A 581209
JOHN STUART MILL
H. TAINE

B
ARTES
LIBRARY
1837
VERITAS
SCIENTIA
OF THE
UNIVERSITY OF MICHIGAN
E-PLURIBUS UNUM
LUCBUR
}
SI-QUAERIS PENINSULAM AMOE NAMEN
CIRCUMSPICE
B
1607
T133
27921
ENGLISH POSITIVISM.
A STUDY
ON

JOHN STUART MILL.
Adolphe
Cappole
By H. TAINE.
Translated from the French
(WITH THE AUTHOR'S PERMISSION),
By T. D. HAYE.
LONDON:
SIMPKIN, MARSHALL, AND CO.
1870.
LONDON
STEVENS AND RICHARDSON, PRINTERS, 5, CREAT QUEEN STREET,
LINCOLN'S INN FIELDS, W. C.
PREFACE
TABLE OF CONTENTS.
PAGE
vi
INTRODUCTION.
I. Philosophy in England-Organization of
Positive Science-Want of General Ideas
II. Why Metaphysics are neglected—Autho-
rity of Religion
III. Indications of Free Thought-New Exe-
gesis-Stuart Mill-His Works-His
Order of Mind-To what School of
Philosophy he belongs-Value of the
higher Speculation in estimating Human
Civilization .
PART I.
EXPOSITION OF MILL'S PHILOSOPHY.
I. The Subject-matter of Logic-How it
differs from Psychology and from Meta-
physics
II. A Judgment, what-What it is we know
of the External and Inner Worlds-
The whole object of Science is to add or
connect Facts
III. The System based on this view of the
Nature of our Knowledge
1
3
6
11
14
24
IV. The Theory of Definitions-Its Impor-
tance-Refutation of the Old Theory-
There are no Definitions of Things, but
of Names only
25
iv
CONTENTS.
PAGE
V. The Theory of Proof-The Ordinary
Theory-Its Refutation-What is the
really fundamental part of a Syllogism. 34
VI. The Theory of Axioms-The Ordinary
Theory-Its Refutation-Axioms are
but a certain kind of Truths of Expe-
rience.
VII. The Theory of Induction-The Cause of a
Fact is no more than its invariable
Antecedent-Experience our only Proof
of the Stability of the Laws of Nature
-What is a Law-By what methods
Laws are discovered-The Methods of
Agreement, of Difference, of Residues,
and of Concomitant Variations
VIII. Examples and Applications-The Theory
of Dew
IX. Deduction-Its Province and Method
X. Comparison of the Methods of Induction
and Deduction-Former employment of
the first-Modern employment of the
second-Sciences in which the first is
required-Sciences in which the second
is required-Positive Character of Mill's
Work-His Predecessor's
XI. Limits of our Knowledge-It is not cer-
tain that all Events happen in accor-
dance with Law-Chance in Nature
PART II.
42
49
63.
75
79
84
I. Accordance of this Philosophy with the
English Mind-Alliance of the Positive
and Religious Spirits-By what Faculty
we arrive at the knowledge of Causation 95
II. There is neither Substance nor Force, but
only Facts and Laws-Abstraction-
Its Nature-Its part in Science
999
CONTENTS.
V
III. The Theory of Definitions-They explain
the abstract generating eleinents of
Things
IV. The Theory of Proof-The Basis of Proof
in Syllogism is an Abstract Law .
V. The Theory of Axioms-Axioms are rela-
tions between Abstract Truths-They
may
tity
be reduced to the Axiom of Iden-
VI. The Theory of Induction-Its Methods
are of Elimination or Abstraction
VII. The two great operations of the mind,
Experience and Abstraction-The two
great manifestations of things, Sensible
Facts and Abstract Laws-Why we
ought to pass to the second by the first
Meaning and extent of the Axiom of
Causation
•
VIII. It is possible to arrive at the knowledge of
First Elements-Error of German Meta-
physicians-They neglect Chance and
Local Perturbations-What might be
known by a philosophizing Ant-Idea
and Limits of Metaphysical Science-
Its State in the three Nations that
think.
EPILOGUE-Oxford at Sunrise
PAGE.
105
108
111
116
118
124
. 132
* X
*
The References are to the Fourth Edition
of "MILL'S LOGIC."
PREFACE.
WHEN this Study first appeared, Mr. Mill
did me the honour to write to me that it
would not be possible to give in a few pages
a more exact and complete notion of the
contents of his work, considered as a body
of philosophical teaching. "But," he added,
66
I think you are wrong in regarding the
views I adopt as especially English. They
were so in the first half of the eighteenth
century, from the time of Locke to that of
the reaction against Hume. This reaction,
beginning in Scotland, assumed long ago
the German form, and ended by prevailing
universally. When I wrote my book I
stood almost alone in my opinions, and
though they have met with a degree of
sympathy which I by no means expected,
we may still count in England twenty à
viii
PREFACE.
priori and spiritualist philosophers for every
partisan of the doctrine of Experience."
This remark is very true. I myself could
have made it, having been brought up in
the doctrines of Scotch philosophy, and the
writings of Reid. I simply answer that
there are philosophers whom we do not
count, and that all such, whether English
or not, spiritualist or not, may be neglected
without much harm. Once in a half cen-
tury, or perhaps in a century, or two cen-
turies, some thinker appears; Bacon and
Hume in England, Descartes and Condillac
in France, Kant and Hegel in Germany.
At other times the stage is unoccupied, or
ordinary men come forward, and offer the
public that which the public likes-Sen-
sualists or Idealists, according to the ten-
dency of the day, with sufficient instruction
and skill to play leading parts, and enough
capacity to re-set old airs, well drilled in the
works of their predecessors, but destitute of
real invention—simple executant musicians,
who stand in the place of composers. In
Europe, at present, the stage is a blank.
PREFACE.
ix
The Germans adapt and alter effete French
materialism. The French listen from habit,
but somewhat wearily and distractedly, to
the scraps of melody and eloquent common-
place which their instructors have repeated
to them for the last thirty years. In this
deep silence, and from among these dull
mediocrities, a master comes forward to
speak. Nothing of the sort has been seen
since Hegel.
b
A STUDY ON MILL.
די
I.
WHEN at Oxford the other year during the
meeting of the British Association, I met
among the few students still in residence a
young Englishman, a man of ability, with
whom I became intimate. In the evenings
we went to the New Museum, which was
well filled with specimens. Short lectures
were delivered there, and models of ma-
chinery were set to work; ladies were
present, and watched the proceedings with
interest, and at their close, on the last
evening, "God save the Queen' was sung.
I admired this zeal, this solidity of mind,
this organization of science, these voluntary
subscriptions, this aptitude for association
and for labour, this great machine pushed
B
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2
:
on by so many arms, and so well fitted to
accumulate, criticise, and classify facts. But
yet, amidst this abundance, there was a
dearth when I read the Transactions, I
imagined myself assisting at a congress of
heads of manufactories. All these learned
men were engaged in verifying details and
exchanging recipes. I seemed to hear fore-
men telling one another their processes for
tanning leather or dyeing cotton. There
was a lack of general ideas. I used to
lament this to my friend, and at night, by
his lamp, we discussed its reasons, while
the university city lay wrapped in silence-
below.
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8
30
II.
ONE day, I said to him: "You are wanting
in philosophy; I mean in what Germans call
metaphysics. You have learned men; but
you have no thinkers. Your God impedes
you; for out of respect to Him, (your
Supreme Cause) you do not venture to reason
on causes. He is far the most important
personage in England, and I see how He
merits His position; not only as forming
a part of your constitution, but as the
guardian of your morality, the judge in
final appeal on all questions whatsoever,
and an advantageous substitute for the
prefects and gendarmes with whom conti-
nental nations are still encumbered. Never-
theless, the rank you accord Him has the
inconvenience of all official positions-it
produces a cant, prejudice, intolerance, and
courtiers. Close by you have poor Mr. Max
Müller, who, in order to acclimatise here the
B 2
4
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study of Sanscrit, was forced to discover in
the Vedas the worship of a moral god--
that is to say, the religion of Paley and
Addison. A few days ago, in. London, I
read a Queen's proclamation forbidding
people to play cards, even at home, on Sun-
days. It seems that, if I were robbed, I
should not be able to bring the thief to
justice without first taking a religious oath,
and, if I refused, the judge would send me
away, deny me justice, and insult me into
the bargain. Every year, when we read in
your papers the speech from the throne, we
find there the inevitable mention of Divine
Providence, which comes in mechanically,
like the apostrophe to the immortal gods in
the fourth page of a rhetorical declamation;
and once, as you know, when the pious.
sentence was omitted, a second communica-
tion was made to Parliament for the express
purpose of supplying it. All this formality
and pedantry indicates to my mind a
celestial monarchy, and naturally it re-
sembles all others: I mean that it rests.
more willingly on tradition and custom
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5
than on examination and reason. Never
did monarchy invite men to verify its cre-
dentials. As, however, yours is useful,
moral, and well adapted to you, you are not
revolted by it, but submit to it without
difficulty; at heart you are attached to it,
and would fear, in touching it, to upset the
constitution and morality. You ascribe this
dominion to the Most High amidst public
homage; you turn away and bring your-
selves down to matters of fact, to minute
dissections, to the operations of the labora-
tory. You betake yourselves to culling
plants and collecting shells.
deprived of its head and crown.
Science is
But all is
for the best, for practical life is benefited,
and dogma is preserved intact."
6
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}
III.
"You are truly French," said he; "you
stride over the facts, and with one bound
you are settled in a theory. You must
know that we do possess thinkers, and need
not go far from here to find them-at
Christ Church, for example. One of them,
the professor of Greek, has spoken so pro-
foundly on inspiration, the creation, and
final causes, as to have incurred persecution.
Look at this little collection which has
recently appeared-Essays and Reviews.
Your philosophic freedoms of the last cen-
tury, the latest conclusions of geology and
cosmogony, the
the intrepidities of German
exegesis, are here in abridgment. Some
things you will not find-the buffoonery of
Voltaire, the misty jargon of Germany, and
the prosaic coarseness of Comte. To my
mind the loss is small. Wait twenty years,
and you will find in London the ideas of
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ས་
Paris and Berlin."-"But they will still be
the ideas of Paris and Berlin. Whom have
"Who then
you original?"- "Stuart Mill."_"
is he?"-"A political writer. His little book
On Liberty is as admirable as the Social
Contract is abominable."-"That is a bold
assertion."-"Not so; for Mill decides as
strongly for the liberty of the individual,
as Rousseau for the despotism of the state."
"Very well; but that is not enough to
make up a philosopher. What more is he?"
"An economist, who raises himself above
his science, and subordinates production to
man, not man to production."-" Well; but
even that is not enough to make up a philo-
sopher. Is he anything else?"-"A logician."
-"Well; but of what school?"-" Of his
own. I told you he was original.”—“ Is he
Hegelian ?"-" Not at all. He is too fond of
facts and proofs."-" Is he a follower of Port
Royal?"-"Still less. He is too well ac-
quainted with modern science."-
"Is he an
imitator of Condillac ?"-" No, indeed. Con-
dillac has merely taught him to write well."
-"Who then are his allies?"-"Locke and
8
A STUDY ON MILL.
со
Comte in the first rank; then Hume and
Newton."" Is he a system-monger?-a
speculative reformer?"-"He has too much
sense for that. All he does is to construct the
best theories, and lay down the best practical
rules. He does not attitudinize majestically
in the character of a reformer of science; he
does not declare, like your Germans, that his
book is destined to inaugurate a new era
for the human race. He proceeds step by
step, slowly, and often creepingly, over a
multitude of particular facts. He excels in
giving precision to an idea; in disentangling
a principle; in tracing it through a number
of different facts; in refuting, in distin-
guishing, in reasoning. He has the astute-
ness, the patience, the method, and the
sagacity of a lawyer."
lawyer."-" Very well. You
admit I was right. A lawyer; an ally of
Locke, of Newton, of Comte, and of Hume;
all we have here is the English philosophy.
But no matter. Has he attained a great con-
ception of the universe?"-"Yes."" Has
he a complete personal idea of nature and of
the mind?" "Yes."-"Has he arranged the
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9
""
66
operations and discoveries of the intellect
under a single principle which puts them all
in a new light?"—"Yes. But this principle
has to be discovered."-"That is for you to
do, and I hope you will undertake it. But
we shall fall into abstract generalities."
"There is no harm in that."-" But this close
reasoning will be like a quick-set hedge."—
"We will prick our fingers with it."-" But
three men out of four cast aside such specu-
lations as idle."-" So much the worse for
them. For in what does the life of a nation
or an age consist except in the formation of
such theories? Man is but thoroughly man
when so engaged. If some inhabitant of
another planet were to descend here to ask us
the nature of our race, it would be necessary
to show him the five or six great ideas
which we have formed of the mind and of
the universe. That alone would give him
the measure of our intelligence. Explain
to me your theory, and I shall go away
better instructed than from having seen
the masses of brick you call London and
Manchester!
""
§ I.
ca
EXPERIENCE.
I.
LET us begin then, like logicians, at the
beginning. Mill has written on Logic.
What is Logic? It is a science, and has
for its subject all other sciences, for if we
have traversed the universe, and know
every part of it-stars, earth, sun, heat,
gravity, chemical affinities, the species of
minerals, geological changes, plants, animals,
human events, and all that classifications
and theories embrace and explain, there
still remain these classifications and these
theories to be learnt. Not only have we an
order of beings, but also an order of the
thoughts which represent them; not only
plants and animals, but also botany and
12
A STUDY ON MILL.
zoology; not only lines, surfaces, volumes,
and numbers, but also geometry and arith-
metic. Sciences, then, are things as real as
? facts themselves, and therefore as capable as
facts of becoming the subject of study. We
can analyse them as we analyse facts; we
can investigate their elements, their compo-
sition, their order, their relations, and their
object. There is, therefore, a science of
sciences, and this it is which we call logic,
and which forms the subject of Mill's work.
