst the above examples it will be noticed that
some have been included, the conclusions of which are
by no means absolutely certain. In these cases, the
deficiency of proof is due not to any formal inconclusive-
ness in the Method of Concomitant Variations, or in that
of Difference, on which it is based, but to the existence
of a doubt as to whether the requirements of these
methods have been stringently fulfilled. In any but the
Experimental Sciences it is always extremely difl&cult to

*• M. Brachet's Historical Grammar of the French Tongue, Mr.
Kitchia's Translation, p. 88.

METHOD OF CONCOMITANT VARIATIONS. 193

assure ourselves that we are acquainted with all the cir-
ciunstances which may influence, or may be influenced
by, any given phenomenon. Moreover, as is the case, for
instance, with regard to the concomitance between cere-
bral development and the manifestation of intelligence,
there may be many known points of difference between
the observed cases besides those which are taken into ac-
count, and the value of the conclusion will depend on the
extent to which we have ascertained that these other points
of difference are not pertinent, or not equally pertinent,
with those which we have taken into account, to the cir-
cumstance or circumstances which we are investigating.

The application of the Method of Concomitant Varia-
tions to determine the numerical relations subsisting
between two phenomena may be illustrated from the ex-
periments by which the measure of the accelerating force
of gravity was established. The fact that the higher the
point from which a body falls the greater is the velocity
acquired is patent to observation, though, if we analyse
the process by which we arrive at the conclusion, it
is by the Method of Concomitant Variations. The rate
of acceleration, however, is a very difl&cult and delicate
problem to solve. By Attwood's machine (which it is
unnecessary to describe here) it is shown (i) that gravity
is an uniformly accelerating force, that is, that the incre-
ments of velocity in equal times are equal ; (2) that the rate
of increase varies slightly at different places on the earth's
surface ; (3) that, in the latitude of Greenwich, in vacuo,
and at high-water mark, the rate of acceleration for every

194 . INDUCTIVE METHODS.

second of time is 32*19 inches, the space traversed in the
first second of time, if the body fall from rest, being half
that quantity, so that the spaces traversed in successive
units of time vary as the odd nimibers i, 3, 5 . . . .
(2«— i). A slight degree of attention will show that
it is by the Method of Concomitant Variations that all
these conclusions are obtained ^.

The conclusions based on statistics in moral and
social enquiries are also instances of this application of
the Method of Concomitant Variations. It is argued
that, if the same causes continue to operate with like
intensity and no new causes intervene, the numerical
relations established between two classes of social pheno-
mena, as, for instance, deficient education and crime,
may be expected to remain constant.

Briefly to review these Methods, it will be seen that
we can only arrive at absolute certainty by means of
one or other of the Methods of Difference, Residues, or
Concomitant Variations, while the Method of Agreement
and the Joint Method of Agreement and Difference give
conclusions only of more or less probability, a probability,
however, which sometimes amounts to moral certainty.
The Joint Method of Agreement and Difference, or the
Double Method of Agreement, possesses one advantage
over all the other Methods, namely that, supposing it to
have been satisfactorily ascertained by this Method that

^ The student who wishes for more detailed information on this
subject is referred to Professor Price's Infinitesimal Calculus^ vol. iii.
chap, viii. sect. 3.

INDUCTIVE METHODS. 1 95

A is the cause of a, it will follow that it is the only
cause.

It should also be borne in mind that a wide distinction
exists between those cases in which the induction indicates
the precise character of the causal connection which
subsists between two or more phenomena and those in
which it simply points out that there exists a causal
connection of some kind or other. In the latter case
a new induction is required in order to show what the
nature of the causal connection is.

It may be noticed, finally, that the Inductive Methods
are strictly reducible to two only, the Method of Agree-
ment and the Method of Difference ; the Joint Method of
Agreement and Difference being a double employment of
the Method of Agreement, the Method of Concomitant
Variations being a series of employments of the Method
of Difference, and the Method of Residues being, strictly
speaking, a deductive method employed in an inductive
enquiry.

Note I . — In the preceding chapter no allusion, or only
a casual one, has been made to a circumstance which
frequently occasions an insuperable difficulty in the appli-
cation of the Inductive Methods, namely, the Intermixture
of Effects. It has been supposed that the antecedents
A, B, C, D, &c. are followed by the consequents a, j3, y, 8, €,
&c,, the effects being regarded as heterogeneous and not
homogeneous. But, suppose the effect o€ K.\.c>\ifc a^^"^\si

o a

196 INDUCTIVE METHODS.

be— ", of C to be y, of D to be ^, and of E to be — -, the

total effect of A, B, C, D, E will be - + -^ . It is obvious

how difl&cult it would be in this case to discover either
the exact portion of the effect which is due to each cause
or the several causes which operate to produce the total
effect. We might have, in fact, as in mechanical action
and reaction, A producing a and B producing — a, each
cause thus neutralising the effect of the other, so that
we might entertain no suspicion that the causes A and B
were in operation at all. In these cases, our main re-
source is Deduction combined with the Method of Re-
sidues. Having ascertained separately by one or other
of the various inductive methods, or from previous de-
ductions, the effects, say of A, B, C, D, we calculate
deductively their combined effect, and then, by subtracting
the sum of the known causes from the total aggregate
of causes and the known portion of the effect from the
total effect, we simplify, if we do not solve, the problem.
On the insufficiency, under ordinary circumstances, of the
Inductive Methods, without the aid of Deduction, to
grapple with cases of this kind, and on the nature of the
assistance rendered by Deduction, the reader may con-
sult Mr. Mill's Logic^ Bk. III. ch. x. § 4-8, and ch. xi.

In cases of this kind, where the action of one cause
is augmented, diminished, or wholly counteracted by that
of another, it must not be supposed that any part of its
appropriate effect has failed to be produced, even though
it may have disappeared wholly or partially in the total

INDUCTIVE METHODS. 1 97

result. An object may remain at rest, . when subject
to two equal forces acting in opposite directions, but
we cannot say of either of these forces that it is in-
operative : each, it is true, prevents any visible effect
resulting from the other ; but then this is the very effect
which it produces, and the correct mode of describing
either of the opposing forces would be to say that
it has a tendency to make the given object move with
a certain velocity in a certain direction. The student
cannot too constantly bear in mind that every cause has
a tendency to produce its full effect, though other causes
may prevent that effect from manifesting itself with all
the intensity with which it would manifest itself, if it acted
alone ; that there are, strictly speaking, no exceptions to
laws of nature, though these laws, in their manifold action
and reaction, may modify or even neutralise each other.
The aphorism * Every rule has an exception,' is only true,
even in Grammar, either because the rule is inexactly
stated or because it conflicts with some other rule known
or unknown.

Note 2. — The Canons for the Inductive Methods were
first stated by Mr. Mill, and the importance now attached
to them in most analyses of inductive enquiries is mainly
due to his influence. The methods are, however, as
Mr. Mill himself states, ' distinctly recognised' in Sir John
Herschel's Discourse on the Study of Natural Philosophy^
so often quoted in this work, 'though not so clearly
characterised and defined, nor their correlation so fully
shown, as has appeared to me desirabk.' Iw^^^^^^'^^

198 INDUCTIVE METHODS.

Book of Bacon's Novum Organum, we find some approxi-
mations, very rough, it is true, to fonnal inductive me-
thods. Tlie 'instantiae crucis' have akeady been adduced
as examples of the Method of Difference, and the 'in-
stantiae solitariae' as including examples of both the
Method of Agreement and the Method of Difference ;
but the part of the Novum Organum to which I am now
alluding, and which is intended to be of more universal
application than the ' instantiae crucis' and the 'instantia^
solitariae,' is contained in the early Aphorisms of the
Second BooL Certain Tables of Instances are there
given for the purpose of providing materials with which
to conduct an investigation into what Bacon called the
* Form,' corresponding pretty nearly to what we should
call the 'Cause,' of Heat. The instances are very far
from satisfying the conditions of Mr. Mill's Methods, but
the principles on which they are arranged in Tables
bear a close analogy to the principles on which the
Canons are constructed. The best mode, perhaps, of
enabling the student to perceive the extent of the resem-
blance is to state the conditions with which the instances
in Bacon's Tables would be required to conform, in
order to satisfy the requirements of Mr. Mill's Methods.

If the 'Instantiae convenientes in natura calidi'^^ were
80 related to one another that, besides the given pheno-
menon (heat), only one other circumstance were common
to tbem all, that other circiunstance might be regarded,

^ Nctmm Organum, Bk. II. Aph. zi.

INDUCTIVE METHODS, 1 99

with more or less probability, as the cause (or effect) of
heat, or, at least, as connected with it through some fact
of causation. Such instances would then come under the
Method of Agreement.

If one instance in the Table of Agreement (' Instantiae
convenientes in natura calidi') were so related to one of the
instances in the Table of Privation (' Instantiae in proximo,
quae privantur natura calidi')^^ as to have every circum-
stance in common with it, except that the former, besides
presenting the phenomenon of heat which is supposed
to be absent in the latter, also presented some other
circumstance which was absent from the latter, this other
circumstance would be the cause, or a necessary part of
the cause (or effect), of heat. This would represent the
Method of Difference.

If, in the * Tabula graduum, sive comparativae in
calido'^ we could discover some one phenomenon which
increased or diminished proportionately with the increase
or diminution of heat, that phenomenon would be the
cause or the effect of heat, or, at least, connected with it
through some fact of causation, and would answer to the
Method of Concomitant Variations. If it could be shown
that this phenomenon and heat were the only circum-
stances which varied concurrently, then the phenomenon
would be proved to be either the cause or the effect of
heat, and would come under the rider to this last Method
(p. 176).

The * Exemplum exclusivae, sive rejectionis naturarum

« Novum Organum, Bk. II. Aph, xiv. ^ \^. K^.tSv,

aOO INDUCTIVE METHODS.

a forma calidi'** bears some, though, it must be acknow-
ledged, a very slight, resemblance to the Method of
Residues. These *rejectiones' consist in excluding some
possible explanation of the phenomenon, either because
an instance, which does not present the phenomenon,
does present the assigned cause, or because an in-
stance, which does present the phenomenon, does not
present the assigned cause*"*. As an instance of the
former, we may take the following * rejectio' : * Per radios
lunae (which were then supposed to be cold) et aliarum
stellarum rejice lucem et lumen.' As instances of the
latter, we may take the two following : * Per radios solis,
rejice naturam elementarem (that is, * terrestrial nature,'
which is composed of *the four elements'); Per ignem
communem, et maxime per ignes subterraneos (qui re-
motissimi sunt, et plurimum intercluduntur a radiis coeles-
tibus) rejice naturam coelestem.' By a succession of these
*rejectiones' we limit the number of possible explana-
tions, amongst which we are to look for the true one.
Bacon's * rejections,' however, lead to a purely negative
result; they may save us from unnecessary trouble
in seeking for a cause when it cannot be found,
but they do not, like the Method of Residues, leave a
definite number of antecedents which either constitute the
cause, or amongst which we know that the cause is to
be sought.

** Novum OrganutUt Bk. II. Aph. xviii.

** The latter, of course, is not a legitimate argument. The effect may
be dne to seyera\ distinct causes, a fact which was not recognised by Bacon.

INDUCTIVE METHODS. 201

Note 3. — ^Dr. Whewell (in a pamphlet published in
1849, which is now embodied in the Philosophy 0/ Dis-
covery^ questions the utility of the Four Methods.
* Upon these methods/ he says, * the obvious thing to
remark is, that they take for granted the very thing which
is most difficult to discover, the reduction of the pheno-
mena to formulae such as are here presented to us/ He
also objects that, as a matter of fact, no discoveries have
ever been made by the employment of these methods.
' Who will carry these formulae through the history of
the sciences, as they have really grown up, and show us
that these four methods have been operative in their for-
mation ; or that any light is thrown upon the steps of
their progress by reference to these formulae?'

The first objection is, as Mr. Mill points out, of the
same character with the objections raised by Locke and
other writers of the eighteenth century against the Rules
of Syllogistic Reasoning. The reply, in either case, is
that Logic does not profess to supply arguments, but to
test them. Men have certainly reasoned, and reasoned
with the greatest force, without any conscious use of the
rules of Logic. But it is the province of a system of
Logic to analyse the arguments commonly, employed, to
discriminate between those which are correct and those
which are incorrect, and thus to enable men to detect, in
the case of others, and to avoid, in their own case,

^ See Pbilosopby of Discovery ^ ch. xxii. The criticism of Mr. Mill's
Methods will be found in §§ 38-48. Mr. Mill replies in a note at the.
end of 6k. III. ch. ix.

202 INDUCTIVE METHODS.

erroneous methods of reasoning. To think of appro-
priate arguments is undoubtedly more difficult than to
test them ; but this does not obviate the necessity of sub-
mitting them to a test. Nor is it a more real objection
that men, who know nothing of the technical rules of
Logic, often reason faultlessly themselves, and show re-
markable acuteness in detecting inconclusive reasoning
in the arguments of others. Many men speak grammati-
cally without having learnt any system of grammar; in
the same manner, many men reason logically without
having leamt any system of Logic. But the great ma-
jority of men, there can be little doubt, may derive
assistance both from one and the other. Grammar
fulfils its functions when it raises the student to the level
of the most correct speakers ; similarly. Logic fulfils its
functions when it raises the student to the level of the
best reasoners. As applied to the syllogistic rules and
formulae, this defence would now be generally admitted,
but it holds equally good of the methods into which it
may be shown that our inductive arguments may ulti-
mately be analysed. * The business of Inductive Logic^'
says Mr. Mill, * is to provide rules and models (such as
the Syllogism and its rules are for ratiocination) to which
if inductive arguments conform, those arguments are
conclusive, and not otherwise. This is what the Four
Methods profess to be, and what I believe they are
universally considered to be by experimental philoso-
phers, who had practised all of them long before any
one sought to reduce the practice to theory/

INDUCTIVE METHODS. 203

With regard to the second objection, that these me-
thods have not been operative in the formation of the
sciences, Dr. Whewell seems to ignore the distinction
between the conscious and the unconscious employment
of a method. It is undoubtedly true that in records of
scientific investigations we seldom find the formal lan-
guage in which the Inductive Canons are expressed. It
seems to me equally true that in such records we inva-
riably detect the employment of the Canons themselves.
Discoveries are of two kinds : they are either entirely the
result of patient research, or they are first suggested to
the mind by some brilliant thought, and afterwards
verified by rigorous proof. In the forrner case, the
discoverer must have made sure of his ground as he
proceeded, and, so far as his method was inductive, he
could only do so by appealing, consciously or uncon-
sciously, to one or more of the inductive methods ; if he
acted otherwise, he arrived at a true result by mere
accident. In discussing the latter case, we must repeat
what has already been stated, that it is not the oflSce of
Logic, either inductive or deductive, to suggest thoughts,
but to analyse and to test them. Now, in the case we are
supposing, the discovery really consists of two parts —
the original conception and the subsequent process by
which it is determined to be the true explanation of
the phenomenon. However striking and appropriate
the conception, we have no right to regard it as the
true explanation of the phenomenon till it has been
subjected to the most rigorous investl^tiQiT^.. 'Wsj&\!K5i^^-

a04 INDUCTIVE METHODS.

tigation must be either inductive or deductive, or both.
But, so far as it is inductive, it must conform to the
requirements of the Inductive Canons, or else it will not
result in positive proof, or even approximate closely
to it. As in the former case, imless the discoverer
has, consciously or unconsciously, employed one or
more of these Canons in the inductive part of his rea-
soning, he has no right to feel any confidence in the
result of his researches.

-tr^QS^sy^'^^

CHAPTER IV.
Of Imperfect Inductions.

AN argument from the particular to the general, or
from particulars to adjacent particulars, may fall short of
absolute proof, or even of moral certainty, while it com-
mends itself as possessing more or less of probability.
Arguments of this character may be called Imperfect
Inductions. Under this head fall imperfect applications
of the experimental or inductive methods, the argument
from analogy, and incomplete cases of Inductio per sim-
plicem enumerationem.

The Inductio per stmplicem enumerationem is, as al-
ready noticed^, when complete, a deductive, and not an
inductive, argument. When incomplete, it is an induc-
tive argument, for it is an inference of the unknown
from the known. This form of Induction possesses the
force of demonstration only when, as in the case of the
Laws of Universal Causation and of the Uniformity of
Nature, it is grounded upon universal experience, and

* Sec p. 117, note 2, and Deductive Logic, Part I I. chap. i. appended
Note 2.

2,o6 IMPERFECT INDUCTIONS.

we feel assured that, if there had been at any time or
were now in any place any instance to the contrary, it
would not have escaped our notice. But, in ordinary
cases, the incomplete Inductio per simplicem enumera-
Honem affords only a presmnption, sometimes very slight,
sometimes tolerably strong, in favour of the position
which it is adduced to establish. I perceive, say in five,
ten, or twenty cases, that the phenomenon a is attended
by the phenomenon 3, and, knowing of no cases in
which the one phenomenon is not attended by the
other, I begin to suspect that a and h are connected
together in the way of causation. Such a surmise may
afterwards be proved by the aid of one or other of the
five methods to be correct, and, in that case, it is taken
out of the category of inductions per simplicem enumera-
Honem J and becomes an instance of a scientific induction.
But, if neither proved nor disproved, it still has a certain
amount of probability in its favour, that amount depend-
ing on the two following considerations: (i) the num-
ber of positive instances which have occurred to us ;
(2) the likelihood, if there be any negative instances, of
our having met with them. The first of these considera-
tions deserves little weight, unless supported by the other.
A native of the North of Europe, some centuries ago,
might, if the mere accumulation of positive instances were
sufiicient, have taken it for a certain truth that all men
had white complexions. His own personal observation,
as well as the reports of travellers and the traditions of
his race, would have furnished numberless instances in

INDUCTIO PER SIMP. ENUM. 20J

favour of the position. But, before drawing the inference,
he ought to have reflected that he possessed information
about a small portion only of the inhabitants of the
earth's surface, that a difference of climate might produce
a difference of complexion, and that there was no reason
for supposing that the anatomical structure of man, or
the various characteristics which we denominate human,
are necessarily connected with a skin of one particular
colour. But, on the other hand, we may affirm with
tolerable certainty that all the varieties of beings pos-
sessing the physical structure of man have the capacity of
articulate speech ; for, if there were any races exhibiting
the one set of phenomena without the other, there is
every probability, with our present knowledge of the
earth's surface, that we should be acquainted with their
existence. In this instance the first consideration, which
in itself would deserve little weight, is converted into a
certainty almost absolute by the support which it derives
from the second.

It cannot be too strongly impressed on the mind of
the student that a mere simplex enumeration that is, a mere
assemblage of positive instances, unless we have reason to
suppose that, were there any instances to the contrary,
they would have become known to us, is simply worthless.
' Inductio per simplicem enumerationem res puerilis est.'
But if the simplex enumeratio be accompanied by a well-
grounded conviction that there are no instances to the
contrary, it may afford a very high degree of probability,
and, if we can assure ourselves tiaaX ^^^x^ ^x^ \nk» '^sv-

io8 IMPERFECT INDUCTIONS.

Stances to the contrary, to us individually it will afford
certainty.

It might seem that an Inductio per Simplicem Enum-
erationem is always an employment of the Method of
Agreement. But there is this essential difference. The
Inductio per Simplicem Enumerationem simply enume-
rates instances without selection or precaution; whereas
the whole force of the Method of Agreement consists in
the choice and variety of the instances on which the in-
ference is based.

The term * Empirical Generalisation' or * Empirical
Law' might be conveniently appropriated to express the
result of an Inductio per Simplicem Enumerationem.
Though these expressions are employed with great lati-
tude, it is usually regarded as characteristic of an Em-
pirical Law or Generalisation that it can only be received
as true within the limits of the data from which it is
derived, that at another time, at another place, or under
different circumstances from those under which the
observations were made, it might be found to break
down^. It is true that, owing to the conflict of causes,
this description applies to many of the conclusions arrived
at by means of the Inductive Methods, but it is peculiarly
applicable to the results of the Inductio per Simplicem
Enumerationem, and it would be extremely convenient to
possess an expression by which the results of this method

^ See Herschel's Discourse on the Study of Natural Philosophy, § 187,
and Miirs Logic, Bk. III. ch. xvi. § 4.

ANALOGY. a09

might be at once distinguished from those of scientific
induction on the one hand, and those of analogy (to be
discussed presendy) on the other. Instances of Empirical
Laws in this restricted sense are such generalisations as that
certain animals or flowers are of a certain colour, that
certain tribes of men are less capable of civilisation than
others, and, perhaps, that certain appearances of sky are
indicative of certain changes ,of weather. There are, of
course, some cases in which it is difficult to determine
whether a given conclusion has been arrived at by the
Inductio per Simplicem Enumerationem or by an imper-
fect application of the Method of Agreement, that is to
say, whether it is based on instances taken indifferently,
or on selected instances ^

Another form of imperfect induction is the Argument
from Analogy*. Here we do not argue from a niunber

' I have ayoided any special discussion of what are called ' Empirical
Laws/ both on account of the extremely indeterminate use of the ex-
pression, and because such a discussion is calculated, in my opinion,
needlessly to perplex the student by the complicated questions to which
it leads. The advanced student can refer to Mr. Mill's Logic, Bk. III.
ch. XV., and Bk. V. ch. v. § 4, but he will be introduced, I venture to
think, to more difficulties than he will find solved.

* It will be observed that the word 'Analogy* is here employed in the
sense of ' resemblance.* In the stricter and more ancient meaning of the
term, it signifies an equality of relations ({(T^n/t \6r^fw). See Aristotle's
Ethics, Bk. V. 3. (8). The reader will find the two significations of the
word 'Analogy* discriminated in the Elements of Deductive Logic,
Part III. ch. i. note 2.

Archbishop Whately defines Analogy as a Resemblance of Relations.
This definition, if intended to represent the ancient sv^^&Ka^^ssa. ^sS. "^^

P

a 10 IMPERTECT INDUCTIONS.

of instances, as in the case of Inductio per Simplicem
Enumerationem, but from a number of points of resem-
blance. The argument is not, that because S, T, U, V,
W, &c. exhibit the union of m with a, 3, r, we may
therefore expect to find m in Z, or wherever else a,
bf c may occur; but that, because X and Y (any two
or more instances) agree in the possession of certain
qualities a, 3, r, we may expect to find the quality m
which is presented by X exhibited also in Y. The
argument is based, not on the niimber of instances in
which the two sets of qualities are found united, but on
the number of qualities which are found to be common
to two or more instances : the argument is not that
I have so often observed a, 3, c in conjunction with m
that I believe these qualities to be conjoined invariably,
but that I know X and Y to resemble each other in so

word, is incorrect. The Aristotelian Analogy is an equality^ not a
resemblance of relations. The instance given in Etb. Nic. i. 6. (12) is
that, in man, the reason {vovs) bears to the living principle (^wx^) the
same relation that the faculty of vision {oipts) bears to the body {awpa) ;
ofs ycLp kv aijiMTi &f/i9, iv ^vxj? ^ovs. The assertion, in this instance, it
will be noticed, is that the relation to each other of the two former
members of the analogy is, not similar to, but the same as, that of the
two latter. The Aristotelian term avaXoylat in fact, exactly corresponds
with the term Proportion as employed by mathematicians, and it was
by the word Proportio, when not availing themselves of the Greek word
Analogia itself, that the Romans expressed this form of argument. See
Quinctilian, Inst. Or at. i. 6 : ' Analogic^ quam proxime ex Graeco trans-
ferentes in Latinum proportionem vocaverunt, haec vis est : Ut id, quod
dubium est, ad aliquid simile, de quo non quaeritur, referat ; ut incerta
certis probet.' I am indebted for this quotation to Mr. Austin's Lectures
on Jurisprudence t vol. iii. p. 255.

ANALOGY. 2 1 I

many points that I believe them to resemble each other
in all.

Thus, because the moon resembles the earth in being
a large spheroid revolving round another body, as well
as in various other particulars, it may be argued that
it probably resembles the earth also in sustaining animal
and vegetable life on its surface. But, if every ground
of resemblance furnishes a probable reason for assigning
to the one body any property known to belong to the
other, it is evident that every ground of dissimilarity will
also furnish a probable reason for denying of the first
body any prpperty known to belong to the second. In
estimating, therefore, the value of an analogical argument,,
we must strike a balance between the known points of
resemblance and the known -points of difference, and
according as the one or the other preponderate, and in
the proportion in which the one or the other prepon-
derate, is the weight of the argument to be regarded
as inclining. If, for instance, the phenomenon A is known
to resemble the phenomenon B in four points, whereas
the known points of difference between them are three,
and it is discovered that some new property belongs to
A but it is uncertain whether it also belongs to B, the
value of the analogical argument that it does belong to
B will be represented by 4 : 3.

Before, however, we are justified in drawing this in-
ference, it is necessary to observe certain cautions.

In the first place, we must have no evidence that there
is any causal connection between the ne^ ^\q^^\^?^ •xs:^

p 2

212 IMPERFECT INDUCTIONS.

any of the known points of resemblance or difference.
If we have such evidence, the argument ceases to be
analogical, and, if not a perfect induction, is an imper-
fect induction of the kind to be described presently.
We know, for instance, that animal and vegetable life on
the surface of the earth could not exist without moisture ;
but, so far as we are able to ascertain, there is no moisture
on the surface of the moon. Hence we appear to be
justified in concluding, not by analogy, but by the Method
of Difference (assuming, of course, the accuracy of the
observations), that animal and vegetable life, in the sense
ordinarily attached to those terms, are not to be found on
the moon's surface*. Again, we happen to know two men
who bear a considerable resemblance to each other in
character and opinions. One of these men acts in a par-
ticular way, and we infer, analogically, that the other will
act similarly. But, suppose we ascertain that the act of
the former man was due to some particular characteristic,
say avarice. The inference will now no longer depend
on the ratio of the known points of resemblance to the
known points of difference in the characters and opinions
of the two men, that is, on analogy, but it will depend
mainly on the presence or absence, the strength or weak-
ness, of this particular characteristic in the second man,

* See the Essay of the Plurality of Worlds (usually attributed to Dr-
Whewell), ch. ix. sect. 7-9. The whole of this essay furnishes excellent
examples of the employment of the Argument from Analogy, and also
illustrates the extreme caution and delicacy which are requisite in esti-
mating its value.

ANALOGY. 213

and, in a subsidiary degree, on the presence or absence,
the strength or weakness, of corroborating or counter-
vailing motives; that is, it will depend, not on analogy,
but on other modes of induction.

Secondly, though there must be no evidence to con-
nect the property in question with any of the known
points of resemblance or diflference, there must, on the
other hand, be no evidence to disconnect it. If there
be such evidence, the point of resemblance or diflference
with which we know or believe it to be unconnected
must, in estimating the value of the analogy, be left out
of consideration. The reason is obvious. When we are
enquiring whether this property is more likely to be
connected with the known points of resemblance or the
known points of diflference, it is plain that we must only
take into account those points with which there is, at
least, some chance of its being connected.

