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Title: Essays: Scientific, Political, & Speculative; Vol. 2 of 3

Author: Herbert Spencer

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*** START OF THE PROJECT GUTENBERG EBOOK ESSAYS:
SCIENTIFIC, POLITICAL, & SPECULATIVE; VOL. 2 OF 3 ***

E S S AY S :
S C IE N T IF IC ,
P OL IT IC A L , &
S P E C U L AT IV E .
BY

HERBERT SPENCER.
LIBRARY EDITION,
(otherwise fifth thousand,)
Containing Seven Essays not before Republished, and various other additions .

VOL. II.

WILLIAMS AND NORGATE,
14, HENRIETTA STREET, COVENT GARDEN, LONDON;
AND 20, SOUTH FREDERICK STREET, EDINBURGH.
1891.

LONDON:
G. NORMAN AND SON, PRINTERS, HART STREET,
COVENT GARDEN.

CONTENTS OF VOL. II.

PAGE

THE GENESIS OF SCIENCE 1

THE CLASSIFICATION OF THE SCIENCES 74

REASONS FOR DISSENTING FROM THE PHILOSOPHY OF M. COMTE 118

ON LAWS IN GENERAL, AND THE ORDER OF THEIR DISCOVERY 145

THE VALUATION OF EVIDENCE 161

WHAT IS ELECTRICITY? 168

MILL versus HAMILTON—THE TEST OF TRUTH 188

REPLIES TO CRITICISMS 218

PROF. GREEN’S EXPLANATIONS 321

THE PHILOSOPHY OF STYLE 333

USE AND BEAUTY 370

THE SOURCES OF ARCHITECTURAL TYPES 375

GRACEFULNESS 381

PERSONAL BEAUTY 387

THE ORIGIN AND FUNCTION OF MUSIC 400

THE PHYSIOLOGY OF LAUGHTER 452
(For Index, see Volume III. )

THE GENESIS OF SCIENCE.
[First published in The British Quarterly Review for July 1854 .]

There still prevails among men a vague notion that scientific knowledge
differs in nature from ordinary knowledge. By the Greeks, with whom
Mathematics—literally things learnt —was alone considered as knowledge
proper, the distinction must have been strongly felt; and it has ever since
maintained itself in the general mind. Though, considering the contrast
between the achievements of science and those of daily unmethodic
thinking, it is not surprising that such a distinction has been assumed; yet it
needs but to rise a little above the common point of view, to see that it is but
a superficial distinction. The same faculties are employed in both cases; and
in both cases their mode of operation is fundamentally the same. If we say
that science is organized knowledge, we are met by the truth that all
knowledge is organized in a greater or less degree—that the commonest
actions of the household and the field presuppose facts colligated,
inferences drawn, results expected; and that the general success of these
actions proves the data by which they were guided to have been correctly
put together. If, again, we say that science is prevision—is a seeing
beforehand—is a knowing in what {2} times, places, combinations, or
sequences, specified phenomena will be found; we are obliged to confess
that the definition includes much that is foreign to science in its ordinary
acceptation: for example, a child’s knowledge of an apple. This, as far as it
goes, consists in previsions. When a child sees a certain form and colours, it
knows that if it puts out its hand it will have certain impressions of

resistance, and roundness, and smoothness; and if it bites, a certain taste.
And manifestly its general acquaintance with surrounding objects is of like
nature—is made up of facts concerning them, grouped so that any part of a
group being perceived, the existence of the other facts included in it is
foreseen. If, once more, we say that science is exact prevision, we still fail
to establish the supposed difference. Not only do we find that much of what
we call science is not exact, and that some of it, as physiology, can never
become exact; but we find further, that many of the previsions constituting
the common stock alike of wise and foolish, are exact. That an unsupported
body will fall; that a lighted candle will go out when immersed in water;
that ice will melt when thrown on the fire—these, and many like predictions
relating to the familiar properties of things, have as high a degree of
accuracy as predictions are capable of. It is true that the results foreseen are
of a very general character; but it is none the less true that they are correct
as far as they go: and this is all that is requisite to fulfil the definition. There
is perfect accordance between the anticipated phenomena and the actual
ones; and no more than this can be said of the highest achievements of the
sciences specially characterized as exact.
Seeing thus that the assumed distinction between scientific knowledge
and common knowledge cannot be sustained; and yet feeling, as we must,
that however impossible it may be to draw a line between them, the two are
not practically identical; there arises the question—What is the relationship
{3} between them? A partial answer to this question may be drawn from the
illustrations just given. On reconsidering them, it will be observed that
those portions of ordinary knowledge which are identical in character with
scientific knowledge, comprehend only such combinations of phenomena as
are directly cognizable by the senses, and are of simple, invariable nature.
That the smoke from a fire which she is lighting will ascend, and that the
fire will presently boil the water placed over it, are previsions which the
servant-girl makes equally well with the most learned physicist; but they are
previsions concerning phenomena in constant and direct relation—
phenomena that follow visibly and immediately after their antecedents—
phenomena of which the causation is neither remote nor obscure—

phenomena which may be predicted by the simplest possible act of
reasoning. If, now, we pass to the previsions constituting science—that an
eclipse of the moon will happen at a specified time; that when a barometer
is taken to the top of a mountain of known height, the mercurial column
will descend a stated number of inches; that the poles of a galvanic battery
immersed in water will give off, the one an inflammable and the other an
inflaming gas, in definite ratio—we perceive that the relations involved are
not of a kind habitually presented to our senses. They depend, some of
them, on special combinations of causes; and in some of them the
connexion between antecedents and consequents is established only by an
elaborate series of inferences. A broad distinction, therefore, between
scientific knowledge and common knowledge is its remoteness from
perception. If we regard the cases in their most general aspect, we see that
the labourer who, on hearing certain notes in the adjacent hedge, can
describe the particular form and colours of the bird making them, and the
astronomer who, having calculated a transit of Venus, can delineate the
black spot entering on the sun’s disc, as it will appear through the telescope,
at a specified hour, do {4} essentially the same thing. Each knows that on
fulfilling the requisite conditions, he shall have a preconceived impression
—that after a definite series of actions will come a group of sensations of a
foreknown kind. The difference, then, is neither in the fundamental
character of the mental acts; nor in the correctness of the previsions
accomplished by them; but in the complexity of the processes required to
achieve the previsions. Much of our common knowledge is, as far as it
goes, precise. Science does not increase its precision. What then does it do?
It reduces other knowledge to the same degree of precision. That certainty
which direct perception gives us respecting coexistences and sequences of
the simplest and most accessible kind, science gives us respecting
coexistences and sequences, complex in their dependencies, or inaccessible
to immediate observation. In brief, regarded from this point of view, science
may be called an extension of the perceptions by means of reasoning .
On further considering the matter, however, it will perhaps be felt that
this definition does not express the whole fact—that inseparable as science

may be from common knowledge, and completely as we may fill up the gap
between the simplest previsions of the child and the most recondite ones of
the physicist, by interposing a series of previsions in which the complexity
of reasoning involved is greater and greater, there is yet a difference
between the two beyond that above described. And this is true. But the
difference is still not such as enables us to draw the assumed line of
demarcation. It is a difference not between common knowledge and
scientific knowledge; but between the successive phases of science itself, or
knowledge itself—whichever we choose to call it. In its earlier phases
science attains only to certainty of foresight; in its later phases it further
attains to completeness . We begin by discovering a relation; we end by
discovering the relation. Our first achievement is to foretell the kind {5} of
phenomenon which will occur under specified conditions; our last
achievement is to foretell not only the kind but the amount . Or, to reduce
the proposition to its most definite form—undeveloped science is
qualitative prevision; developed science is quantitative prevision.
This will at once be perceived to express the remaining distinction
between the lower and the higher stages of positive knowledge. The
prediction that a piece of lead will take more force to lift it than a piece of
wood of equal size, exhibits certainty, but not completeness, of foresight.
The kind of effect in which the one body will exceed the other is foreseen;
but not the amount by which it will exceed. There is qualitative prevision
only. On the other hand, the predictions that at a stated time two particular
planets will be in conjunction; that by means of a lever having arms in a
given ratio, a known force will raise just so many pounds; that to
decompose a given quantity of sulphate of iron by carbonate of soda will
require so many grains—these predictions show foreknowledge, not only of
the nature of the effects to be produced, but of the magnitude, either of the
effects themselves, of the agencies producing them, or of the distance in
time or space at which they will be produced. There is both qualitative
provision and quantitative prevision. And this is the unexpressed difference
which leads us to consider certain orders of knowledge as especially
scientific when contrasted with knowledge in general. Are the phenomena