It is no part of logic to analyse the opera-
tions of the mind, memory, association of
ideas, external perception, &c., which belongs
to psychology; or to discuss the value of
such operations, the veracity of our con-
sciousness, the certainty of our elementary
knowledge, which belongs to metaphysics;
but we assume our faculties to be at work,
and admit their primary discoveries. We
take the instrument as nature furnishes it,
and trust to its accuracy. We leave to
others the task of taking its mechanism to
pieces, and the curiosity which criticises its
results. Setting out from its primitive
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13
operations, we enquire how they aid each
other, how they combine together, how one
is convertible into another, how, by addi-
tions, combinations, and conversions, they
finally make up a growing system of con-
nected truths. We construct a theory of
science, as others construct theories of vege-
tation, of the mind, or of numbers. Such is
the idea of logic; and it is plain that it has,
as other sciences, a real subject-matter, its
distinct province, an evident importance, its
proper method, and a certain future.
X
II.
L
THIS being premised, we observe that all
these sciences which form the subject of
logic are nothing more than collections of
✓ propositions; and all that each proposition
does is to connect or separate a subject and
an attribute—that is to say, a name and
another name; a quality and a substance-
that is to say, a thing and another thing.
We must consider, then, what it is we
understand by a thing, and what it is we
indicate by a name; in other words, what
it is we know in objects, what it is we con-
nect or separate, what it is that forms the
matter of all our propositions and all our
science. There is a point in which all our
several items of knowledge resemble one
another. There is a common element which,
by continued repetition, makes up all our
A STUDY ON MILL.
15
ideas. There is, as it were, a little primi-
tive crystal which, indefinitely and diversely
added to itself, forms the total mass, and
which once known, teaches us beforehand
the laws and the composition of the com-
plex bodies which it has formed.
Now, when we consider attentively the
idea we form of a thing, what do we find in
it? To commence with Substances-that is
to say, Bodies and Minds. This table is
* It is certain, then, that a part of our notion of a
body consists of the notion of a number of sensations of
our own, or of other sentient beings, habitually occur-
ring simultaneously. My conception of the table at
which I am writing is compounded of its visible form
and size, which are complex sensations of sight; its
tangible form and size, which are complex sensations of
our organs of touch and of our muscles; its weight,
which is also a sensation of touch and of the muscles;
its colour, which is a sensation of sight; its hardness,
which is a sensation of the muscles; its composition,
which is another word for all the varieties of sensa-
tion which we receive, under various circumstances
from the wood of which it is made; and so forth.
All or most of these various sensations frequently
are, and, as we learn by experience, always might
be, experienced simultaneously, or in many different
orders of succession, at our own choice and hence
the thought of any one of them makes us think
:
16
A STUDY ON MILL.
brown, and judging by the eye, it is three
feet in length, breadth, and height; which
means that it forms a little spot in the field
of vision; or, in other words, that it produces
a certain sensation on the optic nerve.
It
weighs ten pounds; which means, that to
lift it requires less effort than a weight of
eleven and greater than a weight of nine
pounds; or, in other words, that it produces
a certain muscular sensation. It is hard
and square; which again means that if first
pressed and then run over by the hand, it
will give rise to two different kinds of mus-
cular sensation; and so forth. On closely
examining what I know of it, I find nothing,
except the impressions it makes on me.
Our idea of a body comprises nothing more
than this: we know nothing of it but the
sensations it excites in us; we determine it
by the nature, number, and order of these
✓ sensations; we are ignorant of its inner
of the others, and the whole becomes mentally amalga-
mated into one mixed state of consciousness, which, in
the language of Locke and Hartley, is termed a Com-
plex Idea.—Vol. i., p. 62.
A STUDY ON MILL.
17
nature, if such there be; we affirm simply
that it is the unknown cause of these sen-
sations. When we say that a body has
existed in the absence of our sensations, all
we mean is, that if we had been within
range of it during the time in question,
we should have had sensations which we
have not had. We define it only by means
of our impressions, present or past, future
or possible, complex or simple. This is so
true that philosophers like Berkeley have
maintained with some show of truth that
matter is a creature of the imagination, and
that the whole world of sense is reducible to
an order of sensations. However this may
be, it is so, as far as our knowledge is con-
cerned ; and the judgments which make up
our sciences, refer merely to the impressions
by which things are manifested to us.
So again with the mind. We may readily
admit that there is in us a soul, an
66 ego,
a subject or recipient of our sensations and
other modes of being, and distinct from
those sensations and modes of being, but of
it we know nothing. All that we are aware
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18
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of, says Mill,* even in our own minds, is a
certain thread of consciousness, a series of
feelings—that is, of sensations, thoughts, emo-
tions, and volitions, more or less numerous
and complicated. We have no clearer
notion of mind than of matter, and can
affirm no more of it than of matter. So that
substances, of whatever kind, bodies or
minds, within us or without us, are never
*For, as our conception of a body is that of an un-
known exciting cause of sensations, so our conception of
a mind is that of an unknown recipient, or percipient, of
them; and not of them alone, but of all our other feel-
ings. As body is the mysterious something which excites
the mind to feel, so mind is the mysterious something
which feels, and thinks. It is unnecessary to give in the
case of mind, as we gave in the case of matter, a particular
statement of the sceptical system by which its existence
as a Thing in itself, distinct from the series of what are
denominated its states, is called in question. But it is
necessary to remark, that on the inmost nature of the
thinking principle, as well as on the inmost nature of
matter, we are, and with our faculties must always
All which we are aware
remain, entirely in the dark.
of, even in our own minds, is (in the words of Mr.
Mill) a certain "thread of consciousness;" a series of
feelings, that is, of sensations, thoughts, emotions, and
volitions, more or less numerous and complicated.-
Vol. i., p. 68.
A STUDY ON MILL.
19
anore to us than tissues, more or less complex,
more or less regular, of which our feelings
and modes of being form all the threads.
This is even clearer in the case of attri-
butes than of substances. We say that snow
is white, meaning that when in sight of
snow we have the sensation of whiteness.
We say that fire is hot, meaning that when
near the fire we have the sensation of heat.
We call a mind devout, superstitious, medi-
tative, or gay, simply meaning that the ideas,
the emotions, the volitions, designated by
these words, recur frequently in the series of
its modes of being.*
* Every attribute of mind consists either in being
itself affected in a certain way, or affecting other minds
in a certain way. Considered in itself, we can predicate
nothing of it but the series of its own feelings. When
we say of any mind, that it is devout, or superstitious,
or meditative, or cheerful, we mean that the ideas,
emotions, or volitions, implied in those words, form a
frequently recurring part of the series of feelings, or
states of consciousness, which fill up the sentient exis-
tence of that mind.
In addition, however, to those attributes of a mind
which are grounded on its own states of feeling, attri-
butes may also be ascribed to it, in the same manner
0 2
20
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>
Again, we call bodies heavy, divisible,
moveable, &c., meaning that when let go
they will fall, when cut they will separate,
when pushed they will move,-in other
words, that under such and such circum-
as to a body, grounded on the feelings which it excites
in other minds. A mind does not, indeed, like a body,
excite sensations, but it may excite thoughts or emo-
tions. The most important example of attributes
ascribed on this ground, is the employment of terms
expressive of approbation or blame. When, for ex-
ample, we say of any character, or (in other words) of
any mind, that it is admirable, we mean that the con-
templation of it excites the sentiment of admiration ;
and, indeed somewhat more, for the word implies that
we not only feel admiration, but approve that senti-
ment in ourselves. In some cases, under the sem-
blance of a single attribute, two are really predicated:
one of them, a state of the mind itself; the other, a
state with which other minds are affected by thinking
of it. As when we say of any one that he is generous.
The word generosity expresses a certain state of mind,
but being a term of praise, it also expresses that this
state of mind excites in us another mental state, called
approbation. The assertion made, therefore, is twofold,
and of the following purport: Certain feelings form
habitually a part of this person's sentient existence ;
and the idea of those feelings of his, excites the senti-
ment of approbation in ourselves or others.-Vol. i.,
p. 80,
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21
1
stances they will produce such and such
feelings in our muscles, or our sight. An
attribute invariably marks some one, or
some series of our modes of being. In vain
do we disguise these modes of being, by
hiding them under abstract names, by
grouping, dividing, and transforming them,
till we can sometimes scarcely recognise
them. We still find them, and find nothing
but them, whenever we examine our words
and ideas with sufficient minuteness. Ana-
lyse, says Mill, an abstract proposition—
for example, a generous person is worthy
of honour. The word generous denotes
* Take the following example: A generous person
is worthy of honour. Who would expect to recognise
here a case of co-existence between phenomena? But
so it is.
The attribute which causes a person to be
termed generous, is ascribed to him on the ground of
states of his mind, and particulars of his conduct : both
are phenomena; the former are facts of internal con-
sciousness, the latter, so far as distinct from the former,
are physical facts, or perceptions of the senses. Worthy
of honour, admits a similar analysis. Honour, as here
used, means a state of approving and admiring emotion,
followed on occasion by corresponding outward acts.
Worthy of honour" commotes all this, together with
..66
✓
22
A STUDY ON MILL.
certain habitual states of mind and certain
habitual particularities of conduct--that is
to say, internal modes of being and external
sensible facts. The word honour expresses
a sentiment of approbation and admiration,
followed on occasion by corresponding out-
ward acts. The word worthy indicates that
we approve of the act of showing honour.
All these are phenomena or states of mind
followed or accompanied by physical facts.
We may turn about then as we please, but
shall still find ourselves in the same circle.
Whether the object of thought be attribute
or substance, concrete or abstract, compound
or simple, its material is to us the same-it
an approval of the act of showing honour. All these
are phenomena; states of internal consciousness, accom-
panied or followed by physical facts.
When we say,
A generous person is worthy of honour, we affirm co-
existence between the two complicated phenomena
connoted by the two terms respectively. We affirm
that wherever and whenever the inward feelings and
outward facts implied in the word generosity have
place, then and there the existence and manifestation
of an inward feeling, honour, would be followed in our
minds by another inward feeling, approval.-Vol. i.„
P. 110.
A STUDY ON MILL.
23
is made up of our modes of being only.
Our mind is to nature what a thermometer
is to a boiler: we define the properties of
nature by the feelings of our mind as we
indicate states of heat by the variations
of the thermometer. We know nothing of
one or of the other but states and changes;
we make up the one and the other of iso-
lated and transient facts; a thing is nothing
more to us than a collection of phenomena.
These are the only elements of our know-
ledge; and in every case every effort of
science must be the addition or connection
of fact to fact.
III.
THIS little phrase sums up the whole system.
Familiarise yourself with it, for it explains
all Mill's theories. His definitions and
his innovations commence alike from this
starting-point. In all forms and degrees of
knowledge, he has recognised the knowledge
only of facts, and of their relations.
Now logic, as you know, has two corner-
stones, the Theories of Definition and of
Proof. Since the days of Aristotle, logi-
cians have passed their time in polishing
them. They have only dared to touch
them respectfully, as if they were holy.
The utmost that any innovator has occa-
sionally ventured on, has been to turn them
carefully in order to put them in a better
light. Mill overturns, cuts, pares away,
and replaces them both in a similar manner,
and by the same means.
IV.
I AM quite aware that people are laughed
at now-a-days for reasoning on definitions ;
but you,
I hope, are not guilty of this
absurdity. No theory is more fruitful in
universal and important consequences; it
is the root by which the tree of science.
grows and lives. For in defining things
we mark out their nature. To introduce a
new idea of definition is to introduce a new
idea of the nature of things, of what beings
are, of what they are composed, and of the
elements into which they are capable of
being resolved. In this lies the merit of
these dry speculations; the philosopher
seems occupied with matters of mere con-
vention, while, in fact, he is mapping out
the universe.
Take, say logicians, an animal, a plant,
a sentiment, a geometrical figure, an object
26
A STUDY ON MILL.
or a group of objects. No doubt the object
has its properties, but it has also its essence.
It manifests itself to the outer world by an
indefinite number of effects and qualities;
but all these modes of being are the con-
sequences or the results of its inner nature.
There is in it a certain hidden substratum
which alone is primitive and important,
without which it can neither exist nor be
conceived, and which constitutes its being
and our notion of it. * Definitions they
consider to be propositions denoting this
essence, and assert that such propositions.
constitute the most valuable part of our
knowledge. Mill, on the contrary, holds
that propositions of this kind teach us
nothing; they acquaint us with the mean-
ing of a word, and are simply verbal.t
*According to the idealist school of logicians, we
discover this being by examining our notion of it; and
the idea, on analysis, shows us the essence. According
to the classifying school, we arrive at the being by
placing the object in its group, and define the notion by
stating the genus and the difference. Both agree that
we are capable of arriving at the essence.
An essential proposition, then, is one which is
A STUDY ON MILL.
27
What do I learn by being told that man
is a reasonable animal, or that a triangle is
a space contained by three lines? The first
part of such a phrase expresses by an
abbreviation what the second part expresses
in a developed phrase. You tell me the
same thing twice-you put the same fact
into two different expressions-you do not
add one fact to another, but a fact to its
equivalent; your proposition is not in-
structive-you might collect a million such,
and my mind would remain completely
empty-I should have read a dictionary,
but not have acquired a single piece of
knowledge. They tell us that essential
propositions are important, and those con-
purely verbal; which asserts of a thing under a parti-
cular name, only what is asserted of it in the fact of
calling it by that name; and which therefore either
gives no information, or gives it respecting the name,
not the thing. Non-essential, or accidental propositions,
on the contrary, may be called real propositions, in
opposition to verbal. They predicate of a thing, some
fact not involved in the signification of the name by
which the proposition speaks of it; some attribute not
connoted by that name.-Vol. i., p. 127.