Thirdly, we must have no reason to suspect that any
of the known points of resemblance or diflference of
which the argument takes account, are causally connected
with each other. If the compared phenomena agree in
the possession of the properties a, 3, c, </, e^ and of these
properties b is an eflfect of (or causally connected with)
a, and </ is an eflfect of (or causally connected with) r,
the only properties which ought to be taken into account
in estimating the value of the analogy are a, Cy e. The
moon is supposed to diflfer from the earth in having
no clouds and no water, but, as these two properties
are mutually connected in the ^^^ ^ ^'»»&^ •m^^

214 IMPERFECT INDUCTIONS.

effect, they can only be allowed to count as one
item in instituting a comparison, for the purposes
of analogy, between the known points of resemblance
and the known points of difference in the two bodies.
The enormous difference, on the other hand, between the
maximum and minimum temperature of any place on the
moon's surface, owing to the extreme length of the lunar
days and nights, constitutes a distinct point of difference,
and, as such, furnishes an additional argument against
the habitation of the moon. When we ask to which
side the argument from analogy inclines, we are asking
whether it is more probable that the property in question
(known to belong to the one phenomenon, but not
tnown either to belong or not to belong to the other) is
connected, by way of causation, with one of the known
points of resemblance or with one of the known points of
difference ; but, in calculating the probability, it is essen-
tial that every point should, so far as we know, be in-
dependent of every other ; for it is only in virtue of each
being supposed to be an ultimate property or to point to
an ultimate property that it has any claim to be taken
into the account. Thus, if any two of the properties
are found to be joint effects of the same cause or to
stand to each other in the relation of cause and eflfect,
they furnish only one argument instead of two. If we
say of A that he is likely, under some particular con-
juncture of circumstances, to act in the same manner as
B, because they are both of them vain and selfish, we
should not strengthen our argument by adding a number

ANALOGY, 215

of characteristics which are deducible from vanity and
selfishness, or by adducing a number of individual acts
in which these qualities have been exhibited.

Fourthly, it is only when we have reason to suppose
that we are acquainted with a considerable proportion of
the properties of two objects, that the argument from
analogy can have much weight. If we know only a few
properties out of a large number, they may happen to be
precisely those which are exceptional rather than repre-
sentative, points of similarity where the objects themselves
are mainly dissimilar, or points of dissimilarity where the
objects are mainly similar. Thus, we know that in some
respects the planet Mars closely resembles the earth, as,
for instance, in having an atmosphere, a surface dis-
tributed into land and water, and a temperature in which
life similar to that on our own globe might exist ;
but it would be very rask to conclude from these data
that it also resembles the earth in sustaining animal and
vegetable life on its surface ; for, though life, such as we
understand it, does not appear to be impossible on the
planet Mars as it is on many of the other celestial bodies,
the number of properties with which we are acquainted is
so small as compared with the number of properties with
which we are unacquainted that there is little or nothing
on which to ground a rational conclusion. On the other
hand, the analogy by which Kepler boldly extended the
three laws gained from the observation of the motion of
Mars to the temaining planets was a perfectly sound one ;
for the orbit of a planet, as compared with tke oftrwi^^^

2l6 IMPERFECT INDUCTIONS.

of its surface, is a very simple phenomenon, and what was
known of the orbits of the other planets made it appear
more likely that they would correspond with the orbit
of Mars than that they would differ from it.

The value of the Argument from Analogy, then, we see,
depends on the ratio of the ascertained points of resem-
blance to (i) the ascertained points of difference, (2) the
entire assemblage of the properties of the objects com-
pared. If the ascertained resemblances are numerous,
the ascertained differences, few, and we have reason to
think that we are well acquainted with the objects com- .
pared, the argument from analogy is very forcible. If,
on the other hand, the ascertained resemblances only
slightly exceed in number the ascertained differences, or
if we have reason to suppose that there are numerous pro-
perties in the compared objects with which we are un-
acquainted, the value of the argfument from analogy may
be very slight. It is commonly said that the value of an
argiunent from analogy ranges from certainty to zero.
If it reaches certainty, the argument becomes a com-
plete induction; if it falls to zero, it ceases to be an
argument at all ; if the probability is expressed by
less than one-half, that is, if the number of ascertained
resemblances be less than the number of ascertained
differences, it is usual to say that analogy is against
the possession by the one object of a quality known
to belong to the other, or, in other words, in favour
of their differing in the possession of this quality rather
than agreeing in it.

ANALOGY. 217

* Besides the competition between analogy and diver-
sity,' says Mr. Mill*, 'there may be a competition of
conflicting analogies/ An object may be known to
resemble one object in some particulars and another in
others, and it may be a question with which of the two
it ought to be classed, or which of the two it is likely to
resemble in some unknown property. Thus, for some
time it was a question whether a sponge was an animal
or a vegetable substance ; and it is often by conflicting
analogies that we attempt to determine to which of two
or more masters a painting or a statue should be
ascribed.

The extreme caution which is requisite in employing
the Argument from Analogy may be illustrated by the
following scientific errors which have resulted from a
hasty and inconsiderate employment of this mode of
reasoning.

Mr. Grove, in his Correlation of Physical Forces^ ^ while
combating the once fashionable doctrine of electrical
fluids, brings into juxta-position two very interesting
instances of hasty analogies.

* The progressive stages,' he says, * in the History of Phy-
sical Philosophy will account in a great measure for the adop-
tion by the early electricians of the theories of fluids.

* The ancients, when they witnessed a natural phenomenon,
removed from ordinary analogies, and unexplained by any
mechanical action known to them, referred it to a soul, a

• Mill's Logic, Bk. III. ch. xx. § 2.
' Fifth edition, p. 135.

2l8 IMPERFECT INDUCTIONS.

spiritual or preternatural power : thus amber and the magnet
were supposed by Thales to have a soul ; the functions of
digestion, assimilation, &c., were supposed by Paracelsus to
be effected by a spirit (the Archaeus). Air and gases were
also at first deemed spiritual, but subsequently became in-
vested with a more material character; and the word gas,
from gehtf a ghost or spirit, affords us an instance of the
gradual transmission of a spiritual into a physical conception.

* The establishment by Torricelli of the ponderable cha-
racter of air and gas, showed that substances which had been
deemed spiritual and essentially different from ponderable
matter were possessed of its attributes. A less superstitious
mode of reasoning ensued, and now aeriform fluids were
shewn to be analogous in many of their actions to liquids or
known fluids. A belief in the existence of other fluids, differ-
ing from air as this differed from water, grew up, and when a
new phenomenon presented itself, recourse was had to a
hypothetic fluid for explaining the phenomenon and connect-
ing it with others ; the mind once possessed of the idea of a
fluid, soon invested it with the necessary powers and pro-
perties, and grafted upon it a luxuriant vegetation of ima-
ginary offshoots.'

Most of our readers will be aware of the difficulties
experienced by the early geologists in accounting for
the fact that the strata of our own and other northern
countries often contain remains of animals and shells
akin to those which are now to be found only in the
torrid zone. This difficulty is easily explained by sup-
posing a different distribution of land and water over the
surface of the globe from that which at present exists.
But we must pause before we admit the inference that,
because these animals and shells are akm to those which

ANALOGY. 219

are now found only in warm climates, they must, there-
fore, have subsisted in a similar temperature.

*When reasoning on such phenomena,' says Sir Charles
LyelP, * the reader must always bear in mind that the fossil
individuals belonged to species of elephant, rhinoceros, hippo-
potamus, bear, tiger, and hyaena, distinct from those which
now dwell within or near the tropics. Dr. Fleming, in a
discussion on this subject, has well remarked that a near
resemblance in form and osteological structure is not always
followed, in the existing creation, by a similarity of geo-
graphical distribution; and we must therefore be on our
guard against deciding too confidently, from mere analogy of
anatomical structure, respecting the habits and physiological
peculiarities of species now no more. " The zebra delights to
roam over the tropical plains ; while the horse can maintain
its existence throughout an Iceland winter. The buffalo, like
the zebra, prefers a high temperature, and cannot thrive even
where the common ox prospers. The musk ox, on the other
hand, though nearly resembling the buffalo, prefers the stinted
herbage of the arctic regions, and is able, by its periodical
migrations, to outlive a northern winter. The jackal (Cams
aureus) inhabits Africa, the warmer parts of Asia, and Greece ;
while the isatis (Cams lagopus) resides in the arctic regions.
The African hare and the polar hare have their geographical
distribution expressed in their trivial names;" and different
species of bears thrive in tropical, temperate, and arctic
latitudes.

* Recent investigations have placed beyond all doubt the
important fact that a species of tiger, identical with that of
Bengal, is common in the neighbourhood of Lake Aral, near
Sussac, in the forty-fifth degree of north latitude ; and from
time to time this animal is now seen in Siberia, in a latitude

® Lyell's Principles of Geology, ch. vi. (ninth edition) ; cK« tl. (^vskc^x
edition).

220 IMPERFECT INDUCTIONS,

as far north as the parallel of Berlin and Hamburgh. Hum-
boldt remarks that the part of Southern Asia now inhabited
by this Indian species of tiger is separated from the Himalaya
by two great chains of mountains, each covered with perpetual
snow, — the chain of Kuenlun, lat. 35° N., and that of Mouz-
tagh, lat. 42°,— so that it is impossible that these animals
should merely have made excursions from India, so as to
have penetrated in summer to the forty-eighth and fifty-third
degrees of nqrth latitude. They must remain all the winter
north of the Mouztagh, or Celestial Mountains. The last
tiger, killed in 1828, on the Lena, in lat. 5 2 J', was in a
climate colder than that of Petersburg and Stockholm.'

Neither in Analogy nor in Induction by Simple Enu-
meration is there supposed to be any clue to a fact of
Causation. When we begin to suspect that any one
circumstance or set of circumstances is the cause or the
effect of another, or connected with it in the way of
causation, we ought at once to attempt to apply one or
more of the Experimental Methods. If we can satisfy
ourselves that their conditions, or those of any one of
them, have been rigorously fulfilled, we have, of course,
obtained a Valid Induction, giving us either absolute or
moral certainty. But something considerably short of
a rigorous fulfilment of these conditions may still lead
to a conclusion, possessing more or less of probability.
We may, for instance, to take the Method of Agreement,
feel uncertain whether a and b (any two circumstances) are
the only material circumstances which the cases we have
examined exhibit in common; but still we may have
examined so many, so various, and so well selected in-

INCOMPLETE INDUCTIONS. 22t

stances, that we may be justified in regarding it as highly
probable that the two circumstances stand to each other
in the relation of cause and effect, or are, at least, con-
nected in the way of causation. Similarly, to take
the Method of Difference, in the act of introducing
a new antecedent, we may have unwittingly introduced
some other new antecedent, or, in omitting an antecedent,
we may have unwittingly introduced or omitted some
other antecedent; but still we may have exercised such
extreme caution as to justify us in feeling an assurance
amounting almost, though not altogether, to certainty
that the experiment has been rightly performed. The
less our assurance of this fact, the slighter is the prob-
ability of the conclusion.

There remains one case, which is attended with some
perplexity. It sometimes happens that, though we may be
unable to establish a fact of causation between two par-
ticular phenomena, we may be able to shew that some one
phenomenon stands in a causal relation to some one or
other of a definite number of other phenomena. Thus,
supposing a vegetable to be transplanted to a distant
part of the world, we may be able to assure ourselves,
by excluding other causes of difference, that any new
qualities which it may assume are due either to difference
of climate, or to difference of soil, or to both these causes
conjointly, though our knowledge may not enable us to
assign amongst these alternatives the particular cause or
combination of causes to which the effect \^ ^^. ^^-^

2M IMPERFECT INDUCTIONS.

ought such an Inference to be classified as a perfect or
an imperfect Induction? If we content ourselves with
stating the alternatives, the inference should be regarded,
so far as it goes, as a Perfect Induction ; for we do not
state more than we conceive ourselves to be absolutely
warranted in doing. But, if, on any grounds, we suppose
one of these alternatives to be more probable than the
others, and we state this as our conclusion, the inference
is, of course, only a probable one, and should rank as
an Imperfect Induction.

The same remarks will apply to those cases in which
there is any uncertainty as to the nature of the fact of
causation. If the inference be, say, that the two pheno-
mena either are one cause and the other eflfect, or stand
to each other in the relation of cause and eflfect, though
we may be unable to determine which of the two is
cause and which is eflfect, or are joint eflfects of the
same cause (adding any other alternatives which the par-
ticular case may require), the inference is, so far as it
goes, a Perfect Induction. But, if one or some only of
these alternatives be selected, on any groimds short of
absolute or moral certainty, to the exclusion of the
others, the inference is only probable, and must be re-
garded as merely an Imperfect Induction.

Briefly to sum up the contents of this chapter. Imper-
fect Inductions are the results either of an Inductio per
Simplicem Enumerationem (to which we propose to ap-
propriate the expression 'Empirical Generalisations'), or

INCOMPLETE INDUCTIONS, 223

of the Argument from Analogy (which we call Analogies),
or of an imperfect fulfilment of one or other of the Induc-
tive Methods (to which we might, perhaps, advantageously
appropriate the expression 'Incomplete Inductions'). In
the two former cases there is supposed to be no clue
to a Fact of Causation, while in the last we conceive our-
selves to be on the way towards establishing one.

».«»«««««>• •**»»»»..,.

CHAPTER V.

On the relation of Induction to Dedtcction^

and on Verification.

THE results of our inductions are summed up in
general propositions, which are not unfrequently stated
in the shape of mathematical formulae. These general
propositions, the results of inductive reasoning, become,
in turn, the data from which deductive reasoning pro-
ceeds. Though the major premiss of any particular
deductive argument may itself be the result of deduction,
it will invariably be found, as pointed out long ago by
Aristotle^, that the ultimate major premiss of a chain of
deductive reasoning is a result of induction. There must
be some limit to the generality of the propositions under
which our deductive inferences can be subsumed, and,
when we have reached this limit, the only evidence on
which the ultimate major premiss can repose, if it depend
on evidence at all, must be inductive. Thus, most of
the deductions in the science of Astronomy, and many

Ik tSjv Ka$6\ov. Eitrlv &pa dpxo^ k( &v 6 (rvWoyifffxds, S)v oit/e tan
avXXoyi<rfJi6r (irayor^ &pa. — Eib. Nic, vi. 3 (3). Cf. Etb. Nic. vi. 6.
8 (g) ; Metaphysics, i. I ; Posterior Analytics, ii. 19.

RELATION OF INDUCTION TO DEDUCTION. 22^

of those in the science of Mechanics, depend ultimately
on the Law of Universal Gravitation ; but this Law itself
is the result of an induction based upon a variety of facts,
including both the fall of bodies to the earth and the
motion of the planets in their orbits. Again, a large
number of geometrical deductions may be traced up to
the ultimate major premiss : * Things that are equal to
the same thing are equal to one another/ But this
proposition, if not referred directly to induction, is
classed under the head of intuitive conceptions, the most
probable, though perhaps not the most commonly re-
ceived, explanation of which is that which derives them
from the accumulated experience of generations, trans-
mitted hereditarily from father to son.

A Deductive Inference combines the results of previous
inductions or deductions, and evolves new propositions
as the consequence, or, to put the matter in a slightly
different point of view, as expressing the total result,
of these combinations. We append a few easy examples
of the manner in which the results of induction are em-
ployed in a deductive argument.

To begin with a very simple instance, but one which
will serve as a good illustration of the stage at which
our investigations cease to be inductive and become
deductive; — suppose we have ascertained, by previous
inductions, that A produces a, B produces b, C pro-
duces — f, D produces |^, and E produces f, we know,
by calculation, that is, by deductive reasoning, that the
total effect of A, B, C, D, E is b -f ^. Iiv ^3ci^ ^•^^^ "^^

226 RELATION OF INDUCTION TO DEDUCTION,

simple rules of Algebra, governing the addition and sub-^
traction of quantities, combined with the special data
here furnished, are the premisses from which our de-
ductive reasoning proceeds.

The proposition proved in Euclid, Book i. Prop. 38,
that * Triangles upon equal bases, and between the same
parallels, are equal to one another,' is derived from, or
is the total result of, the previous deductions (i) that
* Parallelograms upon equal bases, and between the same
parallels, are equal to one another,' (2) that * Triangles
formed by the diagonal of a parallelogram are each of
them equal to half the parallelogram' (i. 34), and (3) the
previous induction that *the halves of equal things are
equal.'

What is called the Hydrostatic Paradox, namely, that
a man standing on the upper of two boards, which
form the ends of an air-tight leather bag, and blowing
through a small tube opening into the space between the
board, can easily raise his own weight, is a combination
of two propositions, both gained from experience by
means of induction, these propositions being (i) that
fluids transmit pressure equally in all directions, (2) that
the greater the pressure brought to bear on any surface
from below, the greater the weight which it will sustain
{otherwise expressed by the Mechanical Law that action
and reaction are equal).

To take another very simple instance of a similar kind.
One of the earliest and easiest problems in the Science
of Optics is the following : * A conical pencil of rays is

AND VERIFICATION. 227

incident upon a plane reflecting surface; to determine
the form of the reflected pencil/ The solution, that the
reflected pencil will be a cone having for its vertex a
certain imaginary point, which can be geometrically deter-
mined, on the other side of the surface, is derived from a
combination of the experimental truth, gained by induc-
tion, that ' the angle of reflexion is equal to the angle
of incidence' with the geometrical propositions stated in
Euclid i. 8 and i. 29.

In the Science of Political Economy, Ricardo's Theory
of Rent, namely that ' the rent of land represents the
pecuniary value of the advantages which such land pos-
sesses over the worst land in cultivation,' is an easy
deduction from two principles which are supplied by
every one's experience, namely, (i) that land varies in
value, and (2) that there is some land either so bad or so
disadvantageously situated as to be not worth the culti-
vating^.

Professor Cairnes' work on the Slave Power furnishes
a remarkable example of the successful application of the
deductive method to the determination of economical
questions. The economical effects of slavery are thus
traced. We learn from observation and induction that
slave labour is subject to certahi characteristic defects:
it is given reluctantly; it is unskilful; and, lastly, it is
wanting in versatility. As a consequence of these cha-
racteristics, it can only be employed with profit when

' The student will find an easy exposition of this Theory in Fawcett's
Manual of Political Economy ^ Bk. II. ch. iii. ad init.

228 RELATION OF INDUCTION TO DEDUCTION,

it is possible to organise it on a large scale. It re-
quires constant supervision, and this for small numbers
or for dispersed workmen would be too costly to be re-
munerative. The slaves must, consequently, be worked in
large gangs. Now there are only four products which
repay this mode of cultivation, namely, cotton, sugar,
tobacco, and rice. Hence a coimtry in which slave
labour prevails is practically restricted to these four
products, for it is another characteristic of slave labour,
under its modern form, that free labour cannot exist
side by side with it. But, besides restricting cultivation
to these four products, some or all of which have a pe-
culiar tendency to exhaust the soil, slave labour, from its
want of versatility, imposes a still further restriction.
* The difficulty of teaching the slave anything is so great
— the result of the compulsory ignorance in which he is
kept, combined with want of intelligent interest in his
work — that the only chance of rendering his labour
profitable is, when he has once learned a lesson, to keep
him to that lesson for life. Accordingly where agricul-
tural operations are carried on by slaves, the business of
each gang is always restricted to the raising of a single
product. Whatever crop be best suited to the character
of the soil and the nature of slave industry, whether
cotton, tobacco, sugar, or rice, that crop is cultivated,
and that crop only. Rotation of crops is thus precluded
by the conditions of the case. The soil is tasked again
and again to peld the same product, and the inevitable
result follows. After a short series of years its fertility

AND VERIFICATION. 22,()

is completely exhausted, the planter abandons the ground
which he has rendered worthless, and passes on to seek
in new soils for that fertility under which alone the
agencies at his disposal can be profitably employed.'
Thus, from the characteristics of slave labour may be
deduced the economical effects of exhaustion of the soil
on which it prevails, and the consequent necessity of
constantly seeking to extend the area of cultivation.
From the peculiar character of the crops which can
alone be successfully raised by slave labour may be ex-
plained the former prevalence of slavery in the Southern,
and its absence in the Northern, States of the American
Union ; and from the necessity of constantly seeking
fertile virgin soil for the employment of slave labour may
be explained the former policy of the Southern States,
which was invariably endeavouring to bring newly consti-
tuted States under the dominion of slave institutions^

These examples of the combination of inductive with
deductive reasoning might be multiplied to any extent.
Mechanics, Astronomy, and the Mathematico-physical
sciences generally, furnish, perhaps, the most striking
instances of them. The great importance of deduction
as an instrument for the ascertainment of physical truths
could hardly be illustrated more appropriately than by the
following cases adduced by Sir John Herschel* : —

^ See Professor Cairnes on the Slave Power, ch. ii. His arguments are
stated in a condensed form in Fawcett's Manual of Political Economy,
Bk. II. ch. xi.

* Discourse on tbe Study of Natural PbUosopby, § 399.

230 RELATION OF INDUCTION TO DEDUCTION,

' It had been objected to the doctrine of Copernicus, that,
were it true, Venus [and, it might have been added. Mercury,
as the other inferior planet] should appear sometimes homed
like the moon. To this he answered by admitting the con-
clusion, and averring that, should we ever be able to see its
actual shape, it would appear so. It is easy to imagine -with
what force the application would strike every mind when the
telescope confirmed this prediction, and showed the planet just
as both the philosopher and his objectors had agreed it ought
to appear. The history of science affords perhaps only one
instance analogous to this. When Dr. Hutton expounded his
theory of the consolidation of rocks by the application of heat,
at a great depth below the bed of the ocean, and especially
of that of marble by actual fusion ; it was objected that,
whatever might be the case with others, with calcareous or
marble rocks, at least, it was impossible to grant such a cause
of consolidation, since heat decomposes their substance and
converts it into quicklime, by driving off the carbonic acid,
and leaving a substance perfectly infusible, and incapable even
of agglutination by heat. To this he replied, that the pressure
under which the heat was applied would prevent the escape
of the carbonic acid; and that being retained, it might be
expected to give that fusibility to the compound which the
simple quicklime wanted. The next generation saw this an-
ticipation converted into an observed fact, and verified by the
direct experiments of Sir James Hall, who actually succeeded
in melting marble, by retaining its carbonic acid under violent
pressure.'

The instances just adduced naturally lead to a discus-
sion of the place to be assigned in scientific enquiry to
the process called Verification. In Deductive Reasoning,
especially when it involves elaborate calculations, there is

AND VERIFICATION. 23I

always great danger lest we should have omitted to take
into account some particular agency or element, or have
miscalculated its effects, or have formed a false estimate
of the combined effect of the various agencies or elements
in operation. The only remedy against these possible
errors, besides the employment of great caution in the
conduct of the deductive process itself, is to be found in
Verification, a word which, in its stricter sense, appears
to be applied to the process of testing, by means of an
appeal to facts, the validity of the conclusions already
arrived at by a course of deductive reasoning. Thus it
had been deductively inferred from the Copernican
theory that the planets Venus and Mercury ought to
pass through phases, like the moon, and the application
of the telescope, by means of which they were actually
seen to assume these phases, furnished a triumphant
verification of the inference. Every occurrence of an
eclipse of the sun or moon or of the transit or occul-
tation of a star, when it accords with the previous calcu-
lations of astronomers, is also an instance of Verification
in this, the stricter, sense of the term. But the word is
often used in a looser sense and extended to all cases
in which an appeal is made to facts, as, for instance,
when we perform an experiment in order to test the truth
of a hypothesis, or where we put in action the Method of
Difference in order to supplement the characteristic un-
certainty attaching to the employment of the Method of
Agreement. Of the process denoted by this looser sense
of the word, instances will readily occur to every one.

^3^ RELATION OF INDUCTION TO DEDUCTION^

Thus, the diminution in the periods of Encke's comet has
been regarded as a verification of the theory that space
is filled with an interstellar medium ; or, to take an in-
stance from a very different class of subjects, the recent
breaking-up of the slave-system in the Southern States of
America may be regarded as a verification of the pre-
diction that slave and free institutions could not long
co-exist under the same political form of government.
For an instance of a case in which the Method of Dif-
ference is called in to verify a previous employment of
the Method of Agreement, we may refer back to the
enquiry into the cause of crystallization, already adduced
in our discussion of those two methods ^

There is a still wider application of the word Veri-
fication, by which it is extended to any corroboration of
one mode of proof by means of another. It thus in-
cludes a deductive proof adduced in corroboration of an
inductive one. The most common instance of this kind
of verification is the inclusion of a partial under a
more general law, the partial law having been arrived at
inductively, and it being subsequently shown that the
more general law leads deductively to it. Thus, the
phenomena of the Tides had, prior to the epoch of
Newton, been partially explained by the inductive me-
thod. Newton, by deducing these phenomena from the
Law of Universal Gravitation, not only afforded a much
more complete explanation, but also furnished the most
convincing verification of the results already arrived at.

» See pp.135, 6; H7. 8.

AND VERIFICATION. 233

Similarly, the laws of falling bodies on the earth's sur-
face, which had already been proved inductively, were,
from the time of Newton, brought under the law of uni-
versal gravitation, and proved deductively from it. The
same was also the case with Kepler's Laws, when they
were proved deductively from the theorem of the Central
Force.

It frequently happens that what may be called a re-
sidual phenomenon affords an unexpected, and, on that
accoimt, a striking verification of some law which is not
immediately the object of investigation. Thus, to recur
to an instance already adduced for another purpose,
when it was found that the difference between the ob-
served and calculated velocities of sound was exactly
accounted for by the law of the development of heat by
compression, this law acquired so novel and striking a
confirmation as to leave no doubt of its truth or univer-
sality.

The following examples, both taken from Lyell's
Principles of Geology^, will be interesting, the one as
affording a verification, though by no means a complete
one, of the bold theory of cosmical clouds, the other as
presenting an instance of a very plausible theory which
fails to receive any verification from an appeal to facts.

• Ch. viii. (ninth edition) ; ch. xiii. (tenth edition). The fornaer passage
appears not to be embodied in the last edition. Various other theories
have been proposed in order to account for the appearance of temporary
stars. See Guillemin, The Heavens, and Lardner's Handbook o/AstrO'
nomy, third edition, edited and revised by £. Dunkin.

^34 RELATION OF INDUCTION TO DEDUCTION^

* There is still another astronomical suggestion respecting
the possible causes of secular variations in the terrestrial
climates which deserves notice. It has long been known that
certain stars are liable to great and periodical fluctuations in
splendour, and Sir J. Herschel has lately ascertained (Jan.
1840), that a large and brilliant star, called alpha Orionis, sus-
tained, in the course of six weeks, a loss of nearly half its
light. "This phenomenon," he remarks, "cannot fail to
awaken attention, and revive those speculations which \rere
first put forth by my father Sir W. Herschel, respecting the
possibility of a change in the lustre of our sun itself. If there
really be a community of nature between the sun and fixed
stars, every proof that we obtain of the extensive prevalence
of such periodical changes in those remote bodies, adds to the
probability of finding something of the kind nearer home."
Referring then to the possible bearing of such facts on ancient
revolutions, in terrestrial climates, he says, that, "it is a
matter of observed fact, that many stars have undergone, in
past ages, within the records of astronomical history, very
extensive changes in apparent lustre, without a change of
distance adequate to producing such an effect. If our sun
were even intrinsically much brighter than at present, the
mean temperature of the surface of our globe would, of
course, be proportionally greater. I speak now not of perio-
dical, but of secular changes. But the argument is compli-
cated with the consideration of the possibly imperfect
transparency of the celestial spaces, and with the cause of
that imperfect transparency, which may be due to material
non-luminous particles diffused irregularly in patches analo-
gous to nebulae, but of greater extent — to cosmical cloueLsy in
short - of whose existence we have, I think, some indication
in the singular and apparently capricious phenomena of tem-
porary stars, and perhaps in the recent extraordinary sudden
increase and hardly less sudden diminution of 17 Argus,"

'The gradual diminution of the supposed primitive heat

AND VERIFICATION. 235

of the globe has been resorted to by many geologists as the
principal cause of alterations of climate. The matter of our
planet is imagined, in accordance with the conjectures of
Leibnitz, to have been originally in an intensely heated state,
and to have been parting ever since with portions of its heat,
and at the same time contracting its dimensions. There are,
undoubtedly, good grounds for inferring from recent observa-
tion and experiment, that the temperature of the earth in-
creases as we descend from the surface to that slight depth
to which man can penetrate : but there are no positive proofs
of a secular decrease of internal heat accompanied by con-
traction. ' On the contrary, La Place has shown, by reference
to astronomical observations made in the time of Hipparchus,
that in the last two thousand years at least there has been no
sensible contraction of the globe by cooling; for had this
been the case, even to an extremely small amount, the day
would have been shortened, whereas its length has certainly
not dimmished during that period by ^^th of a second.'