measurable ? is the test which we un­con­scious­ly employ. Space is
measurable: hence Geometry. Force and space are measurable: hence
Statics. Time, force, and space are measurable: hence Dynamics. The
invention of the barometer enabled men to extend the principles of
mechanics to the atmosphere; and Aerostatics existed. When a thermometer
was devised there arose a science of heat, which was before impossible. Of
such external agents as we have found no measures but our sensations {6}
we have no sciences. We have no science of smells; nor have we one of
tastes. We have a science of the relations of sounds differing in pitch,
because we have discovered a way to measure these relations; but we have
no science of sounds in respect to their loudness or their timbre , because we
have got no measures of loudness and timbre . Obviously it is this reduction
of the sensible phenomena it presents, to relations of magnitude, which
gives to any division of knowledge its specially scientific character.
Originally men’s knowledge of weights and forces was like their present
knowledge of smells and tastes—a knowledge not extending beyond that
given by the unaided sensations; and it remained so until weighing
instruments and dynamometers were invented. Before there were hour-
glasses and clepsydras, most phenomena could be estimated as to their
durations and intervals, with no greater precision than degrees of hardness
can be estimated by the fingers. Until a thermometric scale was contrived,
men’s judgments respecting relative amounts of heat stood on the same
footing with their present judgments respecting relative amounts of sound.
And as in these initial stages, with no aids to observation, only the roughest
comparisons of cases could be made, and only the most marked differences
perceived, it resulted that only the most simple laws of dependence could be
ascertained—only those laws which, being uncomplicated with others, and
not disturbed in their manifestations, required no niceties of observation to
disentangle them. Whence it appears not only that in proportion as
knowledge becomes quantitative do its previsions become complete as well
as certain, but that until its assumption of a quantitative character it is
necessarily confined to the most elementary relations.

Moreover it is to be remarked that while, on the one hand, we can
discover the laws of the greater part of phenomena only by investigating
them quantitatively; on the other hand we can extend the range of our
quantitative {7} previsions only as fast as we detect the laws of the results
we predict. For clearly the ability to specify the magnitude of a result
inaccessible to direct measurement, implies knowledge of its mode of
dependence on something which can be measured—implies that we know
the particular fact dealt with to be an instance of some more general fact.
Thus the extent to which our quantitative previsions have been carried in
any direction, indicates the depth to which our knowledge reaches in that
direction. And here, as another aspect of the same fact, it may be observed
that as we pass from qualitative to quantitative prevision, we pass from
inductive science to deductive science. Science while purely inductive is
purely qualitative; when inaccurately quantitative it usually consists of part
induction, part deduction; and it becomes accurately quantitative only when
wholly deductive. We do not mean that the deductive and the quantitative
are coextensive; for there is manifestly much deduction that is qualitative
only. We mean that all quantitative prevision is reached deductively; and
that induction can achieve only qualitative prevision.
Still, however, it must not be supposed that these distinctions enable us to
separate ordinary knowledge from science; much as they seem to do so.
While they show in what consists the broad contrast between the extreme
forms of the two, they yet lead us to recognize their essential identity, and
once more prove the difference to be one of degree only. For, on the one
hand, much of our common knowledge is to some extent quantitative;
seeing that the amount of the foreseen result is known within certain wide
limits. And, on the other hand, the highest quantitative prevision does not
reach the exact truth, but only a near approach to it. Without clocks the
savage knows that the day is longer in the summer than in the winter;
without scales he knows that stone is heavier than flesh; that is, he can
foresee respecting certain results that their amounts will exceed these, and
be less than {8} those—he knows about what they will be. And, with his

most delicate instruments and most elaborate calculations, all that the man
of science can do, is to reduce the difference between the foreseen and the
actual results to an unimportant quantity. Moreover, it must be borne in
mind not only that all the sciences are qualitative in their first stages,—not
only that some of them, as Chemistry, have but lately reached the
quantitative stage—but that the most advanced sciences have attained to
their present power of determining quantities not present to the senses, or
not directly measurable, by a slow process of improvement extending
through thousands of years. So that science and the knowledge of the
uncultured are alike in the nature of their previsions, widely as they differ in
range; they possess a common imperfection, though this is immensely
greater in the last than in the first; and the transition from the one to the
other has been through a series of steps by which the imperfection has been
rendered continually less, and the range continually wider.
These facts, that science and ordinary knowledge are allied in nature, and
that the one is but a perfected and extended form of the other, must
necessarily underlie the whole theory of science, its progress, and the
relations of its parts to each other. There must be incompleteness in any
history of the sciences, which, leaving out of view the first steps of their
genesis, commences with them only when they assume definite forms.
There must be grave defects, if not a general untruth, in a philosophy of the
sciences considered in their interdependence and development, which
neglects the inquiry how they came to be distinct sciences, and how they
were severally evolved out of the chaos of primitive ideas. Not only a direct
consideration of the matter, but all analogy, goes to show that in the earlier
and simpler stages must be sought the key to all subsequent intricacies. The
time was when the anatomy and physiology of the human being were
studied {9} by themselves—when the adult man was analyzed and the
relations of parts and of functions investigated, without reference either to
the relations exhibited in the embryo or to the homologous relations
existing in other creatures. Now, however, it has become manifest that no
true conceptions are possible under such conditions. Anatomists and
physiologists find that the real natures of organs and tissues can be

ascertained only by tracing their early evolution; and that the affinities
between existing genera can be satisfactorily made out only by examining
the fossil genera to which they are akin. Well, is it not clear that the like
must be true concerning all things that undergo development? Is not science
a growth? Has not science, too, its embryology? And must not the neglect
of its embryology lead to a mis­un­der­stand­ing of the principles of its
evolution and of its existing organization?
There are à priori reasons, therefore, for doubting the truth of all
philosophies of the sciences which tacitly proceed upon the common notion
that scientific knowledge and ordinary knowledge are separate; instead of
commencing, as they should, by affiliating the one upon the other, and
showing how it gradually came to be dis­tin­guish­able from the other. We
may expect to find their gen­er­al­i­za­tions essentially artificial; and we shall
not be deceived. Some illustrations of this may here be fitly introduced, by
way of preliminary to a brief sketch of the genesis of science from the point
of view indicated. And we cannot more readily find such illustrations than
by glancing at a few of the various clas­si­fi­ca­tions of the sciences that have
from time to time been proposed. To consider all of them would take too
much space: we must content ourselves with some of the latest.

Commencing with those which may be soonest disposed of, let us notice,
first, the arrangement propounded by Oken. An abstract of it runs thus:―
Part I. M ATHESIS. —Pneu­ma­to­geny : Pri­mary Act, Pri­mary Cons­cious­ness, {10} God, Pri­mary Rest,
Time, Polarity, Motion, Man, Space, Point, Line, Surface, Globe, Rotation.—Hylogeny :
Gravity, Matter, Ether, Hea­venly Bodies, Light, Heat, Fire.
(He explains that M ATHESIS is the doctrine of the whole; Pneu­ma­to­geny being the doctrine
of im­ma­terial to­ta­li­ties, and Hylogeny that of material to­ta­li­ties.)
Part II. O NTOLOGY. —Cosmogeny : Rest, Centre, Motion, Line, Planets, Form, Pla­ne­tary Sys­tem,
Comets.—Stöchiogeny : Con­den­sa­tion, Sim­ple Mat­ter, Elements, Air, Water, Earth.—
Stöchiology : Func­tions of the Ele­ments, &c. &c.—King­doms of Na­ture : In­di­vi­duals.
(He says in explanation that ‘O NTOLOGY teaches us the phenomena of matter. The first of
these are the heavenly bodies comprehended by Cosmogeny . These divide into elements.—
Stöchiogeny. The earth element divides into minerals—Mineralogy . These unite into one
collective body—Geogeny . The whole in singulars is the living, or Organic , which again
divides into plants and animals. Biology , therefore, divides into Organogeny , Phytosophy ,
Zoosophy .’)
F IRST K INGDOM. —M INERALS. Mineralogy , Geology .