28
A STUDY ON MILL.
cerning qualities merely accessory; but the
contrary is the truth, for propositions re-
lating to qualities are the important ones,
and the others merely accessory. I learn
nothing by being told that a circle is
a figure formed by the revolution of a
straight line about one of its points as
centre; I learn a fact when told that the
chords which subtend equal arcs of the
circle are themselves equal, or that three
given points are sufficient to determine the
circumference. What we call the nature of
a being is the connected system of facts
which make up that being. The nature of
a carnivorous mammal consists in the com-
bination of the property of giving milk, and
all its implied peculiarities of structure, with
sharp teeth, with hunting instincts, and
the corresponding faculties. Such are the
elements which compose its nature. They
are facts linked together as mesh to mesh
in a net. Some of them we perceive, but
we can also see that far beyond our pre-
sent knowledge and future experience, the
net extends to infinity its multiplied and
A STUDY ON MILL.
29*
1
interlacing threads. The essence or nature
of a being is the indefinite sum of its pro-
perties. "No definition," says Mill, "ex-
presses this nature in all its entirety, and
every proposition expresses some part of
this nature." Give up, then, the vain hope
of eliminating from properties a primitive
and mysterious being, the source and sum-
mary of the whole-leave entities to Duns
Scotus; do not imagine that either the
examination of your ideas in the German
fashion, or the classification of objects ac-
cording to genera and species in the manner
of the schoolmen-that the revival of the
nominal science of the Middle Ages, or the
riddles of Hegelian metaphysics—will ever
* The definition, they say, unfolds the nature of
the thing but no definition can unfold its whole
nature; and every proposition in which any quality
whatever is predicated of the thing, unfolds some part
of its nature. The true state of the case we take to be
this. All definitions are of names, and of names only;
but, in some definitions, it is clearly apparent, that
nothing is intended except to explain the meaning of the
word; while in others, besides explaining the meaning of
the word, it is intended to be implied that there exists
a thing, corresponding to the word.-Vol. i., p. 162.
30
A STUDY ON MILL.
enable you to dispense with experience. There
are no definitions of things; what definitions.
there are define names only. No phrase can
tell me what a horse is, but there are phrases
which will inform me what is meant by
these five letters. No phrase can exhaust
the inexhaustible sum of the qualities which
make up a being, but many phrases point
out the facts which correspond to a word.
Here definition is possible, for an analysis
may always be made which will enable us
to pass from the abstract and summary
term to the attributes which it represents,
and from these attributes to the feelings,
whether internal, or of the senses which
serve for their foundation. By it, we pass
from the term dog to the attributes mammi-
ferous, carnivorous, &c., which it represents;
and from these to the sensations of sight, of
the touch, of the scalpel on which they are
founded. It reduces the compound to the
simple, the derived to the primitive. It
brings back our knowledge to its origin.
It transforms words into facts. If some
definitions, like those of geometry, seem
A STUDY ON MILL.
31
capable of giving rise to long sequences of
new truth, it is through their comprising
the affirination of a fact in addition to the
explanation of a word. In the definition of
a triangle there are two distinct proposi-
tions: the one stating that there may exist
a figure bounded by three straight lines,
the other that such a figure is called a
triangle; the first is a postulate, the second
a definition. The first is hidden, the second
lies on the surface. The first may be true.
or false, the second is not susceptible of
either truth or falsehood. The first is the
source of all possible theorems as to triangles,
* The definition above given of a triangle, obviously
comprises not one, but two propositions, perfectly dis-
tinguishable. The one is, "There may exist a figure,
bounded by three straight lines" the other, "And
this figure may be termed a triangle." The former of
these propositions is not a definition at all: the latter
is a mere nominal definition, or explanation of the use
and application of a term. The first is susceptible of
truth or falsehood, and may therefore be made the
foundation of a train of reasoning: the latter can
neither be true nor false; the only character it is sus-
ceptible of is that of conformity to the ordinary usage
of language.-Vol. i., p. 162.
32
A STUDY ON MILL.
the second does but resume in a word the
facts contained in the other. The first is a
truth, the second a convention; the first a
part of science, the second an expedient of
language. The first expresses a possible
relation between three straight lines, the
'second names this relation; the first alone
is fruitful, for it alone conforms to the
nature of fruitful propositions and connects
two facts. Let us, then, understand exactly
the nature of our knowledge: it relates
either to words, or to things, or to both at
once. If it relates to words, as in defini-
tions of names, it attempts to refer back
from the words to our primitive feelings;
that is to say, to the facts which constitute
their elements. If it relates to beings, as
in propositions about things, it attempts to
link fact to fact, to connect the finite
number of known properties with the in-
finite number of properties to be known.
If both are involved, as in the above-
mentioned definition of names, which con-
ceal (as it were) a proposition relating to a
thing, it attempts to do both, but to do no
A STUDY ON MILL.
33
co
more. Its operation is everywhere the same.
In every case it is either a matter of expla-
nation—that is, of reverting to the facts; or
of teaching—that is, of the connection of
facts.
V.
THE first rampart, then, is destroyed; I
suppose you will await our philosopher
behind the second-the Theory of Proof.
This theory has for two thousand years
passed for an acquired, definite, impregnable
truth. Many have pronounced it useless,
but no one has ventured to question its
truth. It has been considered on all sides
as an established theorem.
Well, let us examine it.
What is a
proof? According to logicians it is a syllo-
gism, and a syllogism is a group of three
propositions of this kind :-
All men are mortal ;
Prince Albert is a man ;
Therefore Prince Albert is mortal.
Here we have the type of a proof, and
every complete proof is conformable to this
A STUDY ON MILL.
35
type. Now, what is there, according to
logicians, in this proof? A general propo-
sition concerning all men which gives rise
to a particular proposition concerning a
certain man.
We pass from the first to the
second, because the second is contained in
the first; from the general to the particular,
because the particular is comprised in the
general. The second is but an instance of
the first; its truth is contained beforehand
in the truth of the first; and it is for this
reason that it is a truth. In fact, when the
conclusion is no longer contained in the
premises, the reasoning is false; and all the
complicated rules of the Middle Ages have
been reduced by the Port Royalists to this
single rule, "The conclusion must be con-
tained in the premises." Thus the course
of the human mind in its reasonings, con-
sists in recognising in the individual that
which is known of the class; in affirming in
detail what has been established in general;
in stating a second time, and instance by
instance, that which has been stated once
for all at first.
D 2
36
A STUDY ON MILL.
Not at all, says Mill, for if so, our reason-
ing is useless. It is not a progress, but a
repetition. When I have affirmed that all
men are mortal, I have thereby affirmed
that Prince Albert is mortal. In speaking
of the whole class—that is to say, of all, the
individuals of the class-I have spoken of
each individual, and therefore of Prince
Albert, who is one of them. I say nothing
new, then, when I now speak expressly of
him. My conclusion teaches me nothing; it
adds nothing to my positive knowledge; it
does but put in a new form a piece of
knowledge which I already possessed; it is
not fruitful, it is purely verbal. If, then,
reasoning be what logicians represent it,
reasoning is not instructive; I know as
much of the subject before commencing
my reasoning as after I have finished it.
I have transformed words into other words;
I have manœuvred without gaining ground.
But this cannot be, for reasoning does, in
fact, teach us new truths. I learn a new
truth when I discover that Prince Albert is
mortal, and I discover it by reasoning, for
A STUDY ON MILL.
37
since he is still alive I cannot have learnt it
by direct observation. Thus logicians are
wrong, and we must abandon this scholastic
theory of the syllogism which reduces
reasoning to substitutions of words, and
seek for a positive theory of proof which
will explain how it is that, by the process of
reasoning, we discover facts. For this pur-
pose, it is sufficient to observe that general
propositions are not the true proof of par-
ticular propositions. They seem so, but are
not. It is not from the mortality of all
men that I conclude Prince Albert to be
mortal—the premises are elsewhere, and in
the background. The general proposition
is but a memento, a sort of abbreviating
register, to which I have consigned the
results of my experience. This memento.
may be considered as a note-book to which
we refer to refresh our memory; our know-
ledge does not come from the book, but
from what we have seen. The whole value
of our notes is derived from the facts
they recall. My general proposition has no
value except from the particular facts which
38
A STUDY ON MILL.
it sums up. "The mortality of John, Thomas,
and Company is, after all, the whole evidence
which we have for the mortality of Prince
Albert."-"The true reason which makes
us believe that Prince Albert will die is,
that his ancestors, and our ancestors, and all
the other persons who were their contem-
poraries, are dead. These facts are the true
premises of our reasoning." It is from them
that we have gathered the general proposi-
tion; they have taught us its extent and
its truth; its office is limited to mentioning
them in a shorter form; it derives all its
* The mortality of John, Thomas, and Company is,
after all, the whole evidence we have for the mortality
of the Duke of Wellington. Not one iota is added to
the proof by interpolating a general proposition. Since
the individual cases are all the evidence we can possess,
evidence which no logical form into which we choose to
throw it can make greater than it is; and since that
evidence is either sufficient in itself, or, if insufficient
for the one purpose, cannot be sufficient for the other;
I am unable to see why we should be forbidden to take
the shortest cut from these sufficient premises to the
conclusion, and constrained to travel the "high priori
road" by the arbitrary fiat of logicians.-Vol. i.,
p. 211.
A STUDY ON MILL.
39
substance from them; they are acting
through it and by it to lead us to the con-
clusion to which it apparently gives rise.
It is but their representative, and on occa-
sion they dispense with it. Children, igno-
rant persons, and animals know that the
sun will rise, that water will drown them,
that fire will burn them, without the aid of
a general proposition. They reason, and
we, too, frequently reason, not from the
general to the particular, but from parti-
cular to particular. "The mind always
passes from observed to unobserved cases,
either with or without commemorative
formulæ. We only employ them for conve-
nience."* "If we had a sufficiently capacious
*All inference is from particulars to particulars:
general propositions are merely registers of such infer-
ences already made, and short formulæ for making
more: the major premiss of a syllogism, consequently,
is a formula of this description: and the conclusion is
not an inference drawn from the formula, but an infer-
ence drawn according to the formula: the real logical
antecedent, or premise, being the particular facts from
which the general proposition was collected by induc-
tion. Those facts, and the individual instances which
40
A STUDY ON MILL.
memory, and the faculty of maintaining
order among a huge mass of details, we
should be able to reason without employing
a single general proposition."* Here, as
before, logicians have blundered; they have
given the highest rank to verbal propositions,
and left the really fruitful operations in the
background. They have given precedence
to words over facts. They have kept alive
the nominal science of the Middle Ages.
They have mistaken the explanation of
names for the nature of things, and the
supplied them, may have been forgotten; but a record
remains, not indeed descriptive of the facts themselves,
but showing how those cases may be distinguished
respecting which the facts, when known, were con-
sidered to warrant a given inference. According to
the indications of this record we draw our conclusion;
which is, to all intents and purposes, a conclusion from
the forgotten facts. For this it is essential that we
should read the record correctly and the rules of the
syllogism are a set of precautions to ensure our doing
so.—Vol. i., p. 218.
* If we had sufficiently capacious memories, and a
sufficient power of maintaining order among a huge
mass of details, the reasoning could go on without
any general propositions; they are mere formulæ for
inferring particulars from particulars.—Vol. i., p. 240.
A STUDY ON MILL.
41
transformation of ideas for the progress of
the mind. We must upset this in logic as
we have upset it in science—we must exalt
the particular and instructive facts, and
give them that authority and importance in
theory which our practice has conferred on
them for the last three hundred years.
VI.
A PHILOSOPHICAL fortress remains in which
Idealists shelter themselves. At the origin
of all proof are Axioms, from which all proof
is derived. Two straight lines cannot enclose
a space; things which are equal to the same
thing are equal to one another; if equals
be added to equals the wholes are equal.
These propositions are instructive, for they
express, not meanings of words, but rela-
tions of things; and moreover, they are
fruitful, for the sciences of arithmetic, al-
gebra, and geometry are derived from their
truth. On the other hand, they are not
founded on experience, for we know that
two straight lines cannot enclose a space
from our mental conception of them without
the necessity of actually following them
with our eyes. For this purpose we do not
A STUDY ON MILL.
43
require the evidence of our senses,―our
belief arises wholly and with full force from
the simple comparison of our ideas. Besides,
experience does not follow our two lines
for more than a limited distance-for ten,
twenty, or a thousand feet; and the axiom
is true for a thousand, ten thousand, or a
million miles, and for an unlimited distance.
So that, beyond the point at which expe-
rience ceases, it cannot be experience that
establishes the axiom. Finally, the axiom
is a necessary truth-that is to say, its
contrary is inconceivable. We cannot ima-
gine a space enclosed by two straight
lines; for as soon as we imagine a space
to be enclosed, the two lines cease to be
straight; and as soon as we imagine the two
lines to be straight, the space ceases to be
enclosed. In the assertion of axioms, the
two constituent ideas are inevitably con-
nected. In the negation of axioms, the two
constituent ideas inevitably repel each other.
Now this is not so with truths of experience;
they state an accidental, not a necessary
connection; they lay down the connection of
1
44
A STUDY ON MILL.
certain facts, not that they must be con-
nected; they show us that bodies are heavy,
not that they are necessarily heavy. Thus,
axioms are not and cannot be the results of
experience. They are not so, because we
can form them mentally without the aid of
experience; they cannot be so, because the
nature and range of their truths lie with-
out the limits of experimental truths. They
have another and a deeper source. They
spring elsewhere, and have a wider scope.
Not so, answers Mill. Here again you
reason scholastically, and overlook the facts
hidden behind your conceptions; for con-
sider your first argument.
first argument. No doubt you
can discover, without employing your eyes,
and by purely mental contemplation, that
two straight lines cannot enclose a space,
but this contemplation is but a displaced
experiment in which imaginary lines take
the place of real lines, and you construct a
figure in your mind instead of on paper.
Your imagination fulfils the office of a dia-
gram on paper. You trust to it as you would
to the diagram, and it answers equally
A STUDY ON MILL.