In this case, however, no argument can fairly be de-
duced from the non-verification of the theory, as the
period of our observation, when compared with the
enormous geological eras of which it is necessary to
take account in these speculations, is so short as possibly
to be infinitesimal. The theory receives no verification
from the facts to which we appeal, but we cannot say
that it is disproved, or even rendered improbabk, by
their failure to support it.

It need hardly be remarked that any verification of
one inductive proof by another, or of an induction by
a deduction, or of a deduction by an induction, should
conform to the laws of deductive or inductive reasoning

2^6 RELATION OF INDUCTION TO DEDUCTION,

as the case may be. Verification is not a distinct mode
of proof, but is simply a confirmation of one proof by
another, sometimes of a deduction by an induction,
sometimes of an induction by a deduction, and, finally,
sometimes of one induction or deduction by another.

The student will, of course, understand that it is not
always necessary to employ Verification. A proof may
be so cogent as to need no confirmation. It would be
absurd, for instance, to appeal to actual measurement
as a verification of the proposition enimciated in Euclid^
i. 47.

CHAPTER VI.
On the Fallacies incident to Induction.

THE errors incidental to inductive reasoning and to
its various subsidiary processes have already, to a great
extent, been brought before our notice in the preceding
chapters. In laying down the conditions essential for the
correct conduct of a process, the mistakes which result
from its incorrect conduct necessarily form part of our
enquiry. Though, therefore, it may be convenient to pass
the inductive fallacies in review, it is assumed that the
student is already acquainted with the principal errors to
which his processes and methods are liable.

A. To begin with the subsidiary processes, the errors
incident to the process of observation, or * the fallacies
of mis-observation,' are well classified by Mr. Mill as
those which arise from Non-observation and those which
arise from Mal-observation.

I. Non-observation may consist either (i) in neglect-
ing some of the instances, or (2) in neglecting some of
the circumstances, attendant on a given instance.

(i) With respect to the non-observation of instances, it

1
.4

2^8 FALLACIES INCIDENT

was long ago pointed out bj Bacon ^ that there is in the
human mind a pecuHar tendency to dwell on affirmadTe
and to oveiiook negative instances. Familiar examples
of this tendency will readily occur to every one. We
think it a * curious coincidence' that we should suddenfy
meet a man of whom we have just been talking, that
some event should happen of which we dreamt the night
before, or that the predictions of a fortune-teller or an
almanac should be verified by the facts. The expLa,-
nation of these 'curious coincidences' is that our at-
tention is arrested by the affirmative instances, whereas

' ' Intdlectos homanas in m qtue semd placaenmt (ant qnia recepta
font et credita, ant quia dekctant) alia etiam omnia trahit ad sofin-
gatiooem et consensom com illis: et licet major sit instantiamm ris
et copia, qax occorrnnt in contrariom; tamcn eas aut non obserrat,
ant contemnit, aut distinguendo summovet et rejicit« non sine xnagno
et pemicioso prxjodicio, qoo prioribus iUis syllepsibns aoctoritas maneat
iniriolata, Itaqoe recte respondit ille, qoi, com sospensa tabula in templo
ei monstraretur eorum qui vota solverant quod naufiagii periculo elapsi
tint, atque interrogando premeretur, anne turn quidem Deorum numeo
agnosceret, qoxsivit denuo, " At ubi sunt illi depicti qui post vota
noncupata perierint?'' Eadem ratio est iere omnis soperstitionis, at
in astrologicis, in somniis, ominibos, nemesibus, et hujusmodi ; in quibos
homines delectati hujusmodi vanitatibus advertunt eventus, ubi implentnr ;
ast ubi fallunt, licet multo frequentius, tamen negligunt et prxterennt.
At longe sobtilius serpit hoc malum in philosophiis et scientiis ; in quibus
quod semel placuit reliqua (licet multo firmiora et potiora) inficit, et in
ordinem redigit Quinetiam licet abfiierit ea, quam diximus, delectatio
et vanitas, is tamen homano intellectui error est proprius ft perpetuus, ut
magis moveatur et excitetur affinnativis, quam negativis; cum rite et
ordine aequum se utrique prxbere debeat ; quin contra, in omni axiomate
vero constituendo, major est vis instantis negative. — Novum Organum,
Bk. I. Aph. zlvi.

TO INDUCTION. 239

the numberless instances in which there is no corre-
spondence between the one set of facts and the other
altogether escape our notice. We probably talk scores
of times dm'ing the day of persons whom we do not
meet immediately afterwards; we frequentiy dream in
the most circmnstantial manner of events which never
occur; and, where one prediction of a fortune-teller is
verified, scores are probably falsified. The weather-pro-
phets of the almanacs possess a considerable advantage
in the fact that, whereas, at all times, there is at least
a considerable chance of their predictions turning out
true, there are certain periods, such as the equinoxes,
at which particular kinds of weather may be anticipated
with a probability amounting almost to certainty.

In former generations * coincidences' of this kind were
regarded not simply as 'curious' and 'remarkable,' but
as proofs of some causal connection between the events.
To talk of a person was supposed to render his presence
more likely; a verified prediction was regarded as evi-
dence of second- sight ; and a comet which was observed
to be followed by a war was supposed to be, if not
the cause of the war, at least a messenger sent from
Heaven to proclaim its approach. The tendency to take
note of afiirmative, and to overlook negative instances,
is one of the causes of that hasty generalisation of which
we shall speak in a subsequent part of this chapter ^.

^ The following remarks of Sir John Herschel, in speaking of the verifica-
tion of * signs of the weather/ are so apposite, that I append them in a note.
* We would strongly recommend any of our readers whose occupations

240 FALLACIES INCIDENT

This tendency is considerably intensified, if the af-
firmative instances are regarded as illustrations of some
preconceived theory", or if the evidence afForded by
them be supplemented by some powerful afFection of
the mind *. It seldom happens that men can hold them-
selves entirely indifferent with respect to two rival
opinions and apply themselves to the comparatively un-

lead them to attend to the '* signs of the weather," and who, from
hearing a particular weather adage often repeated, and from noticing
themselves a few remarkable instances of its verification, have ** begun
to put faith in it,** to commence keeping a note-book, and to set down
without bias all the instances which occur to them of the recognised
antecedent, and the occurrence or non-occurrence of the expected con-
sequent, not omitting also to set down the cases in which it is left
undecided; and after so collecting a considerable number of instances
(not less than a hundred), proceed to form his judgment on a fair com-
parison of the favourable, the unfavourable, and the undecided cases :
remembering always that the absence of a majority one way or the other
would he in itself an improbability^ and that, therefore, to have any
weight, the majority should be a very decided one, and that not only
in itself, but in reference to the neutral instances. We are all involun-
tarily much more strongly impressed by the fulfilment than by the failure
of a prediction, and it is only when thus placing ourselves face to face
with fact and experience, that we can fully divest ourselves of this
bias.' — Familiar Lectures on Scientific Subjects^ Lecture IV.

^ ' Habet enim unusquisque (praeter aberrationes naturas humanae in
genere) specum sive cavemam quandam individuam, quae lumen naturae

frangit et corrumpit ; vel propter differentias impressionum

prout occurrunt in animo praeoccupato et praedisposito, aut in animo
aequo et sedato.' — Bacon's Novum Organum^ Bk. I. Aph. xlii.

^ * Intellectus humanus luminis sicci non est ; sed recipit infusionem a
voluntate et affectibus ; id quod generat ad quod vult scientias : quod
enim mavult homo verum esse, id potius credit.' — Novum Organum,
Bk. J. Aph. xlix.

TO INDUCTION. 24 1

exciting task of collecting evidence impartially on either
side. To avoid taking a side on imperfect information,
even where our interests or passions are not directly
concerned, is one of the last and most difficult lessons
learned by the scientific intellect, and by ordinary men
it is regarded as a sign of a peculiarly frigid temper-
ament, if not of an indifference to truth. Thus, when
the theory involved in the idea of witchcraft had once
been conceived and accepted, and especially when it
had led to the invention of a new crime, it came to
be held that the burden of proof lay with those who
called its reality in question. Every story which con-
firmed the theory would be greedily received, while
instances in which the supposed powers of the witch
had failed, if noticed at all, would either leave but
a slight impression on the mind or be easily ac-
coimted for by supposing the intervention of a higher
power. To the numerous class engaged in the ad-
ministration of the laws, a not unnatural reluctance
to question the justice of the principles on which they
and their predecessors had been in the habit of act-
ing would furnish an additional inducement to pass
lightly over negative instances. Fear, or dread of
eccentricity, would operate in the case of others ;
and thus a theory of the most preposterous character,
which, to a mind not preoccupied, received little or no
confirmation from facts ^ and the truth of which could

* When a person was convinced that he was subject to the evil
practices of a witch, this conviction would, of course, soixifitbcEsft& "^x«c»^^'ft.

34^ FALLACIES' INCIDENT

easily have been brought to the test, maintained it&
ground, and throughout many centuries continued to pro-
duce the most mischievous results. The extent of the
bias to which the mind, in its observation of instances is
exposed from the influence of strong affections, is patent
to every one. A man of a desponding temperament will
dwell on the number of those who have failed, a man of
a sanguine temperament on the number of those who have
succeeded, in their respective professions. A man with
strong sympathies will see only virtues or good traits of
character, where one of a malevolent or critical dispo-
sition will see only vices or blemishes. An ardent ad-
herent of a religious sect or a political party will see
nothing but good in those who agree with him, nothing
but evil in those who adopt a different creed or profess
to be guided by different principles of policy.

Not only will a preconceived opinion or a powerful
affection come in aid of men's natural tendency to dwell
on affirmative and overlook negative instances, but they
will often cause men to adhere to theories for which
whatever may have been the history of their formation
there is absolutely no support whatever in fact. Thus
the theory, which prevailed down to the time of Galileo,
that bodies fall to the earth in times inversely propor-
tional to their weights, so that a body weighing, say,
five pounds, would fall in a time five times as short as a

the ill effects attributed to witchcraft itself. In other cases, some event,
such as a death or an illness, which occurred in the ordinary course of
nature, would confirm the suspicion.

TO INDUCTION. 243

body weighing one pound, rested on absolutely no evi-
dence except the fact that, in consequence of the re-
sistance of the air, the heavier body reaches the ground
in a somewhat shorter time than the lighter one; still,
till Galileo made his experiments, at the end of the
sixteenth century, from the leaning tower of Pisa, no
one thought of bringing to a decisive test a theory which
it was so easy to prove or disprove. Even, without
having recourse to experiment, one would have imagined
that the most casual observations of fallmg bodies would
have revealed, to a mind not strongly pre-occupied, the
strange inaccuracy of this theory. The reception ac-
corded to the theory that the weight of the elements
increased in a tenfold ratio, so that earth was ten
times heavier than water, water ten times heavier than
air, and air ten times heavier than fire, seems still more
astounding ^ The idea of an uniform ratio, and the
particular ratio selected, rested solely upon fancy.

In Sir Thomas Browne's Enquiries into Vulgar and
Common Errors '', we have an examination of the proposi-
tion that ' men weigh heavier dead than alive, and before
meat than after/ Here are two extraordinary paradoxes
which it was perfectly easy for any one to bring to a
decisive test; and still, though an appeal to facts would
at once have been fatal to them, they appear to have met
with a very general reception. The grounds assigned
for the prevalence of the latter opinion are so curious
that they deserve to be transcribed. * ]\Iany are also of

• Novum Organum, Bk. I. Aph. xlv. ' Bk. IV. ch. vii.

B 2

244 FALLACIES INCIDENT

opinion, and some learned men maintain, that men are
lighter after meals than before, and that by a supply
and addition of spirits obscuring the gross ponderosity
of the aliment ingested ; but the contrary hereof we have
found in the trial of sundry persons in different sex and
ages. And we conceive men may mistake, if they dis-
tinguish not the sense of levity unto themselves, and in
regard of the scale, or decision of trutination. For after
a draught of wine, a man may seem lighter in himself
from sudden refection, although he be heavier in the
balance, from a corporal and ponderous addition; but
a man in the morning is lighter in the scale, because
in sleep some pounds have perspired ; and is also lighter
unto himself, because he is refected.' It will be noticed
that * spirits' are supposed to possess the property of
positive levity, and that, consequently, they are regarded
as making any body into which they enter lighter than
it was before. The theory that certain bodies are
positively light is itself an instance of a fallacy of
non-observation, but, as will be seen presently, of non-
observation of circumstances not of instances.

Another extraordinary instance of a statement which
obtained acceptance without any foimdation whatever m
fact is noticed in an article in the Quarterly Review for
January, 1865, on * Aristotle's History of Animals.' Here,
however, there appears to be no assignable reason for the
mistake.

* Aristotle held some peculiar notions with respect to the
skull. He says, " that part of the head which is covered with

TO INDUCTION. 245

hair is called the cranium; the fore part of this is called
the sinciput; this is the last formed, being the last part in
the body which becomes hard." He correctly alludes here
to the opening in the frontal bone of a young infant, which
gradually becomes hardened by ossification ; " the hinder part
is the occiput, and between the occiput and sinciput is the
crown of the head : the brain is placed beneath the sinciput,
and the occiput is empty (!). The skull has sutures ; in women
there is but one placed in a circle (!); men have generally
three joined in one, and a man's skull has been seen without
any sutures at all." The often repeated question as to how
far Aristotle's observations are the result of his own investi-
gation, naturally suggests itself again here ; had Aristotle ever
dissected a human body, he never would have asserted a
proposition so manifestly false as that the back of the head is
empty, or that women have only one suture placed in a
circle.*

The passage here noticed occurs in the Historia Am-
maimm, Bk. I. ch. vii. Cp. Bk. III. eh. vii.

A still more remarkable instance of this description of
fallacy is noticed in Mr. Lecky's History of European
Morals from Augustus to Charlemagne'^,

* Aristotle, the greatest naturalist of Greece, had observed
that it was a curious fact, that on the sea-shore no animal
ever dies except during the ebbing of the tide. Several cen-
turies later, Pliny, the greatest naturalist of an empire that
was washed by many tidal seas, directed his attention to this
statement. He declared that after careful observations which
had been made in Gaul, it had been found to be inaccurate,
for what Aristotle stated of all animals, was in fact only true
of man. It was in 1727 and the two following years, that

• Vol. i. p. 394.

246 FALLACIES INCIDENT

scientific observations made at Rochefort and at Brest finally
dissipated the delusion.*

The influence of some strong passion or affection in
causing men to accept theories without any support from
observation or experiment, and often in direct defiance
of them, may be illustrated from almost all the more
powerful feelings of human nature. The mythologies of
every nation are full of the wildest and most improbable
stories, originating partly in the strength of the religious
sentiment, partly in that love of the marvellous which
seems to be connatural to every race of mankind, partly
in later misinterpretations of that poetical language in
which early races are wont to clothe their ideas. Thus,
stories of the transformation of men into beasts, of
rivers flowing backwards, of images falling down from
heaven, besides other tales still more fantastic, have been
greedily received by generation after generation in spite
of all the analogies of nature and without one single
instance to confirm them. The beliefs in ghosts, spirit-
rapping, and similar phenomena, seem to have their
origia in man's insatiable craving for the marvellous,
acting often in combination with the feelings of fear,
hope, or curiosity. One of the most powerful agents
in human affairs is the passion of avarice or the insa-
tiable desire for the accumulation of wealth. In the
middle ages, this passion led the alchemists, contrary to
all experience, to the belief that it was open to men to
become suddenly and enormously rich by discovering the
secret of transmuting other metals into gold. In modem

TO INDUCTION. 247

times it has frequently led, and still leads, men to embark
in the most desperate speculations, which no scientific
calculation of chances would justify. In a lottery, for
instance (which is a comparatively innocuous form of
speculation), the value of the chance is, owing to the
expenses of management and the profit required by the
projectors, invariably much less than the price paid for
the ticket. But, perhaps, the most remarkable exempli-
fication of the imreasoning desire for sudden accessions
of wealth is to be found in the pertinacity with which,
in spite of every warning, men would, till within the
last few years, expend large fortimes in sinking shafts
for coal and other minerals in strata in which the uni-
versal experience of geologists and miners testified against
their occurrence. In this, as in many other cases, the
observations of competent authorities went for nothing ;
the passion was so absorbing that it alone determined
action.

The fallacies due to non-observation of instances may
be further exemplified by the tendency of the mind to
acquiesce in the first instances which offer themselves ^
especially if they be of a striking kind^**, instead of care-

® * Axiomata, quae in usu sunt, ex tenui et manipulari experientia, et
paucis particularibus, quae ut plurimum occummt fluxere; et sunt fere
ad mensuram eonim facta et exteusa.' — Novum Organum^ Bk. 1.
Aph. XXV.

'^ • Intdlectus humanus illis, quae simul et subito mentem ferire et
subire possunt, maxime movetur; a quibus phantasia impleri et inflari
consuevit : reliqua vero modo quodam, licet imperceptibili, ita se habere
fingit et supponit, quomodo se habent pauca ilia quibus mens obsidetur ;
ad ilium vero transcursum ad instaivtias Ttmo\aL% ^ \«X«to^\iK»s^ '^^-^

248 FALLACIES INCIDENT

fully searching for other instances of a similar nature
with which to compare and by means of which to in-
terpret them. Thus, the phenomena of thunder and
lightning would probably have received a much earlier
explanation, had men's attention been sooner directed
to the instances of electricity which nature presents of
a less striking kind and on a smaller scale. Again, the
difficulties presented to early speculators by volcanoes
and earthquakes would have been considerably dimi-
nished, had they been aware of the fact that there is
hardly any portion of the earth's surface which is not
undergoing a constant change of level by the process
either of elevation or of subsidence, though such change
is usually imperceptible to each single generation. The
mistakes originating in this source of error are count-
less. We observe certain peculiarities in some particular
representative of a class, profession, or nation, and then
proceed to argue as if all the members of the class,
profession, or nation were like him. Or, a person on
his travels in some country is unfavourably impressed
with the hotel-keepers, porters, and carriage-drivers, and
then proceeds to denounce the whole nation to which
they belong, as if the characteristics of a few exceptional
classes were the characteristics of a nationality ^^

quas axiomata tanquam igne probantur, tardus omnino intellectus est
et inhabilis, nisi hoc illi per duras leges et violentum imperium im-
ponatur.* — Novum Organum^ Bk. I. Aph. xlvii.

^^ The history of the French language furnishes a striking instance of
non-observation and of the curious and baseless theories to which it may
lead : * It is well known that before certain feminine substantives, such

TO INDUCTION. 249

The student must have already perceived that we are
trenching on Fallacies of Generalisation. When we
proceed to treat insufficient evidence, or the absence of
evidence, or popular beliefs which run counter to all
the evidence available, as if they afforded perfectly suf-
ficient evidence, the fallacy is one of inference, and, if

as messe, mere, soif, faim, peur, &c., the adjective grand keeps its
masculine tennination, grand* niesse, grand* mere , &c. Why so ?
Grammarians, who are puzzled by nothing, tell us without hesitation
that grand is here put for grande, and that the apostrophe marks the
suppression of the final e. But the good sense of every scholar protests
against this : after having learnt in childhood that e mute is cut off
before a vowel, and never before a consonant, he is told that the e
is here cut off without the slightest reason in such phrases as grand*-
route, &c. The real explanation is in fact a very different one. In its
beginning, French grammar was simply the continuation and prolonga-
tion of Latin grammar ; consequently the Old French adjectives followed
in all points the Latin adjective; those adjectives which had two termina-
tions for masculine and feminine in Latin (as bonus, bona) had two in
Old French, whereas those Latin adjectives which had but one (as grandis,
fords, &c.), had only one in French. In the thirteenth century men
said une grand femme, grandis femina ; une ante mortel, mortalis anima ;
une coutume cruel, crudelis; une plaine vert, viridis planities, &c. In
the fourteenth century the meaning of this distinction was no longer
understood ; and men, deeming it a mere irregularity, altered the form
of the second to that of the first class of adjectives, and wrote grande,
verte, forte, &c., after the pattern of bonne, &c. A trace of the older
and more correct form survives in such expressions as grand^mere, grand^-
route, grand'faim, grand'garde, &c., which are the ddbris of the older
language. In the seventeenth century, Vaugelas and the grammarians
of the age, in their ignorance of the historic reason of this usage,
pompously decreed that the form of these words arose from an euphonic
suppression of the e mute, which must be indicated by an apostrophe.'
— Brachet's Historical Grammar of the French Tongue, Mr. Kitchin's
Transl., Preface, p. vi.

250 FALLACIES INCIDENT

the simulated inference be inductive, it is a FaUacy of
Greneralisation. But the absence or insufficiency of the
evidence, if due to our not having kept our minds
sufficientiy open to facts or not having taken sufficient
pains to collect all the facts pertinent to the question,
is a Fallacy of Non-observation, and is a defect in the
preliminary process rather than in the inductive in-
ference itself. It is believed that all the instances de-
scribed above fall imder this head, though the inferences
founded upon them, where they possess any show^ of
justification at all, are cases of unwarranted Inductio per
Simplicem Enumerationem, and so afiford illustrations of
Fallacies of Generalisation.

(2) The second division of the Fallacies of Non-obser-
vation is the fallacy which arises from overlooking some
of the material circumstances attendant on a given in-
stance. Here the defect is not in the number or per-
tinency of the instances, but in their character; the
description of the instances themselves is untrustworthy.
Till we have ascertained that we are fully acquainted with
all the material circumstances of the cases examined, we
cannot rely upon our facts, and, consequently, we have
no right to proceed to ground any inference upon them.
'The circumstances/ says Sir John HerscheP^ 'which
accompany any observed fact, are main features in its
observation, at least until it is ascertained by sufficient
experience what circumstances have nothing to do with

" Herschel's Discourse on the Study of Natural Philosophy , § m.

TO INDUCTION, 25 1

it, and might therefore have been left unobserved without
sacrificing the fad. In observing and recording a fact,
therefore, altogether new, we ought not to omit any cir-
cumstance capable of being noted, lest some one of the
omitted circumstances should be essentially connected
with the fact, . . . For instance, in the fall of meteoric
stones, flashes of fire are seen proceeding from a cloud,
and a loud rattling noise like thunder is heard. These
circumstances, and the sudden stroke and destruction
ensuing, long caused them to be confoimded with an
effect of lightning, and called thunderbolts. But one
circumstance is enough to mark the difference : the flash
and sound have been perceived occasionally to emanate
from a very small cloud insulated in a clear sky; a com-
bination of circumstances which never happens in a
thimder storm, but which is undoubtedly intimately con-
nected with their real origin/

The extreme difficulty of obtaining, by means of the
thermometer, a correct measure of the temperature of
the atmosphere, owing to the conduction of heat by the
stand and its radiation from surrounding objects, together
with the errors constantly made by observers from not
sufficiently providing against, or allowing for, these
sources of interference, will serve to every one as a
familiar illustration of the great importance of the caution
which it is here intended to furnish.

The following examples, adduced by Mr. MilP', are

" System 0/ Logic, Bk. V. ch, iv, % i^.

2^2 FALLACIES INCIDENT

50 interesting and appropriate, that I take the liberty
of transcribing them :—

* Such, for instance [namely the imperfect observation of
particular facts], 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 appear-
ances ; 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 com-
bustion ; 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 circum-
stance 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, more-
over, 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 allf to be let alone for seven days, at the
end of which period the bandages were removed, when the

TO INDUCTION. 253

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 upon the total ex-
clusion of air from the wound, and upon the sanative opera-
tions 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

The next example I extract from Bp. Wilkins' very
curious tractate, entitled A Discovery of a New World,
or a Discourse tending to prove that *tis probable there may
be another Habitable World in the Moon : —

* He [that is, * a late reverend and learned Bishop,'
writing * under the feigned name of Domingo Gonsales*^]
supposeth that there is a natural and usual passage for many
creatures betwixt our earth and this planet. Thus, he says,
those great multitude of locusts wherewith divers countries
have been destroyed, do proceed from thence. And if we
peruse the authors who treat of them, we shall find that many
times they fly in numberless troops or swarms, and for sundry
days together before they fall are seen over those places in
great high clouds, such as coming nearer, are of extension
enough to obscure the day, and hinder the light of the sun.
From which, together with divers other such relations, he
concludes that *tis not altogether improbable they should

" Dr. Paris* Pbarmacologia, pp. 23-24.

^' The small tract here referred to is republished in vol. viii. of the
Harleian Miscellanies (Park's Edition). The author was Francis
Godwin, afterwards Bishop of Hereford, and author of the Vell-known
book De Prcesulibus Anglice Commentarius,

aS4 FALLACIES INCIDENT

proceed from the moon. Thus, likewise, he supposes the
swallows, cuckoos, nightingales, with divers other fowl, which
are with us only half a year, to fly up thither when they go
from us. Amongst which kind, there is a wild swan in the
East Indies, which at certain seasons of the year do constantly
take their flight thither. Now, this bird being of a great
strength, able to continue for a long flight, as also going
usually in flocks like our wild geese, he supposeth that
many of them together might be thought to carry the weight
of a man; especially if an engine were so contrived (as he
thinks it might) that each of them should bear an equal share
in the burden. So that by this means, 'tis easily conceivable,
how once a year a man might finish such voyage ; going along
with these birds at the beginning of winter, and again return-
ing with them at the spring ^^'

A more accurate and extended series of observations
would, of course, have shewn that the birds and locusts
migrated from other parts of the earth's surface.

It is not necessary to multiply examples of the errors
arising from slovenliness and inattention in the collec-
tion or examination of our instances. The necessity of
maintaining the strictest caution and accuracy in the
conduct of our observations and experiments has already
been insisted upon in the Second Chapter of this work.

II. Besides the errors which originate in the neglect of
instances or of some of the circumstances which are con-
nected with a given instance, there is another class of
errors derived from mistaking for observation that which
is not observation at all, but inference. To this class of

" Wilklns* Discovery of a New World, Fifth Edition, p. i6o.

TO INDUCTION. 2^5

errors Mr. Mill gives the name of Fallacies of Mal-
Observation. That which is strictly matter of observa-
tion or perception does not admit of being called in
question; it is the ultimate basis of all our reasoning,
and, if we are to repose any confidence whatever in the
exercise of our faculties, must be taken for granted. But
there are few of our perceptions, even of those which to
the unphilosophical observer appear to be the simplest,
which are not inextricably blended with inference. Thus,
as is well known to every student of psychology, in what
are familiarly called the perceptions of distance and of
form, the only perception proper is that of the various
tints of colour reflected on the retina of the eye, and it is
by a combination of this with perceptions of touch that the
mind gains its power of determining form and distance.
Now a judgment of this kind, which is really due to in-
ference, is, especially by the uneducated and unreflecting,
perpetually mistaken for that which is due to direct ob-
servation ; and thus what is really only an inference from
facts is often emphatically asserted to be itself a matter of
fact. *In proportion,' says Mr. Mill", *to any person's
deficiency of knowledge and mental cultivation, is gene-
rally 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

" MiU's Logic, Bk. V. ch. iv. § 5,

256 FALLACIES INCIDENT

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 diffi-
culty of inducing witnesses to restrain within any mode-
rate limits the intermixture of their inferences with the
narrative of their perceptions, is well known to experi-
enced cross-examiners; and still more is this the case
when ignorant persons attempt to describe any natural
phenomenon. " The simplest narrative," says Dugald
Stewart, "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 state-
ments. 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 phrase-
ology 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 difiicult of all arts, that of
the faithful inierpretation of nature.'"

No better instance can be given of the Fallacy of
Mal-Observation than that adduced by Mr. Mill and
many other authors of the confusion between observation
and inference, namely, what was called the common-sense
argument against the truth of the Copernican System.
That the earth should move round the sun, men said, was

TO INDUCTION. 257

impossible ; for, every day, they saw the sun rise and set
and perform his course in the heavens. They felt the earth
at rest, they saw the sun in motion, and it was absurd to
call upon them to disbelieve the direct evidence of their
senses. It need hardly be said that what they mistook
for the direct evidence of their senses was really an in-
ference. What they saw was consistent with one or
other of two hypotheses, that the sun moved round the
earth, or that the earth moved round the sun; and,
neglecting to take any accoimt of the latter, they assumed
the former. If it were not for the impressions of a con-
trary kind derived from the actual motion of the car-
riage, a man, whirled along in a railway train, might
with equal justice maintain, by an appeal to the evidence
of his eyesight, that the trees and the houses were run-
ning past him.