Part III. B IOLOGY. —Organosophy , Phy­to­geny , Phyto-phy­si­ol­ogy , Phy­to­logy , Zoogeny , Phy­si­‐
ology , Zoology , Psy­cho­logy .
A glance over this confused scheme shows that it is an attempt to classify
knowledge, not after the order in which it has been, or may be, built up in
the human con­scious­ness; but after an assumed order of creation. It is a
pseudo-scientific cosmogony, akin to those which men have enunciated
from the earliest times downwards; and only a little more respectable. As
such it will not be thought worthy of much consideration by those who, like
ourselves, hold that experience is the sole origin of knowledge. Otherwise,
it might have been needful to dwell on the incongruities of the arrangement
—to ask how motion can be treated of before space? how there can be
rotation without matter to rotate? how polarity can be dealt with without
involving points and lines? But it will serve our present purpose just to
indicate a few of the absurdities resulting from the doctrine which Oken
seems to hold in common with Hegel, that “to philosophize on Nature is to
re-think the great thought of Creation.” Here is a sample:―
“Mathematics is the universal science; so also is {11} Physio-philosophy,
although it is only a part, or rather but a condition of the universe; both are
one, or mutually congruent.
“Mathematics is, however, a science of mere forms without substance.
Physio-philosophy is, therefore, mathematics endowed with substance .”
From the English point of view it is sufficiently amusing to find such a
dogma not only gravely stated, but stated as an unquestionable truth. Here
we see the experiences of quantitative relations which men have gathered
from surrounding bodies and generalized (experiences which had been
scarcely at all generalized at the beginning of the historic period)—we find
these generalized experiences, these intellectual abstractions, elevated into
concrete actualities, projected back into Nature, and considered as the
internal frame-work of things—the skeleton by which matter is sustained.
But this new form of the old realism, is by no means the most startling of
the physio-philosophic principles. We presently read that,
“The highest mathematical idea, or the fundamental principle of all
mathematics is the zero = 0.” * * *

“Zero is in itself nothing. Mathematics is based upon nothing, and,
consequently , arises out of nothing.
“Out of nothing, therefore , it is possible for something to arise; for
mathematics, consisting of propositions, is a something in relation to 0.”
By such “consequentlys” and “therefores” it is, that men philosophize
when they “re-think the great thought of creation.” By dogmas that pretend
to be reasons, nothing is made to generate mathematics; and by clothing
mathematics with matter, we have the universe! If now we deny, as we do
deny, that the highest mathematical idea is the zero—if, on the other hand,
we assert, as we do assert, that the fundamental idea underlying all
mathematics, is that of equality; the whole of Oken’s cosmogony
disappears. And here, indeed, we may see illustrated, the distinctive
peculiarity of the German method of procedure in these {12} matters—the
bastard à priori method, as it may be termed. The legitimate à priori
method sets out with propositions of which the negation is inconceivable;
the à priori method as illegitimately applied, sets out either with
propositions of which the negation is not inconceivable, or with
propositions like Oken’s, of which the affirmation is inconceivable.
It is needless to proceed further with the analysis; else might we detail
the steps by which Oken arrives at the conclusions that “the planets are
coagulated colours, for they are coagulated light”; that “the sphere is the
expanded nothing;” that gravity is “a weighty nothing, a heavy essence,
striving towards a centre;” that “the earth is the identical, water the
indifferent, air the different; or the first the centre, the second the radius, the
last the periphery of the general globe or of fire.” To comment on them
would be nearly as absurd as are the propositions themselves. Let us pass
on to another of the German systems of knowledge—that of Hegel.
The simple fact that Hegel puts Jacob Bœhme on a par with Bacon,
suffices alone to show that his stand-point is far remote from the one
usually regarded as scientific: so far remote, indeed, that it is not easy to
find any common basis on which to found a criticism. Those who hold that
the mind is moulded into conformity with surrounding things by the agency
of surrounding things, are necessarily at a loss how to deal with those who,

like Schelling and Hegel, assert that surrounding things are solidified mind
—that Nature is “petrified intelligence.” However, let us briefly glance at
Hegel’s clas­si­fi­ca­tion. He divides philosophy into three parts:―
1. Logic , or the science of the idea in itself, the pure idea.
2. The Philosophy of Nature , or the science of the idea considered under
its other form—of the idea as Nature.
3. The Philosophy of the Mind , or the science of the idea in its return to
itself.
Of these, the second is divided into the natural sciences, {13} commonly
so-called; so that in its more detailed form the series runs thus:—Logic,
Mechanics, Physics, Organic Physics, Psychology.
Now, if we believe with Hegel, first, that thought is the true essence of
man; second, that thought is the essence of the world; and that, therefore,
there is nothing but thought; his clas­si­fi­ca­tion, beginning with the science
of pure thought, may be acceptable. But otherwise, it is an obvious
objection to his arrangement, that thought implies things thought of—that
there can be no logical forms without the substance of experience—that the
science of ideas and the science of things must have a simultaneous origin.
Hegel, however, anticipates this objection, and, in his obstinate idealism,
replies, that the contrary is true. He affirms that all contained in the forms,
to become something, requires to be thought; and that logical forms are the
foundations of all things.
It is not surprising that, starting from such premises, and reasoning after
this fashion, Hegel finds his way to strange conclusions. Out of space and
time he proceeds to build up motion , matter , repulsion , attraction , weight ,
and inertia . He then goes on to logically evolve the solar system. In doing
this he widely diverges from the Newtonian theory; reaches by syllogism
the conviction that the planets are the most perfect celestial bodies; and, not
being able to bring the stars within his theory, says that they are mere
formal existences and not living matter, and that as compared with the solar
system they are as little admirable as a cutaneous eruption or a swarm of
flies.1 Results so absurd might be left as self-disproved, were it not that
speculators of this class are not alarmed by any amount of incongruity with

established beliefs. The only efficient mode of treating systems like this of
{14} Hegel, is to show that they are self-destructive—that by their first steps
they ignore that authority on which all their subsequent steps depend. If
Hegel professes, as he manifestly does, to develop his scheme by reasoning
—if he presents successive inferences as necessarily following from certain
premises; he implies the postulate that a belief which necessarily follows
after certain antecedents is a true belief; and did an opponent reply to one of
his inferences that, though it was impossible to think the opposite, yet the
opposite was true, he would consider the reply irrational. The procedure,
however, which he would thus condemn as destructive of all thinking
whatever, is just the procedure exhibited in the enunciation of his own first
principles. Mankind find themselves unable to conceive that there can be
thought without things thought of. Hegel, however, asserts that there can be
thought without things thought of. That ultimate test of a true proposition—
the inability of the human mind to conceive the negation of it—which in all
the successive steps of his arguments he considers valid, he considers
invalid where it suits his convenience to do so; and yet at the same time
denies the right of an opponent to follow his example. If it is competent for
him to posit dogmas which are the direct negations of what human con­‐
scious­ness recognizes; then is it also competent for his antagonists to stop
him at any moment by saying, that though the particular inference he is
drawing seems to his mind, and to all minds, necessarily to follow from the
premises, yet it is not true, but the contrary inference is true. Or, to state the
dilemma in another form:—If he sets out with inconceivable propositions,
then may he with equal propriety make all his succeeding propositions
inconceivable ones—may at every step throughout his reasoning draw the
opposite conclusion to that which seems involved.
Hegel’s mode of procedure being thus essentially suicidal, the Hegelian
clas­si­fi­ca­tion which depends upon {15} it, falls to the ground. Let us
consider next that of M. Comte.
As all his readers must admit, M. Comte presents us with a scheme of the
sciences which, unlike the foregoing ones, demands respectful