45
well, for, in the matter of figures and lines,
the imagination exactly reproduces the sen-
sation. What you have seen with your
eyes open, you will see again in a precisely
similar manner a moment afterwards with
your eyes closed, and you can study geome-
trical properties transferred to the field of
mental sight as accurately as in the field of
actual sight. There are, then, mental experi-
ments as there are ocular ones, and it is
after such an experiment that you deny to
two straight lines, even when prolonged to in-
finity, the property of enclosing a space. For
this purpose, there is no need to follow the
lines to infinity-you have merely to imagine
yourself at the point where they converge,
and there you have the impression of a
bent line—that is, of one which is no longer
straight. Your
Your presence there in imagina-
*For though, in order actually to see that two
given lines never meet, it would be necessary to follow
them to infinity; yet without doing so we may know
that if they ever do meet, or if, after diverging from
one another, they begin again to approach, this must
take place not at an infinite, but at a finite distance.
Supposing, therefore, such to be the case, we can
46
A STUDY ON MILL.
tion is equivalent to your actual presence;
and you can affirm by it as much, and as
positively, as your actual presence would have
enabled you to do. The first amounts to the
second in a more manageable form, with
greater range and flexibility; it is like using
a telescope in place of the naked eye; and,
as the evidence of the telescope gives rise to
propositions of experience, so will the evi-
dence of the imagination.
Again, the argument distinguishing
axioms from propositions of experience, on
the ground that the contraries of the latter
are conceivable while the contraries of
transport ourselves thither in imagination, and can
frame a mental image of the appearance which one or
both of the lines must present at that point, which we
may rely on as being precisely similar to the reality.
Now, whether we fix our contemplation upon this
imaginary picture, or call to mind the generalizations
we have had occasion to make from former ocular
observation, we learn by the evidence of experience,
that a line which, after diverging from another straight
line, begins to approach to it, produces the impression
on our senses which we describe by the expression,
"a bent line," not by the expression, "a straight
line."--Vol. i.,
p. 264.
A STUDY ON MILL.
47
axioms are inconceivable, is nugatory, for
there is no such distinction. There is
nothing to prevent the contraries of certain
propositions of experience being conceivable,
and the contraries of others inconceivable.
It depends on the constitution of our minds.
It is possible that the mind may sometimes
be able to contradict its experience, and
sometimes not. It is possible that our con-
ceptions may sometimes differ from our
perceptions, and sometimes not. It is pos-
sible that external sight may sometimes
be opposed to internal, and sometimes not.
Now, we have seen that, in the case of
figures, our mental sight exactly reproduces
our actual sight. Therefore, in axioms of
figure, the mental sight cannot be opposed
to the actual; imagination cannot contra-
dict sensation. In other words, the con-
traries of such axioms will be inconceivable.
Thus axioms, even though their contraries
be inconceivable, are a kind of experimental
truths; and it is on account of their being
experimental truths that their contraries
are inconceivable. At every point this
48
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conclusion, the abridgment of the system,
presents itself:—that every instructive or
fruitful proposition is derived from expe-
rience, and is nothing but a connecting
together of facts.
VIL
HENCE it follows that Induction is the sole -
key to nature. This theory is Mill's master-
piece. No one but so thorough-going
partisan of experience could have con-
structed the theory of Induction. What,
then, is Induction? It is the operation
which discovers and proves general pro-
positions. It is the process by which we
conclude that what is true of certain indi-
viduals of a class is true of all the class, or
that what is true at a particular time will
be true at all times, under similar circum-
stances.* It is the reasoning by which we
* Induction, then, is that operation of the mind, by
which we infer that what we know to be true in a
particular case or cases, will be true in all cases which
resemble the former in certain assignable respects. In
other words, Induction is the process by which we
E
50
A STUDY ON MILL.
conclude that all men will die, from having
observed that Peter, John, and a greater or
less number of men, have died. In short,
induction connects mortality with the
quality of man; that is to say, connects two
general facts found to be successive, and
asserts that one of them is the Cause of the
other.
This amounts to saying that the course
of nature is uniform. But induction does
not set out from this axiom, but leads us
up to it; we do not find it at the com-
mencement, but at the conclusion of our
researches.* At starting, experience pre-
conclude that what is true of certain individuals of a
class is true of the whole class, or that what is true at
certain times will be true in similar circumstances at
all times.-Vol. i., p. 315.
*We must first observe, that there is a principle
implied in the very statement of what Induction is;
an assumption with regard to the course of nature and
the order of the universe: namely, that there are such
things in nature as parallel cases; that what happens
once, will, under a sufficient degree of similarity of
circumstances, happen again, and not only again, but
as often as the same circumstances recur. This, I say,
is an assumption, involved in every case of induction.
A STUDY ON MILL.
51
supposes nothing beyond itself. No à priori
principle comes to authorise or guide her.
We observe that this stone has fallen, that
this coal has burnt us, that this man is
dead, and we have no other means of per-
forming induction than the collection and
comparison of these little isolated and
transient facts. Simple practical experience
shows us that the sun gives light, that
bodies fall, that water quenches thirst, and
we have no other means of extending or
criticising these inductions than by other
similar inductions. Each observation and
each induction derives its value from itself,
and from similar ones. Experience is in-
variably the test of experience, and induc-
tion the test of induction.
The body of our knowledge has not, then,
a soul distinct from it, and vivifying it; it
And, if we consult the actual course of nature, we find
that the assumption is warranted. The universe, so
far as known to us, is so constituted, that whatever is
true in any one case, is true in all cases of a certain
description; the only difficulty is, to find what
description.-Vol. i., p. 337.
E 2
52
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subsists by the harmony of its parts taken
as a whole, and by the vitality of each part
taken separately. We should disbelieve a
traveller who told us of men with heads
underneath their shoulders, but we should
not refuse to believe a traveller who said
that there were black swans, and yet our
experience is the same in the two cases. We
have never seen any but white swans, and
have never seen men with their heads else-
where than on their shoulders. How comes
it, then, that the second testimony appears
more credible to us than the first? "Appa-
rently because there is less constancy in
the colours of animals, than in their general
anatomical structure. But how do we know
this? Evidently by experience.* It appears,
* Why is it that, with exactly the same amount of
evidence, both negative and positive, we did not reject
the assertion that there are black swans, while we
should refuse credence to any testimony which asserted
that there were men wearing their heads underneath
their shoulders? The first assertion was more credible
than the latter. But why more credible? So long as
neither phenomenon had been actually witnessed, what
reason was there for finding the one harder to be
A STUDY ON MILL.
53
then, that we have need of experience to
inform us in what degree, in what cases or
sorts of cases, experience is to be relied on.
Experience must be consulted in order to
learn under what circumstances arguments
from it will be valid. We have no ulterior
test to which we can subject experience in
general, but we make experience its own
test." Experience is all we have and all we
can have.
believed than the other? Apparently because there
is less constancy in the colours of animals, than in the
general structure of their internal anatomy. But how
do we know this? Doubtless, from experience. It
appears, then, that we need experience to inform us,
in what degree, and in what cases, or sorts of cases,
experience is to be relied on. Experience must be
consulted in order to learn from it under what circum-
stances arguments from it will be valid. We have no
ulterior test to which we subject experience in general;
but we make experience its own test. Experience
testifies, that among the uniformities which it exhibits
or seems to exhibit, some are more to be relied on
than others; and uniformity, therefore, may be pre-
sumed, from any given number of instances, with a
greater degree of assurance, in proportion as the case
belongs to a class in which the uniformities have
hitherto been found more uniform.-Vol. i., p. 351.
54
A STUDY ON MILL.
!
Let us then consider how it is that, by
experience alone, we are able to form general
propositions, and especially those, the most
numerous and most important of all, which
connect two successive events, by saying that
the first is the cause of the second.
We have here a great word, Cause; let us
examine it. It comprises a whole philosophy
in itself. From the notion we have of Cause
depend all our notions of nature. To give a
new idea of Causation is to give a new form
to human thought; and we shall see how
Mill, like Comte and Hume, but better than
either of them, has put this idea into a new
shape.
What, then, is a cause? When Mill says
that the contact of iron with moist air pro-
duces rust, or that heat dilates bodies, he
does not speak of the mysterious link by
which metaphysicians connect cause and
effect. He does not busy himself with the
intimate force or generative virtue which
certain philosophers insert between the thing
producing and the product.
"The only
notion," he says, "of which induction has
A STUDY ON MILL.
55
need, may be attained by experience. We
learn by experience that there is in nature an
invariable order of succession, and that each
fact is always preceded by another fact. We
call the invariable antecedent, cause, and
the invariable consequent, effect."* No other
foundation underlies these two words. We
wish simply to say that at every time, and
place, the contact of iron with moisture will
be followed by the appearance of rust; the
application of heat by the dilation of bodies.
"The real cause is the series of conditions-
the whole of the antecedents without which
the effect would not arrive.t
There is
* The only notion of a cause, which the theory of
induction requires, is such a notion as can be gained
from experience. The Law of Causation, the recog-
nition of which is the main pillar of inductive science,
is but the familiar truth, that invariability of succes-
sion is found by observation to obtain between every
fact in nature and some other fact which has preceded
it; independently of all consideration respecting the
ulterior mode of production of phenomena, and of
every other question regarding the nature of "Things
in themselves.”—Vol. i., p. 359.
+ The real Cause, is the whole of these antecedents.-
Vol. i., p. 360.
56
A STUDY ON MILL.
no scientific foundation for distinguishing
between the cause of a phenomenon and the
conditions of its happening.
The
distinction drawn between the patient and
the agent is purely verbal.
The
cause is the sum of negative and positive
conditions taken together; the whole of
the circumstances and contingencies of
every kind, which, once given, are in-
variably followed by the consequence."*
Much argument has been expended on the
word necessary.
"That which is necessary,
that which cannot but be, is that which will
happen, whatever suppositions may be made
about other things." That is all we mean
by saying that the notion of cause includes
* The cause, then, philosophically speaking, is the
sum total of the conditions, positive and negative, taken
together; the whole of the contingencies of every
description, which being realised, the consequent
invariably follows.-Vol. i., p. 365.
+ If there be any meaning which confessedly belongs
to the term necessity, it is unconditionalness. That
which is necessary, that which must be, means that
which will be, whatever supposition we may make in
regard to all other things.-Vol. i., p. 372.
A STUDY ON MILL.
57
that of necessity. We mean that the ante-
cedent is sufficient and complete, that there
is no need to suppose any additional antece-
dent, that all requisite conditions are con-
tained in it, and that no other condition
need exist. To follow unconditionally, then,
is the whole notion of cause and effect. We
can attain no other. Philosophers are mis-
taken when they discover in our will a
different type of causation, and give it as an
example of efficient cause in act and in
exercise. Nothing of the sort is to be found
there, but there, as elsewhere, we find constant
successions only. We do not find fact engen-
dering fact, but fact accompanying fact. "Our
will produces our bodily actions as cold pro-
duces ice, or as a spark produces an explosion
of gunpowder." There, as elsewhere, we find
an antecedent-the resolution or state of
mind, and a consequent-the effort or phy-
sical sensation. Experience connects them,
and enables us to foresee that the effort will
follow the resolution, just as it enables us to
foresee that the explosion of gunpowder will
follow the contact of the spark. Let us give
58
A STUDY ON MILL.
t
up, then, all psychological illusions, and seek
only, under the names of cause and effect, for
phenomena which form pairs without ex-
ception or condition.
Now, Mill discovers four, and only four,
methods for the establishment of these con-
nections of phenomena; namely, the Methods
✔of Agreement, of Difference, of Residues, and
of Concomitant Variations. These are the
only means by which we can penetrate into
nature. There are no other, and these pre-
vail in every direction. And all of them
employ the same artifice; that is to say,
elimination-for induction is, in fact, nothing
more than this. You have two groups, one
of antecedents, and one of consequents, each
of them containing more or less elements-
ten, for example. To what antecedent is each
consequent joined? Is the first consequent
joined to the first antecedent, or to the third,
or sixth? All the difficulty and the only
possible solution lie here. To resolve the
difficulty, and effect the solution, elimination
is required, that is to say-the exclusion of
those antecedents which are not connected
A STUDY ON MILL.
59
with the consequent we are considering. But
as we are not able actually to exclude them,
and as in nature the pair of phenomena we are
seeking is always surrounded with circum-
stances, we collect different cases, which, by
their diversity, enable us mentally to clear
away those circumstances, and discover the
pair we are in search of. In short, we can
only perform induction by discovering pairs
of phenomena; we can only form these pairs
by elimination; we can only eliminate by
means of comparisons.
On the Four Methods of Experimental Inquiry.
If we take fifty crucibles of molten matter and let
them cool, and fifty solutions and let them evaporate,
all will crystallize. Sulphur, sugar, alum, salt,-sub-
stances, temperatures, circumstances-all are as different
as they can be. We find one, and only one, common
fact-the change from the liquid to the solid state—and
conclude, therefore, that this change is the invariable
antecedent of crystallization. Here we have an
example of the Method of Agreement. Its canon is :—
"I. If two or more instances of the phenomenon
under investigation have only one circumstance in
common, the circumstance in which alone all the
instances agree, is the cause (or effect) of the given
phenomenon."-Vol. i., p. 422.
60
A STUDY ON MILL.
A bird in the air breathes; plunged into carbonic
acid gas, it ceases to breathe. In other words,
in the second case, suffocation ensues. In other
respects the two cases are as similar as possible,
since we have the same bird in both, and they take
place in immediate succession. They differ only in
the circumstance of immersion in carbonic acid gas
being substituted for immersion in the atmosphere,
and we conclude that this circumstance is invariably
followed by suffocation. The Method of Difference is
here employed.
Its canon is :-
“II. If an instance in which the phenomenon under
investigation occurs, and an instance in which it does not
occur, have every circumstance in common save one,
that one occurring only in the former; the circumstance
in which alone the two instances differ, is the effect, or
the cause, or a necessary part of the cause, of the
phenomenon."-Vol. i., p. 423.
[A combination of these methods is sometimes em-
ployed, and is termed the Indirect Method of Difference,
or the Joint Method of Agreement and Difference. It
is, in fact, a double employment of the Method of
Agreement, first applying that method to instances in
which the phenomenon in question occurs, and then
to instances in which it does not occur. The following
is its canon :—-
'III. If two or more instances in which the pheno-
menon occurs have only one circumstance in common,
while two or more instances in which it does not
occur have nothing in common, save the absence of
A STUDY ON MILL.