Ventriloquism supplies another familiar instance of the
same error. A man who had never before been imposed
upon by the tricks of a ventriloquist, and who was not
aware of the character of the deception, would be positive
in maintaining that he had the direct evidence of the
sense of hearing in support of his belief that the sound
he heard proceeded from a particular person or a par-
ticular part of the building other than that from which it
really did. The fact, of course, is that the sound itself is
all that is directly perceived by the sense of hearing ; the
reference of it to a particular person or a particular place
is an act of inference grounded upon constant, or at
least frequent, association. What is do\\fc \s^ '^'^ ^^sv-

258 FALLACIES INCIDENT

triloquist is not to deceive the sense of hearing, but to
mislead the faculty of judgment.

What are called 'delusions' and 'hallucinations' fur-
nish a further instance of Mal-observation. It seems to
be now pretty generally agreed that these are due to
morbid affections of the sensory ganglia. ' The patient's
senses,' says Dr. Maudsley^®, speaking of what he calls
sensorial insanity y ' are possessed with hallucinations, their
ganglionic central cells being in a state of convulsive
action ; before the eyes are blood-red flames of fire, amidst
which whosoever happens to present himself, appears as
a devil, or otherwise horribly transformed ; the ears are
filled with a terrible roaring noise, or resound with a voice
imperatively commanding him to save himself; the smell
is perhaps one of sulphurous stifling ; and the desperate
and violent actions are, like the furious acts of the ele-
phant, the convulsive re-actions to such fearful halluci-
nations. The individual in such a state is a machine set
in destructive motion, and he perpetrates the extremest
violence or the most desperate murder without conscious-
ness at the time, and without memory of it afterwards.'
What is here said of delusions in that extreme form in
which they assume unmistakeably the character of mad-
ness applies equally, as an explanation, to those less
obtrusive, though far more frequent, forms in which they
produce semi-insanity, monomania, melancholy, or par-
tial and temporary deception. In all these cases, the
sensations are really experienced; the error consists in

" Maudsley, The Physiology and Pathology ofMind, ch. iv. p. loi.

TO INDUCTION. 259

referring the cause of the sensations to external objects
rather than to the morbid condition or action of the
brain itself. The testimony of others, or the inherent
improbability of the things perceived, ought to be re-
garded, though they seldom are, as sufficient proof that
the evidence of the senses is given under abnormal and
untrustworthy conditions.

The description here given of the errors originating
in Non-observation or Mal-observation includes, as will
already have been perceived, the errors incident to arti-
ficial as well as to natural observation, that is, to experi-
ment as well as to observation proper.

III. The errors incidental to the other operations
preliminary to induction, namely, classification, nomen-
clature, terminology, and hypothesis, will be sufiiciently
apparent on a perusal of the sections appropriated to
the discussion of those processes. In the steps inter-
mediate between the observation of individual facts and
the inductive inference itself, it is in the employment
of artificial instead of natural classifications, and in
the neglect of the rules designed to guard against the
formation of illegitimate hypotheses, that the danger of
error mainly Ues.

B. The fallacies incidental to the performance of the in-
ductive process itself may be called Fallacies of General-
isation. An error of this class is committed whenever,
in arguments grounded on experience, we overrate the
value of the evidence before us; that is, whenever we

s 2

26o FALLACIES INCIDENT

accept an imperfect induction as a perfect one, or when-
ever, in an induction confessedly imperfect, we under-
estimate the amount of imperfection.

Of the imperfect inductions, the argument from analogy
is little likely to be mistaken for a perfect induction. The
strength of the analogy is often grossly exaggerated, and
an argument which possesses little or no probability is
often adduced as afifording highly probable evidence; but,
as this kind of argument is very seldom^* treated as
affording absolute certainty, the discussion of false ana-
logies may be reserved till we have completed the treat-
ment of those errors which consist in regarding imperfect
as perfect inductions.

Excluding analogy, there are, as we have seen, two
forms of imperfect induction, that which employs the
incomplete Inductio per Simplicem Enumerationem and
that which consists in an imperfect fulfilment of the
conditions of the inductive methods. An argument of
either of these classes may be, and frequently is, mis-
taken for a perfect induction. We shall first notice the
case in which scientific induction is simulated by the
incomplete Inductio per Simplicem Enimierationem.

IV. When men first begin to argue from their experience
of the past to their expectation of the future, or from
the observation of what immediately surrounds them to
the properties of distant objects, they seem naturally to

^ The geological example on p. 219 may perhaps be an instance of
an analogical argument thus regarded. Many writers have certainly
treated the inference as if its certainty admitted of no doubt.

TO INDUCTION. 26 1

fall into this unscientific and unreflective mode of rea-
soning. They have constantly seen two phenomena in
conjmiction, and, consequently, they cannot imagine them
to be dissevered, or they have never seen two phenomena
in conjunction, and, consequently, they cannot imagine
them to be associated. The difficulties experienced by
children in accommodating their conceptions to the
wider experiences of men ; the tendency of the unin-
structed, and frequently even of the instructed, to invest
with the peculiar circumstances of their own time or
country the men of a former generation or of another
land ; the prejudices entertained against those of another
creed, or party, or nationality, as if moral excellence
were never dissociated from particular opinions or a
particular lineage, — ^are all evidences of the limited
character of our first efi*orts at generalisation. It is
long before men learn to discriminate between the
material and immaterial circumstances attendant on
any given phenomenon, to perceive the irrelevancy of
the immaterial circumstances, and to recognise the
necessity of insisting on a repetition of all the mate-
rial circumstances before they can anticipate a similar
effect. But not only is the Inductio per Simplicem
Enumerationem the mode of generalisation natural to
immature and uninstructed minds; it is the method
which, till the time of Bacon '^, or at least till the era

^ Bacon seems to be never weary of condemning this unscientific
procedure. Thus, in addition to the aphorism already quoted (p. 1 1 7)t
we have, amongst others, the following em^baAxc '^'&^<^« 5" K»ssa!a^».

262 FALLACIES INCIDENT

of those great discoveries which shortly preceded the
time of Bacon, was almost universal. Aristotle, it is
true, requires that an induction should be based on an
examination of all the instances; but this requirement
being in the vast majority of cases impossible of ful-
filment, he was obliged, whenever he had recourse to
experience, to content himself with an inspection of
those cases which were nearest at hand. Thus, in the
very passage^ in which he emphatically asserts that the
minor premiss of the inductive syllogism (for he repre-
sents induction under the syllogistic form) should include
all the instances, he argues that all animals which are
deficient in bile are long-lived, because he finds this to

qusB in usu sunt, ex tenoi et manipulari experientia, et paucis particulari-
bus, qux ut plurimum occumint, fluxere; et sunt fere ad mensuram
eorum facta et extensa : ut nil minim sit, si ad nova particularia non
ducant. Quod si forte instantia aliqua, non prius animadversa aut
cognita, se offerat, axioma distinctione aliqua frivola salvatur, ubi emen-
dari ipsum verius foret/ Nov. Org. Bk. I. Aph. xxv. * At philosophiae
genus empiricum placita magis deformia et monstrosa educit, qnam
sopbisticum aut rationale genus; quia non in luce notionum vulgarinm
(qusB licet tenuis sit et superficialis, tamen est quodammodo universalis,
et ad multa pertinens) sed in paucorum experimentorum angustiis et

obscuritate fiindatum est Sed tamen circa hujusmodi philosophias

cautio nullo modo praetermittenda erat ; quia mente jam prxvidemus et
auguramur, si quando homines, nostris monitis excitati, ad experientiam
se serio contulerint (valere jussis doctrinis sophisticis) turn demum, propter
praematuram et praeproperam intellectus festinationem et saltum sive
volatum ad generalia et rerum principia, fore ut magnum ab hujusmodi
philosophiis periculum immineat ; cui malo etiam nunc obviam ire debe-
mus.* Aph. Ixiv.
^ Analytica Priora^ ii. 23.

TO INDUCTION, 263

be the case with the man, the horse, and the mule.
Aristotle's works, and especially those on Natural His-
tory, abound in rash generalisations of this kind. *It
is a fact,' says Mr. Lewes ^^, *that normally in turtles,
and exceptionally in elephants, horses, and oxen, there
is an ossification of the septimi of the heart. Aristotle
saw or heard of one of these "bones" in the hearts of
a horse and an ox, and forthwith generalised the obser-
vation thus : " The heart is destitute of bones except in
horses and in a species of ox ; these, however, in con-
sequence of their size, have something bony as a support,
just as we find throughout the whole body^." His
Spanish follower Funes Y Mendo9a improves on this
by saying that the bone acts like a stick to support
the weight of the heart, which is very great.'

There is another passage in which Aristotle tells us
that the cranium of a dog consists of a single bone^.
* It is probable,' says the author of the review previously
quoted^', *that Aristotle had got hold of the cranium
of an old individual in which the sutures had become
obliterated.'

The employment of the Inductio per Simplicem Enu-
merationem prevailed so universally from the time of
Aristotle to the rise of modem science that it seems

^ Lewes* Aristotle^ ch. xvi. § 399.
^ De Partihus Animalium, Bk. III. ch. iv.

** rd filv ydtp Ix** fiovdffrtov rd Kpaviov, &a'ntp 6 icuow^ ra h\ ffvy-
K€ifi«voVt &<Tir(p ayOpomot. Hiitoria Animaliumy Bk. III. ch. vii.
* Quarterly Review^ No. 233, Art. ii.

264 FALLACIES INCIDENT

unnecessary to multiply instances of it during that period.
But it may be instructive to illustrate from the history
of more modern times the peculiar facility with which
some even of the greatest discoverers have lapsed into
this erroneous form of reasoning.

'Bichat,' says Mr. Lewes^^, 'tried to establish a gene-
ralisation which has been much admired, namely, that all the
organs of Animal life are double and symmetrical, while all
the organs of Vegetal life are single and asymmetrical. Un-
happily the facts do not fit. In the commencement almost
e^ery organ is double and symmetrical ; and only in the later
stages of development do the difierences appear. Even in the
matured organism we find many striking exceptions to Bichat's
generalisation. Thus the parotid, sublingual, and mammary
glands, the lungs, the kidneys, ovaries and testes, are all
vegetal organs, and all generally double. And if the heart
and uterus are classed as single organs, then must the brain
and spinal cord be classed thus. While in birds the liver is
double and symmetrical.*

*It is in a great degree true,* we are informed by Dr,
Paris'", * that the sensible qualities of plants, such as colour
taste, and smell, have an intimate relation to their properties,
and may often lead by analogy to an indication of their
powers ; we have an example of this in the dark and gloomy
aspect of the Luridce, which is indicative of their narcotic and
very dangerous qualities, as Datura, Hyoscyamus, Atropa^ and
Nicotiana, Colour is certainly in many cases a test of activity •
the deepest of coloured flowers, the Digitalis, for example
are the most active, and when the leaves of powerful plants
lose their green hue, we may conclude that a corresponding

2« Lewes* Aristotle, ch. xvi. § 399 d.

^ Pbarmacologia, ninth cd. fp. no, in.

TO INDUCTION. 26^

deterioration has taken place with respect to their virtues;
but Linnaeus ascribed too much importance to such an indica-
tion, and his aphorisms are unsupported by facts; for in-
stance, he says, ''Color pallidus iruipidum, viridis crudum,
luteus amarumy ruber acidumy albus dulce, niger ingratum,
indicat."'

The early history of Geology presents, in the con-
troversy which was long carried on between the Nep-
tunians and Vulcanians, a remarkable instance of the
errors arising from a partial induction, as well as of the
tenacity with which men will cling to views to which they
have once, committed themselves. The Neptmiians, the
student need hardly be told, referred all geological phe-
nomena to the influence of water, while the Vulcanians
greatly exaggerated the action of heat in the past his-
tory pf the globe, and the number of formations to be
ascribed to an igneous origin. Of the Neptunians, the
great Saxon geologist Werner was the chief.

* Werner,* says Sir Charles Lyell ^*, * had not travelled to
distant countries; he had merely explored a small portion
of Germany, and conceived, and persuaded others to believe,
that the whole surface of our planet, and all the mountain
chains in the world, were made after the model of his own
province. It became a ruling object of ambition in the minds
of his pupils to confirm the generalisations of their great
master, and to discover in the most distant parts of the globe
his " universal formations," which he supposed had been each
in succession simultaneously precipitated over the whole earth
from a common menstruum or "chaotic fluid." It now
appears that the Saxon professor had misinterpreted many

* Lyell's Principles 0/ Geology ^ Bk, I, cVu v»i «

266 FALLACIES INCIDENT

of the most important appearances even in the immediate
neighbourhood of Freyberg. Thus, for example, within a
day's journey of his school, the porphyry, called by him
primitive, has been found not only to send forth veins or
dikes through strata of the coal formation, but to overlie
them in mass/

* In regard to basalt and other igneous rocks, Werner's
theory was original, but it was also extremely erroneous.
The basalts of Saxony and Hesse, to which his observations
were chiefly confined, consisted of tabular masses capping the
hills, and not connected with the levels of existing valleys,
like many in Auvergne and the Vivarais. These basalts, SaA
all other rocks of the same family in other countries, were,
according to him, chemical precipitates from water. He
denied that they were the products of submarine volcanoes ;
and even taught that, in the primeval ages of the world, there
were no volcanoes.*

After describing the complete demolition of this theory
by some of Werner's contemporaries, Sir Charles Lyell
adds : —

'Notwithstanding this mass of evidence, the scholars of
Werner were prepared to support iiis opinions to their utmost
extent ; maintaining, in the fulness of their faith, that even
obsidian was an aqueous precipitate. As they were blinded
by their veneration for the great teacher, they were impatient
of opposition, and soon imbibed the spirit of a faction ; and
their opponents, the Vulcanists, were not long in becoming
contaminated with the same intemperate zeal. Ridicule and
irony were weapons more frequently employed than argument
by the rival sects, till at last the controversy was carried on
with a degree of bitterness almost unprecedented in questions
of physical science. Desmarest alone, who had long before
provided ample materials for refuting such a theory, kept

TO INDUCTION, 267

aloof from the strife; and whenever a zealous Neptunist
wished to draw the old man into an argument, he was satisfied
with replying " Go and see." '

It is remarked by Mr. Mill that the Method of Simple
Enmneration, though almost banished from the physical
sciences, is still the common and received method of
induction in whatever relates to man and society. The
reason of this is to be sought in the extraordinary dif-
ficulty of subjecting this class of speculations to the
more scientific methods. Moral and social phenomena
are so complex that it is often next to impossible
to discover by elimination the true connection between
any two events or sets of facts. Take, for instance, such
questions as the influence of any particular form of
government upon the welfare of the people among whom
it is established, the effects of religion, or of any particular
form of religion, upon morals, the social and political
conditions most favourable to the development of art,
or literature, or science, or commerce. Here, if it be
required to discover the cause of a given effect, there are
given a set of consequents constantly varying in their
character and intensity, and a set of antecedents, often
very numerous, any one of which may have an appreci-
able influence in the production of the effect in ques-
tion ; and it is obvious that to detect the precise degree
in which the effect is due to any one of these antecedents,
even supposing the task to be possible, will require the
utmost skill, patience, and dispassionateness in the
selection and comparison of instances. Nor, if it be

268 FALLACIES INCIDENT

required to discover the effect of a given cause, will the
task be much simplified; for, though it may be possible
to fix the precise time at which a new cause — say a new
form of religion, a new form of government, or a new
commercial tariff — was introduced, yet, before it can be
argued that any novel event which may appear to have
resulted from it, is really due to it, as an effect to a cause,
the enquirer is bound to satisfy himself (i) that the intro-
duction of the new cause was not accompanied by other
causes which may have wholly or partially produced the
supposed effect, (2) that the new cause and the supposed
effect are not joint effects of some common cause which
he may have overlooked. It is the extreme difficulty of
bringing this class of questions within the requirements
of scientific induction, that has led, on the one hand, to
the employment of the loose Method of Inductio per
Simplicem Enumerationem, or of a mere appeal to un-
sifted experience, and on the other to the disbelief in the
possibility of arriving at any satisfactory conclusions upon
them. At the ' same time, there can be little doubt that
moral and social enquiries are beginning to emerge from
the chaotic state of confusion in which they have hitherto
been sunk, and that what are now dignified with the titles
of the moral and political sciences, however imperfect
they may be, are beginning to be something more than
mere collections of random guesses, or conclusions drawn
from the first undisciplined impressions of the teaching of
experience.

To the class of fallacies originating in the employment

TO INDUCTION. 269

of the incomplete Inductio per Simplicem Enumerationem
may perhaps be referred the illegithnate use of the Argu-
ment from Authority. The opinions or predictions of a
certain man or of a certain class of men upon some parti-
cular question or questions have been subsequently found
to be verified by the issue of events or an examination of
the facts. From this it is sufficiently rash to infer, without
further warrant, that the correspondence between these
predictions or opinions and the subsequent events or
ascertained facts is the result of knowledge, and not of
what we call accident; but, not content even with this,
men are apt to draw the far more unwarrantable in-
ference that this person or class of persons is to be
accepted as an authority on all matters, or at least on
all matters of the same or of an analogous kind. It is
on this principle that a savage, or even an uneducated man
in a civilised commimity, will trust implicitly any person
for whom he has conceived a general respect. In nine
cases out of ten he probably acts more wisely in trust-
ing to such a person than in trusting to himself. But
the same habit of mind, which is a virtue among un-
educated men and in primitive states of society, be-
comes one of the most serious obstacles to progress
and knowledge when men, either individually or col-
lectively, have attained that stage at which they are
able to enquire for themselves. We have to learn not
only that men are to be trusted exclusively within the
limits of their own experience, in their own profession
or pursuit, but that even within those Iixx\Lt<& ^^ •ia^-

ajO FALLACIES INCIDENT

thority is apt to become tyrannical and irrational unless
it is constantly confronted with facts and subjected to
the criticism of others.

But an imdiscriminating submission to the authority of
contemporaries, of which we have hitherto exclusively
spoken, has been but a slight source of error when com-
pared with undiscriminating submission to the authority of
past generations^. The latter involves a kind of com-
pound fallacy. The authority of an Aristotle or a Galen
has come, by the process already described, to be re-
ceived without question and without limit by his own or
by the succeeding generation; and then, by the con-
stant repetition of a similar process, it is received from
that generation by the leading minds of the next, from
them by their contemporaries, and so on, respect for
tradition being blended with respect for a great name,
and both these resting for their support on the de-
ference paid to established authority. Many of the
propositions accepted without the slightest hesitation
by previous generations on this kind of authority now

^ Of this tendency we have many * glaring instances/ as Bacon would
call them. The error has been, so to say, canonised in the proverb
*Mallem cum Platone errare.' There is a characteristic anecdote of
Scheiner, who contests with Galileo the honour of having been the first
to observe the spots in the sun. * Scheiner was a monk; and, on com-
municating to the superior of his order the account of the spots, received
in reply from that learned father a solemn admonition against such
heretical notions : — " I have searched through Aristotle,** he said, ** and
can find nothing of the kind mentioned : be assured, therefore, that it
is A deception of your senses, or of your glasses."* Baden PoweH'i
0/ Natural Pbilosopby, p. 171.

TO INDUCTION. 27 1

appear to us patently absurd, nor is it without effort
that we can realise the universality of their former re-
ception^. Instances of such propositions have already
been given under the head of the Fallacies of Non-
Observation, to the production of which the undue de-
votion to authority has, perhaps, contributed more than
any other cause ^^. But in subjects lying remote from

** The increasing unwillingness of men to accept a proposition on
mere authority is thus forcibly put by Bentham, Booh of Fallacies^
Part I. ch. i., first published, in French by M. Dumont, in 1815, and in
English by * A Friend/ in 1824.

* As the world grows older, if at the same time it grows wiser (which
it will do, unless the period shall have arrived at which experience, the
mother of wisdom, shall have become barren), the influence of authority
will in each situation, and particularly in parliament, become less and less/

* Take any part of the field of moral science, private morality, consti-
tutional law, private law; go back a few centuries, and you will find
argument consisting of reference to authority, not exclusively, but in as
large a proportion as possible. As experience has increased, authority
has been gradually set aside, and reasoning, drawn from facts, and guided
by reference to the end in view, true or false, has taken its place.

******

* In mechanics, in astronomy, in mathematics, in the new-bom science
of chemistry — no one has at this time of day either effrontery or folly
enough to avow, or so much as to insinuate, that the most desirable state
of these branches of useful knowledge, the most rational and eligible
course, is to substitute decision on the ground of authority to decision
on the ground of direct and specific evidence.*

^ It might appear that the illegitimate use of the Argument from
Authority should be classed amongst the Fallacies of Non-Observation,
but, though a blind devotion to authority is one of the most powerful
influences in leading men to neglect observation and experiment, the dis-
position to bow thus unduly to it is itself a fact which requires explana-
tion, and one which it is here attempted to explain.

2T2 FALLACIES INCIDENT

ordinary observation, propositions almost equally absurd
have held tiieir ground till quite recently ; some continue
to maintain themselves, and others no doubt will be
propounded to take advantage of the credulity of man-
kind.

*To give a general currency,* says Dr. Paris ^, *to a hypo-
thetical opinion, or medicinal reputation to an inert substance,
nothing more is required than the talismanic aid of a few
great names ; when once established upon such a basis, inge-
nuity, argument, and even experiment, may open their inef-
fectual batteries ; the laconic sentiment of the Roman satirist
is ever opposed to remonstrance : — " Marcus dixit f ita est,**
A physician cannot err in the opinion of the public, if he
implicitiy obeys the dogmas of authority. In the most bar-
barous ages of ancient Egypt, he was punished or rewarded
according to the extent of his success; but to escape the
former it was only necessary to show that an orthodox plan
of cure had been followed, such as was prescribed in the
acknowledged writings of liermes. It is an instinct in our
nature to follow the track pointed out by a few leaders*
we are gregarious animals, in a moral as well as a physical
sense, and we are addicted to routine because it is always
easier to follow the opinions of others than to reason and
judge for ourselves ; and thus do one half of the world live
as alms-folks on the opinions of the other half. What but
such a temper could have upheld the preposterous system of
Galen for more than thirteen centuries, and have enabled
it to give universal laws in medicine to Europe, Africa, and
part of Asia ? What, but the spell of authority, could have
inspired a general belief that the sooty washings of resin could
act as a universal remedy ? What, but a blind devotion to
authority, or an insuperable attachment to established custom

32

Dr. Paris' Pbarmacologia, Introduction, p. 76, &c.

TO INDUCTION. 273

and routine, could have so long preserved from oblivion the
absurd medicines which abound in our earlier dispensatories ?
for example, the '^ Decoctum ad Ictericoj*' of the Edinburgh
College, which never had any foundation but that of the
doctrine of signatures in favour of the Curcuma and CMi-
donium majus ; and it is only within a few years that the
Iheriaca Andromacbi^ in its ancient form, has been dismissed
from our Pharmacopoeia. The Codex Medicamentarius
of Paris still cherishes the many-headed monster of phar-
macy, under the appropriate title of ^^ Ekctuarium Opiatum
Polupbarmacum^

»>»

* The same devotion to authority which induces us to re-
tain an accustomed remedy with pertinacity, will frequently
oppose the introduction of a novel practice with asperity,
unless indeed it be supported by authority of still greater
weight and consideration. The history of various articles
of diet and medicine will prove in a striking manner how
greatly their reputation and fate have depended upon
authority. It was not until many years after Ipecacuan
had been imported into Europe, that Helvetius, under the
patronage of Louis XIV, succeeded in introducing it into
practice: and to the eulogy of Katharine, queen of Charles
II, we are indebted for the general introduction of tea into
England.*

*The history of the warm bath presents us with another
curious instance of the vicissitudes to which the reputation
of our valuable resources is so universally exposed; that
which for so many ages was esteemed the greatest luxury
in health, and the most efficacious remedy in disease, fell into
total disrepute in the reign of Augustus, for no other reason
than because Antonius Musa had cured the emperor of a
dangerous malady by the use of the cold bath. The most
frigid water that could be procured was, in consequence,

T

274 FALLACIES INCIDENT

recommended on every occasion : thus Horace, in his epistle

to Vala, exclaims —

** Caput ac stomachum supponere fontibns audent
Qusinis, Gabiosque petunt, et frigida rura." — Epist. xv. lib. i.

* This practice, however, was doomed but to an ephemeral
popularity, for although it had restored the emperor to health,
it shortly afterwards killed his nephew and son-in-law, Mar-
cellus ; an event which at once deprived the remedy of its
credit and the physician of his popularity.

*The history of the Peruvian bark would furnish a very
curious illustration of the overbearing influence of authority
in giving celebrity to a medicine, or in depriving it of that
reputation to which its virtues entitle it. This heroic remedy
was first brought to Spain in the year 1632, and we learn
from Villerobel that it remained for seven years in that
country before any trial was made of its powers, a certain
ecclesiastic of Alcala being the first person in Spain to whom
it was administered in the year 1639 ; but even at this period
its use was limited, and it would have sunk into oblivion but
for the supreme power of the Roman church, by whose
auspices it was enabled to gain a temporary triumph over
the passions and prejudices which opposed its introduction.
Innocent the Tenth, at the intercession of Cardinal de Lugo,
who was formerly a Spanish Jesuit, ordered that the nature
and effects of it should be duly examined, and upon being
reported as both innocent and salutary, it immediately rose
into public notice ; its career, however, was suddenly stopped
by its having unfortunately failed, in the autumn of 1652, to
cure Leopold, Archduke of Austria, of a quartan intermittent;
this disappointment kindled the resentment of the prince's
principal physician, Chifletius, who published a violent philippic
against the virtues of Peruvian bark, which so fomented the
prejudices against its use, that it had nearly fallen into total
neglect and disrepute.*

V. The errors incident to the employment of the va-

TO INDUCTION. 275

nous Inductive Methods have already been pointed out in
our detailed description of each of these Methods, but it
may be useful in this place to take note of certain forms
of fallacy which appear to be common to them all.

The Inductive Methods may all be regarded as de-
vices for the elimination of extraneous circumstances and
for the establishment of a causal connection between some
two phenomena, a and b, the connection which it is sought
to establish being generally that of cause and effect.
Now, in our investigation, we may either have mistaken
the precise relation between a and b, or we may have
overlooked some other material circumstance or group
of circumstances, c. In the former case, the most
common sources of error are either the inversion of
cause and effect or the neglect of their reciprocal action,
the 'mutuality of cause and effect,' as it is called by
Sir G. C Lewis. In the latter case (supposing a to
be the presumed cause, and b the presumed effect), it
seems open to us to have committed any of the following
errors: (i) to have mistaken a for the cause, when the
real cause is r; (2) to have mistaken a for the sole cause,
when a and c are the joint causes, either (a) as both
contributing to the total effect, or (iS) as being both essen-
tial to the production of any effect whatever''; (3) to

® The distinction may be illustrated by a familiar example. If a
cistern is filled by two pipes, the water passing through each contributts
to the total amount of water in the cistern. But, if the cistern is filled
by one pipe having two taps, one above the other, both taps must be
turned m order that the cistern may receive any water whatever.

T 2

276 FALLACIES INCIDENT

have mistaken a for the cause of by when they are really
both of them effects of c ; (4) to have mistaken a for
the proximate cause of 3, when it is really only the re-
mote cause, c, which has escaped our attention, being
the proximate cause.

To begin with the latter class of errors.