consideration. Widely as we differ from him, we cheerfully bear witness to
the largeness of his views, the clearness of his reasoning, and the value of
his speculations as contributing to intellectual progress. Did we believe a
serial arrangement of the sciences to be possible, that of M. Comte would
certainly be the one we should adopt. His fundamental propositions are
thoroughly intelligible; and, if not true, have a great semblance of truth. His
successive steps are logically co-ordinated; and he supports his conclusions
by a considerable amount of evidence—evidence which, so long as it is not
critically examined, or not met by counter evidence, seems to substantiate
his positions. But it only needs to assume that antagonistic attitude which
ought to be assumed towards new doctrines, in the belief that, if true, they
will prosper by conquering objectors—it needs but to test his leading
doctrines either by other facts than those he cites, or by his own facts
differently applied, to show that they will not stand. We will proceed thus to
deal with the general principle on which he bases his hierarchy of the
sciences.
In the condensed translation of the Positive Philosophy , by Miss
Martineau, M. Comte says:—“Our problem is, then, to find the one
rational order, amongst a host of possible systems.” . . “This order is
determined by the degree of simplicity, or, what comes to the same thing, of
generality of their phenomena.” And the arrangement he deduces runs thus:
—Mathematics , Astronomy , Physics , Chemistry , Physiology , Social
Physics . This he asserts to be “the true filiation of the sciences.” He asserts
further, that the principle of progression from a greater to a less degree of
generality, “which gives this order to the whole body of science, arranges
the parts of each science.” And, {16} finally, he asserts that the gradations
thus established à priori among the sciences and the parts of each science,
“is in essential conformity with the order which has spontaneously taken
place among the branches of natural philosophy;” or, in other words—
corresponds with the order of historic development.
Let us compare these assertions with the facts. That there may be perfect
fairness, let us make no choice, but take as the field for our comparison, the
succeeding section treating of the first science—Mathematics; and let us

use none but M. Comte’s own facts, and his own admissions. Confining
ourselves to this one science, we are limited to comparisons between its
several parts. M. Comte says, that the parts of each science must be
arranged in the order of their decreasing generality; and that this order of
decreasing generality agrees with the order of historic development. Our
inquiry will be, then, whether the history of mathematics confirms this
statement.
Carrying out his principle, M. Comte divides Mathematics into “Abstract
Mathematics, or the Calculus (taking the word in its most extended sense)
and Concrete Mathematics, which is composed of General Geometry and of
Rational Mechanics.” The subject-matter of the first of these is number ; the
subject-matter of the second includes space , time , motion , force . The one
possesses the highest possible degree of generality; for all things whatever
admit of enumeration. The others are less general; seeing that there are
endless phenomena that are not cognizable either by general geometry or
rational mechanics. In conformity with the alleged law, therefore, the
evolution of the calculus must throughout have preceded the evolution of
the concrete sub-sciences. Now somewhat awkwardly for him, the first
remark M. Comte makes bearing on this point is, that “from an historical
point of view, mathematical analysis appears to have arisen out of the
contemplation of geometrical and mechanical facts.” True, he goes {17} on
to say that, “it is not the less independent of these sciences logically
speaking;” for that “analytical ideas are, above all others, universal,
abstract, and simple; and geometrical conceptions are necessarily founded
on them.” We will not take advantage of this last passage to charge M.
Comte with teaching, after the fashion of Hegel, that there can be thought
without things thought of. We are content simply to compare the assertion,
that analysis arose out of the contemplation of geometrical and mechanical
facts, with the assertion that geometrical conceptions are founded upon
analytical ones. Literally interpreted they exactly cancel each other.
Interpreted, however, in a liberal sense, they imply, what we believe to be
demonstrable, that the two had a simultaneous origin . The passage is either
nonsense, or it is an admission that abstract and concrete mathematics are

coeval. Thus, at the very first step, the alleged congruity between the order
of generality and the order of evolution, does not hold good.
But may it not be that though abstract and concrete mathematics took
their rise at the same time, the one afterwards developed more rapidly than
the other; and has ever since remained in advance of it? No: and again we
call M. Comte himself as witness. Fortunately for his argument he has said
nothing respecting the early stages of the concrete and abstract divisions
after their divergence from a common root; otherwise the advent of Algebra
long after the Greek geometry had reached a high development, would have
been an inconvenient fact for him to deal with. But passing over this, and
limiting ourselves to his own statements, we find, at the opening of the next
chapter, the admission, that “the historical development of the abstract
portion of mathematical science has, since the time of Descartes, been for
the most part determined by that of the concrete.” Further on we read
respecting algebraic functions that “most functions were concrete in their
origin—even those which are at present the most purely {18} abstract; and
the ancients discovered only through geometrical definitions elementary
algebraic properties of functions to which a numerical value was not
attached till long afterwards, rendering abstract to us what was concrete to
the old geometers.” How do these statements tally with his doctrine? Again,
having divided the calculus into algebraic and arithmetical, M. Comte
admits, as perforce he must, that the algebraic is more general than the
arithmetical; yet he will not say that algebra preceded arithmetic in point of
time. And again, having divided the calculus of functions into the calculus
of direct functions (common algebra) and the calculus of indirect functions
(transcendental analysis), he is obliged to speak of this last as possessing a
higher generality than the first; yet it is far more modern. Indeed, by
implication, M. Comte himself confesses this incongruity; for he says:—“It
might seem that the transcendental analysis ought to be studied before the
ordinary, as it provides the equations which the other has to resolve. But
though the transcendental is logically independent of the ordinary , it is best
to follow the usual method of study, taking the ordinary first.” In all these
cases, then, as well as at the close of the section where he predicts that

mathematicians will in time “create procedures of a wider generality ,” M.
Comte makes admissions that are diametrically opposed to the alleged law.
In the succeeding chapters treating of the concrete department of
mathematics, we find similar contradictions. M. Comte himself names the
geometry of the ancients special geometry and that of the moderns general
geometry. He admits that while “the ancients studied geometry with
reference to the bodies under notice, or specially; the moderns study it with
reference to the phenomena to be considered, or generally.” He admits that
while “the ancients extracted all they could out of one line or surface before
passing to another,” “the moderns, since Descartes, employ themselves on
questions {19} which relate to any figure whatever.” These facts are the
reverse of what, according to his theory, they should be. So, too, in
mechanics. Before dividing it into statics and dynamics, M. Comte treats of
the three laws of motion , and is obliged to do so; for statics, the more
general of the two divisions, though it does not involve motion, is
impossible as a science until the laws of motion are ascertained. Yet the
laws of motion pertain to dynamics, the more special of the divisions.
Further on he points out that after Archimedes, who discovered the law of
equilibrium of the lever, statics made no progress until the establishment of
dynamics enabled us to seek “the conditions of equilibrium through the
laws of the composition of forces.” And he adds—“At this day this is the
method universally employed . At the first glance it does not appear the most
rational—dynamics being more complicated than statics, and precedence
being natural to the simpler. It would, in fact, be more philosophical to refer
dynamics to statics, as has since been done.” Sundry discoveries are
afterwards detailed, showing how completely the development of statics has
been achieved by considering its problems dynamically; and before the
close of the section M. Comte remarks that “before hydrostatics could be
comprehended under statics, it was necessary that the abstract theory of
equilibrium should be made so general as to apply directly to fluids as well
as solids. This was accomplished when Lagrange supplied, as the basis of
the whole of rational mechanics, the single principle of virtual velocities.”
In which statement we have two facts directly at variance with M. Comte’s