61
that circumstance; the circumstance in which alone the
two sets of instances differ, is the effect, or the cause,
or a necessary part of the cause, of the phenomenon."]
-Vol. i., p. 429.
If we take two groups-one of antecedents and one
of consequents and can succeed in connecting by
previous investigations all the antecedents but one to
their respective consequents, and all the consequents
but one to their respective antecedents, we conclude
that the remaining antecedent is connected to the
remaining consequent. For example, scientific men
had calculated what ought to be the velocity of sound
according to the laws of the propagation of sonorous
waves, but found that a sound actually travelled quicker
than their calculations had indicated. This surplus
or residue of speed was a consequent for which an
antecedent had to be found. Laplace discovered the
antecedent in the heat developed by the condensation
of each sonorous wave, and this new element, when
introduced into the calculation, rendered it perfectly
accurate. This is an example of the Method of
Residues, the canon of which is as follows :-
"IV. Subduct from any phenomenon such part as
is known by previous inductions to be the effect of
certain antecedents, and the residue of the phenomenon.
is the effect of the remaining antecedents."-Vol. i.,
p. 431.
Let us take two facts-as the presence of the earth and
the oscillation of the pendulum, or again the presence of
62
A STUDY ON MILL.
the moon and the flow of the tide. To connect these
phenomena directly, we should have to suppress the
first of them and see if this suppression would occasion
the stoppage of the second. Now, in both instances,
such suppression is impossible. So we employ an indirect.
means of connecting the phenomena. We observe
that all the variations of the one correspond to certain
variations of the other; that all the oscillations of the
pendulum correspond to certain different positions of
the earth; that all states of the tide correspond to
positions of the moon. From this we conclude that
the second fact is the antecedent of the first. These
are examples of the Method of Concomitant Variations.
Its canon is :-
"V. Whatever phenomenon varies in any manner
whenever another phenomenon varies in some par-
ticular manner, is either a cause or an effect of that
phenomenon, or is connected with it through some
fact of causation."-Vol. i., p. 435.
"The Method of Agreement," says Mill (vol. i.,
p. 424), "stands on the ground that whatever can be
eliminated, is not connected with the phenomenon by
any law. The Method of Difference has for its founda-
tion, that whatever can not be eliminated, is connected
with the phenomenon by a law." The Method of
Residues is a case of the Method of Differences. The
Method of Concomitant Variations is another case of the
same method; with this distinction, that it is applied,
not to the phenomena, but to their variations.
VIII.
THESE are the rules: an example will make
them clearer. We will take Dr. Wells's
theory of dew, which will show you the
methods in exercise. Nearly all of them
are employed in it. I will give it you in
Mill's own words, which are so clear that
you must have the pleasure of considering
them.*
We must begin by separating dew from
rain, and the moisture of fogs, and by de-
fining it as "the spontaneous appearance
of moisture on substances exposed in the
open air, when no rain or visible wet is
falling." What is the cause of the pheno-
mena we have thus defined, and how was
that cause discovered?
* Vol. i., pp. 451-9. Mr. Mill quotes from Sir
John Herschel's Discourse on the Study of Natural
Philosophy.
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A STUDY ON MILL.
In the first place, "we have analogous
phenomena in 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.' Comparing these cases, we find that
they all contain the phenomenon which was
proposed as the subject of investigation.
Now, all these instances agree in one point,
the coldness of the object dewed, in compa-
rison with the air in contact with it.' But
there still remains the most important case
of all, that of nocturnal dew: does the same
circumstance exist in this case?
'Is it a
fact that the object dewed is colder than the
air? Certainly not, one would at first be
inclined to say; for what is to make it so?
But . the experiment is easy: we have
only to lay a thermometer in contact with the
dewed substance, and to hang one at a little
distance above it, out of reach of its influ-
A STUDY ON MILL.
65
ence. The experiment has therefore been
made; the question has been asked, and the
answer has been invariably in the affirma-
tive. Whenever an object contracts dew, it
is colder than the air.'
"Here then is a complete application of
the Method of Agreement, establishing the
fact of an invariable connection between the
deposition of dew on a surface, and the cold-
ness of that surface compared with the ex-
ternal air. But which of these is cause, and
which effect? or are they both effects of
something else? On this subject the Method
of Agreement can afford us no light we
must call in a more potent method. • We
must collect more facts, or, which comes to
the same thing, vary the circumstances;
since every instance in which the circum-
stances differ is a fresh fact: and especially,
we must note the contrary or negative cases,
i. e., where no dew is produced:' a compa-
rison between instances of dew and in-
stances of no dew, being the condition neces-
sary to bring the Method of Difference into
play.
T
66
A STUDY ON MILL.
•
"Now, first, no dew is produced on the
surface of polished metals, but it is very
copiously on glass, both exposed with their
faces upwards, and in some cases the hori-
zontal under side of a horizontal plate of glass
is also dewed.' Here is an instance in which
the effect is produced, and another instance
in which it is not produced; but we cannot
yet pronounce, as the canon of the Method
of Difference requires, that the latter instance
agrees with the former in all its circum-
stances except one; for the differences be-
tween glass and polished metal are mani-
fold, and the only thing we can as yet be
sure of is, that the cause of dew will be
found among the circumstances by which
the former substance is distinguished from
the latter." To detect this particular cir-
cumstance of difference we have but one
practicable method, that of Concomitant
Variations. In the cases of polished metal
and polished glass, the contrast shows evi-
dently that the substance has much to do
with the phenomenon; therefore let the
substance alone be diversified as much as
66 6
A STUDY ON MILL.
67
possible, by exposing polished surfaces of
various kinds. This done, a scale of inten-
sity becomes obvious. Those polished sub-
stances are found to be most strongly dewed
which conduct heat worst; while those
which conduct well, resist dew most effec-
tually.'" Hence we conclude, that “cæteris
paribus the deposition of dew is in some
proportion to the power which the body
possesses of resisting the passage of heat;
and that this, therefore, (or something con-
nected with this,) must be at least one of
the causes which assist in producing the
deposition of the dew on the surface.
'But if we expose rough surfaces instead
of polished, we sometimes find this law in-
terfered with. Thus, roughened iron, espe-
cially if painted over or blackened, becomes
dewed sooner than varnished paper: the
kind of surface, therefore, has a great influ-
ence. Expose, then, the same material in
very diversified states as to surface' (that
is, employ the Method of Difference to as-
certain concomitance of variations,) and
another scale of intensity becomes at once
F 2
68
A STUDY ON MILL.
> ""
6
apparent; those surfaces which part with
their heat most readily by radiation, are found
to contract dew most copiously.' Hence we
conclude, "that cæteris paribus the depo-
sition of dew is also in some proportion to
the power of radiating heat; and that the
quality of doing this abundantly (or some
cause on which that quality depends) is
another of the causes which promote the
deposition of dew on the surface. Again,
the influence ascertained to exist of sub-
stance and surface leads us to consider that
of texture: and here, again, we are pre-
sented on trial with remarkable differences,
and with a third scale of intensity, pointing
out substances of a close firm texture, such
as stones, metals, &c., as unfavourable, but
those of a loose one, as cloth, velvet, wool,
eider-down, cotton, &c., as eminently favour-
able to the contraction of dew.' The Me-
thod of Concomitant Variations is here, for
the third time, had recourse to; and, as
before, from necessity, since the texture of
no substance is absolutely firm or absolutely
loose.
Looseness of texture, therefore, or
A STUDY ON MILL.
69
something which is the cause of that quality,
is another circumstance which promotes the
deposition of dew; but this third cause
resolves itself into the first, viz., the quality
of resisting the passage of heat: for sub-
stances of loose texture 'are precisely those
which are best adapted for clothing, or for
impeding the free passage of heat from the
skin into the air, so as to allow their outer
surfaces to be very cold, while they remain
warm within.'
"It thus appears 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 circumstance 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 quantity of it, is formed, and which
are also extremely various, agree (as far as
we can observe) in nothing except in not
70
A STUDY ON MILL.
having this same property." We can now
revert to our previous inquiry as to whether
the coldness was the cause of dew, or its
66
effect. This doubt we are now able to
resolve. We have found that, in every such
instance, the substance on which dew is
deposited, is one, which, by its own proper-
ties or laws, would, if exposed in the night,
become colder than the surrounding air.
The coldness therefore, being accounted for
independently of the dew, while it is proved
that there is a connection between the two,
it must be the dew that depends on the
coldness; or in other words, the coldness is
the cause of the dew.
"This law of causation, already so amply
established, admits, however, of efficient
additional corroboration in no less than
three ways. First, by deduction from the
known laws of aqueous vapour when diffused
through air or any
other gas;
gas; and though
we have not yet come to the Deductive
Method, we will not omit what is necessary
to render this speculation complete. It is
known by direct experiment that only a
A STUDY ON MILL.
71
limited quantity of water can remain sus-
pended in the state of vapour at each degree
of temperature, and that this maximum
grows less and less as the temperature
diminishes. From this it follows, deduc-
tively, that if there is already as much va-
pour suspended as the air will contain at its
existing temperature, any lowering of that
temperature will cause a portion of the va-
pour to be condensed, and become water.
But, again, we know deductively, from the
laws of heat, that the contact of the air with
a body colder than itself, will necessarily
lower the temperature of the stratum of air
immediately applied to its surface; and will
therefore cause it to part with a portion of
its water, which accordingly will, by the
ordinary laws of gravitation or cohesion,
attach itself to the surface of the body,
thereby constituting dew. This deductive
proof, it will have been seen, has the advan-
tage of proving at once causation as well as
co-existence; and it has the additional ad-
vantage that it also accounts for the excep-
tions to the occurrence of the phenomenon,
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A STUDY ON MILL.
the cases in which, although the body is
colder than the air, yet no dew is deposited;
by showing that this will necessarily be the
case when the air is so under-supplied with
aqueous vapour, comparatively to its tempe-
rature, that even when somewhat cooled by
the contact of the colder body, it can still
continue to hold in suspension all the vapour
which was previously suspended in it: thus
in a very dry summer there are no dews, in
a very dry winter no hoar-frost.
"The second corroboration of the theory is
by direct experiment, according to the canon
of the Method of Difference. We can, by
cooling the surface of any body, find in all
cases some temperature, (more or less inferior
to that of the surrounding air, according to
its hygrometrical condition,) at which dew
will begin to be deposited. Here, too, there-
fore, the causation is directly proved. We
can, it is true, accomplish this only on a
small scale; but we have ample reason to
conclude that the same operation, if con-
ducted in Nature's great laboratory, would
equally produce the effect.
A STUDY ON MILL.
73
cr
And, finally, even on that great scale we
are able to verify the result. The case is
one of those rare cases, as we have shown
them to be, in which nature works the ex-
periment for us in the same manner in
which we ourselves perform it; introducing
into the previous state of things a single and
perfectly definite new circumstance, and ma-
nifesting the effect so rapidly that there is
not time for any other material change in the
pre-existing circumstances. It is observed
that dew is never copiously deposited in
situations much screened from the open sky,
and not at all in a cloudy night; but, if the
clouds withdraw, even for a few minutes, and
leave a clear opening, a deposition of dew
presently begins, and goes on increasing.
Dew formed in clear intervals
will often even evaporate again when the
sky becomes thickly overcast.' The proof,
therefore, is complete, that the presence or
absence of an uninterrupted communication
with the sky causes the deposition or non-
deposition of dew. Now, since a clear sky is
nothing but the absence of clouds, and it is
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A STUDY ON MILL.
a known property of clouds, as of all other
bodies between which and any given object
nothing intervenes but an elastic fluid, that
they tend to raise or keep up the superficial
temperature of the object by radiating heat
to it, we see at once that the disappearance.
of clouds will cause the surface to cool; so
that Nature, in this case, produces a change
in the antecedent by definite and known
means, and the consequent follows accord-
ingly a natural experiment which satisfies
the requisitions of the Method of Difference.'
""
IX.
THESE four are not all the methods of sci-
ence, but they lead us up to the others. They
are all connected and no one has pointed
out their connection so well as Mill. These
processes of isolation are ineffectual in many
cases; namely, in those in which the effect
is produced by a concurrence of causes, and
cannot therefore be reduced into its ele-
ments. Methods depending on isolation
are then impracticable. We cannot elimi-
nate, and so cannot perform induction. This
grave difficulty presents itself in almost all
cases of movement: for nearly every move-
ment is the effect of a concurrence of forces
and the respective effects of the different
forces are found so mixed up in it, that we
cannot separate them without destroying it,
and it seems impossible to know what part
76
A STUDY ON MILL.
each force has in the production of the
movement.
Take, for instance, a body acted on by
two forces whose directions form an angle.
It moves along the diagonal. Each element
of its movement at any moment-the force,
the speed, the position-is the combined
effect of the two impelling forces. Their
several effects are so intimately combined
that we cannot isolate either of them, and
refer it to its causing force. To perceive
the effects separately, we should have to
consider the movements apart-that is, to
suppress the actual movement and replace
it by others. Neither the Method of Agree-
ment, nor of Difference, nor of Residues, nor
of Concomitant Variations, which are all
decomposing and eliminative, can serve us
with a phenomenon which by its nature ex-
cludes all elimination, and all decomposition.
We must therefore evade the obstacle; and
here it is that we avail ourselves of De-
duction-the last key to nature. Aban-
doning the study of the actual phenomenon,
we turn to simpler cases; we establish their
A STUDY ON MILL.
77
laws, and we connect each to its cause by
the ordinary methods of induction. Then,
assuming the concurrence of two or more of
these causes, we determine from their known
laws what will be their total effect. We
then examine whether the actual movement
corresponds precisely to the predicted move-
ment; and if so, we attribute it to the
causes from which we have deduced it.
Thus, to discover the causes of the planetary
motions, we seek by simple induction the
laws of two causes: the one being the force
of primitive impulsion in the direction of
the tangent, and the other an accelerating
attracting force. From these laws obtained
by induction, we deduce by calculation the
movement of a body under their combined
influence; and having verified that the ob-
served planetary movements coincide exactly
with the predicted movements, we conclude
that the two forces in question are actually
the causes of the movements in question.