(i) The following extract from Mr. Lewes* Physiology
of Common Life^ may serve as an illustration of the first
subdivision : —

* One very general, indeed almost universal, misconception
on this subject (asphyxia or suffocation) is, that carbonic acid
is poisonous in the blood ; but the truth seems to be that the
carbonic acid is noxious only when it prevents the access
of oxygen. There is always carbonic acid in the blood, both
venous and arterial. Its accumulation in the blood is only
fatal when there is such an accumulation in the atmosphere
as will prevent its exhalation ; its mere presence in the blood
seems to be quite harmless, even in large quantities, provided
always that it be not retained there to the exclusion of
oxygen. Carbonic acid, when absorbed into the blood, which
is alkaline, cannot there exert its irritant action as an acid,
because it will either be transformed into a carbonate or be
dissolved. Bernard has injected large quantities into the
veins and arteries, and under the skin of rabbits, and found
no noxious effect ensue. The more carbonic acid there is
in the blood, the more will be exhaled, provided always that
the air be not already so charged with it as to prevent this
exhalation.'

Here there are really two antecedents, the presence
of carbonic acid and the absence of oxygen, and the
noxious effects, which are erroneously ascribed to the

2* Vol. i. p. 383.

TO INDUCTION, 277

former cause, ought properly to be referred to the
latter.

The above extract exemplifies this error as vitiating
an application of the Method of Agreement. In the
following extracts from Dr. Paris' Pharmacologia, it will
be seen also to vitiate applications of the Method of
Difference : —

* Soranus, who was contemporary with Galen, and wrote
the life of Hippocrates, tells us that honey proved an easy
remedy for the aphthae of children ; but instead of at once
referring the fact to the medical qualities of the honey, he
very gravely explains it, from its having been taken from
bees that hived near the tomb of Hippocrates ^ ! *

*In my life of Sir Humphry Davy, I have published an
anecdote which was communicated to me by the late Mr.
Coleridge, and which bears so strikingly upon the present
subject that I must be excused for repeating it. As soon
as the powers of nitrous oxide were discovered. Dr. Beddoes
at once concluded that it must necessarily be a specific for
paralysis: a patient was selected for the trial, and the
management of it was entrusted to Davy. Previous to the
administration of the gas, he inserted a small pocket thermo-
meter under the tongue of the patient, as he was accustomed
to do upon such occasions, to ascertain the degree of animal
temperature, with a view to future comparison. The paralytic
man, wholly ignorant of the nature of the process to which
he was to submit, but deeply impressed, from the represent-
ations of Dr. Beddoes, with the certainty of its success, no
sooner felt the thermometer under his tongue, than he
concluded the talisman was in full operation, and in a burst
of enthusiasm declared that he already experienced the effect

^ Pkarmacologiat p. so.

278 FALLACIES INCIDENT

of its benign influence throughout his whole body: the
opportunity was too tempting to be lost ; Davy cast an
intelligent glance at Mr. Coleridge, and desired his patient
to renew his visit on the following day, when the same
ceremony was performed, and repeated every succeeding day
for a fortnight, the patient gradually improving during that
period, when he was dismissed as ciu-ed, no other application
having been used ^.'

'Amongst the numerous instances which have been cited
to show the power of faith over disease, or of the mind over
the bodily organs, the cures performed by royal touch have been
considered the most extraordinary : but it would appear, upon
the authority of Wiseman, that the cures which were thus
effected were in reality produced by a very different cause ;
for he states that part of the duty of the royal physicians and
Serjeant surgeons was to select such patients afflicted with
scrofula as evinced a tendency towards recovery, and that
they took especial care to choose those who approached the
age of puberty. In short, those only were produced whom
Nature had shown a disposition to cure ; and as the touch of
the king, like the sympathetic power of Digby, secured the
patient from the mischievous importimities of art, so were the
efforts of Nature left free and uncontrolled, and the cure of
the disease was not retarded or opposed by the administration
of adverse remedies. The wonderful cures of Valentine
Greatricks, performed in 1666, which were witnessed by
contemporary prelates, members of parliament, and fellows
of the Royal Society, amongst whom was the celebrated
Mr. Boyle, would probably, upon investigation, admit of
a similar explanation. It deserves, however, to be noticed,
that in all records of extraordinary cures performed by
mysterious agents, there has always been a desire to conceal

•'* Pbarmacologiat p. 28.

TO INDUCTION. 279

the remedies, and other curative means which might have
been simultaneously administered. Thus Oribasius com-
mends, in high terms, a necklace of peony-root for the cure
of epilepsy ; but we learn that he always took care to accom-
pany its use with copious evacuations, although he assigns
to them not the least share of credit in the cure. In later
times, we have an excellent specimen of this species of
deception, presented to us in a work on scrofula by Mr.
Morley, written, as we were informed, for the sole purpose
of restoring the much-injured character and use of the
vervain ; in which the author directs the root of that plant
to be tied with a yard of<ivbite satin riband around the neck ;
— but mark — during the period of its application, he calls
to his aid the most active medicines in the materia medica.
" It is unquestionable," says Voltaire, speaking of sorceries,
"that certain words and ceremonies will effectually destroy
a flock of sheep, if administered with a sufficient portion
of arsenic^." '

* Our inability upon all occasions to appreciate the efforts of
nature in the cure of disease, must necessarily render our
notions, with respect to the powers of art, liable to numerous
errors and deceptions. Hence protracted or (wire-drawn
cures ought to be very cautiously received as evidences of the
success of medical treatment. Many diseases require only
time to enable nature to remove them. All the long train
connected with hysteria are cured by time; the solution of
which, as Mr. Travers has observed, is to be found in the
fact, that the hysteric period wanes, and the restlessness of
the temperament undergoes a slow but salutary change.
Nothing, certainly, is more natural, although it may be very
erroneous, than to attribute the cure of a disease to the last
medicine that had been administered ; the advocates even of
amulets and charms have been thus enabled to appeal to

^ Pbarmacdogiaf p. 30.

a8o FALLACIES INCIDENT

the testimony of what they call experience, in justification
of their superstition^.'

Of a similar character was the old superstition, noticed
by Sir Thomas Browne ^ and many other authors, that
the hardest stone could be broken by goat's blood : —

' And, first, we hear it in every mouth, and in many good
authors read it, that a diamond, which is the hardest of
stones, not yielding unto steel, emery, or any thing but its
own powder, is yet made soft, or broke by the blood of a
goat. . . . But this, I perceive, is easier affirmed than
proved. For lapidaries, and such as profess the art of cutting
this stone, do generally deny it; and they that seem to
countenance it have in their deliveries so qualified it, that
little from thence of moment can be inferred for it. For
first, the holy fathers, without a further enquiry, did take it
for granted, and rested upon the authority of the first deliver-
ers. . . . But the words of Pliny, from whom most likely
the rest at first derived it, if strictly considered, do rather
overthrow, than any way advantage this effect. His words
are these: Hircino rumpitur sanguine, nee aliter quam recenti,
calidoque macerata, et sic quoque multis ictibus, tunc etiatn prtBter^
quam eximias incudes malleosque ferreos frangens. That is, it is
broken with goat's blood, but not except it be fresh and warm,
and that not without many blows, and then also it will break
the best anvils and hammers of iron.*

The example of Sir Kenelm Digby's sympathetic pow-
der (already quoted p. 252) also illustrates this class of
fallacies *°.

^ PbarmacologiOt p. 88.

* Enquiry into Vulgar and Common Errors^ Bk. II, ch. v. Collected
Works, vol. ii. pp. 334, 335.

*® These instances, together with many others in this chapter, il-
lustrate the ancient fallacies *Non causa pro causa* and * Post hoc, ergo

TO INDUCTION. 28 1

(2) When an effect is the joint result of two or more
causes, the causes may either simply contribute towards
the production of the total result, though one only would
produce some portion of it, or they may all be essential
to the production of any result whatever. It would be
convenient if, in the former case, we could speak of the
causes 2l% joint causes^ in the latter 2k% joint conditions ^ but
to do so would perhaps be too great an innovation on
established language.

(a) An instance of supposing that a phenomenon is en-
tirely due to one cause, when it seems in reality to be only
partially due to it, is furnished by the notion, apparently
erroneous, that the heart is the sole cause of the cir-
culation of the blood.

* What is it,* says Mr. Lewes *^, * which causes the blood to
circulate ? " The heart," answers an unhesitating reader.
That the heart pumps blood incessantly into the arteries, and
that this pumping must drive the stream onwards with great

propter hoc* It will probably have already occurred to the student that
some of the examples just cited might have been equally well adduced as
examples of the fallacy of noii-observation. It, in fact, frequently happens
that the same error may be assigned indifferently to two or more sources
of deception. * From the elliptical form,' says Archbishop Whately
{Elements of Logic ^ Bk, iii. §1), * in which all reasoning is usually ex-
pressed, and the peculiarly involved and oblique form in which fallacy is
for the most part conveyed, it must of course be often a matter of doubt,
or rather of arbitrary choice, not only to which genus each hind of fallacy
should be referred, but even to which kind to refer any one individual
fallacy.* Thus, so intimately are our intellectual operations blended, that
it is often extremely difficult to decide whether a mistake be mainly due
to defective observation or erroneous reasoning.
** Physiology 0/ Common Life, vol. i. p. 323.

282 FALLACIES INCIDENT

force, there is no doubt; but although the most powerful
agent in the circulation, the heart is not the sole agent - and
the more we study this difficult question, the more our doubts
gather round the explanation.

* Let a few of the difficulties be stated. There have been
cases of men and animals bom without a heart ; these ** acar-
diac monsters" did not live, indeed could not live ; but they
had grown and developed in the womb, and consequently
their blood must have circulated. In most of these cases
there has been a twin embryo, which was perfect ; and the
circulation in both was formerly attributed to the heart of
the one ; but it has been fully established that this is not the
case. Further, Dr. Carpenter reminds us that " it has occa-
sionally been noticed that a degeneration in the structure of
the heart has taken place, during life, to such an extent that
scarcely any muscular tissue could at last be detected in
it, but without any such interruption to the circulation as
must have been anticipated if this organ furnishes the sole
impelling force." On the other hand, an influence acting on
the capillaries will give a complete check to the action of
the heart although that organ is itself perfectly healthy and
vigorous.*

Mr. Lewes then proceeds to discuss the subject at
greater length, but the above quotation will be sufficient
for our purpose.

A familiar instance of this error occurs in the vulgar
notion that the mean annual temperature of a place is
exclusively determined by its latitude. The reader need
hardly be told that in this case there are many other
causes at work, namely, elevation, distance from the sea,
proximity of mountain chains, and the like.

When a number of causes contribute towards the total

TO INDUCTION. %%i

effect, it is plain that, as in the last instance, they may
operate in the way of modifying, counteracting, or even
frustrating*^ each other's influence. This is a considera-
tion which it is often of the utmost importance to bear
in mind, as will be obvious from the following examples,
extracted, the former from Dr. Paris' Pharmacologia *^, the
latter from Sir G. C. Lewis' Methods of Observation and
Reasoning in Politics **.

* In ordering saline draughts as vehicles for active medicines,
it is very important that they should be rendered perfectly
neutral; the effect of a predominating acid or alkali may
produce decompositions fatal to the efficacy of the remedy,
as the practitioner will fully understand by a reference to the
Acetate of Ammonia^ and other preparations in the Table of
Incompatibles. In prescribing them to be taken in a state of
effervescence, we must consider whether the disengaged car-
bonic acid may not invalidate the powers of the remedies
simultaneously given with them. I should certainly recom-
mend such a form to be avoided, in all cases where a salt
of lead had been administered, for the carbonic acid retained
in the stomach might probably convert it into a carbonate,

* But it is to be borne in mind that, in estimating negative
instances, due allowance must be made for the occasional

frustration of causes For example : it might be

argued, from the occurrence of several cases in which the
absence of high import duties and of commercial restrictions
was accompanied with abundance and cheapness of com-
modities, that the former was the cause of the latter. Certain

*^ We sometimes speak of causes * wholly or partially counteracting
each other/ It would be an advantage, if we could appropriate the
word frustration to express complete counteraction.

^ p. 498. ** Vol. i. p. 386.

284 FALLACIES INCIDENT

instances might then occur, in which the former existed with-
out the latter; but each of these exceptional cases might
be accounted for, by showing that there was a special circum-
stance, such as a deficient supply, or interruption of inter-
course by war or blockade, which partially obstructed, and for
a time suspended, the operation of the former cause. Again :
it might be shown, by the evidence of facts, that the operation
of a new law had been generally beneficial, with the exception
of certain districts, where its enforcement had been prevented
or retarded by certain peculiar and accidental circumstances.
Exceptions of this kind,' which admit of an adequate special
explanation, serve rather to confirm the general inference
than to weaken it ; inasmuch as they raise the presumption
that, but for the partial obstruction to the cause, it would
have operated in these as in the other instances where no
obstructions existed*^.*

* It is probably from observing this case of the problem
of causation, that the popular error has arisen of supposing
that a rule is sometimes proved by its exceptions. Every
exception to a general proposition must, in so far as it is
an exception, detract from the application of the proposition,
and consequently disprove [or rather go towards disproving]
it. Thus, if it were asserted that all cloven-footed animals
ruminate, this assertion certainly would receive no confirm-
ation from the fact, that certain cloven-footed animals — such
as the hog — do not ruminate. If, however, the exception,
as in the case which we have been examining, admitted
of a peculiar explanation, and it could be shown that the
n'uus or tendency of the cause was the same in the excep-
tional as in the other instances, but that in the former it
was counteracted and overcome, while in the latter it was
not — then the exception may be said not to invalidate, but
rather to confirm the rule.*

^ Sir G. C. Lewis' Methods of Observation and Reasoning in Politics,
vjl. i. p. 386.

TO INDUCTION. 285

The above passage is noteworthy, as furnishing a good
comment on the maxim, Exceptio probat regulam, a
maxim which is, of course, only applicable where the
exceptions are apparent, and where they admit of ex-
planation in conformity with the rule.

(/3) That every event depends upon the concurrence of
a number of causes, positive and negative, or, as they
are often called, conditions, has already been pointed
out (Chap. I. pp. 10-12). Thus, the burning of a
fire depends not only on the application of a lighted
match and the supply of fuel, but also on the presence
of atmospheric air, or rather of the oxygen which it
contains, though, from the universal presence of air, we
are less apt to think of the latter cause than of the former
ones. The importance, however, of not overlooking this
consideration is shewn by the extent to which we can
augment the temperature by constantly bringing fresh
currents of air into contact with any heated mass, as well
as by the familiar phenomenon of the increased bright-
ness with which a fire bums on a frosty day, when the
atmosphere is more than ordinarily dry, or free from
aqueous vapour.

The importance of bearing in mind that an event
depends upon a concurrence of causes may be further
illustrated by the boiling-point of water. The point at
which water boils depends upon two causes or con-
ditions, the temperature of the water and the pressure
of the atmosphere. Now, as the latter varies at diflferent
heights and in different states of weather, water does not

286 FALLACIES INCIDENT

always boil at the same temperature^ the boiling-point
being, as a rule, diminished by i** for every 590 feet that
we ascend, so that, whereas at the sea level water boils
at about 212° Fahrenheit, on the top of Mont Blanc it
boils at about 185°. It is obvious that any one, not bear-
ing in mind this fact, might be exposed to the greatest
practical inconveniences.

The following quotations from Dr. Paris' JPharmaco-
hgia will furnish a suflfieient illustration of the importance
of this consideration and of the errors which may result
from neglecting it.

* In some cases of irritability of stomach, the addition of a
small quantity of opium will impart efficacy to a remedy
otherwise inert ; an emetic will often thus be rendered more
active, as I have frequently witnessed in my practice. In
some states of mania, and affections of the brain, emetics will
wholly fail, unless the stomach be previously influenced and
prepared by a narcotic. I have often also found that the
system has been rendered more susceptible of the influence
of mercury by its combination with antimony and opium.
So, again, when the system is in that condition which is
indicated by a hot and dry skin, squill will fail in exciting
expectoration; but administer it in conjunction with am-
monia, and in some cases with Ant'tmomal Wine and a saline
draughty and its operation will be promoted. As a diuretic,
Squill is by no means active, when singly administered, but
Calomel^ or some mercurial, when in combination with it,
appears to direct its influence to the kidneys, and in some
unknown manner to render these organs more susceptible of
its influence*'*.*

*• PbarmacolopOt p. 388.

TO INDUCTION. 287

*It has been determined by the most ample experience,
that substances will produce effects upon the living system,
when presented in a state of simple mechanical mixture,
very different from those which the same medicinal ingre-
dients will occasion when they are combined by the agency
of chemical affinity. To illustrate this by a simple case, — a
body suspended in a mixtiu^e in the form of a powder, will
act very differently if held in solution by a fluid. The rela-
tive effects of alcohol in the form of what is termed " spirit"
and in that of wine, may be explained upon the same prin-
ciple ; in the former case, it is in a state of mixture, in the
latter, in that of combination. It has been demonstrated
beyond all doubt, that a bottle of port, madeira, or sherry,
actually contains as much alcohol as exists in a pint of
brandy; and yet how different the effect! — a fact which
affords a very striking illustration of the extraordinary
powers of chemical con^ination in modifying the activity
of substances upon the living system '"^.^

* It has been very generally supposed that substances,
whose application does not produce any sensible action upon
the healthy system, cannot possess medicinal energy ; and, on
the contrary, that those which occasion an obvious effect
must necessarily prove active in the cure or palliation of
disease. To this general proposition, imder certain limita-
tions and restrictions, we may perhaps venture to yield our
assent ; but it cannot be too early, nor too forcibly impressed
upon the mind of the young practitioner, that medicinej are,
for the most part, but relative agents , producing their ejffects in
reference only to the state of the living frame. We must, there-
fore, concur with Sir Gilbert Blane in stating that the virtues
of medicines cannot be fairly essayed, nor beneficially ascer-
tained, by trying their effects on sound subjects, because that
particular morbid condition does not exist which they may be

** Pbarmaeologia, pp. 426, 427.

288 FALLACIES INCIDENT

exclusively calculated to remove ; thus, in a robust state of
the body, the effects of steel, in commendation of which, in
certain diseases, professional opinion is unanimous, may be
wholly imperceptible. Bitter tonics, also, may either prove
entirely inert, or they may give strength, relax the bowels, or
induce constipation, according to the particular condition of
the patient to whom they are administered ; so again in a
healthy state of the stomach, a few grains of soda or magnesia
will not occasion the least sensible effect, but where that
organ is infested with a morbid acid, immediate relief will
follow the ingestion of the one, and purgation that of the
other. By not reasoning upon such facts, physicians have, in
my opinion, very unphilosophically advanced to conclusions
respecting the inefficacy of certain agents. They have ad-
ministered particular preparations in large doses, and not
having observed any visible effects, have at once denounced
them as inert. I might allude, for instance, to the tris-tutraU
of bismuth, a substance which, however powerless in health, I
am well satisfied, from ample experience, is highly effica-
cious in controlling certain morbid states of the stomach.
Dr. Robertson has well observed, that disease calls forth
the powers, and modifies the influence of medicines. That
which agitates the calm of health may soothe the irritation
of illness, and that which without opposition is inert, may
act powerfully where it meets with an opponent. Experi-
ments should be made on the sick, in order to determine how
the sick will be affected, and nothing should be pronounced
feeble, merely because it has done nothing where there was
nothing to be done*\*

To adduce one more illustration: insanity, though
sometimes due to a number of causes, each one of
which simply contributes to and augments the affection,

^ Pbarmacologiaf pp. 133, 134.

TO INDUCTION. ^89

which would still exist, though in a weaker degree,
even if some of them were absent, appears at other
times to be the joint result of a number of causes, the
presence of every one of which seems to be essential to
the production of any effect so definite as to deserve the
name of mental derangement. The train, in these cases,
appears to be laid by a number of precedent circum-
stances, and the addition of some one other circumstance
seems to be the spark which produces the conflagration.

*When we are told,* says Dr. Maudsley**, *that a man
has become deranged from anxiety or grief, we have
learned very little if we rest content with that. How does it
happen that another man, subjected to an exactly similar
cause of grief, does not go mad ? It is certain that the entire
causes cannot be the same where the effects are so different ;
and what we want to have laid bare is the conspiracy of
conditions, internal and external, by which a mental shock,
inoperative in one case, has had such serious consequences
in another. A complete biographical account of the indi-
vidual, not neglecting the consideration of his hereditary
antecedents, would alone suffice to set forth distinctly the
causation of his insanity. If all the circumstances, internal
and external, were duly scanned and weighed, it would be
found that there is no accident in madness; the disease,
whatever form it might take, by whatsoever complex con-
currence of conditions, or by how many successive links of
causation, it might be generated, would be traceable as the
inevitable consequence of certain antecedents, as plainly as
the explosion of gunpowder may be traced to its causes,
whether the train of events of which it is the issue be long

*' Physiology and Pathology of Mind, Part II. ch. i. p. 325.

U

290 FALLACIES INCIDENT

or short. The germs of insanity are sometimes latent in
the foundations of the character, and the final outbreak is
perhaps the explosion of a long train of antecedent prepa-
rations.

(3) The phenomena of insanity also furnish a good illus-
tration of the next source of error, the mistaking of joint
effects for cause and effect. In this, as in many other
diseases, symptoms are often mistaken for causes. Thus,
it is not uncommon to hear violent religious excitement
or inordinate grief adduced as causes of insanity, whereas
these are probably, in the vast majority of cases, due to
precisely the same combination of physical and mental
causes which, when they operate with greater intensity,
ultimately issue in definite and unmistakable insanity.

We have an instructive instance of the same error
in some of the speculations respecting the origin of
fevers. In Abdominal Typhus (the so-called TyphoVd
or Enteric Fever of the English Physicians) the febrile
symptoms (Pyrexia, Erethism, &c.) have been as-
cribed to certain lesions of the glandular structures
of the intestines; but a wider observation has shown
that the other symptoms often precede by some time
the formation of the lesions, and that the fever may
even run a fatal course, though it may be impossible,
in a post-mortem examination, to detect the specific
lesions in question. Practically, the correction of this
and similar errors is of great importance, as much mis-
chief may be done, and much time may be lost, by a
mode of treatment which, through mistaking sjmtiptoms

TO INDUCTION. 291

for causes, or co-eflfects for cause and effect, addresses
itself only to the consequences of the malady, and leaves
the real source of evil unattacked.

The following anecdote, told by Dr. Paris, affords an
amusing illustration of the extent to which the ignorant,
in reasoning on cause and effect, may be deceived by an
invariable, or even frequent, concurrence of events.

* It should,' says he'^, ^be kept in mind, that two events
may arise from a common cause, and be co- existent,
and yet have not the most remote analogy to, or de-
pendence upon, each other. It was a general belief at
St. Kilda, that the arrival of a ship gave all the inhabitants
colds. Dr. John Campbell took a great deal of pains to
ascertain the fact, and to explain it as the effect of effluvia
arising from human bodies ; the simple truth, however, was,
that the situation of St. Kilda renders a north-east wind
indispensably necessary before a stranger can land, — the
wind, not the stranger, occasioned the epidemic'

In speculations on the history of language, languages,
which recent investigation has shown to be related col-
laterally, were by older philologers erroneously regarded
as standing to each other in the relation of parent and
child. I extract from Professor Max Mtiller's Lectures
on the Science of Language^^ the foUovring illustration,
which will aheady be familiar to many of my readers : —

* A glance at the modem history of language will make
this clearer. There never could be any doubt that the so-

"• Pbarmacologia, p. 89 " First Series Lecture V,

U 2

293 FALLACIES INCIDENT

called Romance languages, Italian, Wallachian, Provenga
French, Spanish, and Portuguese, were closely related to ei
other. Everybody could see that they were all derived fr
Latin. But one of the most distinguished French schoi;
Raynouard, who has done more for the history of the F
mance languages and literature than any one else, maintah
that ProveiifaJ only was the daughter of Latin ; when
French, Italian, Spanish, and Portuguese were the daughl
of Provencal. He maintained that Latin passed, from 1
seventh to the ninth century, through an intermediate sta
which he called Langue Romane, and which he eadeavoui
to prove was the same as the Proven9al of Southern FraO'
the language of the Troubadours. According to him, it v
only after Latin had passed through this uniform metamt
phosis, represented by the Langue Romane or Provenf
that it became broken up into the various Romance dialei
of Italy, France, Spain, and Portugal. This theory, whi
was vigorously attacked by August Wilhelm von Schleg
and afterwards minutely criticised by Sir Comewall Lew
can only be refuted by a comparison of the Proven)
grammar with that of the other Romance dialects. And hei
if you take the auxiliary verb Ib be, and compare its fon
in Proven9al and French, you will see at once that, 1
several points, French has preserved the original Latin fbn
in a more primitive state than Proven5al, and that, therefoi
it is impossible to classify French as the daughter of Pr
venial, and as the granddaughter of Latin. We have
Proven 5 al ; —

" The met relationship of French to Provenj»l may be repretenl
thus ; the Pensant Latin becime in the South of France the L»n|
d'Oe (or Provenfal), ind in the North the Langue d'Oi], of which 1
French (or the dialed of the Isle de France) was the principal diale
and his in its modem tonn became the language of the natjon. *
Brachet'i HisloriccU Qrammar (Mr. Khcbui's Tiaoilation), p. 13,

TO INDUCTION. ^93

senij corresponding to the French nous sommes^
et% „ *vous etes,

son ,y Us sontf

and it would be a grammatical miracle if crippled forms, such
as sem, etz, and son, had been changed back again into the
more healthy, more primitive, more Latin, sommes, etes, sont ;
sumus, estis, sunt.

Let us apply the same test to Sanskrit, Greek, and Latin ;
and we shall see how their mutual genealogical position is
equally determined by a comparison of their grammatical
forms. It is as impossible to derive Latin from Greek, or
Greek from Sanskrit, as it is to treat French as a modification
of Provengal. Keeping to the auxiliary verb to be, we find
that / am is in

Sanskrit Greek Lithuanian

asmi esmi esmi.

The root is as, the termination mi.

Now, the termination of the second person is si, which,
together with as, or es, would make,

as'si eS'Si es'si.

But here Sanskrit, as far back as its history can be traced,
has reduced assi to asi ; and it would be impossible to suppose
that the perfect, or, as they are sometimes called, organic,
forms in Greek and Lithuanian, es-si, could first have passed
through the mutilated state of the Sanskrit asi.

The third person is the same in Sanskrit, Greek, and
Lithuanian, as-ti or es-ti; and, with the loss of the final /, we
recognise the Latin est, Gothic ist, and Russian est*.

The same auxiliary, verb can be made to furnish sufficient
proof that Latin never could have passed through the Greek,
or what used to be called the Pelasgic stage, but that both
are independent modifications of the same original language.
In the singular, Latin is less primitive than Greek ; for sum
stands for es-um, es for es-is, est for es-ti. In the first person

294 FALLACIES INCIDENT

plural, too, sumus stands for es-umus, the Greek ej^meSf the
Sanskrit *smas. The second person «-^w, is equal to Greek
es-te^ and more primitive than Sanskrit stba. But in the third
person phiral Latin is more primitive than Greek. The
regular form would be as-anti; this, in Sanskrit^ is changed
into janti. In Greek, the initial s is dropped, and the iEolic
enti is finally reduced to eisi. The Latin, on the contrary,
has kept the radical j, and it would be perfectly impossible
to derive the Latin sunt from the Greek eLsL'

(4) A not uncommon som"ce of error is the confusion
of the proximate with the primary or remote cause of
a phenomenon. To be on our guard against this error
is often of the utmost practical importance ; for the re-
moval of the proximate cause may only temporarily
remove the eflfect, and the primary cause may, after a
time, reproduce it ; or, again, the removal of the primary
cause may still leave the proximate cause in full action.
This is well exemplified in Mr. Lewes' account of Thirst.