doctrine;—first, that the simpler science, statics, reached its present
development only by the aid of the principle of virtual velocities, which
belongs to the more complex science, dynamics; and that this “single
principle” underlying all rational mechanics—this most general form which
includes alike the relations of statical, {20} hydrostatical, and dynamical
forces—was reached so late as the time of Lagrange.
Thus it is not true that the historical succession of the divisions of
mathematics has corresponded with the order of decreasing generality. It is
not true that abstract mathematics was evolved antecedently to, and
independently of, concrete mathematics. It is not true that of the
subdivisions of abstract mathematics, the more general came before the
more special. And it is not true that concrete mathematics, in either of its
two sections, began with the most abstract and advanced to the less abstract
truths.
It may be well to mention, parenthetically, that, in defending his alleged
law of progression from the general to the special, M. Comte somewhere
comments upon the two meanings of the word general , and the resulting
liability to confusion. Without now discussing whether the asserted
distinction exists in other cases, it is manifest that it does not exist here. In
sundry of the instances above quoted, the endeavours made by M. Comte
himself to disguise, or to explain away, the precedence of the special over
the general, clearly indicate that the generality spoken of is of the kind
meant by his formula. And it needs but a brief consideration of the matter to
show that, even did he attempt it, he could not distinguish this generality
which, as above proved, frequently comes last, from the generality which
he says always comes first. For what is the nature of that mental process by
which objects, dimensions, weights, times, and the rest, are found capable
of having their relations expressed numerically? It is the formation of
certain abstract conceptions of unity, duality, and multiplicity, which are
applicable to all things alike. It is the invention of general symbols serving
to express the numerical relations of entities, whatever be their special
characters. And what is the nature of the mental process by which numbers
are found capable of having their relations expressed algebraically? It is the

same. {21} It is the formation of certain abstract conceptions of numerical
functions which are constant whatever be the magnitudes of the numbers. It
is the invention of general symbols serving to express the relations between
numbers, as numbers express the relations between things. Just as
arithmetic deals with the common properties of lines, areas, bulks, forces,
periods; so does algebra deal with the common properties of the numbers
which arithmetic presents.
Having shown that M. Comte’s alleged law of progression does not hold
among the several parts of the same science, let us see how it agrees with
the facts when applied to the separate sciences. “Astronomy,” says M.
Comte (Positive Philosophy , Book III.), “was a positive science, in its
geometrical aspect, from the earliest days of the school of Alexandria; but
Physics, which we are now to consider, had no positive character at all till
Galileo made his great discoveries on the fall of heavy bodies.” On this, our
comment is simply that it is a mis­rep­re­sen­ta­tion based upon an arbitrary
misuse of words—a mere verbal artifice. By choosing to exclude from
terrestrial physics those laws of magnitude, motion, and position, which he
includes in celestial physics, M. Comte makes it appear that the last owes
nothing to the first. Not only is this unwarrantable, but it is radically
inconsistent with his own scheme of divisions. At the outset he says—and
as the point is important we quote from the original—“Pour la physique
inorganique nous voyons d’abord, en nous conformant toujours à l’ordre de
généralité et de dépendance des phénomènes, qu’elle doit être partagée en
deux sections distinctes, suivant qu’elle considère les phénomènes généraux
de l’univers, ou, en particulier, ceux que présentent les corps terrestres.
D’où la physique céleste, ou l’astronomie, soit géométrique, soit
mechanique; et la physique terrestre.” Here then we have inorganic physics
clearly divided into celestial physics and terrestrial physics —the
phenomena presented by the universe, and the {22} phenomena presented by
earthly bodies. If now celestial bodies and terrestrial bodies exhibit sundry
leading phenomena in common, as they do, how can the generalization of
these common phenomena be considered as pertaining to the one class

rather than to the other? If inorganic physics includes geometry (which M.
Comte has made it do by comprehending geometrical astronomy in its sub-
section, celestial physics); and if its other sub-section, terrestrial physics,
treats of things having geometrical properties; how can the laws of
geometrical relations be excluded from terrestrial physics? Clearly if
celestial physics includes the geometry of objects in the heavens, terrestrial
physics includes the geometry of objects on the earth. And if terrestrial
physics includes terrestrial geometry, while celestial physics includes
celestial geometry, then the geometrical part of terrestrial physics precedes
the geometrical part of celestial physics; seeing that geometry gained its
first ideas from surrounding objects. Until men had learnt geometrical
relations from bodies on the earth, it was impossible for them to understand
the geometrical relations of bodies in the heavens. So, too, with celestial
mechanics, which had terrestrial mechanics for its parent. The very
conception of force , which underlies the whole of mechanical astronomy, is
borrowed from our earthly experiences; and the leading laws of mechanical
action as exhibited in scales, levers, projectiles, &c., had to be ascertained
before the dynamics of the Solar System could be entered upon. What were
the laws made use of by Newton in working out his grand discovery? The
law of falling bodies disclosed by Galileo; that of the composition of forces
also disclosed by Galileo; and that of centrifugal force found out by
Huyghens—all of them gen­er­al­i­za­tions of terrestrial physics. Yet, with facts
like these before him, M. Comte places astronomy before physics in order
of evolution! He does not compare the geometrical parts of the two
together, and the mechanical parts of the two {23} together; for this would
by no means suit his hypothesis. But he compares the geometrical part of
the one with the mechanical part of the other, and so gives a semblance of
truth to his position. He is led away by a verbal illusion. Had he confined
his attention to the things and disregarded the words, he would have seen
that before mankind scientifically co-ordinated any one class of phenomena
displayed in the heavens, they had previously co-ordinated a parallel class
of phenomena displayed on the surface of the earth.

Were it needful we could fill a score pages with the incongruities of M.
Comte’s scheme. But the foregoing samples will suffice. So far is his law of
evolution of the sciences from being tenable, that, by following his
example, and arbitrarily ignoring one class of facts, it would be possible to
present, with great plausibility, just the opposite generalization to that
which he enunciates. While he asserts that the rational order of the sciences,
like the order of their historic development, “is determined by the degree of
simplicity, or, what comes to the same thing, of generality of their
phenomena;” it might contrariwise be asserted that, commencing with the
complex and the special, mankind have progressed step by step to a
knowledge of greater simplicity and wider generality. So much evidence is
there of this as to have drawn from Whewell, in his History of the Inductive
Sciences , the remark that “the reader has already seen repeatedly in the
course of this history, complex and derivative principles presenting
themselves to men’s minds before simple and elementary ones.” Even from
M. Comte’s own work, numerous facts, admissions, and arguments, might
be picked out, tending to show this. We have already quoted his words in
proof that both abstract and concrete mathematics have progressed towards
a higher degree of generality, and that he looks forward to a higher
generality still. Just to strengthen this adverse hypothesis, let us take a
further instance. {24} From the particular case of the scales, the law of
equilibrium of which was familiar to the earliest nations known,
Archimedes advanced to the more general case of the lever of which the
arms may or may not be equal; the law of equilibrium of which includes
that of the scales. By the help of Galileo’s discovery concerning the
composition of forces, D’Alembert “established, for the first time, the
equations of equilibrium of any system of forces applied to the different
points of a solid body”—equations which include all cases of levers and an
infinity of cases besides. Clearly this is progress towards a higher generality
—towards a knowledge more independent of special circumstances—
towards a study of phenomena “the most disengaged from the incidents of
particular cases;” which is M. Comte’s definition of “the most simple
phenomena.” Does it not indeed follow from the admitted fact, that mental