To the Deductive Method," says Mill,
"the human mind is indebted for its most
66
conspicuous triumphs in the investigation
78
A STUDY ON MILL.
of nature. To it we owe all the theories by
which vast and complicated phenomena are
embraced under a few simple laws." Our
deviations have served us better than the
direct path. We have derived efficiency
from imperfection.
:
X
IF now we compare the two methods-their
aptitude, their functions, their provinces-we
shall find, in epitome, the history, divisions,
hopes, and limits of human knowledge. The
first belongs to its earliest, the other to its
later stages. The first became predominant
in Bacon's time, and is losing its relative
importance; the latter, which then lost its
supremacy, is now beginning to regain it.
So that science, having passed from the
deductive to the experimental state, is now
passing from the experimental to the de-
ductive. Induction has for its province
phenomena which are capable of being de-
composed, and on which we are able to ex-
periment. Deduction has for its province
phenomena which are not capable of being
* Vol. i., p. 526.
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A STUDY ON MILL.
decomposed, or on which we cannot experi-
ment. The first is efficacious in physics,
chemistry, zoology, and botany, in the
earlier stages of each science, and, above
all, when the phenomena are comparatively
simple, within our reach, and capable of
being modified by means at our disposal.
The second is efficacious in astronomy, in
the higher branches of physics, in physio-
logy, in history, in the higher grades of each
science, and, above all, where the pheno-
mena are very complicated, as in animal
and social life, or placed beyond our reach,
as the movements of the heavenly bodies,
and the changes of the atmosphere. When
the
proper method is not employed, science
is at a stand-still: when it is employed,
science advances. Here lies the whole secret
of its past and present states. If the phy-
sical sciences were stationary till the time of
Bacon, it was because deduction was em-
ployed, when there was need of induction.
If physiology and the moral sciences are now
making slow progress, it is because we at-
tempt induction when deduction should be
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81
employed. It is by deduction, and from
the laws of physics and chemistry, that phy-
siological phenomena must be explained. It
is by deduction, and from the laws of the
mind, that historical phenomena are capable
of explanation.* And that which has be-
come the instrument of these two sciences,
it is the object of all the others to employ.
All tend to become deductive, and aim at
being summed up in a few general proposi-
tions, from which the rest may be deduced.
The fewer these propositions are, the fewer
suppositions and postulates a science requires,
the more advanced and perfect it has be-
come. Such a reduction is its final state.
Astronomy, acoustics, and optics afford us
models. We shall be acquainted with na-
ture when we shall have deduced its millions
of facts from two or three laws.
* See Chapter 9, Book vi., v. 2, p. 478, on the
Physical or Concrete Deductive Method as applied to
Sociology; and Chapter 13, Book iii, for explanations,
after Liebig, of Decomposition, Respiration, the action.
of poisons, &c. A whole book is devoted to the logic
of the moral sciences; I know no better treatise on the
subject.
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I venture to say that the theory which
you have just heard is perfect. I have
omitted many of its characteristics, but you
have seen enough of it to recognise that
nowhere has induction been explained so
completely and precisely, with such an
abundance of fine and just distinctions,
with such exact and extensive applications,
with such a knowledge of actual practice
and of acquired discoveries, with so com-
plete an exclusion of à priori principles and
of metaphysical suppositions, and in a spirit
more in conformity with the rigorous pro-
cedure of modern experimental science.
You asked me, just now, what we had
effected in philosophy. I reply, the theory
of Induction. Mill is the last of that great
line of philosophers, commencing with Bacon,
and continued through Hobbes, Newton,
Locke, Hume, and Herschell, to our own
times. They have applied our national
spirit to philosophy; they have been posi-
tive and practical; they have not soared
above their facts; they have not attempted
extraordinary paths; they have purged the
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83
mind of its illusions, presumptions, and
dreams; they have employed it in the only
direction in which it is capable of acting.
All they have aimed at has been to light
and mark out the already trodden ways of
the progressive sciences. They have refused
to spend their labour in other than explored
and verified paths; they have aided the
great modern work, the discovery of appli-
cable laws; they have contributed, as culti-
vators of special sciences do, to the increase
of man's power. Find me many philoso-
phers who have done as much.
G 2
XI.
You will tell me that our philosopher has
cut off his wings to strengthen his legs.
True and he has acted wisely. Experience
marks out the career which she opens to us;
she gives us an object to aim at; but also
lays down limits within which we are con-
fined. We have but to regard the elements
of which our experience is composed, and
the facts from which it sets out, to under-
stand that its range is limited. Its nature
and its method confine its progress to a few
steps. And first of all, the ultimate laws
of nature cannot possibly be less numerous
than the several distinct species of our sen-
sations. We can easily reduce a movement
to another movement, but not the sensation
of heat to that of smell, or of colour, or of
*
* Vol. ii., p. 4.
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85
sound, nor one nor the other to a movement.
We can easily connect together phenomena
differing in degree, but not phenomena
differing in species. We find distinct sen-
sations at the bottom of all our knowledge,
as simple indecomposable elements abso-
lutely separate one from another; absolutely
incapable of being reduced one to another.
Let experience do what she will, she can-
not suppress the diversities on which she is
founded. Again, do what she will, she can-
not escape from the conditions she acts
under. Whatever may be her province,
it is bounded by time and space: the fact
which she observes is limited and influenced
by an infinite number of other facts to which
she cannot attain. She is obliged to suppose
or to recognise some primordial state whence
she starts, and which she cannot explain. *
There exist in nature a number of Permanent
Causes, which have subsisted ever since the human
race has been in existence, and for an indefinite and
probably an enormous length of time previous. The
sun, the earth, and planets, with their various consti-
tuents, air, water, and the other distinguishable sub-
stances, whether simple or compound, of which nature
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Every problem has its accidental or arbi-
trary data; from these the rest may be
deduced, but there is nothing from which
these can be deduced. The sun, the earth,
the planets, the initial impulsion of the
heavenly bodies, the primitive chemical pro-
perties of substances, are such facts.* By
is made up, are such Permanent Causes. They have
existed, and the effects or consequences which they
were fitted to produce have taken place, (as often as the
other conditions of the production met,) from the very
beginning of our experience. But we can give no
account of the origin of the Permanent Causes them-
selves.—Vol. i., p. 378.
* The resolution of the laws of the heavenly motions
established the previously unknown ultimate property
of a mutual attraction between all bodies: the resolu-
tion, so far as it has yet proceeded, of the laws of
crystallization, or chemical composition, electricity, mag-
netism, &c., points to various polarities, ultimately
inherent in the particles of which bodies are composed;
the comparative atomic weights of different kinds of
bodies were ascertained by resolving, into more general
laws, the uniformities observed in the proportions in
which substances combine with one another; and so
forth. Thus, although every resolution of a complex
uniformity into simpler and more elementary laws has
an apparent tendency to diminish the number of the
ultimate properties, and really does remove many pro-
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87
the help of these all things are capable of
explanation, but these themselves we cannot
explain. Why, asks Mill, did these particular
natural agents exist originally, and no others?
-why are they commingled in such and such
proportions ?-and why distributed in such
and such a manner throughout space? Here,
he says, is a question we cannot answer, and,
more than this, we can discover nothing
regular in the distribution itself; we can
reduce it to no uniformity, to no law. The
assemblage of these agents can be nothing
more to us than a pure accident.* And
perties from the list; yet, (since the result of this
simplifying process is to trace up an ever greater
variety of different effects to the same agents,) the
further we advance in this direction, the greater num-
ber of distinct properties we are forced to recognise in
one and the same object: the coexistences of which
properties must accordingly be ranked among the ulti-
mate generalities of nature.-Vol. ii., p. 108.
* Why these particular natural agents existed origi-
nally and no others, or why they are commingled in
such and such proportions, and distributed in such and
such a manner throughout space, is a question we
cannot answer. More than this: we can discover no-
thing regular in the distribution itself; we can reduce
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astronomy, which afforded us just now the
model of a perfected science, now affords us
an example of a limited science. We can
predict the innumerable positions of all the
planetary bodies, but are obliged to assume
not only their primitive impulsion and its
amount, not only the force and law of attrac-
tion, but also the masses and distances of all
the bodies in question. We comprehend
millions of facts, but it is by means of some
hundred facts which we do not comprehend.
We attain necessary consequences, but it is
by means of accidental antecedents; so that,
if the theory of our universe were completed,
there would remain two great blanks: one
at the commencement of the physical world;
and one at the commencement of the moral
world; the one comprising the elements of
being; the other the elements of experience:
the one relating to primitive sensations; the
it to no uniformity, to no law. There are no means
by which, from the distribution of these causes or
agents in one part of space, we could conjecture
whether a similar distribution prevails in another.-
Vol. i., p. 378.
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89
other to primitive agents.
"Our know-
<<
ledge" says Royer Collard, consists in
driving back ignorance as far as possible."
Can we even affirm that these irreducible
facts are so in appearance only, and in con-
sequence of the laws of our mind? Can we
assert that they have causes like the derived
facts whose causes they are? Can we con-
clude that every event, at every period of
time, and every part of space, happens ac-
cording to law, and that this little world
of ours, so full of uniformity, is a sort of
epitome of the universe? Can we, by the
aid of axioms, leave our confined precinct
and affirm anything of the universe? In no
way. And here it is that Mill pushes his
principle to its furthest consequences. For
the law which attributes a cause to every
event, has to him no other foundation, value,
or extent than what it derives from expe-
rience. It has no inherent necessity:
it
derives all its authority from the great
number of cases in which it has been recog-
nised to be true; it does but sum up a
mass of observations; it connects two states
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of facts which, considered in themselves, have
no intimate connection; it joins antecedents
generally to consequents generally, just as the
law of gravitation joins a particular antece-
dent to a particular consequent; it establishes
a couple, as do all experimental laws, and
participates in their uncertainty as in their
restrictions. Listen to this bold assertion;
"I am convinced that any one accustomed to
abstraction and to analysis, who will fairly
exercise his faculties for the purpose, will,
when his imagination has once learnt to
entertain the notion, find no difficulty in con-
ceiving that in some one, for instance, of the
many firmaments into which sidereal astro-
nomy now divides the universe, events may
succeed one another at random, without any
fixed law; nor can anything in our experi-
ence, or in our mental nature, constitute a
sufficient, or indeed any, reason for be-
lieving that this is nowhere the case."*
* I am convinced that any one accustomed to abstrac-
tion and analysis, who will fairly exert his faculties for
the purpose, will, when his imagination has once learnt
to entertain the notion, find no difficulty in conceiving
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91
Practically we may trust in so well-estab-
lished a law, but "in distant parts of the
stellar regions where the phenomena may
be entirely unlike those with which we are
acquainted, it would be folly to affirm confi-
dently that this general law prevails, any more
than those special laws which we have found
to hold universally on our own planet."*
that in some one, for instance, of the many firmaments
into which sidereal astronomy now divides the universe,
events may succeed one another at random, without
any fixed law; nor can anything in our experience, or
in our mental nature, constitute a sufficient, or indeed
any, reason for believing that this is nowhere the case.
The grounds, therefore, which warrant us in rejecting
such a supposition with respect to any of the phenomena
of which we have experience, must be sought elsewhere
than in any supposed necessity of our intellectual
faculties. Vol. ii., p. 95.
* In distant parts of the stellar regions where the
phenomena may be entirely unlike those with which
we are acquainted, it would be folly to affirm confi-
dently that this general law prevails, any more than
those special ones which we have found to hold univer-
sally on our own planet. The uniformity in the succes-
sion of events, otherwise called the law of causation,
must be received not as a law of the universe, but of
that portion of it only which is within the range of our
means of sure observation, with a reasonable degree of
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We are, then, inevitably driven back from
the infinite; our faculties and our assertions
can in no way attain to it; we remain con-
fined in a very small circle; our mind cannot
carry itself beyond the range of its expe-
rience; we cannot establish any universal
and necessary connection between facts;
perhaps, indeed, no such universal and ne-
cessary connection exists. Mill stops here.
But there can be no doubt, that by carrying
out his idea to its full extent, we should
arrive at the conception of the world as a
simple collection of facts, the existence and
connections of which would be attributable
to no internal necessity, but which would
be simple arbitrary accidentally-existing
.facts. Sometimes, as in our system, they
would be found assembled in such a way as
to bring about regular recurrences; some-
times they would be so assembled that
extension to adjacent cases. To extend it further is to
make a supposition without evidence, and to which, in
the absence of any ground from experience for estimat-
ing its degree of probability, it would be idle to attempt
to assign any. Vol. ii., p. 104.
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93
nothing of the sort would occur. Chance
would be, as Democritus taught, at the
foundation of all things. Laws themselves
would be the result of chance, and some-
times we should find them, sometimes not.
It would be with things, as it is with some
numbers-decimal fractions, for example,
which, according to the hazard of what may
be their two primitive factors, sometimes
recur regularly, and sometimes not. Here
is, no doubt, a high and original conception.
It is the final consequence of the primitive
leading idea, which we discovered at the
commencement of the system, which has
transformed the theories of Definition, of
Propositions, and of the Syllogism; which
has reduced axioms to truths of experience;
which has developed and brought to perfec-
tion the theory of induction; which has
established the aim, the limits, the province,
and the methods of science; which has,
everywhere, in nature and in science, sup-
pressed all interior connections; which has
replaced the necessary by the accidental;
cause by antecedent; and which consists in
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maintaining that every assertion which is
not merely verbal, forms in effect a couple-
that is to say, joins together two facts which
were separate by their nature.
§ II.
ABSTRACTION.
I.
AN abyss of chance, and an abyss of igno-
rance. The prospect is sombre; but what
matter, if it be true? At all events, in this
theory of science we have the theory of
English science. Seldom, I grant you, has
a thinker better summed up in his teaching
the practice of his country; seldom has any
one set forth, both by his denials and his
assertions, the limits and the province of
his race.