'The sensation of Thirst is not merely a sensation de-
pendent on a deficiency of liquid in the system, but a local sen-
sation dependent on a local disturbance : the more water these
men (the prisoners confined in the Black Hole at Calcutta)
drank, the more dreadful seemed their thirst ; and the mere
sight of water rendered the sensation, which before was
endurable, quite intolerable. The increase of the sensation
following a supply 6i water, would be wholly inexplicable to
those who maintain that the proximate cause of Thirst is
deficiency of liquid; but is not wholly inexplicable, if we
regard the deficiency as the primary, not the proximate
cause; for this primary cause having set up a feverish con-
dition in the mouth and throat, that condition would continue
after the original cause had ceased to exist. The stimulus

TO INDUCTION. 295

of cold water is only a momentary relief in this case, and
exaggerates the sensation by stimulating a greater flow o(
blood to the parts. If, instead of cold water, a little luke-
warm tea, or milk-and-water, had been dnmk, permanent
relief would have been attained ; or if, instead of cold water,
a lump of ice had been taken into the mouth, and allowed
to melt there, the effect would have been very different —
a transitory application of cold increasing the flow of blood,
a continuous application driving it away.

*We must not, however, forget that although, where a
deficiency of liquid has occasioned a feverish condition of the
mouth and throat, no supply of cold liquid will at once re-
move that condition, the relief of the Systemic sensation
not immediately producing relief of the local sensation, never-
theless, so long as the system is in need of liquid, the feeling
of thirst must continue. Claude Bernard observed that a
dog which had an opening in its stomach drank unceasingly,
because the water ran out as fast as it was swallowed; in
vain the water moistened mouth and throat on its way to
the stomach. Thirst was not appeased because the water
was not absorbed. The dog drank till fatigue forced it to
pause, and a few minutes afterwards recommenced the same
hopeless toil ; but no sooner was the opening closed, and the
water retained in the stomach, from whence it was absorbed
into the system, than thirst quickly vanished*'.'

In studying the history of a language, it is often
most important to bear in mind that words ultimately
derived from one language are proximately derived
through the medium of another. Thus, 'there are in-
deed,' says M. Brachet'^, * some few Greek words in early

® Lewes' Physiology of Common Life, vol. i. pp. 45-47.
^ Historical Grammar, Mr. Kitchio's Translation, p. 37.

2g6 FALLACIES INCIDENT

French, such as ckhe, somme, parole; but these do not
come straight from the Greek ko^cl, aayfia, n-apafioXij, but
through the Latin which first adopted them and handed
them on/ And again : —

* When Jerome translated the Old Testament into Latin
he incorporated into his version certain Hebrew "words which
had no Latin equivalents, as seraphim, Gehenna, pascha, &c. ;
from Latin they passed at a later time into French (seraphiny
gene, pdque'). But they entered French from the Latin, not
from the Hebrew. The same is the case with the Arabic;
its relations with French have been purely accidental. To
say nothing of those words which express oriental things
such as Alcoran, bey, cadi, cara'vane, dervicbe, firmany jamssaire,
&c., which were brought into the west by travellers, the
French language received, in the middle ages, many Arabic
words from another source : the Crusades, the scientific
greatness of the Arabians, the study of oriental philosophies,
much followed in France between the twelfth and fourteenth
centuries, enriched the vocabulary of the language with many
words belonging to the three sciences which the Arabians
cultivated successfully: in astronomy it gave such words as
azimuth, nadir, zenith; in alchemy, alcali, alcool, alambic,
alchimie, elixir, sirop; in mathematics, algebre, n^ro, chiffre.
But even so these words did not come directly from Arabic
to French ; they passed through the hands of the scientific
Latin of the middle ages. In fact, the oriental languages
have had little or no popular or direct influence on French ".*

The non-recognition of these intermediate channels
through which the words of one language have been
introduced into another, has often led to the most erro-

" Historical Grammar, p. 22, a. 2.

TO INDUCTION. %()']

neous theories as to the connection of languages or the
relations subsisting between the people speaking them.
Thus, it was once a favourite theory that all languages
are derived from Hebrew, and the occurrence in dif-
ferent languages of the same words has often, without
any other ground, been regarded as a proof of the con-
nection of the most diverse races.

We add an example from the science of Political
Economy. It has often been supposed that high prices
produce high wages. A sudden rise in the price of any
particular class of commodities may lead, by a desire
on the part of the producers to increase the supply, and
by a consequent increase in the demand for labour in
that particular department, to a temporary rise in wages.
But a rise in prices produces no permanent rise in wages,
unless it leads to an increased accmnulation of capital,
that is, an augmentation of the fund available for the
further production of wealth aiid, consequently, for the
payment of wages '^^. Here the rise in prices is the
remote or primary, and the increased accumulation of
capital is the proximate, cause of the phenomenon ; but,
as counteracting causes, such as reckless speculation or
the adoption of a more luxurious style of living on the
part of the capitalists, may prevent the rise in prices
from being followed by an increased accumulation of
. capital, it is often of great importance to distinguish the
two.

We have, thus far, discussed those errors which ori-

^ See Mill's Politieal Economy, Bk. II. ch. zi. § a.

298 FALLACIES INCIDENT

ginate in overlooking the presence of some third circum-^
stance. But, even when all the circumstances except the
cause and effect (or what we suppose to be such) have
been eliminated, we may still commit an error, either
from mistaking the cause for the effect, or from neglect-
ing to take account of their mutual action and reaction,
and being thus led erroneously to assign to one of the
two exclusively the whole share in the production of the
ultimate effect.

(5) The importance of not overlooking this latter source
of error is well illustrated by the following remarks of
Sir G. C. Lewis ^^:—

*An additional source of error in determining political
causation is likewise to be found in the mutuality of cause
and effect. It happens sometimes that when a relation of
causation is established between two facts, it is hard to
decide which, in the given case, is the cause and which the
effect, because they act and re-act upon each other, each
phenomenon being in turn cause and effect. Thus, habits
of industry may produce wealth ; while the acquisition of
wealth may promote industry: again, habits of study may
sharpen the understanding, and the increased acuteness of
the understanding may afterwards increase the appetite for
study. So an excess of population may, by impoverishing the
labouring classes, be the cause of their living in bad dwellings;
and, again, bad dwellings, by deteriorating the moral habits
of the poor, may stimulate population. The general intelli-
gence and good sense of a people may promote its good
government, and the goodness of the government may, in its
turn, increase the intelligence of the people, and contribute

^ On Methods of Observation and Reasoning in Politics, vol. i. p. 375.

TO INDUCTION. , 299

to the formation of sound opinions among them. Dnmken-
ness is in general the consequence of a low degree of intelli-
gence, as may be observed both among savages and in civilized
countries. But, in return, a habit of drunkenness prevents
the cultivation of the intellect, and strengthens the cause
out of which it grows. As Plato remarks, education im-
proves nature, and nature facilitates education. National
character, again, is both effect and cause : it re-acts on the
circumstances from which it arises. The national peculiarities
of a people, its race, physical structure, climate, territory,
&c., form originally a certain character, which tends to
create certain institutions, political and domestic, in har-
mony with that character. These institutions strengthen,
perpetuate, and reproduce the character out of which they
grew, and so on in succession, each new effect becoming,
in its turn, a new cause. Thus a brave, energetic, restless
nation, exposed to attack from neighbours, organises military
institutions: these institutions promote and maintain a war-
like spirit : this warlike spirit, again, assists the development
of the military organisation, and it is further promoted by
territorial conquests and success in war, which may be its
result— each successive effect thus adding to the cause out
of which it sprung.'

The difference between the calculated and observed
velocities of sound (already noticed*®) furnishes another
illustration of the importance of attending to the mutual
action of cause and effect. The wave of sound, in its
passage through the air, developes heat by compression,
and this heat, by augmenting the elasticity of the air,
increases, in turn, the velocity with which the sound
is transmitted. Thus the effect re-acts upon, and pro-

" pp. 171, 173.

I

1

300 FALLACIES INCIDEITT

motes the operation of, the original cause. It was fp
overlooking this fact that Newton's calctUation of
velocity of sound fell short of the observed velocity
about one-sixth of the actual rate.

Malthus' speculations on the increase of populat
illustrate another form of the same error. He foi
that, in many cases, population increased faster than ft
increased. He inferred that this increase of populat
once begun would continue under all circumstano
and that therefore a time was at hand, in many coi
tries, when the bulk of the people would be redui
almost to a state of starvation. He did not obse;
that in this case, the effect re-acts upon the cause ; n
however, in the way of promotii^ but of retarding
operation. The tendency of an increase of populati
is certainly to diminish the supply of food; but, in
tempting to forecast the ultimate results of this tt
dency, Malthus did not take sufficient account of t
fact that the diminution in the supply of food h;
in its turn, a tendency to arrest the increase of pop
lation.

Instances of the tendency of an effect to re-act up"
its cause, in the way of diminishing its intensity, are ve
frequent in human aff^rs. Thus, when a man discove
that he is labouring under a disease, the addition
prudence which he is induced to exercise will ofti
not only arrest or retard the progress of the diseaf
but lead to the prolongation of his life beyond the usu
term. Again, when a deficiency of sanitary arrang

TO INDUCTION, 30r

merits has led to an increased mortality or the outbreak
of a pestilence, the attention thus directed to the noxious
influences at work will often result in their removal, or,
at least, in some considerable alleviation of them. It
is plain that, in speculating on the future, these are
considerations which ought not to be left out of ac-
count.

(6) We may invert cause and effect, mistaking one
for the other. This error is not infrequent in his-
torical speculations, as, for instance, when some great
event, such as the religious reformation of the sixteenth
century, or the French Revolution, is assigned as the
cause of a general change of opinion or of certain mental
and social habits, whereas, in reality, the gradual, and
often imobserved, operation of this change has been the
cause, and not the effect, of the historical event. In
a case of this kind, however, the event may, in turn,
have intensified, and, perhaps, given the sanction of
authority to, the causes which produced it.

Again, a particular form of government, monarchical,
aristocratical, democratical, or the like, is often assigned
as the cause of certain peculiarities of social feeling or
national character, whereas it would probably be far
more correct to regard the form of government as due,
in the first instance, to these peculiarities, though it, in
turn, may have intensified the causes to which it was
originally due.

In meteorological speculations it has been questioned
whether the "electrical phenomenon of lightning is the

302 FALLACIES INCIDENT

cause or eflfect of the sudden precipitations of rain and
hail which it generally accompanies. Sir John Herschel
(in opposition to the ordinary opinion**') maintains that
it is the effect, and argues thus : —

* Whatever may be the state of the ultimate molecules of
vapour, it seems impossible but that when a great multitude
of them lose their vaporous state by cold, and coalesce into
a drop or snow spangle, however minute, that drop will have
collected and retained on its surface (according to the laws
of electric equilibrium) the whole electricity of its con-
stituent molecules, which will therefore have some finite,
though very feeble tension. Now, suppose any number (looo
for instance) of such globules to coalesce, or that by successive
deposition one should gradually grow to looo times its original
volume. The diameter will be only lo, and the surface loo
times increased. But the electric contents being the sum
of those of the elementary globules, will be increased one
thousandfold, and being spread entirely over the surface, will
have a tenfold density (j,e, tension).

♦ * * * 4c

* It will easily be seen, that when thousands of these electri-
ferous globules again further coalesce into rain drops, a great
and sudden increase of tension at their surface must take
place. Their electricity, then, is enabled to spring from drop
to drop, and rushing in an instant of time from all parts of
the cloud to the surface, a flash is produced. Accordingly,
in thunder-storms, it is the commonest of all phenomena to
find each great flash succeeded by a sudden rush of rain at
such an interval of time as may be supposed to have been
occupied in its descent. The sudden precipitation of large
quantities of rain, and especially of hail, which is formed in
a cold region where the insulating power of the air is great

* Herschel's Meteorology ^ §§ 135, 137.

TO INDUCTION, 303

is almost sure to be accompanied with lightning, which the
usual perversity of meteorologists, where electricity is in
question, long persisted, and even yet persists, with few ex-
ceptions, in regarding as the cause, and not the consequence,
of the precipitation.'

A question has also been raised whether the copious
precipitation of rain which usually takes place in the
centre of a cyclone is the cause or the eflfect of the
cyclone. The more probable view is that the partial
vacuum produced by the rain-fall, and the consequent
inrush of the surrounding atmosphere, is the cause of
the cyclone.

Professor Rogers, in his recently published Manual of
Political Economy^, calls in question the received opinion
on the relation between the increase of population and
the cultivation of inferior soils. Though I cannot accept
his position, the passage will serve as an instance of
the difficulty frequently experienced in determining which
of two phenomena or events is cause and which is
effect.

'There is not a shadow of evidence in support of the
statement that inferior lands have been occupied and cul-
tivated as population increases. The increase of population
has not preceded but followed this occupation and cultivation.
It is not the pressure of population on the means of sub-
sistence which has led men to cultivate inferior soils, but the
fact that these soils being cultivated in another way, or taken
into cultivation, an increased population became possible.
How could an increased population have stimulated greater

60

p. 153.

304 FALLACIES ZZfCmETT

hbcnr ia. agricuitare, wfioi a ^imltu re i«»*st : bv^ ijj,^_k,|
the mcaas oq whicii tbat iiicrEa»i popizLitKxi conli bate
exited ^^r To make inareased popalatioa tfie cam^ of m-
proved agricuitnre is to cxjmmit the absurd blazidcr of coh
foundxng caise and effect.'

Whfle agreeizig wish the ordmarv tbeorr that Ae
pressure of popoknon leads, in the first instance, to
the cultivation of inferior lands, I shoold admit that die

ideriz^

possible a larger population, reacts iq>on and intensifies
the original cause, an increased population leading to die
culdvation of fresh lands, that rendering possible a still
larger population, this in turn leading to the cnltivatioD
of fresh lands, and so on, till the process is arrested
by counteracting causes. If this view be correct, die
ordinary theory is more jusdy open to the cham
of neglecting to take into account the 'mutuality' of
cause and effect, noticed a few pages back, than of
inverting their relatidlL

VI. The Argument from Analogy, as has already been
stated, consists in drawing the conclusion that, because
two phenomena resemble each other in certain observed
points, they also resemble each other in certain other
points beyond the range of our observation. The con-
ditions to which such an inference, in order to be leei-
timate, must conform, need not be here repeated. If
the conditions be not fulfilled, we may commit the error

*^ This question appears to ignore the fact that a population may hare
an insufficient supply of food, though it may just be able to sustain life.

TO INDUCTION. 305

either of over-estimating the force of the analogy; of
mistaking the direction in which it points, so as to regard
an analogy which makes against a certain position as
making for it, or the reverse; or, lastly, of supposing
grounds of analogy to subsist where there really are
none. The two former errors have been sufl&ciently ex-
emplified in the chapter on Imperfect Inductions.

When we exaggerate the value of analogical evidence,
or mistake the conclusion to be drawn from it, we may
be led to do so either by over-rating the number of
ascertained points of resemblance as compared with
ascertained points of diflference, or the reverse, or by
miscalculating the extent of our knowledge of the pheno-
mena. The examples referred to illustrate both sources
of error. Thus, for instance, the points in which elec-
tricity resembles a fluid are obvious, while the points of
difference are far less obtrusive, and, moreover, the un-
known properties of electricity are probably out of all
proportion to those which we know. In this case, too,
when we include the consideration of heat, light, and
simUar agencies, the argument from analogy may be
used against, rather than in favour of, the identification
of electricity with a fluid.

The student need, however, hardly be reminded that
an analogy which in one state of knowledge appears
to be a strong one may, as knowledge advances, become
extremely faint, worthless, or even positively unfavourable
to the position which it was originally adduced to support.

The term False Analogy is, strictly speaking, applied

X

3o6 FALLACIES INCIDENT

not to those cases in which we over-estimate the value
of the analogy, or mistake the direction in which the
argument points, but to those cases of analogical in-
ference in which there exists no ground for any analogy
whatever. Two phenomena. A, B, resemble each other
in the possession of the properties a, b^ c. The pheno-
menon A is observed also to present the property d^ and
hence it is inferred as probable that the same property
is to be found also in B. Now it has already been
pointed out that if we have any reason to suppose i
to be causally connected with any of the properties
a, b, Cy the argument ceases to be analogical, and b^
comes inductive. But if, on the other hand, we have
any reason to suppose that d is causally connected with
none of the properties a, 3, r, there is no room for any
inference whatever. The whole force of the Argument
from Analogy consists in the chance of d being causally
connected with a, b, ox c] if we have reason to believe
that this is the case, the argument becomes more than
analogical; if we have reason to believe that it is not
the case, we are debarred from employing the argument
altogether. Thus, in a certain sense, the Argument from
Analogy is based on our ignorance; it is the result of
a calculation of chances, which an accession of know-
ledge may invalidate, by either augmenting, diminishing,
or annihilating. Of False Analogy, in its strict sense,
that is to say, the error of supposing that similarity or
dissimilarity in certain points is an evidence of similarity
or dissimilarity in other points, when more careful re-

TO INDUCTION. 307

flection or observation would lead to the belief that there
is probably no connection whatever between the ob-
served points from which the Analogy proceeds, and the
unobserved points to which it argues, instances are
extremely numerous in almost every branch of knowledge.
As this, form of Fallacy is so common, we shall subjoin
several examples of it.

The following excellent illustration is quoted by Mr.
Mill from Archbishop Whately's Rhetoric *^ :

* It would be admitted that a great and permanent diminu-
tion 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 sove-
reign would be twice as large ; if only half as easy, it would

«2 MiU's Logic, Bk. V. ch. v. § 6 ; Whately's Rhetoric, Part I. ch. ii.
§ 7. The passage does not occur in the earlier editions of Whately's
Rhetoric.

X 2

308 FALLACIES INCIDENT

hi of the size of a half-sovereign, and this (besides the trifling
circumstance of the cheapness or clearness of gold ornaments)
would be all the difference. The analogy, therefore, fails in
the point essential to the argument/

Respect for antiquity is often urged by an argument
so sweeping as to assume the form of a False AnaIog}^
'Who are we/ it is said, *that we should presume to
think that we know better than previous generations?'
Now, on many matters of fact, there can be no question
that the belief of previous generations, when properly
examined and sifted, must be accepted as final, inasmuch
as they were contemporary with, or at least nearer than
ourselves to, the original sources of information. To
infer from this just and limited deference the necessity of
an undiscriminating submission to the opinions of our
ancestors, would be an instance of the fallacy of Inductio
per simplicem enumerationem. But this, at least in
many cases, seems not to be the nature of the argu-
ment, which appears rather to proceed on the following
grounds : we reverence the opinions of the aged, because
they have had more experience than we have had, and
, therefore, surely, on the same principle, we ought to
accept the opinions of our ancestors who lived in bygone
generations. The point of resemblance is the fact of
having been born at a period prior to ourselves, and
hence it is inferred that the greater experience and the
greater wisdom which are found to be concomitants of
this fact in the case of many of our senior contemporaries
may also be presumed in the case of those who have

TO INDUCTION. 309

long since been dead. It, of course, escapes the notice
of those who have recourse to this argument, that the
average age of the persons living at any one time is
about the same as that of those living at any other, and
that superior wisdom is the consequence not of priority
of birth but of greater experience. Thus far, the fallacy
may be regarded as one of False Analogy, strictly so
called. But there is another consideration which turns
the edge of the argument. Experience grows with time,
each generation not only inheriting the accumulated
experience of previous generations, but adding to the
stock its own acquisitions. 'Recte enim,' says Bacon ^,
* Veritas temporis filia dicitur, non auctoritatis.' * Anti-
quitas saeculi juventus mundi^/

^ Novum Organum, Bk. I. Aph. Ixxxiv. The reference is, perhaps,
to ^schylus, Prometheus Vinctus, I. 981 : &XX* ixdi^aKci v6li/0' 6
yrfpAaKojy xp6vo$. Compare the following sentences in the same
Aphorism : * De antiquitate autem opinio, quam homines de ipsa fovent,
negligens omnino est, et vix verbo ipsi congnia. Mundi enim senium
et grandsBvitas pro antiquitate vere habenda sunt ; quae temporibus
nostris tribui debent, non juniori aetati mundi, qualis apud antiquos fuit.
Ilia enim aetas, respectu nostri, antiqua et major ; respectu mundi ipsius,
nova et minor fuit. Atque revera quemadmodum majorem rerum huma-
narum notitiam, et maturius judicium, ab horoine sene expectamus, quam
a juvene, propter experientiam, et rerum, quas vidit, et audivit, et
cogitavit, varietatem et copiam ; eodem modo et a nostra setate (si vires
suas nosset, et experiri et intendere vellet) majora multo quam a priscis
temporibus expectari par est ; utpote aetate mundi grandiore, et infinitis
cxperimentis et observationibus aucta et cimiulata/ Bentham in his
Book of Fallacies, Part I. ch. ii., and Sydney Smith in his review of that
work {Edinburgh Review, No. Ixxxiv, reprinted in his Collected Works),
have some very apposite and amusing remarks on this subject.
•* De Augmentis Scientiarum, Lib. I. Dr. Whewell in his Pbihsopby

3IO FALLACIES INCIDENT

Bishop Wilkins' Discovery of a New World contains
the following curious extract, translated from the woA
of Cardinal Nicold de Cusa De doctd Ignorantid •* :

* We may conjecture the inhabitants of the sun are like to
the nature of that planet, more clear and bright, more intel-
lectual than those in the moon where they are nearer to the
nature of that duller planet, and those of the earth being
more gross and material than either, so that these intellectual
natures in the sun are more form than matter, those in the

ofDhcovery (chap. xiii. % 4) appears to think that thif celebrated Apho-
riim may be traced to Giordano Bruno. * It is worthy of remark that
a thought which is often quoted from Francis Bacon, occurs in Bruno's
Cena di Centre ^ pubh'shed in 15S4; I mean, the notion that the bter
times are more aged than the earlier. In the course of the dialogue, the
Pedant, who is one of the interlocutors, says, *'In antiquity is wisdom*"
to which the Philosophical Character replies, ** If you knew what too
were talking about, you would see that your prmciple leads to the
opposite result of that which you wish to infer ; — I mean, that we are
older, and have lived longer, than our predecessors." He then proceeds
to apply this, by tracing the course o{ astronomy through the earlier
astronomers up to Copernicus.* See Wagner's edition of Giordano

Bruno*t Works, vol. i. p. 133. In the original the passage runs thus:

* Prudenzio. Sii come la si vuole, io non voglio discostarmi dal parer de
gli antichi; per che dice il saggio: Ne I'antiquitli k la sapienza.
Teofilo. E soggiunge : In molti anni la prudenza. Se roi intendeste
bene quel che dite, vedreste, che dal vostro fondamento s' inferisce il
contrario di quel che pensate : voglio dire, che noi siamo piii vecchi et
abbiamo piU lunga etk, che i nostri predecessori.' Mr. Spedding, how-
ever, in his edition of Bacon, questions whether Bacon intended the
aphorism as a quotation, and thinks it probable that he did not derive
it from any earlier writer. See Ellis and Spedding's edition of B<ie<M
vol. i. p. 458, n. 4.

•' Wilkins* Diicovery o/a New World in the Moon, p. laS ; Cusanus,
De doct(% IgnorantiA, Lib. II. ch. xii.

TO INDUCTION. 3II

earth more matter than form, and those in the moon betwixt
both. This we may guess from the fiery influence of the sun,
the watery and aerous influence of the moon, so also the
material heaviness of the earth. In some such manner like-
wise is it with the regions of the other stars ; for we conjec-
ture that none of them are without inhabitants, but that there
are so many particular worlds and parts of this one universe,
as there are stars, which are innumerable, unless it be to Him
who created all things in number.'

The analogy in this case is founded not, as in the
previous instances, on points of resemblance but on
points of dissimilarity. The sun, the moon, and the
earth are formed of different materials, and, therefore,
it is argued, their inhabitants differ in their intellectual
capacities, the exaltation of intelligence rising in pro-
portion to the * clearness and brightness' of the globe
which they inhabit. Waiving the assumptions as to the
materials of which the three bodies are composed and
the habitation of them all* by intelligent beings, it is
plain that there is no presumption in favour of the
theory that the intelligence of the inhabitants stands in
any relation to the material of the globe on which they
live ; by parity of reasoning, birds ought to be far more
intelligent than men.

The following passage from Bacon's Novum Organum^
furnishes a remarkable example of an admixture of Con-
fusion of Language with False Analogy : * Sed tem-
poribus insequentibus, ex inundatione Barbarorum in

•• Bk. I. Aph. Ixxvii.

31 a FALLACIES INCIDENT

imperium Romanum, postquam doctrina humana vck
naufragium perpessa esset; turn demum philosophiac
Aristotelis et Platonis, tanquam tabulae ex materia leviore
et minus solida, per fluctus temporum servatse sunt'
The student may exercise his sagacity in assigning its
due share to each source of deception.

The arguments for or against the independence of
colonies will often be found to rest on a False Analogy.
Sometimes it is said that, under no circumstances, ought
a colony to rebel against the authority of the mother-
country ; at other times, that, the colony having come to
maturity, the time for its emancipation has arrived. In
each of these cases the argument is suggested by the
term 'mother-country/ Now the relations of the child
to the parent are mainly determined by natural affection,
by early associations, by gratitude for favours received,
and frequently by the fact that, while the child is gra-
dually approaching to the .prime of life, the parent
is gradually receding from it. Similar circumstances
though to a far weaker degree, may undoubtedly de-
termine the relations of a colony to its ' mother-country,'
as, for instance, sympathy of race, the associations of
many of the colonists with their early home, gratitude
for assistance received at the foundation of the colony
or during the earlier years of its existence, the growing
prosperity of the colony or the waning power of the
* mother-country/ But, in addition to the fact that there
are many cases in which these circumstances or some
of them do not exist, or in which they exist only to

TO INDUCTION. 313

the slightest extent, it must be plain, on reflection, that
the justice or injustice, the expediency or inexpediency,
of separation from the mother-country or of repudia-
tion by it must often be settled by considerations totally
distinct from these, and such as receive no elucidation
whatever from the relations between parent and child.

The illusion, originating in a false analogy, that every
conmiunity must, like every individual man, pass through
the three stages of growth, vigour, and decay, is thus
exposed by Sir G. C. Lewis®^ :

* From what has been already said, it follows that the com-
parison which is sometimes instituted between the progress
of a community and the life of a man fails in essentials, and is
therefore misleading. Both a man and a community, indeed,
advance from small beginnings to a state of maturity ; but a
man has an allotted term of life, and a culminating point from
which he descends; whereas a community has no limited
course to run ; it has no necessary period of decline and de-
cay, similar to the old age of a man; its national existence
does not necessarily cease within a certain time. Nations, as
compared with other nations, have periods of prosperity and
power ; but even these periods often ebb and flow, and when
a civilised nation loses its pre-eminence — as Italy in the nine-
teenth, as compared with Italy in the fourteenth and sixteenth
centuries — it does not necessarily lose its civilisation. A po-
litical community is renewed by the perpetual succession of
its members ; new births, immigrations, and new adoptions of
citizens, keep the political body in a state of continuous
youth. No such process as this takes place in an individual
man. If he loses a limb, it is not replaced by a fresh growth.
The effects of disease are but partially repaired; all the

67

Methods of Observation and Reasoning in Politics, vol. ii. p. 438.

314 FALLACIES ISCIDEST

bodily and mental fimctions are gradnallT enfeebled, as fi»
is prolongedy tiD at last decay ineritablj ends in death;
whereas a commitnity might, consistently with the laws d
hmnan nature, hare a duration co-eztensiTe with tliat d
mankind*

' The supposed analogy between the existence of a poG-
tical community and the life of a man seems to hare con-
tributed to the formation of the bdief in a liability to
eorrvpt'um, inherent in erery society. It was a £iToarite
doctrine among some writers of the last ce ntur y , tint every
ctrilised community is filed to reach a period erf* c onmiUi M,
when its healthy and natural action ceases^ and it undergoes
some great deterioration. The notion of an inevitable stage
of corruption in a nation was, indeed, partly suggested by the
commonplaces condemnatory of luxury, derived both from
the classical and ecclesiastical writers; and by the more
modem eulogies of savage life. So £ir, however, as it was
founded on the inevitable periods of decay in aniwiai and
vegetable life, the comparison was delusive; for the two
relations which are brought together do not corre^xMid.
The death of individuals may, indeed, be considered a neces-
sary condition for the progress of the society, into which they
enter as temporary elements. It is by the substitution of
new intelligences, and of natures not hardened to old customs,
for minds whose thoughts and habits have learnt to move
uniformly in the same groove, that progressive changes in
human affairs are effected. The decay and death of the indi-
vidual, therefore, tends not only to prevent the deterioration
of the society, but to promote its improvement.*

Ancient medicine was full of false analogies. We may
take the following example from Dr. Paris'® :

'An example of reasoning by false analogy is presented

•• Pbarmacologiaf p. 64.