advance is from the concrete to the abstract, from the particular to the
general, that the universal and therefore most simple truths are the last to be
discovered? Should we ever succeed in reducing all orders of phenomena to
some single law—say of atomic action, as M. Comte suggests—must not
that law answer to his test of being independent of all others, and therefore
most simple? And would not such a law generalize the phenomena of
gravity, cohesion, atomic affinity, and electric repulsion, just as the laws of
number generalize the quantitative phenomena of space, time and force?
The possibility of saying so much in support of an hypothesis the very
reverse of M. Comte’s, at once proves that his generalization is only a half-
truth. The fact is that neither proposition is correct by itself; and the
actuality is expressed only by putting the two together. The progress of
science is duplex. It is at once from the special to the general, and from the
general to the special. It is analytical and synthetical at the same time.
M. Comte himself observes that the evolution of science {25} has been
accomplished by the division of labour; but he quite misstates the mode in
which this division of labour has operated. As he describes it, it has been
simply an arrangement of phenomena into classes, and the study of each
class by itself. He does not recognize the effect of progress in each class
upon all other classes: he recognizes only the effect on the class succeeding
it in his hierarchical scale. Or if he occasionally admits collateral influences
and inter­com­mun­i­ca­tions, he does it so grudgingly, and so quickly puts the
admissions out of sight and forgets them, as to leave the impression that,
with but trifling exceptions, the sciences aid one another only in the order
of their alleged succession. The fact is, however, that the division of labour
in science, like the division of labour in society, and like the “physiological
division of labour” in individual organisms, has been not only a
specialization of functions, but a continuous helping of each division by all
the others, and of all by each. Every particular class of inquirers has, as it
were, secreted its own particular order of truths from the general mass of
material which observation accumulates; and all other classes of inquirers
have made use of these truths as fast as they were elaborated, with the effect
of enabling them the better to elaborate each its own order of truths. It was

thus in sundry of the cases we have quoted as at variance with M. Comte’s
doctrine. It was thus with the application of Huyghens’s optical discovery to
astronomical observation by Galileo. It was thus with the application of the
isochronism of the pendulum to the making of instruments for measuring
intervals, astronomical and other. It was thus when the discovery that the
refraction and dispersion of light did not follow the same law of variation,
affected both astronomy and physiology by giving us achromatic telescopes
and microscopes. It was thus when Bradley’s discovery of the aberration of
light enabled him to make the first step towards ascertaining the motions of
the stars. {26} It was thus when Cavendish’s torsion-balance experiment
determined the specific gravity of the Earth, and so gave a datum for
calculating the specific gravities of the Sun and Planets. It was thus when
tables of atmospheric refraction enabled observers to write down the real
places of the heavenly bodies instead of their apparent places. It was thus
when the discovery of the different expansibilities of metals by heat, gave
us the means of correcting our chronometrical measurements of
astronomical periods. It was thus when the lines of the prismatic spectrum
were used to distinguish the heavenly bodies that are of like nature with the
sun from those which are not. It was thus when, as recently, an elec­tro-tel­e­‐
graphic instrument was invented for the more accurate registration of
meridional transits. It was thus when the difference in the rates of a clock at
the equator, and nearer the poles, gave data for calculating the oblateness of
the earth, and accounting for the precession of the equinoxes. It was thus—
but it is needless to continue. Here, within our own limited knowledge of its
history, we have named ten additional cases in which the single science of
astronomy has owed its advance to sciences coming after it in M. Comte’s
series. Not only its minor changes, but its greatest revolutions have been
thus determined. Kepler could not have discovered his celebrated laws had
it not been for Tycho Brahe’s accurate observations; and it was only after
some progress in physical and chemical science that the improved
instruments with which those observations were made, became possible.
The heliocentric theory of the Solar System had to wait until the invention
of the telescope before it could be finally established. Nay, even the grand

discovery of all—the law of gravitation—depended for its proof upon an
operation of physical science, the measurement of a degree on the Earth’s
surface. So completely, indeed, did it thus depend, that Newton had actually
abandoned his hypothesis because the {27} length of a degree, as then
stated, brought out wrong results; and it was only after Picart’s more exact
measurement was published, that he returned to his calculations and proved
his great generalization. Now this constant intercommunion which, for
brevity’s sake, we have illustrated in the case of one science only, has been
taking place with all the sciences. Throughout the whole course of their
evolution there has been a continuous consensus of the sciences—a
consensus exhibiting a general correspondence with the consensus of the
faculties in each phase of mental development; the one being an objective
registry of the subjective state of the other.

From our present point of view, then, it becomes obvious that the
conception of a serial arrangement of the sciences is a vicious one. It is not
simply that, as M. Comte admits, such a clas­si­fi­ca­tion “will always involve
something, if not arbitrary, at least artificial;” it is not, as he would have us
believe, that, neglecting minor imperfections such a clas­si­fi­ca­tion may be
substantially true; but it is that any grouping of the sciences in a succession
gives a radically erroneous idea of their genesis and their dependencies.
There is no “one rational order among a host of possible systems.” There is
no “true filiation of the sciences.” The whole hypothesis is fundamentally
false. Indeed, it needs but a glance at its origin to see at once how baseless
it is. Why a series ? What reason have we to suppose that the sciences admit
of a linear arrangement? Where is our warrant for assuming that there is
some succession in which they can be placed? There is no reason; no
warrant. Whence then has arisen the supposition? To use M. Comte’s own
phraseology, we should say, it is a metaphysical conception. It adds another
to the cases constantly occurring, of the human mind being made the
measure of Nature. We are obliged to think in sequence; it is a law of our
minds that we must consider subjects separately, one after another:

therefore {28} Nature must be serial—therefore the sciences must be
classifiable in a succession. See here the birth of the notion, and the sole
evidence of its truth. Men have been obliged when arranging in books their
schemes of education and systems of knowledge, to choose some order or
other. And from inquiring what is the best order, have fallen into the belief
that there is an order which truly represents the facts—have persevered in
seeking such an order; quite overlooking the previous question whether it is
likely that Nature has consulted the convenience of book-making. For
German philosophers, who hold that Nature is “petrified intelligence,” and
that logical forms are the foundations of all things, it is a consistent
hypothesis that as thought is serial, Nature is serial; but that M. Comte, who
is so bitter an opponent of all an­thro­po­mor­phism, even in its most
evanescent shapes, should have committed the mistake of imposing upon
the external world an arrangement which so obviously springs from a
limitation of the human con­scious­ness, is somewhat strange. And it is the
more strange when we call to mind how, at the outset, M. Comte remarks
that in the beginning “toutes les sciences sont cultivées simultanément par
les mêmes esprits ;” that this is “inevitable et même indispensable ;” and
how he further remarks that the different sciences are “comme les diverses
branches d’un tronc unique .” Were it not accounted for by the distorting
influence of a cherished hypothesis, it would be scarcely possible to
understand how, after recognizing truths like these, M. Comte should have
persisted in attempting to construct “une échelle encyclopédique .”
The metaphor which M. Comte has here so inconsistently used to express
the relations of the sciences—branches of one trunk—is an approximation
to the truth, though not the truth itself. It suggests the facts that the sciences
had a common origin; that they have been developing simultaneously; and
that they have been from time to time dividing and sub-dividing. But it fails
to suggest the fact, that the {29} divisions and sub-divisions thus arising do
not remain separate, but now and again re-unite in direct and indirect ways.
They inosculate; they severally send off and receive connecting growths;
and the intercommunion has been ever becoming more frequent, more

intricate, more widely ramified. There has all along been higher
specialization, that there might be a larger generalization; and a deeper
analysis, that there might be a better synthesis. Each larger generalization
has lifted sundry specializations still higher; and each better synthesis has
prepared the way for still deeper analysis.
And here we may fitly enter upon the task awhile since indicated—a
sketch of the Genesis of Science, regarded as a gradual outgrowth from
common knowledge—an extension of the perceptions by the aid of the
reason. We propose to treat it as a psychological process historically
displayed; tracing at the same time the advance from qualitative to
quantitative prevision; the progress from concrete facts to abstract facts, and
the application of such abstract facts to the analysis of new orders of
concrete facts; the simultaneous advance in generalization and
specialization; the continually increasing subdivision and reunion of the
sciences; and their constantly improving consensus .