The operations of which he com-
poses science are those in which you speci-
ally excel, and those which he excludes from
science are the ones in which you are, of all
nations, the most deficient. He has given
us a description of the English, for that of
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the human mind. Here, too, lies his merit,
and here his weakness. In your idea of
knowledge there is a flaw, and its incessant
repetition ends by creating the gulf of
chance, from which, according to his teach-
ing, all things arise, and the gulf of ignorance,
at whose brink, he tells us, our knowledge
ends. And see what happens. By cut-
ting away from science the knowledge
of first causes-that is, of divine things--
you drive men to become sceptical, posi-
tive, utilitarian, if they are cool-headed;
or mystical, enthusiastic, methodistical, if
they have lively imaginations. In the huge
unknown void which you create beside our
little world, men with hot heads and un-
easy consciences find room for all their
dreams; while men of cool judgment, des-
pairing of arriving at any sure knowledge,
have nothing left but to bring themselves
down to the search for practical truths which
may serve to ameliorate our condition. It
seems to me, that these two dispositions.
frequently co-exist in an English mind. The
religious and positive spirits dwell there
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97
side by side, but separate. They form a
strange alliance, and I confess that I prefer
the way in which the Germans have recon-
ciled science with faith.
"But their philosophy is but an ill-written
poetry."-"Perhaps so."-" But what they
call reason, or intuition of principles, is but
the faculty of building up hypotheses."-
"Perhaps so." "But the systems they
have constructed have not held their ground
before experience."-"I do not defend what
they have done." "But their absolute, their
subject, their object, and the rest, are but
big words."-" I give you up their style."-
"What, then, do you defend ?"-" Their
idea of Causation."-" You believe with them
that causes are discovered by a revelation of
the reason?"—"Not at all."-"You believe,
then, with us, that our knowledge of causes
is founded on simple experience?"-"Still
less."—" Is there, then, a faculty other than
experience and reason capable of discovering
causes ?"—"Yes."-"You think there is a
middle course situated between illumina-
tion and observation, capable of arriving at
H
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principles, as they tell us that the first is,
capable of arriving at truths as we find the
second is ?""Yes." What then?"-"Ab- "
straction. Let us return to your original
idea. I will attempt to show you where I
find it incomplete, and how you appear to
me to mutilate the human mind. But you
must give me space: it will be the connected
argument of an advocate."
II.
YOUR starting-point is correct. In fact,
man knows nothing of substances; he knows
nothing of minds or bodies; he is conscious
only of his transient, isolated, internal states.
He avails himself of these to assert and
name exterior states, positions, movements,
and changes, and avails himself of them for
this purpose only. All he can attain to are
facts, internal or external; sometimes tran-
sient, when his impression is not repeated;
sometimes permanent, when his impression,
frequently repeated, leads him to believe
that it will be so whenever and as often as
he pleases. All he grasps are colours, sounds,
resistances, and movements-sometimes mo-
mentary and variable, sometimes constant
and renewed. To group these facts he sup-
poses, by means of an artifice of language,
Uorm
H 2
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the existence of qualities and properties.
We go even further than you: we think
that there are neither minds nor bodies, but
simply groups of present or possible move-
ments, and groups of present or possible
thoughts. We believe that there are no
substances, but only systems of facts. We
look on the notion of substance as a psy-
chological illusion. We consider substance,
force, and all the metaphysical existences of
the moderns as the remains of scholastic
entities. We think the world consists of
facts and laws; of events and the relations
between them; and we admit, with you,
that all we know may be reduced to the
connection or addition of fact to fact.
when this is accomplished a new operation
commences, the most fruitful of all, con-
sisting in the reduction of complex into
simple facts. A magnificent faculty comes
into play, the origin of language, the inter-
preter of nature, the parent of religions and
philosophies, the only real distinction which,
according to its degree, separates man from
the brute, and great from ordinary men. I
Maou
But
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101
mean Abstraction: the power of isolating
the elements of facts, and of considering
them separately. My eyes follow the out-
line of a square, and from it abstraction
derives its two constituent properties—the
equality of its sides and angles. My fingers
touch the surface of a cylinder, and from it
abstraction derives its two generating ele-
ments-the idea of a rectangle, and of the
revolution of this rectangle about one of its
sides as an axis. A hundred thousand facts
of experience display to me, by an infinite
number of details, the series of physiological
operations which make up life, and abstrac-
tion derives the law of this series, which is a
round of constant loss and continual repa-
ration. Twelve hundred pages teach me
Mill's views on the different facts of science,
and abstraction derives his leading idea :-
that those propositions only are fruitful
which connect a fact to another not con-
tained in the first. The case is the same
everywhere. A fact, or series of facts, may
always be resolved into its components. This
resolution it is which forms our problem
Uor M
102
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when we inquire into the nature of an
object. These components are what we are
in search of when we attempt inquiries into
the inner nature of a being. These are what
pass under the names of forces, causes,
laws, essences, primitive properties. They
are not new facts added to the first, but a
portion or extract of them; they are con-
tained in them, and have no existence apart
from the facts themselves. To discover them
we do not pass from one fact to a different
one, but from one to another aspect of the
same fact; from the whole to a part, from
the compound to the components. All we
do is to look at the same thing under two
forms; first, as a whole, then, as divided:
to translate our idea from one language into
another, from the language of the senses into
abstract language, just as we express a curve
by an equation, or a cube as a function of
its side.
It matters little whether this translation
be difficult or not; whether it may not
require the accumulation or comparison of
an immense number of facts, and whether
Mou
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103
our mind may not often succumb before
accomplishing it. However this may be, it
invariably happens that in this operation,
which is evidently a fruitful one, instead of
passing from fact to fact we are employed
with one and the same fact; instead of
adding portion to portion of experimental
knowledge, we set aside a portion of the
first; instead of advancing, we stop to exa-
There are,
mine the ground we stand on.
then, judgments which, though instructive,
are not the results of experience; there are
propositions which, though essential, are not
merely verbal; there is an operation, differ-
ing from experience, which acts by retrench-
ment instead of addition: which instead of
acquiring, devotes itself to what has been
acquired, and which, going farther than ob-
servation, opens a new field to the sciences,
defines their nature, determines their pro-
gress, completes their resources, and marks
ont their end.
This is the great omission of your system.
It leaves Abstraction in the background,
barely mentioned, hidden by the other ope-
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rations of the mind, and treated as an ap-
pendage of Experience; we have but to
re-establish it in the general theory, in
order to enable us to reform its particular
branches in the points in which they are
deficient.
III.
To commence with Definitions. Mill teaches
that there can be no definitions of things,
and that when you define a sphere as the
solid generated by the revolution of a semi-
circle about its diameter, you only define a
name. That such a proposition teaches the
meaning of a name is unquestionable, but it
also teaches a good deal more. It asserts
that all the properties of every sphere may
be derived from this generating formula. It
reduces an infinitely complex system of facts
to two elements. It transforms sensible into
abstract facts. It expresses the essence of
the sphere that is to say, the internal pri-
mordial cause of all its properties. Such is
the nature of every true definition; it is not
confined to the explanation of a name ; it is
not a mere description; it does not simply
point out a distinctive property; its office is
not limited to ticketing an object so as to
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distinguish it from all others. There are
many ways of indicating the object besides
its definition; there are other properties
which belong exclusively to it; a sphere
might be described by saying that it is that
of all bodies which, with equal surface, occu-
pies the most space, or in many other ways.
But such descriptions are not definitions;
they express a characteristic, derived qua-
lity, not a generating and primitive one.
They do not reduce the thing to its factors.
and reconstruct it under our eyes; they do
not show its inner nature and its irreducible
elements. A definition is a proposition
which marks out in an object that quality
from which its others are derived, but
which is not itself derived from any other.
Such a proposition is not verbal, for it
teaches the quality of a thing. It is not
the affirmation of an ordinary quality, for it
shows us the quality which is the source of
the rest. It is an assertion of an extraor-
dinary kind, the most fruitful and precious
of all, which sums up a whole science, and
in which it is the aim of every science to be
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107
summed up.
There is a definition apper-
taining to each science, and one for each
object. It is what we have not always
arrived at, but at which we are always at-
tempting to arrive. We have arrived at
defining the motion of the planets, by the
tangential force and central attraction of
which it is compounded; we can now partly
define a chemical body by the notion of
equivalent, and a living body by the notion
of type. We strive to transform each group
of phenomena into certain laws, forces, or "
abstract notions. We endeavour to attain
to the generating elements in each object as
we do attain them in the sphere, cylinder,
circle, cone, and other mathematical loci.
We reduce natural bodies to two or three
sorts of movement attraction, vibration,
polarization-as we reduce geometrical bo-
dies to two or three sorts of elements-the
point, the movement, the time; and we pro-
nounce our science to be partial or complete,
provisional or definite, accordingly as this
reduction is approximate or absolute, im-
perfect or complete.
IV.
THE Theory of Proof requires similar altera-
tion. According to Mill, the proof of the
mortality of a living man is not derived
from the premiss that all men are mortal,
for that would amount to asserting the same
thing twice over, but from the facts of the
deaths of John, Peter, and others; in short,
of all those of whom we have ever heard.
I answer that the real source of our infer-
ence lies elsewhere, and is neither the mor-
tality of John, Peter, and others, nor the
mortality of all men. A fact is proved,
✓says Aristotle, by pointing out its cause.
We shall prove, then, the mortality of Prince
Albert, by giving a reason why he will die.
And what reason is there? except that the
*
* See the Posterior Analytics, which are much
superior to the Prior-δι' αἰτίων καὶ προτέρων.
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109
human body, being an unstable chemical
compound, must in time be resolved; in
other words, because mortality is joined to
the quality of man. Here is the cause, and
the proof. It is this abstract law which,
present in nature, will cause the Prince's
death, and the presence of which to my
mind shows me that he will die. What really
proves this is the abstract proposition; not
the series of particular propositions, nor the
concrete general proposition. In fact, the
abstract proposition proves the others. If
John, Peter, and others, are dead, it is be-
cause mortality is joined to the quality of
man. If all men are dead, or will die, it
is still because mortality is joined to the
quality of man. Here, once more, the part
played by Abstraction has been overlooked.
Mill has confounded it with Experience.
He has not distinguished the proof from
the materials of the proof, the abstract law
from the finite or indefinite number of its
applications.
The applications comprise
both proof and law, but are themselves
neither proof nor law. The examples of
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Peter, John, and others, contain the cause ;
but they are not the cause. It is not
enough to add up the cases; we must extract
from them the law. Experiments alone
will not do, abstraction is necessary. Here
we have the great scientific operation. Syl-
logism does not pass from the particular to
the particular, as Mill teaches, nor from the
general to the particular, as is taught by
ordinary logicians, but from the abstract to
the concrete that is to say, from the cause
to the effect. This is its title to form part
of science, the links of which it makes and
marks out; it connects principles with
effects; it brings
it brings together the definition
and the phenomenon. It diffuses over the
whole range of science that Abstraction
which definition has carried to its height.
V
AXIOMS, again, are explained by Abstrac-
tion. According to Mill, if we know that
when equal magnitudes are added to equal
magnitudes the wholes are equal, or that
two straight lines cannot enclose a space, it
is by external ocular experiment, or by an
internal experiment by the aid of imagina-
tion. No doubt it is possible thus to arrive
at the conclusion that two straight lines.
cannot enclose a space; but there are other
ways of doing so. We can represent lines
in imagination, but can also form concep-
tions of them by reason.
We can either
study their form or their definition. We
can either study the line itself or its gene-
rating elements. I can picture to myself a
line ready drawn, but can also resolve it
into its elements. I can go back to its for-
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mation and discover the abstract elements
of which it is composed, as in the case of a
cylinder we find that it is generated by the
revolution of a rectangle. It will not do to
say that a straight line is the shortest from
one point to another, for that is a derived
property, but we may call it the line de-
scribed by a point which moves towards
another point, and towards that point only;
and this amounts to saying that two points
are sufficient to determine a straight line;
in other words, that two straight lines,
having two points in common, coincide in
their entire length; whence it appears, that
when the two straight lines approach to en-
close a space, they become one straight line,
and so, nothing is enclosed. Here we have
another way of arriving at a knowledge of
the axiom, and it evidently differs consider-
ably from the first. In the first we verify
it, in the second we deduce it. In the first
we find by experience that it is true, in the
second we prove it to be true. The first
compels us to admit its truth, the second
explains how it is true; the first merely
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113
shows the contrary of the axiom to be incon-
ceivable, the second further shows that its
contrary would involve a contradiction.
When we are given the definition of a
straight line, we find that the axiom that
two straight lines cannot enclose a space is
comprised in it, and may be derived from it,
as a consequent from a principle. It is no-
thing more, in fact, than an identical propo-
sition—that is to say, its subject contains its
attribute. It does not connect two terms
which are separate and irreducible one to
the other, but brings together two, the
second of which is a part of the first. It is
merely an analysis, and this is the case with
all axioms. We have only to decompose
them, to see that they do not pass from an
object to a different one, but are concerned
with one object only. We have but to
resolve the notions of equality, cause, sub-
stance, time, and space into their abstracts,
in order to demonstrate the axioms of equa-
lity, substance, cause, time, and space. There
is only one axiom-that of identity. The
others are applications, or consequences of it.
I
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When this is admitted, it appears at once
that the range of our mind is altered. We
are no longer capable only of relative and
limited knowledge, but also of infinite and
absolute knowledge. We possess in axioms
facts which do not merely accompany one
another, but the one of which includes
the other. If they only accompanied one
another, as Mill says, we should be driven
to conclude with him that this might not
always be the case. We should see no
internal necessity for their connection, and
should not admit it except as far as our
experience went; we should say that the
two facts being isolated in their nature, cir-
cumstances might be found in which they
would be separate. We should only affirm
the truth of axioms relatively to our world
and mind. If, on the contrary, the two
facts are such that the one includes the
other, we should thus establish the necessity
of their connection: wherever the first may
be found it will bring the second with it,
since the second is a part of itself, and there-
fore inseparable from it. No circumstance
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115
can exist between them, and disconnect them,
for they make but one thing under different
aspects. Their connection, then, is absolute
and universal; and we possess truths subject
neither to limitation, to condition, nor restric-
tion. Abstraction restores their value to
axioms, by showing their origin, and we
restore to science her dispossessed dominion,
by restoring to the mind the faculty of
which it was deprived.