TO INDUCTION, 315

to us by Paracelsus, in his work de vita longd, wherein,
speaking of antimony, he exclaims, " Sicut anlimonium finit
aurum, sic, eadem ratione et forma, corpus humanimi purum
reddit." '

The alchemists, or some of them, appear to have
imagined that the same preparation by which they hoped
to convert the baser metals into gold (called metaphori-
cally 'the healthy man') would also be effective in re-
moving the sources of all bodily diseases. Why should
not the impurities of the human body be removable by
the same means as the impurities of the metals ?

* They [that is, the Arabian physicians] conceived,* says the
same author ^^, * that gold was the metallic element in a state
of perfect purity, and that all the other metals differed from
it in proportion only to the extent of their individual con-
tamination ; and hettce the origin of the epithet base^ as
applied to such metals. This hypothesis explains the origin
of alchemy; but in every history we are informed that the
earlier alchemists expected, by the same means that they
hoped to convert the baser metals into gold, to produce an
universal remedy, calculated to prolong indefinitely the span
of human existence.

Ht is difficult to imagine what connexion could exist in
their ideas between the ^^Philosopher's Stoncy* which was to
transmute metals, and a remedy which could arrest the pro-
gress of bodily infirmity : upon searching, however, into the
writings of these times, it appears probable that this conceit
may have originated with the alchemists from the applica-
tion of false analogies, and that the error was subsequently
diffused and exaggerated by a misconstruction of alchemical
metaphors.'

/ •• Pbarmacologia, p. 64.

3l6 FALLACIES INCIDENT

The old maxim that * Nature abhors a vacuum/ the
once fashionable doctrine of the * Social Contract ' or
* Original Compact/ the explanation of moral and phy-
sical facts by applying to them the conceptions of * per-
fect numbers* and * regular solids ^°/ the Pythagorean
theory of the Harmony of the Spheres, the Aristotelian
doctrine of the Mean, and innumerable other instances
with which the student will meet in his reading, will
abundantly illustrate the nature of False Analogy and
its frequency in the reasoning of eariy speculators.

The Argument from Final Causes'^, at least that
extreme form of it which assumes that every natural

'** On this subject the reader will find some very curious informatiou
in Mill's Logic t Bk. V. ch. v. § 6, and WheweU's History of the Induc-
tive Sciences^ 6k. IV. ch. iii. § a.

"'^ * Turn vero, ad ulteriora tendens [intellectus humanus], ad proximiora
recidit, videlicet ad causas finales, quae sunt plane ex natura hominis,
potius quam universi : atque ex hoc fonte philosophiam miris modis
corrupenint.* Bacon, Nov. Org, Lib. I. Aph. xlviii. To prevent mis-
conception, I may state that I am far from denying that the Argument
from Final Causes, if it take sufficient account of the evolution of or-
ganisms and their power of adapting themselves to external circumstances,
and if it be based on the contemplation of Nature as a whole, instead of
on individual objects, may not admit of being stated in such a form as
to occupy once more an important position in any scheme of Natural
Theology. Moreover, even with respect to individual organisms, there
are some cases of adaptation so marvellous, as that, for instance, of the
eye, that it is difficult to exclude the idea of design, whatever may have
been the agency, and however mysterious and prolonged the process, by
which an intelligent Creator may have worked. The student will find
a very temperate statement of the prevalent theory, together with much
useful information on the literature of the subject, in Dr. Acland's

TO INDUCTION. 317

organism was specially designed to subserve some special
object, and fashioned, once for all, in immediate reference
to that object, appears ultimately to repose on a False
Analogy. God or Nature (for both terms are used) is
assimilated to a human artificer, and the argument ap-
pears to rest on the assumption that the motives, con-
ceptions, and contrivances of the one may be regarded
as similar to those of the other. * Nature does nothing
in vain/ * Nature always acts for the best/ * Everything
is designed for some good purpose/ These and similar
maxims express the general principle on which the
argument rests. Of its application to special cases we
may take the following examples.

The instances given by Bacon, in the Advancement of
Learning and the De Augmentis^^, when protesting against

Harveian Oration for 1865. On the other side he may, with most
advantage, consult the works of Mr. Herbert Spencer and Mr. Darwin.

" Advancement of Learning, Bk. II. (Ellis and Spedding's edition,
vol. iii. p. 358). Cf. De Augmentis, iii. 4. It should be noticed, how-
ever, that Bacon allows the use of Final Causes in what he calls * Meta-
physic/ Of the foregoing instances, * and the like,* he says that they
are ' well enquired and collected in Metaphysic ; but in Physic they are
impertinent.' And again : ' Not because these final causes are not true,
and worthy to be enquired, being kept within their own province ; but
because their excursions into the limits of physical causes hath bred a
vastness and solitude in that track.* The rest of the paragraph may be
read with advantage. What Bacon appears to mean (and the distinc-
tion is important) is that we may argue, in Theology or Metaphysics,
from an ascertained case of adaptation to the wisdom or goodness of the
Creator, but that we are not justified in assuming adaptation or design
as an instrument of physical investigation. Those who defend this use
of the argument, would reply that many discoveries (such as, notably,

3l8 FALLACIES INCIDENT

the emplojonent of Final Causes in physical enquiiies,
are the following : ' The hairs of the eye-Kds are for a
quickset and fence about the sight ; the finnness of the
skins and hides of living creatures is to defend than
from the extremities of heat or cold ; the bones are for
the columns or beams, whereupon the frames of the
bodies of living creatures are built ; the leaves of trees
are for protecting of the fruit ; the clouds are for water-
ing of the earth; the solidness of the earth is for the
station and mansion of living creatures.'

The absurd extent to which the argument may be
carried by speculators who attempt to find a Final
Cause for every phenomenon which falls under their
cognisance, will be plain from the examples which foUow.
It would, however, be unjust to charge these absurdities
to the account of those writers of the past generation
who took a more sober, though, perhaps, an erroneous,
view of the argument.

In the TimcBus of Plato ''^ the construction of the whole
universe, and specially of man, is explained on the
principle of Final Causes. The following extract from

Harvey's discovery of the circulation of the blood, which set out from
observing the action of the valves in the veins of many parts of the body,
and enquiring into their purpose) have been suggested by the idea of
adaptation. See Acland's Harveian Oration^ and Dugald Stewart's Pbilo-
sopby of the Human Mind, Part II. ch. xi. (Sir W. Hamilton's edition of
Stewart's Works, vol. iii. p. 335, &c.) This may be, and, in fact, must
be, admitted with respect to physiological enquiries (however the adapt-
ation may be accounted for), and hence Bacon's prohibition is certainly
too absolute.

'' Of Plato, Bacon says truly, that he * ever anchoreth on that shore.'

TO INDUCTION. 319

Mr. Grote's Plato^^ will serve as a specimen of the
method there employed :

* The Demiurgus, having constructed the entire Kosmos,
together with the generated Gods, as well as Necessity would
permit — imposed upon these Gods the task of constructing
Man : the second-best of the four varieties of animals whom
he considered it necessary to include in the Kosmos. He
furnished to them as a basis an immortal rational soul (di-
luted remnant from the soul of the Kosmos); with which
they were directed to combine two mortal souls and a body.
They executed their task as well as the conditions of the pro-
blem admitted. They were obliged to include in the mortal
souls pleasure and pain, audacity and fear, anger, hope, ap-
petite, sensation, &c., with all the concomitant mischiefs. By
such uncongenial adjuncts the immortal rational soul was
unavoidably defiled. The constructing Gods, however, took
care to defile it as little as possible. They reserved the head
as a separate abode for the immortal soul: planting the
mortal soul apart from it in the trunk, and establishing the
neck as an isthmus of separation between the two. Again
the mortal soul was itself not single but double : including
two divisions, a better and a worse. The Gods kept the two
parts separate; placing the better portion in the thoracic
cavity nearer to the head, and the worse portion lower down,
in the abdominal cavity: the two being divided from each
other by the diaphragm, built across the body as a wall of
partition : just as in a dwelling-house, the apartments of the
women are separated from those of the men. Above the
diaphragm and near to the neck, was planted the energetic,
courageous, contentious soul ; so placed as to receive orders
easily from the head, and to aid the rational soul in keeping
under constraint the mutinous soul of appetite, which was

'* Vol. iii. pp. 273-75.

3^0 FALLACIES INCIDENT

planted below the diaphragm. The immortal soul was fas-
tened or anchored in the brain, the two mortal souls in the
line of the spinal marrow continuous with the brain : which
line thus formed the thread of connection between the three.
The heart was established as an outer fortress for the exer-
cise of influence by the immortal soul over the other two.
It was at the same time made the initial pomt of the veins,
— the fountain from whence the current of blood proceeded
to pass forcibly through the veins round to all parts of the
body. The purpose of this arrangement is, that when the
rational soul denounces some proceeding as "wrong (either
on the part of others without, or in the appetitive soul
within), it may stimulate an ebullition of anger in the heart,
and may transmit from thence its exhortations and threats
through the many small blood channels to all the sensitive
parts of the body; which may thus be rendered obedient
everywhere to the orders of our better nature.

* In such ebullitions of anger, as well as in moments of
imminent danger, the heart leaps violently, becoming over-
heated and distended by excess of fire. The Gods foresaw
this, and provided a safeguard against it by placing the lungs
close at hand with the windpipe and trachea. The lungs
were constructed soft and full of internal pores and cavities
like a sponge ; without any bloody — but receiving, instead
of blood, both the air inspired through the trachea, and the
water swallowed to quench thirst. Being thus always cool,
and soft like a cushion, the lungs received and deadened the
violent beating and leaping of the heart ; at the same time
that they cooled down its excessive heat, and rendered it
a more equable minister for the orders of reason.

* The third or lowest soul, of appetite and nutrition, was
placed between the diaphragm and the navel. This region
of the body was set apart like a manger for containing neces-
sary food ; and the appetitive soul was tied up to it like a wild
beast ; indispensable indeed for the continuance of the race

TO INDUCTION. 321

yet a troublesome adjunct, and therefore placed afar oiF, in
order that its bellowings might disturb as little as possible
the deliberations of the rational soul in the cranium for
the good of the whole. The Gods knew that this appe-
titive soul would never listen to reason, and that it must
be kept under subjection altogether by the influence of
phantoms and imagery. They provided an agency for this
purpose in the liver, which they placed close upon the abode
of the appetitive soul. They made the liver compact, smooth,
and brilliant, like a mirror reflecting images: — moreover,
both sweet and bitter on occasions. The thoughts of the
rational soul were thus brought within view of the appetitive
soul, in the form of phantoms or images exhibited on the
mirror of the liver. When the rational soul is displeased,
not only images corresponding to this feeling are impressed,
but the bitter properties of the liver are all called forth. It
becomes crumbled, discoloured, dark, and rough; the gall
bladder is compressed ; the veins carrying the blood are
blocked up, and pain as well as sickness arise. On the con-
trary, when the rational soul is satisfied, so as to send forth
mild and complacent inspirations, — all this bitterness of the
liver is tranquillised, and all its native sweetness called forth.
The whole structure becomes straight and smooth ; and the
images impressed upon it are rendered propitious. It is
thus through the liver, and by means of these images, that
the rational soul maintains its ascendancy over the appetitive
soul ; either to terrify and subdue, or to comfort and encou-
rage it.

* Moreover, the liver was made to serve another purpose.
It was selected as the seat of the prophetic agency ; which
the Gods considered to be indispensable, as a refuge and aid
for the irrational department of man. Though this portion
of the soul had no concern with sense or reason, they would
not shut it out altogether from some glimpse of truth. The
revelations of prophecy were accordingly signified on the liver,

322 FALLACIES INCIDlEI^T

for the instruction and within the easy vIcav of the appetitive
soul ; and chiefly at periods when the functions of the rational
soul are suspended — either during sleep, or disease, or fits of
temporary extasy. For no man in his perfect senses comes
under the influence of a genuine prophetic inspiration. Sense
and intelligence are often required to interpret prophecies,
and to determine what is meant by dreams or signs or prog-
nostics of other kinds : but such revelations are received by
men destitute of sense. To receive them, is the business of
one class of men : to interpret them, that of another. It is a
grave mistake, though often committed, to confound the two.
It was in order to furnish prophecy to man, therefore, that
the Gods devised both the structure and the place of the
liver. During life, the prophetic indications are clearly
marked upon it : but after death they become obscure and
hard to decypher.

*The spleen was placed near the liver, corresponding to
it on the left side, in order to take off from it any impure or
excessive accretions or accumulations, and thus to preserve it
clean and pure.*

Aristotle constantly employs this method of reasoning.
Thus, in a familiar passage of the Ethics ''^ he szys
that ' if it is better for men to attain happiness through
their own exertions than through chance, it is reason-
able to suppose that this will be the case, since every-
thing that depends on Nature ^^ is in the best possible
condition.'

" Efb. Nic. i. 9 (5). Ei 8' kariv o0ra; ^iXriov ^ did n^^i/v c^9ai-
fiovuv, iiXoyov ex^iv ovtojs, tiirtp rd kqt^ <f)vaiv, dts oT6v re iroAAi^ra
I^X^^^t otfTO) iri<f>vK€v.

""* The student will notice the transition from the Demiurgus and
inferior gods of Plato to the 'Nature* of Aristotle. 'And in this,' says

TO INDUCTION. 323

From his physiological works (in which the argument
is most commonly employed) it will be sufficient to ad-
duce one or two examples, which will serve also to show
how a preconceived opinion may lead an author to invent
false facts for the purpose of supporting his theory.

Having fixed the seat of sensation in the heart, in-
asmuch as it is in the centre of the body, rather than
in the brain, as some philosophers had done, it was
necessary to discover some function for the brain. The
necessity of discovering some function for it led to the
fiction of its * coldness,' which was supposed to counteract
the heat of the heart, and so to preserve the body 'in
a mean state ^'^.^ On this account, he supposed, all
animals which have blood are furnished with a brain,
while bloodless animals, having little heat, require nothing
to cool them, and are, therefore, without one. Moreover,
in order to temper the coldness of the brain, blood is

Bacon, * Aristotle is more to be blamed than Plato, seeing that he left
out the fountain of final causes, namely God, and substituted Nature for
God ; and took in final causes themselves rather as the lover of logic
than of theology.* — The Dignity and Advancement of Learning (Trans-
lation of \hcDe Augmentis), Bk. III. ch. iv. (Ellis and Spedding's Edition,
vol. iv. p. 364).

■" Compare the extraordinary fancy (in the same work, Bk. III. ch. iv.)
that the reason why the heart, in man, inclines slightly towards the left
side is that it may temper the greater coldness of that side {vpht rh
Syiaovy t^ Kar&yfnj^iv rSav &piaT€pSt¥' iJu&Xiara yap twk AkXeay fyofl'
Sy$panro$ Ix** KaTof/vyfxiva rd, dpiffT(pd). It is needless to observe
that the left side of man is not colder than the right ; the fact is simply
assumed in order to account for the position of the heart in a manner
conformable to Aristotle's general theories.

Y 2

324 FALLACIES INCIDENT

conveyed to the membrane which envelopes it by means
of veins or channels. But, again, lest the heat so con-
veyed should injure the brain, the veins, instead of being
large and few, are small and many, and the blood con-
veyed, instead of being copious and thick, is thin and
pure^®.

'The viscera are formed out of the blood, and therefore
are only found in sanguineous animals, which necessarily have
a heart; for it is clear that, having blood, which is a fluid,
they must have a vessel to contain it, and hence also Nature
has created veins ; and for these veins the origin must neces-
sarily be one, since one, whenever possible, is better than
many. The heart is the origin of the veins : this is seen in
the fact that they spring from it, and do not go through it ;
also they resemble it in structure. The heart has the chief
position, namely, that of the centre, but more upwards than
downwards, and rather in front than behind : for Nature is
accustomed to seat the noblest in the noblest place, unless
any stronger reason prevails : ot ftrj ri icwXvfi /nfifov^®.'

The work of Bishop Wilkins, already quoted, furnishes
some curious examples of the arguments which, even
within the last two hundred years, have found favour with
men distinguished for their scientific attainments*®.

* But this [namely, a conceit of Philo's, in order to account
for the spots in the moon, that * in the fabrick of the world,

^® De Partibus Animalium^ ii. 7. Cf. Lewes* Aristotle^ § 164, p. 180.

^* De Partibus Animalium, iii. 4. I here quote Mr. Lewes' summary,
given in § 395, p. 310 of his Aristotle,

^ Bishop Wilkins was one of the founders of the Royal Society, and
enjoyed one of the highest scientific reputations of his time.

TO INDUCTION. 325

all things grow perfecter as they grow higher, and this is
the reason why the moon doth not consist of any pure simple
matter, but is mixed with air, which shows so darkly within
her body'] cannot be a sufficient reason ; for though it were
true, that nature did frame everything perfecter, as it was
higher, yet is it as true, that nature frames everything fully
perfect for that office to which she intends it. Now, had she
intended the moon merely to reflect the sun-beams, and give
light, the spots then had not so much argued her providence,
as her unskilfulness and oversight, as if in the haste of her
work, she could not tell how to make that body exactly fit
for that office to which she intended it,

' It is likely then, that she had some other end which
moved her to produce this variety, and this in all probability
was her intent to make it a fit body for habitation,, with the
same conveniences of sea and land, as this inferior world doth
partake of. For since the moon is such a vast, such a solid
and opacous body, like our earth (as was above proved), why
may it not be probable, that those thinner and thicker parts
appearing in her do show the difference betwixt the sea and
land in that other world ? and Galilaeus doubts not, but that
if our earth were visible at the same distance, there would
be the like appearance of it.

' If we consider the moon as another habitable earth, then
the appearances of it will be altogether exact, and beautiful,
and may argue unto that, it is fully accomplished for all those
ends to which Providence did appoint it. But consider it
barely as a star or light, and then there will appear in it much
imperfection and deformity, as being of an impure dark
substance, and so unfit for the office of that nature ^^.*

* Though there are some, who think mountains to be a de-
formity to the earth, as if they were either beat up by the
flood, or else cast up like so many heaps of rubbish left at the

**- A Discovery of a New World in the Moon, pp. 66, 67.

326 FALLACIES INtHDEXT

Creation ; yet, if weU considered, they wfll be found as mud
to conduce to the beauty and conTeniency of the universe, as
any of the other parts. Nature (saith Pliny) purposdy fhmed
them for many excellent uses : poirtly to tame the vicdaice of
greater rivers, to strengthen certain joints within the vans
and bowels of the earth, to break the force of the sea's iiran*
dation, and for the safety of the earth's inhabitants^ vihether
beasts or men®.'

* I have now sufficiently proved that there are hills in the
moon, and hence it may seem likely that there is also a worid-
for since Providence hath some special end in all its worts
certainly then these mountains were not produced in vain*
and what more probable meaning can we conceive there
should be, than to make that place convenient for habi-
tation"?'

* It hath been before confirmed, that there 'was a sphere of
thick vaporous air encompassing the moon, as the first and
second regions do this earth. 1 have now showed, that thence
such exhalations may proceed as do produce the comets.
Now from hence it may probably follow, that there may be
wind also and rain, with such other meteors as are common
amongst us. This consequence is so dependent, that Fro-
mondus dares not deny it, though he would (as he confesses
himself), for if the sun be able to exhale from them such
fumes as may cause comets, why not such as may cause
winds, why not then such also as may cause rain, since I have
above showed that there is sea and land, as with us ? Now
rain seems to be more especially requisite for them, since it
may allay the heat and scorchings of the sun, when he is over
their heads. And Nature hath thus provided for those in
Peru, with the other inhabitants under the line®*.'

^ A Discovery of a New World in the Moorit \>* *J*J.
" Id. p. 91. ®* Id. p. lai

TO INDUCTION. 327

One of the most whimsical applications of the Argu-
ment from Final Causes is to be found in the ' Doctrine
of Signatures/ of which Dr. Paris thus speaks*' : —

* But the most absurd and preposterous hypothesis that has
disgraced the annals of medicine, and bestowed medicinal re-
putation upon substances of no intrinsic worthy is that of the
" Doctrine of Signatures," as it has been called, which is
no less than a belief that every natural substance <ivbicb possesses
any medicinal virtues^ indicateSy by an obvious and <well-marked
external character, the disease for <wbicb it is a remedy , or the
object for <wbicb it sbould be employed. This extraordinary
monster of the fancy has been principally adopted and che-
rished by Paracelsus, Baptista Porta, and CroUius, although
traces of its existence may certainly be discovered in very
ancient authors.

* ♦ ♦ * *

* The conceit, however, did not assume the importance of
a theory until the end of the fourteenth century, at which
period we find several authors engaged in the support of its
truth, and it will not be unamusing to oiFer a specimen of
their sophistry; they affirm that, since man is the lord of
the creation, all other creatures are designed for his use, and
therefore that their beneficial qualities and excellences must
be expressed by such characters as can be seen and under-
stood by every one ; and as man discovers his reason by
speech, and brutes their sensations by various sounds, mo-
tions, and gestures, so the vast variety and diversity of figures,
colours, and consistencies, observable in inanimate creatures,
is certainly designed for some wise purpose. It must be,
in order to manifest those peculiar properties and excellen-
ces, which could not be so effectually done in any other way,
not even by speech, since no language is universal. Thus,

** Pbarmacologia, pp. 47-50.

328 FALLACIES INCIDRXT

the lungs of a fox mtut be a specific for asthma, hecamse that
animal is remarkable for its strong powers of respiratioiL
Turmaick has a brilliant yellow colour, ^rhich indicates that
it has the power of curing jaundice ; by the same rule, Pop^s
must relieve diseases of the head ; • • . . and the Bupljraaa
(eye-bright) acquired fame as an application in complaints of
the eye, because it exhibits a black spot in its corolla resem-
bling the pupil. In the curious work of Cbrysostom Magnem
(Exercit. de Tabaco), we meet with a whimsical account of
the signature of tobacco. "In the first place," says he, "the
manner in which the flowers adhere to the head of the plant
indicates the mfundibulum cerebri, and pitmtary gland ; in the
next place, the three membranes, of which its leaves are com-
posed, announce their value to the stomach, which has three
membranes."

* The blood-stone, the beliotropium of the ancients, from
the occasional small specks or points of a blood-red colour
exhibited on its green surface, is even at this day employed
in many parts of England and Scotland to stop a bleeding
from the nose ; and nettle-tea continues a popular remedy
for urticaria.

* * * * ^

* It is also asserted that some substances bear the signa-
tures of the humours, as the petals of the red rose that of
the blood, and the roots of rhubarb, and the flowers of
saiFron, that of the bile.

* I apprehend that John of Gaddesden, in the fourteenth
century, celebrated by Chaucer, must have been directed by
some remote analogy of this kind, when he ordered the son
of Edward I., who was dangerously ill with the small-pox,
to be wrapped in scarlet cloth, as well as all those who
attended upon him, or came into his presence ; and even
the bed and room in which he was laid were covered with
the same drapery; and so completely did it answer sav
the credulous historians of that day, that the prince was

TO INDUCTION. 329

cured without having so much as a single mark left upon
him.*

In these and similar instances, which might be multi-
plied to almost any extent^®, it is plain that much is
gained by the employment of the vague word Nature.
Presuming that the majority of at least the more modern
writers who have employed the Argument from Final
Causes, if pressed to attach a definite meaning to the
word, would reply that they regard it, in this connection,
as only another name for God, the argument, as em-
ployed in the above and similar examples (we are not
here discussing the more refined employment of it), seems
to rest on the three following assumptions : —

(i) That God [or Nature] acts, not by laws, governing
thie evolution of natural objects, but after the manner of
a human artificer, having in view some special end in the
production of each object and of each separate part of it.

(2) That all objects are designed for the good of man,
or, at least, of sentient or intelligent beings.

(3) That we are so well acquainted with what is, on
the whole, good for ourselves, or others, or the world
at large, as well as with the general plan of the universe,
that we are able, in each case, to pronounce positively

^* The following example (taken from Plutarch, De Stoicorvm Repug-
nantiis, p. 1042, by Mr. Lecky, in his History of European Morals, Jrom
Augustus to Charlemagne, vol. ii. p. 174, note 2) is perhaps unsurpassed
in absurdity : ' Chrysippus maintained that cock-fighting was the final
cause of cocks, these birds being made by Providence in order to inspire
lis by the example of their courage.'

3^0 FALLACIES INCIDENT TO INDUCTION.

on the ends which God [or Nature] proposed to himself
in his constructions*^.

Of these three assumptions, the first and second are,
as we conceive, based on false analogies, the first trans-
ferring to God [or Nature] the habit, observed in the
human artificer, of producing each object with reference
to some special end, and the second the motives which
usually guide the artificer in the selection of those ends.
The third assumption, it need hardly be added, involves
a generalisation from a very narrow range of experience
to operations co-extensive with all space and all time.

Even though these various errors have been avoided,
and the inductive process has been correctly performed,
it is still possible, either through confusion of language,
through mistaking the question at issue, or through
drawing erroneous inferences in our subsequent deduc-
tions, to arrive at false conclusions. But these are con-
siderations which properly appertain to the other branch
of Logic, which is concerned with deductive reasoning.

^ The 'principle* laid down by Descartes {De Principiis Pbilosopbia,
i. 28 ) supplies an appropriate commentary on this assumption : * Ita
denique nullas unquam rationes circa res naturales, a fine, quern Deus
aut natura in lis faciendis sibi proposuit, desumemus ; quia nou tantum
nobis debemus arrogare, ut ejus consiliorum participes nos esse putemus.'

INDEX.

Adxquata causa, why the expres-
sion is not here employed, 113.

Adequate hypotheses, 99-103.

Affirmative instances, tendency of
the mind to notice, rather than
negative instances, 238-243.

Analogy, argument from, 209-220.

— different meanings of the word,

209, 210. -

— fake, fallacy of, 304-330.
Antiquitas saeculi juventus mundi,

origin of the apophthegm,
310.

Antiquity, illegitimate use of the
argument from, 308-316.

Aristotle pointed out the depend-
ence of deduction on induc-
tion, 224.

— his constant employment of

inductio per simplicem enu-
merationem, 262.

— his constant employment of the

argument from final causes,

333.
Authority, illegitimate use of the

argument from, 268-274.
Average of observations, 41.

Bacon, his condemnation of induc-
tio per simplicem enumera-
tionem, 117, 261, 262.

Bacon, his instantuB soUtari<Bt 134,

135-

— his instantia cruets ^ 142, 144.

— his approximation to the in-

ductive methods, 198-200.

— his notice of the tendency to

take account of affirmative
rather than negative instances,

238.

— his criticism of the argument

from final causes, 316-318.
Bain, Professor, his view of the

origin of universal beliefs, 28,

29.
Botany, reasons for the excellence

of its classifications, 48.

— nomenclature of, 82, 83.

— terminology of, 85.

Brown, Dr. Thomas, his view of
the origin and nature of our
conception of cause, 20.

Causal relations, various kinds of,
118-120.

Cause, relation of, to the condi-
tions of a phenomenon, 10-
12.

— nature of our conception of,

15-24.

— origin of our conception of,

20, 21.

33^

INDEX.

Cause, definition of, 20.

— error originating in mistaking

a joint cause for a sole cause,
281-290.