To trace out scientific evolution from its deepest roots would, of course,
involve a complete analysis of the mind. For as science is a development of
that common knowledge acquired by the unaided senses and uncultured
reason, so is that common knowledge itself gradually built up out of the
simplest perceptions. We must, therefore, begin somewhere abruptly; and
the most appropriate stage to take for our point of departure will be the
adult mind of the savage.
Commencing thus, without a proper preliminary analysis, we are
naturally somewhat at a loss how to present, in a satisfactory manner, those
fundamental processes of thought out of which science originates. Perhaps
our argument may {30} be best initiated by the proposition, that all
intelligent action whatever depends upon the discerning of distinctions
among surrounding things. The condition under which only it is possible for
any creature to obtain food and avoid danger, is, that it shall be differently
affected by different objects—that it shall be led to act in one way by one
object, and in another way by another. In the lower orders of creatures this

condition is fulfilled by means of an apparatus which acts automatically. In
the higher orders the actions are partly automatic, partly conscious. And in
man they are almost wholly conscious. Throughout, however, there must
necessarily exist a certain clas­si­fi­ca­tion of things according to their
properties—a clas­si­fi­ca­tion which is either organically registered in the
system, as in the inferior creation, or is formed by conscious experience, as
in ourselves. And it may be further remarked, that the extent to which this
clas­si­fi­ca­tion is carried, roughly indicates the height of intelligence—that,
while the lowest organisms are able to do little more than discriminate
organic from inorganic matter; while the generality of animals carry their
clas­si­fi­ca­tions no further than to a limited number of plants or creatures
serving for food, a limited number of beasts of prey, and a limited number
of places and materials; the most degraded of the human race possess a
knowledge of the distinctive natures of a great variety of substances, plants,
animals, tools, persons, &c.; not only as classes but as individuals.
What now is the mental process by which clas­si­fi­ca­tion is effected?
Manifestly it is a recognition of the likeness or unlikeness of things, either
in respect of their sizes, colours, forms, weights, textures, tastes, &c., or in
respect of their modes of action. By some special mark, sound, or motion,
the savage identifies a certain four-legged creature he sees, as one that is
good for food, and to be caught in a particular way; or as one that is
dangerous; and acts accordingly. He has classed together all the creatures
that are alike in {31} this particular. And manifestly in choosing the wood
out of which to form his bow, the plant with which to poison his arrows, the
bone from which to make his fish-hooks, he identifies them through their
chief sensible properties as belonging to the general classes, wood, plant,
and bone, but distinguishes them as belonging to sub-classes by virtue of
certain properties in which they are unlike the rest of the general classes
they belong to; and so forms genera and species.
And here it becomes manifest that not only is clas­si­fi­ca­tion carried on by
grouping together in the mind things that are like ; but that classes and sub-
classes are formed and arranged according to the degrees of unlikeness .
Things strongly contrasted are alone distinguished in the lower stages of

mental evolution; as may be any day observed in an infant. And gradually
as the powers of discrimination increase, the strong­ly-con­trast­ed classes at
first distinguished, come to be each divided into sub-classes, differing from
each other less than the classes differ; and these sub-classes are again
divided after the same manner. By the continuance of which process, things
are gradually arranged into groups, the members of which are less and less
unlike ; ending, finally, in groups whose members differ only as individuals,
and not specifically. And thus there tends ultimately to arise the notion of
complete likeness . For manifestly, it is impossible that groups should
continue to be subdivided in virtue of smaller and smaller differences,
without there being a simultaneous approximation to the notion of no
difference .
Let us next notice that the recognition of likeness and unlikeness, which
underlies clas­si­fi­ca­tion, and out of which continued clas­si­fi­ca­tion evolves
the idea of complete likeness—let us next notice that it also underlies the
process of naming , and by consequence language . For all language
consists, at the outset, of symbols which are as like to the things
symbolized as it is practicable to make them. The {32} language of signs is a
means of conveying ideas by mimicking the actions or peculiarities of the
things referred to. Verbal language also, in its first stage, is a mode of
suggesting objects or acts by imitating the sounds which the objects make,
or with which the acts are accompanied. Originally these two languages
were used simultaneously. It needs but to watch the gesticulations with
which the savage accompanies his speech—to see a Bushman dramatizing
before an audience his mode of catching game—or to note the extreme
paucity of words in primitive vocabularies; to infer that in the beginning,
attitudes, gestures, and sounds, were all combined to produce as good a
likeness as possible of the things, animals, persons, or events described; and
that as the sounds came to be understood by themselves the gestures fell
into disuse: leaving traces, however, in the manners of the more excitable
civilized races. But be this as it may, it suffices simply to observe, how
many of the words current among barbarous peoples are like the sounds
appertaining to the things signified; how many of our own oldest and

simplest words have the same peculiarity; how children habitually invent
imitative words; and how the sign-language spontaneously formed by deaf
mutes is based on imitative actions—to be convinced that the notion of
likeness is that from which the nomenclature of objects takes its rise. Were
there space we might go on to point out how this law of likeness is
traceable, not only in the origin but in the development of language; how in
primitive tongues the plural is made by a duplication of the singular, which
is a multiplication of the word to make it like the multiplicity of the things;
how the use of metaphor—that prolific source of new words—is a
suggesting of ideas which are like the ideas to be conveyed in some respect
or other; and how, in the copious use of simile, fable, and allegory among
uncivilized races, we see that complex conceptions which there is no direct
language for, are {33} rendered, by presenting known conceptions more or
less like them.
This view is confirmed, and the predominance of this notion of likeness
in primitive thought further illustrated, by the fact that our system of
presenting ideas to the eye originated after the same fashion. Writing and
printing have descended from picture-language. The earliest mode of
permanently registering a fact was by depicting it on a skin and afterwards
on a wall; that is—by exhibiting something as like to the thing to be
remembered as it could be made. Gradually as the practice grew habitual
and extensive, the most frequently repeated forms became fixed, and
presently abbreviated; and, passing through the hieroglyphic and
ideographic phases, the symbols lost all apparent relation to the things
signified: just as the majority of our spoken words have done.
Observe, again, that the same thing is true respecting the genesis of
reasoning. The likeness which is perceived to exist between cases, is the
essence of all early reasoning and of much of our present reasoning. The
savage, having by experience discovered a relation between a certain object
and a certain act, infers that the like relation will be found in future. And
the expressions we use in our arguments—“analogy implies,” “the cases
are not parallel ,” “by parity of reasoning,” “there is no similarity ,”—show
how constantly the idea of likeness underlies our ratiocinative processes.

Still more clearly will this be seen on recognizing the fact that there is a
close connexion between reasoning and clas­si­fi­ca­tion; that the two have a
common root; and that neither can go on without the other. For on the one
hand, it is a familiar truth that the attributing to a body in consequence of
some of its properties, all those other properties in virtue of which it is
referred to a particular class, is an act of inference. And, on the other hand,
the forming of a generalization is the putting together in one class, all those
{34} cases which present like relations; while the drawing a deduction is
essentially the perception that a particular case belongs to a certain class of
cases previously generalized. So that as clas­si­fi­ca­tion is a grouping together
of like things ; reasoning is a grouping together of like relations among
things. Add to which, that while the perfection gradually achieved in clas­si­‐
fi­ca­tion consists in the formation of groups of objects which are completely
alike ; the perfection gradually achieved in reasoning consists in the
formation of groups of cases which are completely alike .
Once more we may contemplate this dominant idea of likeness as
exhibited in art. All art, civilized as well as savage, consists almost wholly
in the making of objects like other objects; either as found in Nature, or as
produced by previous art. If we trace back the varied art-products now
existing, we find that at each stage the divergence from previous patterns is
but small when compared with the agreement; and in the earliest art the
persistency of imitation is yet more conspicuous. The old forms and
ornaments and symbols were held sacred, and perpetually copied. Indeed,
the strong imitative tendency notoriously displayed by the lowest human
races—often seeming to be half automatic, ensures among them a constant
reproducing of likenesses of things, forms, signs, sounds, actions and
whatever else is imitable; and we may even suspect that this aboriginal
peculiarity is in some way connected with the culture and development of
this general conception, which we have found so deep and wide-spread in
its applications.
And now let us go on to consider how, by a further unfolding of this
same fundamental notion, there is a gradual formation of the first germs of
science. This idea of likeness which underlies clas­si­fi­ca­tion, nomenclature,