I 2
VI.
INDUCTION remains to be considered, and
seems to be the triumph of pure experience,
while, in fact, it is the triumph of abstrac-
tion. When I discover that cold produces
dew, and that the passage from the liquid
to the solid state produces crystallization, I
establish a connection between two abstract
facts. Neither cold, nor dew, nor the passage
from the liquid to the solid state, nor crys-
tallization, exist in themselves. They are
portions of phenomena, extracts from com-
plex cases, simple elements included in
compound wholes. I draw them thence,
and isolate them. I isolate dew in general
from all local, temporary, special dews which
I observe. I isolate cold in general from all
the special, various, distinct colds which may
be produced by all differences of texture, all
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117
diversities of substance, all inequalities of tem-
perature, all complications of circumstances.
I connect an abstract antecedent with an
abstract consequent, and I connect them as
Mill himself shows, by subtractions, sup-
pressions, eliminations. I expel from the
two groups which contain them all adjacent
circumstances; I discover the couple under
the surroundings which obscure it; I
detach, by a series of comparisons and
experiments, all the subsidiary accidental
circumstances which are found accompany-
ing it, and finish by laying it bare. I
appear to be considering twenty different
cases, and in reality I consider one only.
I appear to proceed by addition, and in
reality am performing subtraction. All
the methods of Induction, then, are methods
of Abstraction, and all the work of Induction
is the connection of abstract facts.
VII.
WE see now the two great moving powers
of science and the two great manifestations
of nature. There are two operations—
experience and abstraction; two kingdoms
-that of complex facts, and that of simple
elements. The first is the effect, the second
the cause.
The first is contained in the
second, and is capable of being deduced
from it as a consequent from its principle.
The two are equivalent; they are one and
the same thing considered under two aspects.
This magnificent, moving universe-this
tumultuous chaos of mutually dependent
events—this incessant life, infinitely varied
and multiplied, may all be reduced to cer-
tain elements, and the relations between
them. All our efforts amount to the passing
from one to the other, from the complex to
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119
the simple, from facts to laws, from experi-
ments to formulæ. And the reason of this
is evident; for the fact which I perceive by
sense or consciousness is but a fragment
arbitrarily severed by sense or consciousness
from the infinite and continuous web of
being. With differently constituted senses
and consciousness, other fragments would
be intercepted, and it is the chance of their
construction that determines what is actually
perceived. They are like open compasses,
capable of greater or of less extension, and
the area of the circle they describe is not
natural, but artificial. This, indeed, is the
case in two ways, both externally and
internally. For when I consider an event,
I isolate it artificially from its natural sur-
roundings, and I compose it artificially of
elements which do not form a natural group.
When I see a falling stone, I separate the
fall from the antecedent circumstances which
are really connected with it, and I put
together the fall, the form, the structure,
the colour, the sound, and twenty other
circumstances which have really no con-
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nection with it. A fact, then, is an arbitrary
grouping, and at the same time an arbitrary
*
severing; that is to say, an unreal group,
separating things connected, and connecting
things that are separate. So long, therefore,
as we regard nature by simple observation,
we do not see it as it is; and have but a
provisional and illusory idea of it. In
reality, nature is, as it were, a tapestry of
which we only see the reverse, and which,
therefore, we attempt to turn. We apply
ourselves to discovering laws that is to
say, natural groups, really distinct from
their surroundings, and composed of ele-
ments really connected. We discover
couples-that is to say, real compounds and
real connections. We pass from the acci-
dental to the necessary, from the relative to
the absolute, from the appearance to the
reality, and, having found these first couples,
we practice on them the same operation as
we did on the facts, for, though in less
degree, they are of the same nature. Though
* A fact, as was said to me by a man eminent in
physical science, is a superposition of laws.
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121
more abstract, they are still complex. They
may be decomposed and explained. There
is some ulterior reason for their existence.
There is some cause or other which con-
structs and unites them. In their case, as
in that of the facts, we can search for gene-
rating elements into which they may be
resolved, and from which they may be
deduced. And this operation may be con-
tinued until we arrive at elements which
are entirely simple; that is to say, such
that their decomposition would involve a
contradiction. Whether we can find them
or not, they exist; the axiom of causation
would be falsified if they were wanting.
There are, then, elements incapable of de-
composition, and from them are derived the
more general laws; from these, again, the
more special laws; and from these the facts
which we observe; just as in geometry there
are one or two primitive notions from which
the properties of lines are deduced, and from
these the properties of surfaces and solids,
and of all the innumerable forms which
nature can produce or the mind conceive.
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We can now understand the value and
meaning of that axiom of causation which
rules all things, and which Mill has mu-
tilated. There is an inner constraining
force which gives rise to every event, which
connects everything compared and produces
every actual fact. This means, on the one
hand, that there is a reason for everything,
that every fact has its law, that every com-
pound may be reduced to simple elements,
that every product implies factors, that
every quality and every being must be
derived from some superior and anterior
term. And, on the other hand, it means
that the product is equivalent to the factors,
that the two are but one thing under
different aspects, that the cause does not
differ in nature from the effect, that the
generating powers are nothing more than
elementary properties, that the active force
by which we picture Nature to our minds
is nothing but the logical necessity by
which the compound and the simple, the
fact and the law, are transformed one into
the other. Thus we determine beforehand
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123
the limits of all science, and hold the powerful
formula, which, establishing the invincible
connection and spontaneous production of
beings, places the moving spring of Nature,
in Nature, while driving home and fixing in
the heart of every living thing the iron
hooks of necessity.
VIII.
ARE we, then, capable of arriving at a
knowledge of these first elements? For my
part, I think so; and for this reason, that
being abstract, they are not placed without
the facts, but are comprised in them; in
such a way, that all there is to do is to
obtain them from the facts. Besides, as
the most abstract and most general of all
things, there are no facts in which they are
not comprised, and from which we cannot
obtain their idea. However limited our
experience may be, we are able to arrive at
these primary notions, and this is the point
from which the modern school of German
metaphysicians have started in attempting
their vast constructions. They have seized
on the truth that there are simple notions
—that is to say, undecomposable abstract
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125
facts-that the combinations of these en-
gender all others, and that the laws of their
union and of their mutual contrarieties are
the first laws of the universe. They have
attempted to attain to these ideas, and
to reconstruct by pure reason the world
as observation shows it us. They have
broken down in their task, and their
gigantic structure, all factitious and fragile,
hangs in ruins, reminding one of a tempo-
rary scaffolding, serving merely to mark out
the plan of a future building. The fact is,
that with a high notion of our powers they
have not kept in view their limits. For we
are out-flanked on all sides by the infinity
of time and space; we find ourselves thrown
in the midst of this monstrous universe like
a shell on the sea-shore, or an ant on an
ant-hill. Here Mill is right. Chance is
found at the end of all our knowledge, as at
the commencement of all our postulates.
Do what we will we can only mount up,
and that by conjecture, to an initial state;
but this state depends on one preceding it,
which depends on another, and so on, and
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thus we are obliged to accept it as a pure
postulate and to give up attempting to
deduce it, though we see that there is some-
thing from which it may be deduced. This
is the case in all the sciences-in geology,
in natural history, physics, chemistry, psycho-
logy, or history, and the primitive accidental
fact extends its effects into all parts of the
sphere in which it is comprised. If it had
been otherwise, we should not have the
same planets, the same chemical compounds,
the same vegetables, the same animals, the
same races of men, nor, perhaps, any one of
these kinds of beings. If an ant were taken
into another country, it would not see the
same trees, nor insects, nor dispositions of
the soil, nor changes of the atmosphere, nor,
perhaps, any of these forms of being. There
is, then, in every fact and in every object, a
portion which is local and accidental-an im-
mense portion—and it, like the rest, depends
on primitive laws, but not directly—only
through an infinite circuit of consequences,
in such a way that between it and the
primitive laws there is an infinite hiatus,
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127
only to be bridged over by an infinite series
of deductions.
Here, then, we have the inexplicable por-
tion of phenomena, and this it is that
German metaphysicians have attempted to
explain. They have been desirous of de-
ducing from their elementary theorems the
form of the planetary system, the different
laws of physics and of chemistry, the prin-
cipal types of life, the progress of civilization
and of human thought; they have tortured
their universal formulæ with the view of
deriving from them purely special cases;
they have taken indirect and far-fetched
consequences, as direct and intimate ones;
they have omitted or suppressed the great
work which is interposed between the first
laws and the final consequences. They have
discarded Chance from their construction as
material unworthy of science, and the void so
left, and but imperfectly filled up by decep-
tive substitutes, has brought destruction on
their whole edifice.
Does this amount to saying that in the facts
presented us by our little corner of the uni-
128
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verse everything is local? By no means. If
an ant were capable of making experiments,
it might attain to the idea of a physical law,
of a living form, of a representative sensation,
of an abstract thought; for a foot of ground
on which there is a thinking brain includes
all these. However limited, then, be the field
of the mind, it contains general facts--that
is, such as are spread over vast exterior terri-
tories into which its limitation hinders it
from penetrating. If the ant could reason,
it might construct arithmetic, algebra, geo-
metry, mechanics; for a movement of half an
inch comprises time, space, number, force-—
all the materials of mathematics. So, then,
however limited be the field of the mind's
researches, it comprises facts which are uni-
versal-that is to say, spread over all the
region of time and space. Again, if the ant
were a philosopher, it might attain to the
ideas of being, of nothingness, and all the
stock-in-trade of metaphysics; for any phe-
nomenon we please, internal or external,
affords us these materials. So, then, how-
ever limited be the field of a mind's re-
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129
searches, it contains absolute truths-that is
to say, such as must be present in every object.
And this is necessarily so; for in proportion
to the generality of a fact, the fewer are the
objects which we have to examine in order
to meet with it. If it is universal it is met
with everywhere; if it is absolute we cannot
escape meeting it. This is why, in spite of the
narrowness of our experience, metaphysics,
I mean the search for primary causes, is
possible, but on condition only that we re-
main at a great height, that we do not de-
scend into details, that we consider only the
most simple elements of being, and the most
general tendencies of nature. If any one
were to collect the three or four great ideas
in which our sciences end, and the three or
four kinds of existence which make up our
universe; if he were to compare those two
strange quantities which we call duration
and extension, those principal forms or deter-
minations of quantity which we call physical
laws, chemical types, and living species, and
this marvellous representative power, the
Mind, which, without falling into quantity,
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reproduces the two others and itself; if he
were to discover among these three terms-
the
pure quantity, the determined quantity,
and the suppressed quantity*-such an order
that the first must require the second, and the
second the third; if he were to thus establish
that the pure quantity is the necessary com-
mencement of Nature, and that Thought
is the extreme term at which Nature is
wholly suspended; if, then, isolating the
elements of these facts, he should show
that they must combine just as they are
actually combined, and not otherwise; if, in
a word, he proved that there are no other
elements, and can be no others, he would
have sketched out a system of metaphysics
without encroaching on the positive sciences,
and would have attained the source with-
out being obliged to descend to trace the
various streams.
In my opinion, these two great operations,
Experience, as you have described it, and
Abstraction, as I have attempted to define it
*Die aufgehobene Quantitat.
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131
comprise in themselves all the resources of
*the human mind-the one in its practical,
the other in its speculative direction. The
first leads us to consider nature as an
assemblage of facts, the other as a system of
laws; the exclusive employment of the first
is English, that of the second, German. If
there is a place between the two nations, it
is ours. We have extended the English
ideas of the eighteenth century, and now,
in the nineteenth, we are able to give pre-
cision to those of the Germans. Our
pro-
vince seems to be the restraining, correcting,
and completing the two types of mind, one
by the other; the combination of them into
one mind; the expression of their ideas in a
style generally understood, and thus to
make of them the universal mind.
WE went out. As always happens in such
cases, each had given the other matter for
reflection, neither had convinced the other.
But our reflections were short; in the pre-
sence of a fine August morning, all reason-
ings fall to the ground. The old walls, the
rain-worn stones, smiled in the rising sun.
A fresh light shone on their embrasures,
on the keystones of the cloisters, and the
glittering leaves of the ivy. Roses and
honeysuckle climbed the walls, and their
flowers sparkled as they trembled in the
light breeze. The fountains murmured in
the lonely courts. The charming city stood
out from the morning mist as beautiful and
peaceful as a fairy palace, while its robe of
rose-coloured vapour was indented, as embroi-
dery of the renaissance, by a bordering of
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133
towers, cloisters, and palaces, each enclosed
in verdure and decked with flowers. The
architecture of different times had mixed
there ogives, trefoils, statues, and columns ;
time had softened their several tints, the
sun united them in its light, and the ancient
city seemed a shrine to which every age and
every genius had in its turn added a jewel.
Beyond this, the river rolled a sheet of
silver, and mowers stood to the knee in the
high grass of the meadows. Myriads of
buttercups and meadow-sweet, grasses bend-
ing under the weight of their grey heads
steeped in dew, swarmed in the rich soil.
Words cannot paint this freshness of tint
and luxuriance of vegetation. As the line
of shade retreated the flowers appeared bril-
liant with life. On seeing them, virgin and
timid in their gilded veil, one thought of
the blushing cheeks and modest eyes of a
young girl who puts on for the first time her
jewelled necklace. Around, as though to
guard them, enormous trees, four centuries
old, extended in regular lines, and in them
I found a new trace of that practical good
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sense which has accomplished revolutions
without committing ravages; which, while
reforming in all directions, has destroyed
nothing; which has preserved both its con-
stitution and its trees; which has lopped
away dead branches without injuring the
trunk; and to which it is owing, that this
alone among the nations is in the enjoy-
ment not only of the present but of the past.
THE END.
LONDON:
STEVENS AND RICHARDSON, PRINTERS, 5, GREAT QUEEN STREET, W.C.

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