— error originating in the con-

fusion of the proximate with
the primary or remote cause
of a phenomenon, 294-797.

— error due to neglecting to take

into account the mutual ac-
tion and reaction (mutuality)
of cause and effect, 298-301.

— error due to the inversion of

cause and effect, 30 x -304.
Causes, exciting, 12, 13.

— predisposing, 12, 13.

— final, illegitimate employment

of the argument from, 316-

330.
Characteristick, 77, 78.
Chemistry, nomenclature of, 84.
<— method of difference extensively

employed in, 144-145.
Classification, 45-81.

— scientific, distinguished from

that employed in the aflfairs
of ordinary life, 46-47.

— scientific, regarded as subsidiary

to induction, definition of, 47.

— a natural system of, distin-

guished from an artificial sys-
tem of, 49, 50.

— natural, rules for the right con-

duct of, 65-73.
Colligation of facts, a hypothesis

serves for, 92.
Conditions, relation of, to the

cause of a phenomenon, lo-
12.

Consilience of inductions, 1 1 1, in.
Continuity, law of, 75.
Crucial instances, 1 42-1 44.

Darwin, Mr., quoted on the signi-
fication of the word * spedes,'

74.

Deduction, its relation to induc-
tion, 224-230.

Definition, are natural classes <k-
termined by definition «
type, 78-81.

Descartes, his criticism of the argu-
ment from final causes, 330.

Diagnosis, 77, 78.

Empirical generalisations or bwi

208, 209.
Exceptio probat regulam, the

maxim explained, 284, 285.
Exceptions to rules, 197.
Experiment, 33-45.

— distinguished from observation,

33. 34-

— general superiority of, over ob-

servation, 35.

— not open to us in the attempt

to ascertain the cause of a
given eflfect, 36, 37.

— and observation, rules for the

right conduct of, 39-45.
Explanation, in the scientific sense,
what, 91.

Fallacies incident to induction,
^37-330.

INDEX.

333

Fallacies of generalisation, 259-550.

— common to the employment of

the various inductive methods,
274.304.

— the same instance may often

be indifferently ascribed to
several, 281.
Fallacy of non-observation, 237-

354-

— of non-observation of instances,

237-250-

— of non-observation of circum-

stances attendant on a given
instance, 250-254.

— of mai-observation, 254-259.

— arising from treating the in-

ductio per simplicem enu-
merationem as if it were a
valid induction, 260-274.

— of * non causa pro causa,' 276-

281.

— due to the neglect of a joint

cause, 281-290.

— due to mistaking of joint effects

for cause and effect, 290-294.

— due to the confusion of the

proximate with the primary
or remote cause of a phe-
nomenon, 294-297.

— due to neglecting to take into

account the mutual action
and reaction (mutuality) of
cause and effect, 298-301.

— due to the inversion of cause

and effect, 501-304.

— of false analogy, 304-530.

— due to the illegitimate emjdoy*

ment of argument from £nal
causes, 516-350.
Final causes, fallacv due to the ille-
gitimate emplo3niient of the
argument from, 516-550.

Geology abounds in instances of
the employment of the method
of concomitant variations, 185.

Hamilton, Sir W., his criticism of
Hume's theory on the nature
of cause, 18, 19.

Herschel, Sir John, distinctly recog-
nises the inductive methods,
197.

— quoted on our tendency to

notice affirmative rather than
negative instances, 259, 240.
Hume, his view of the nature of our
conception of cause, 15-24.

— injustice done to him by quoting

from his treatise of Human
Nature, 24.
HjTpothesb, 89-115.

— distinction between, and induc-

tion, 8-10, 104-107.

— description of, 90.

— conditions of a legitimate^ 95-

105.

— difference between Mr. Mill and

Dr. Whewell as to the func-
tion of, 107-112.

— gratuitous, 114, 115.

Inductio per simplicem enumera-
tionem, 116, 1 1 7, 205-209.

— complete, 117.

INDEX.

335

Method of concomitant variations,

173-195-

Methods, inductive or experi-
mental, 116-204.

Mill, James, quoted on the origin
of our belief in the law of
universal causation, 29.

Mill, Mr., question between him
and Dr. Whewell, as to whe-
ther inductive inference be
from the particular to the
general, or from particulars
to adjacent particulars, 13-15.

— his view of the origin of uni-

versal beliefs, 28, 29.

— difference between him and

Dr. Whewell as to the func-
tion of hypotheses, 107-112.

— importance now attached to

the inductive methods mainly
due to his influence, 197.

Natural distinguished from artificial
classification, 49, 50.

— classification, rules for the right

conduct of, 65-73.

— groups, arrangement of, in a

natural series, 70-73.

— groups, constant recognition of

new, 74-76.
Newton, his demonstration of a

central force, 105-108.
Nomenclature, 81-84.

Observarion, 33-45.

— distinguished from experiment,

33» 34-

Observation, general emplojrment
of, preceded that of experi-
ment, 34.

— alone open to us in the attempt

to ascertain the cause of a
given effect, 36, 37.

— sciences wholly or mainly de-

pendent on, at a great disad-
vantage, as compared with
those in which we can largely
employ experiment, 37, 38.

— and experiment, rules for the

right conduct of, 39-45.
Observations, importance of taking
an average of, 41.

Physiology frequently employs the
method of concomitant varia-
tions, 185, 186.

Plato, his employment of the
argument from final causes,
318-322.

Plurality of causes, 122-124.

Power, question whether the idea
of, is involved in our concep-
tion of cause, 15-24.

Prediction, value to be attached
to, 108-1 1 1.

Reid, his criticism of Hume's ac-
count of causation, 18, 19.

— his view of the nature of our

conception of cause, 21.

— his view of the origin of uni-

versal beliefs, a6, 27.

Social questions, the extreme dif-
ficulty attendant on their in-
vestigation, 267, 268.

33^

JNDEX^

Species, practice of naturalists in
stopping at, open to question,

73, 74-

Species and varieties, constant re-
cognition of new, 74-76.

Spencer, Herbert, his view of the
origin of universal beliefs, 31,
3a.

Statistics, conclusions based on, are
instances of the application of
the method of concomitant
variations, 194.

Stewart, Dugald, his view of the
nature of our conception of
cause, a I.

Subordination of characters, prin-
ciple of, 67, 68.

Terminology, 84-89.
Type, persistency of, 76.

— are natural classes determined
by definition or, 78-81.

Uniformity of nature, law of, 5, 6.

— converse does not hold true, 6.

— universality of the belief in, 24-

26.

— origin of the belief in, 26-32.
Universal beliefs, various theories as

to the origin of, 26-32.

Universal causation, law of, 4, 5.

— universality of the belief in, 24-

a6.

— origin of the belief in, 26-32.

Variation of circumstances, im-
portance of, 42, 43.

Vera causa, why the expression is
not here employed, 113, 114.

Verification, 230-236.

Whewell, Dr.. question between
him and Mr. Mill as to whether
inductive inference be from
the particular to the general,
or from particulars to adjacent
particulars, 13-15.

— his view of the origin of uni-

versal beliefs. 27. 28.

— his position that natural classes

are determined not by defini-
tion but by type. 78-81.

— his remarks on terminology, 85-

89.

— difference between him and

Mr. MiU as to the function
of hypotheses, 107-112.

— his criticism on the inductive

methods, 201-204,

Zoology, reasons for the excellence
of its classifications. 48.

October, 1871.

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Cioero. Selection of interesting and descriptive passages.

With Notes. By Henry Walford, M.A., Wadham College, Oxford, Assistant
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Also sold separately.
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Cioero. Select Letters. By Albert Watson, M.A., Fellow

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Cicero de Oratope. With Introduction and Notes. By

A. S. Wilkins, M. A., Professor of Latin, Owens Collie, Manchester.

Clarendon Press Series.

Cicero and PUny. Select Epistles (for Schools). With

Notes bvE. R. Bernard, M.A.. Fellow of Maedalen College. Oxford, and
the late C. E. Prichard, M.A., formerly Fellow of Balllol College, Oxford. /»
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ComeUus Nepos. With Notes, by Oscar Browning, M.A.,

Fellow of King's College, Cambridge, and Assistant Master at Eton CoU^e.
Ext. fcap. 8va cMh, as. id.

Horace. With Notes and Introduction. By Edward C.

Wickham, M.A., Fellow and Tutor of New College, Oxford.
Also a small edition for Schools.

Iiivy, Books I-X. By J. R. Seeley, M.A., Fellow of Christ's

College, and Regius Professor of Modem History, Cambridge. Book I. Demy
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Also a small edition for Schools.

Ovid. Selections for the use of Schools. With Introduc-
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Fragrments and Specimens of Early Latin. With Intro-
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College, Oxford.

Selections from the less known Iiatin Poets. By North

Finder, M.A., formerly Fellow of Trinity College, Oxford. Demy 8vo. cloth.

Passages for Translation into Latin. For the use of

Passmen and others. Selected by J. Y. Sai^cnt, M.A., Tutor, formerly Fellow,
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II. MENTAL AND MOBAL PHILOSOPHY.
The Elements of Deductive Logic, designed mainly for

the use of Junior Students in the Universities. By T. Fowler, M.A., Fellow
and Tutor of Lincoln College, Oxford. Fourth Edition, with a Collection of
Examples. Ext. fcap. 8vo. cloth, y. 6d.

The Elements of IndiLCtive Logic, designed mainly for

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A Manual of Political Economy, for the use of Schools.

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Acoustics. By W. F. Donkin, M.A., F.R.S., Savilian Pro-
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8 Clarendon Pras

An EleiDontftry Treatise on Queini nioim By P. G.

Tait. M.A.. PnrfesBor of Nttnril Fhaosophy m idle Uni » enily of E Jia b i gh;
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Edition. Ext. fcapL 8to. lim^ cloth, is. 6d.

A Ck>nr8e of laectnres on Fore Oeometry. By Henry J.

Stephen Smith. M. A., F.R.S.. Fdknr of Baffiol CoQege. and SaWBan Ptafessor
of Geometiy in the Unirersity of Oxford.

A Treatiae on Slectrioity and MagnetJanu By J. Clerk

Maxwell. M. A., F.R.S.. foraetly IVoicssor of Natural Flaiosoi^y, Kbit's Col-
lege, London. In the Press.

A Series of Elementary Works it being arranged, anti ■Wfill shortly be

nfiftfHftcpd.

TV. HI8TOBY.
A Manual of Ancient History. By Geoi^ Rawlinson,

M. A . Camden ProfesstM- of Ancient History, formerly FeOow of Exeter CoQeee,
Oxford. Demy Bra cloth, i\s.

Select Charters and other Illnstrations of liSTigiiaTi

Constitutional History from the Earliest "Hmes to the nan of Edward L
By W. Stubbs, M.A.. Regius Professor oi Modem History m the University
of Oxford. Crown 8vo. cloth, 8r. 6d,

A Constitutional History of Tlngland. By W. Stubbs,

M. A, Kq^us Professor of Modem History in the University of Oxford.

A History of Germany and of the Empire, down to the

close of the Middle Ages. By J. Brirce, B.CL., Fellow of Oriel CoDeee.
Oxford.

A History of Germany, from the Reformation. By Adol-

Ehus W. Ward, M.A., Fellow cX St. Peter's Cdl^e, Cambridge, Ptofessor of
[istory, Owens College. Manchester.

A History of British India. By S.J. Owen, M.A.. Lee's

Reader in Law and History, Christ
History in the University ot Oxfmrd.

Reader in Law and History, Christ Church, and Teacher of Indian Law and
"' - ofC " ■

A History of Greece. By E. A. Freeman, MA., formerly

Fellow of Trinity College, Oxford.

A History of France. By G. W. Kitchin, M.A., formerly '

Censor of Christ Church.

Elements of Law for the use of Students. By William ■

Markby. M.A., one of the Justices of the High Court of Judicature, Calcutta. '
Nearly ready. I

Commentaries on Boman Law ; from the original and the

best modem sources. V^y H. J. Roby, M.A., formeriy Fellow of St. John's
College, Cambridge ; Professor of Law at University College, London.

Clarendon Press Series.

VI. FHTSICAIi SCrBNCE.

Natural Fhilosopliy. In four volumes. By Sir W. Thom-
son, L.L.D., D.C.L., F.R.S., Professor of Natural Philosophy, Glasgow; and
P. G. Tah, M.A., Professor of Natural Philosophy, Edinburgh; formerly Fel-
lows of St. Peter's College, Cambridge. VoL 1. 8va cloth, u. $s.

By the same Authors, a smaller Work on the same subject,

forming a complete Introduction to it, so far as it can be carried out with
Elementary Geometry and Algebra. In the Press.

Descriptive Astronomy. A Handbook for the General

Reader, and also for practical Observatory work. With 234 illustrations and
numerous tables. By G. F. Chambers, F.R.A.S., Barrister-at-Law. DemySvo.
856 pp., cloth, i/. IS.

Chemistry for Students. By A. W. Williamson, Phil.

Doc.. F.R.S., lYofessor of Chemistry, University College, London. A new
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A Treatise on Heat, with numerous Woodcuts and Dia-
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Kew. Second Edition. Ext. fcap. 8to. cloth, js. 6d. yust published.

Forms of Animal Idfe. By G. RoUeston. M.D., F.R.S.,

Linacre Professor of Physiology, Oxford. Illustrated by Descriptions and
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Exercises in Practical Chemistry. By A. G. Vernon

Harcourt, M.A., F.R.S., Senior Student of Christ Church, and Lee's Reader
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Series I. Qualitative Exercises. Crown 8va cloth, 7X. td.
Series II. Quantitative Exercises. ^

The Valley of the Thames : its Physical Geography and

Geology. By John Pliillips, M.A., F.R.S., Professor of Geology, Oxford.
In the Press.

Geology. By J. Phillips, M.A., F.R.S., Professor of Geo-
logy, Oxford.

Mechanics. By Bartholomew Price, M.A., F.R.S., Sedleian

Professor of Natural Philosophy, Oxford.

Optics. By R. B. Clifton, M.A., F.R.S., Professor of Experi-
mental Philosophy, Oxford ; formerly Fellow of St. John's College, Cambridge.

Electricity. By W. Esson, M.A., F.R.S., Fellow and

Mathematical Lecturer of Merton College, Oxford.

Crystallography. By M. H. N. Story-Maskel3aie, M.A.,

Professor of Mineralogy, Oxford ; and Deputy Keeper in the Department of
Minerals, British Museum.

Mineralogy. By the same Author.

Physiological Physios. By G. Griffith, M A., Jesus Col-
lege, Oxford, Assistant Secretary to the British Association, and Natural
Science Master at Harrow School

Magnetism.

VII. ENGIiISH IiANaXTAGE AND IiITSBATTTBE.
A First Beading Book. By Marie Eidiens of Berlin ; and

edited by Anne J. Clough. Ext fcap. 8vo. stiff corvers, 4^>

Oxford Beading Book, Part I. For Little Children.

Ext. fcap. 8vo. stiff covers, td.

Oxford Beading Book, Pait II. For Junior Classes.

ExL fcap. 8vo. stiff covers, 6e[.

On the Principles of Grammar. By E. Thring, MA.,

Head Master of Uppingham School Ext fcap. 8to. ciotA, 4s. 6d.

Grammatical Analysis, designed to serve as an Exercise

atid Composition Book in the English Language. By E. Thring^, M. A., Head
Master of Uppingham School Ext fcap. Svo. cloth, y. 6d.

Specimens of Early English ; being a Series of Extracts

from the most important English Authors. Chronologicall]^ arranged, illustrative
of the progress of the English Languskge and its Dialectic varieties, from A.D.
1250 to A.D. 140a With Grammatical Introduction, Notes, and Glossary. By
R. Morris, Editor of " The Story of Genesis and Exodus." &c. Ext fcap. 8va
doth, js. 6d.

Specimens of English from a.d. 1394 to a.d. 1579 (from

the Crede to Spenser) : selected by W. W. Skeat, M.A., formerly Fellow of
Christ's College, Cambridge. In tfu Press.

The Vision of "William concerning Piers the Plowman,

by William Langland. Edited, with Notes, by W. W. Skeat, M.A., formerly
Fellow of Christ^ College, Cambridge. Ext. fcap. Svo. cioth, 4^ . 60.

The Philology of the English Tongue. By J. Earle,

M.A., formerly Fellow of Oriel College, and Professor of Anglo-Saxon, Oxford.
Ext. fcap. Svo. cloth, 6s. 6d. ynst published.

Tsrpical Selections from the best English Authors from the

Sixteenth to the Nineteenth Century, (to serve as a higher Reading Book,) with
Introductory Notices and Notes, being a Contribution towards a History of
English Literature. Ext. fcap. Svo. cloth, 4J-. td.

Specimens of the Scottish Language; being a Series of

Annotated Extracts illustrative of the Literature and Philology of the Lovdand
Tongue from the Fourteenth to the Nineteenth Century. With Introduction
and Glossary. By A. H. Burgess, M.A.

See also XII, below for other English Classics.

VIII. FKENOH IiANGTTAaE AND IiITEBATUBB.
Brachet's Historical Granmiar of the French Language.

Translated by G. W. Kitchin, M.A., formerly Censor of Christ Church. ExL
fcap. Svo. cloth, 3s. 6d.

Clarendon Press Series, 1 1

An Etymological Dictionary of the French Language, with

a Preface on the Principles of French Etymology. By A. Brachet. Iranslated
by G. W. Kitchin, M.A., formerly Censor of Christ Cliwch. In the Press,

Comeille's Cinna, and Molidre's Les Femmes Savantes.

Edited, with Introduction and Notes, by Gustave Masson. . Ext fcap. 8vo.
cloth, 2S. 6d.

Bacine's Andromaque, and Comeille's Le Menteur. With

Louis Racine's Life of his Father. By the same Editor. Ext fcap. 8vo. doth,

Molidre's Les Fourberies de Scapin, and Bacine's Athalie.

With Voltaire's Life of Moli&re. By the same Editor. Ext fcap. 8vo. cloth,
as. 6d.

Selections from the Correspondence of Madame de S6vign6

and her chief Contemporaries. Intended more especially for Girls' Schools.
By the same Editor. Ext fcap. 8vo. c/oth, 3s.

Voyage autour de ma Chambre, by Xavier de Maistre;

Ourika. by MADAME DE DURAS; La Dot de Suzette, by FlEVEE ; Les Ju-
meaux de I'H&tel Comeille, by Edmond ABOUT ; M€saventures d'un £coher,
by RODOLPHE ToPFFER. By the same Editor. Ext fcap. 8vo. cloth, 2s. bd.

A French Grammar. A Complete Theory of the French

Language, with the rules in Freuch and Ene^lish, and numerous Examples to
serve as first Exercises in the Language. Bv Jules Bu^, Honorary M.A. of
Oxford ; Taylorian Teacher of French, Oxfora : iixaminer in the Oxford Local
Examinations from 1858.

A French. Grammar Test. A Book of Exercises on French

Grammar: each Exercise being preceded by Grammatical Questions. By the
same Author.

Exercises in Translation No. i, from French into English,

with general rules on Translation ; and containing Notes, Hints, and Cautions,
founded on a comparison of the Grammar £md Genius of the two Languages.
By the same Author.

Exercises in Translation No. 2, from English into French,

on the same plan as the preceding book. By the same Author.

IX. GEBMAN' liANGTJAGE AND IiITEBATUBE.
Goethe's Egmont. With a Life of Goethe, &c. By Dr.

Buchheim, Professor of the German Language and Literature in King's Col-
lege. London ; and Examiner in German to the University of London. Extra
fcap. 8vo. cloth, y.

Schiller's Wilhelm Tell. With a Life of Schiller ; an histo-
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the same Editor. Ext fcap. 8vo. cloth, y. 6d.

Iiessing's Minna von Bamhelm. A Comedy. With a Life

of Lessing, Critical Commentary, &c. By the same Editor.

Clarendon Press Series.

X. ABT, &<].

A Handbook of Fiatorkl Art. By R. St. J. Tyrwhitt.
A Treatiae on Harmony. By Sir F. A. Gore Ouseley,

A Troatiaa on Counterpomt, Canon, and Fugue, based

XI. MI8CrBIjI.ANEOirS. {

The Modem Oreek LanEuage in its relation to Ancient

The CultlTation of the Bpeaking Voice. By John HuUah.

XII. A 8EBIES as XNOI.IBH OLASBIOS.

Dej'igmd to meet the 'wanti of StudenU in Englitb Lile-
raturt: under the juperintendence of the Rev. J. S.
Brewer, M.A., of Queen' College, Oxfird, and Prefesjor
of Eighth IJterature at Kin^i College, London,

he (tudcnt of English Lite.
le ontset of bis lailc ; — hit reading it apt to
be too narrow or too diffuie.

Out or tlie van number of authors Kt before him in boolu
professing to deal -with this iubject he kno".i not which to idect ;
he thinks he must read a little of all; hcsonn ahiudontto hope-
less an attempt ; he endi by comcniin^ hinuFlfwith second-hand
information i and professing 10 -iiudy English Literature, he fait*
to master a single English auihor. On the other hand, by con-

Clarendon Press Series. 13

fining his attention to one or two writers, or to one special period
of English Literature, the student narrows his view of it ; he fails
to grasp the subject as a whole ; and in so doing misses one of
the chief objects of his studjr.

How may these errors be avoided ? How may minute reading
be combined with comprehensiveness of view ?

In the hope of famishing an answer to these questions the
Delegates of the Press, acting upon the advice and experience of
Professor Brewer, have determined to issue a series of small
volumes, which shall embrace, in a convenient form and at a
low price, the general extent of English Literature, as repre-
sented in its masterpieces at successive epochs. It is thought
that the student, by confining himself, in the first instance, to
those authors who are most worthy of his attention, will be
saved from the dangers of hasty and indiscriminate reading. By
adopting the course thus marked out for him, he will become
familiar with the productions of the greatest minds in English
Literature ; and should he never be able to pursue the subject
beyond the limits here prescribed, he will have laid the founda-
tion of accurate habits of thought and judgment, which cannot
fail of being serviceable to him hereafter.

The authors and works selected are such as will best serve to
illustrate English Literature in its historical aspect. As * the eye
of history,' without which history cannot be understood, the
literature of a nation is the clearest and most intelligible record
of its life. Its thoughts and its emotions, its graver and its less
serious modes, its progress, or its degeneracy, are told by its best
authors in their best words. This view of the subject will sug-
gest the safest rules for the study of it.

With one exception all writers before the Reformation are
excluded from the Series. However great may be the value of

14 Clarendon Press Series.

literature before that epoch, it is not completely nationid. For
it had no common organ of language; it addressed itself to
special classes ; it dealt mainly with special subjects. Again ; of
writers who flourished after the Reformation, who were pcxHilar
in their day, and reflected the manners and sentiments of their
age, the larger part by far must be excluded from our list.
Common sense tells us that if young persons, who have bat a
limited time at their disposal, read Marlowe or Greene, Burton,
Hakewill or Du Bartas, Shakespeare, Bacon, and Milton will be
comparatively neglected.

Keeping, then, to the best authors in each epoch and here

popular estimation is a safe guide — the student will find the fol-
lowing list of writers amply sufllicient for his purpose : Chaucer
Spenser, Hooker, Shakespeare, Bacon, Milton, Dryden, Bunyan,
Pope, Johnson, Burke, and Cowper. In other words, Chaucer is
the exponent of the Middle Ages in England ; Spenser of the
Reformation and the Tudors; Hooker of the latter years of
Elizabeth ; Shakespeare and Bacon of the transition from Tudor
to Stuart ; Milton of Charles I and the Commonwealth ; Dryden
and Bunyan of the Restoration ; Pope of Anne and the House
of Hanover ; Johnson, Burke, and Cowper of the reign of
George HI to the close of the last century.

The list could be easily enlarged; the names of Jeremy
Taylor, Clarendon, Hobbes, Locke, Swift, Addison, Goldsmith
and others are omitted. But in so wide a field, the difficulty is
to keep the series from becoming unwieldy, without diminishinf
its comprehensiveness. Hereafter, should the plan prove to be
useful, some of the masterpieces of the authors just mentioned
may be added to the list.

The task of selection is not yet finished. For purposes of
education, it would neither be possible, nor, if possible, desirable
to place in the hands of students the whole of the works of the

Clarendon Press Series. 15

authors we have chosen. We must set before them only the
masterpieces of literature, and their studies must be directed, not
only to the greatest minds, but to their choicest productions.
These are to be read again and again, separately and in combina-
tion. Their purport, form, language, bearing on the times, must
be minutely studied, till the student begins to recognise the full
value of each work both in itself and in its relations to those that
go before and those that follow it.

It is especially hoped that this Series may prove useful to
Ladies- Schools and Middle Class Schools ; in which English
Literature must always be a leading subject of instruction.

A General Introduction to the Series. By Professor

Brewer, M.A.

1. Chaucer. The Prologue to the Canterbury Tales ; The

Knightes Tale ; The Nonne Prest his Tale. Edited by R. Morris, Editor for
the liarly English Text Society, &c., &c. Second Edition. Extra fcap. 8vo.
cloth, 2^. 6d.

2. Spenser's Faery Queene. Books I and II. Designed

chiefly for the use of Schools. With Introduction. Notes, and Glossary. By
G. w. Kitchin, M.A., formerly Censor of Christ Church. Extra fcap. 8vo.
ciotA, as. 6d. each.

3. Hooker. Ecclesiastical Polity, Book I. Edited by R. W.

Church, M.A,, Rector of Whatley ; formerly Fellow of Oriel College, Oxford.
Extra fcap. 8vo. ctoth, as.

4. Shakespeare. Select Plays. Edited by W. G. Clark,

M.A., Fellow of Trinity College, Cambridge; and W. Aldis Wright, M.A.,
Trinity College, Cambridge.

I. The Merchant of Venice. Extra fcap. 8vo. stiffcwtrs, is.

II. Richard the Second. Extra fcap. 8vo. stiff covers^ is. 6d.

III. Macbeth. Extra fcap. 8vo. stiff covers, xs. 6d.

5. Bacon. Advancement of Learning. Edited by W. Aldis

Wright, M.A. Extra fcap. 8vo. cUtA, 4s. 6d.

6. Milton. Poems. Edited by R. C. Browne, M.A., and

Associate of King's College, London, a vols. Ext fcap. 8vo. ciotA, dr. 6d.
Sold separately, WoL I. \s.,Vo\. II. y.

1 6 Clarendon Press Series.

7. Dryden. Stanzas on the Death of Oliver Cromwell;

Astraea Redux : Annus MirabOis ; Absalom and Achitophel ; Relifio Laid ;
The Hind and the Panther. Edited by W. D. Christie. M. A.. Trinity College.
Cambridsre. Extra fcap. 8vo. cMh, y. 6d,

I 8. Bunyan. Grace Abounding; The Pilgrim's Progress.

Edited by E. Venables, M.A., Canon of Lincoln.

I

9. Pope. With Introduction and Notes. By Mark Pattison,

B.D., Rector of Lincoln College, Oxford.

I. Essay on Man. Extra fcap. Sra stiff covers^ is. 6el,
II. Epistles and Satires. In tJte Press.

10. Johnson. Rasselas; Lives of Pope and Dryden. Edited

by C. H. O. Daniel, M. A., Fellow and Tutor of Worcester College, Oxford.

11. Burke. Thoughts on the Present Discontents ; the Two

Speeches on America ; Reflections on the French Revolution. By Mark Patti-
son, B.D., Rector of Lincoln College, Oxford.

12. Cowper. The Task, and some of his minor Poems.

Edited by J. C. Shairp, M. A., Principal of the United CoUege, St. Andrews.

Published for the ITniversity by
MACMIIiLAN AJTD GO., IiOmDOIT.

The Delegates op the Press invite suggestions and advice
from all persons interested in education; and will he thankful
for bints, &c., addressed to either the Rev. G. W. KrrcHDf,
St, Gileses Road East, Oxford, or the Secretary to the
Delegates, Clarendon Press, Oxford.

f^

I