language spoken and written, reasoning, and art; and which plays so
important a part because all acts of intelligence are made {35} possible only
by distinguishing among surrounding things, or grouping them into like and
unlike;—this idea we shall find to be the one of which science is the
especial product. Already during the stage we have been describing, there
has existed qualitative prevision in respect to the commoner phenomena
with which savage life is familiar; and we have now to inquire how the
elements of quantitative prevision are evolved. We shall find that they
originate by the perfecting of this same idea of likeness—that they have
their rise in that conception of complete likeness which, as we have seen,
necessarily results from the continued process of clas­si­fi­ca­tion.
For when the process of clas­si­fi­ca­tion has been carried as far as it is
possible for the uncivilized to carry it—when the animal kingdom has been
grouped not merely into quadrupeds, birds, fishes, and insects, but each of
these divided into kinds—when there come to be classes, in each of which
the members differ only as individuals, and not specifically; it is clear that
there must frequently occur an observation of objects which differ so little
as to be in­dis­tin­guish­able. Among several creatures which the savage has
killed and carried home, it must often happen that some one, which he
wished to identify, is so exactly like another that he cannot tell which is
which. Thus, then, there originates the notion of equality . The things which
among ourselves are called equal —whether lines, angles, weights,
temperatures, sounds or colours—are things which produce in us sensations
which cannot be distinguished from each other. It is true that we now apply
the word equal chiefly to the separate traits or relations which objects
exhibit, and not to those combinations of them constituting our conceptions
of the objects; but this limitation of the idea has evidently arisen by
analysis. That the notion of equality originated as alleged, will, we think,
become obvious on remembering that as there were no artificial objects
from which it could have been {36} abstracted, it must have been abstracted
from natural objects; and that the various families of the animal kingdom

chiefly furnish those natural objects which display the requisite exactitude
of likeness.
The experiences out of which this general idea of equality is evolved,
give birth at the same time to a more complex idea of equality; or, rather,
the process just described generates an idea of equality which further
experience separates into two ideas—equality of things and equality of
relations . While organic forms occasionally exhibit this perfection of
likeness out of which the notion of simple equality arises, they more
frequently exhibit only that kind of likeness which we call similarity ; and
which is really compound equality. For the similarity of two creatures of the
same species but of different sizes, is of the same nature as the similarity of
two geometrical figures. In either case, any two parts of the one bear the
same ratio to one another, as the homologous parts of the other. Given in a
species, the proportions found to exist among the bones, and we may, and
zoologists do, predict from any one, the dimensions of the rest; just as,
when knowing the proportions subsisting among the parts of a geometrical
figure, we may, from the length of one, calculate the others. And if, in the
case of similar geometrical figures, the similarity can be established only by
proving exactness of proportion among the homologous parts—if we
express this relation between two parts in the one, and the corresponding
parts in the other, by the formula A is to B as a is to b ; if we otherwise
write this, A to B = a to b ; if, consequently, the fact we prove is that the
relation of A to B equals the relation of a to b ; then it is manifest that the
fundamental conception of similarity is equality of relations . With this
explanation we shall be understood when we say that the notion of equality
of relations is the basis of all exact reasoning. Already it has been shown
that reasoning in general is a recognition {37} of likeness of relations; and
here we further find that while the notion of likeness of things ultimately
evolves the idea of simple equality, the notion of likeness of relations
evolves the idea of equality of relations: of which the one is the concrete
germ of exact science, while the other is its abstract germ. Those who
cannot understand how the recognition of similarity in creatures of the same
kind, can have any alliance with reasoning, will get over the difficulty on

remembering that the phenomena among which equality of relations is thus
perceived, are phenomena of the same order and are present to the senses at
the same time; while those among which developed reason perceives
relations, are generally neither of the same order, nor simultaneously
present. And if, further, they will call to mind how Cuvier and Owen, from
a single part of a creature, as a tooth, construct the rest by a process of
reasoning based on this equality of relations, they will see that the two
things are intimately connected, remote as they at first seem. But we
anticipate. What it concerns us here to observe is, that from familiarity with
organic forms there simultaneously arose the ideas of simple equality , and
equality of relations .
At the same time, too, and out of the same mental processes, came the
first distinct ideas of number . In the earliest stages, the presentation of
several like objects produced merely an indefinite conception of
multiplicity; as it still does among Australians, and Bushmen, and Damaras,
when the number presented exceeds three or four. With such a fact before
us we may safely infer that the first clear numerical conception was that of
duality as contrasted with unity. And this notion of duality must necessarily
have grown up side by side with those of likeness and equality; seeing that
it is impossible to recognize the likeness of two things without also
perceiving that there are two. From the very beginning the conception of
number must have been, as it is still, associated with {38} likeness or
equality of the things numbered; and for the purposes of calculation, an
ideal equality of the things is assumed. Before any absolutely true
numerical results can be reached, it is requisite that the units be absolutely
equal . The only way in which we can establish a numerical relationship
between things that do not yield us like impressions, is to divide them into
parts that do yield us like impressions. Two unlike magnitudes of extension,
force, time, weight, or what not, can have their relative amounts estimated,
only by means of some small unit that is contained many times in both; and
even if we finally write down the greater one as a unit and the other as a
fraction of it, we state, in the denominator of the fraction, the number of
parts into which the unit must be divided to be comparable with the

fraction. It is, indeed, true, that by a modern process of abstraction, we
occasionally apply numbers to unequal units, as the furniture at a sale or the
various animals on a farm, simply as so many separate entities; but no exact
quantitative result can be brought out by calculation with units of this order.
And, indeed, it is the distinctive peculiarity of the calculus in general, that it
proceeds on the hypothesis of that absolute equality of its abstract units,
which no real units possess; and that the exactness of its results holds only
in virtue of this hypothesis. The first ideas of number must necessarily then
have been derived from like or equal magnitudes as seen chiefly in organic
objects; and as the like magnitudes most frequently observed were
magnitudes of extension, it follows that geometry and arithmetic had a
simultaneous origin.
Not only are the first distinct ideas of number co-ordinate with ideas of
likeness and equality, but the first efforts at numeration display the same
relationship. On reading accounts of savage tribes, we find that the method
of counting by the fingers, still followed by many children, is the aboriginal
method. Neglecting the several cases {39} in which the ability to enumerate
does not reach even to the number of fingers on one hand, there are many
cases in which it does not extend beyond ten—the limit of the simple finger
notation. The fact that in so many instances, remote, and seemingly
unrelated nations, have adopted ten as their basic number; together with the
fact that in the remaining instances the basic number is either five (the
fingers of one hand) or twenty (the fingers and toes); of themselves show
that the fingers were the original units of numeration. The still surviving use
of the word digit , as the general name for a figure in arithmetic, is
significant; and it is even said that our word ten (Sax. tyn; Dutch, tien;
German, zehn) means in its primitive expanded form two hands . So that,
originally, to say there were ten things, was to say there were two hands of
them. From all which evidence it is tolerably clear that the earliest mode of
conveying the idea of a number of things, was by holding up as many
fingers as there were things; that is, by using a symbol which was equal , in
respect of multiplicity, to the group symbolized. For which inference there
is, indeed, strong confirmation in the statement that our own soldiers

spontaneously adopted this device in their dealings with the Turks during
the Crimean war. And here it should be remarked that in this re-combination
of the notion of equality with that of multiplicity, by which the first steps in
numeration are effected, we may see one of the earliest of those
inosculations between the diverging branches of science, which are
afterwards of perpetual occurrence.
As this observation suggests, it will be well, before tracing the mode in
which exact science emerges from the inexact judgments of the senses, and
showing the non-serial evolution of its divisions, to note the non-serial
character of those preliminary processes of which all after development is a
continuation. On re-considering them it will be seen that not only are they
divergent branches {40} from a common root,—not only are they
simultaneous in their growth; but that they are mutual aids; and that none
can advance without the rest. That progress of clas­si­fi­ca­tion for which the
unfolding of the perceptions paves the way, is impossible without a
corresponding progress in language, by which greater varieties of objects
are thinkable and expressible. On the one hand clas­si­fi­ca­tion cannot be
carried far without names by which to designate the classes; and on the
other hand language cannot be made faster than things are classified. Again,
the multiplication of classes and the consequent narrowing of each class,
itself involves a greater likeness among the things classed together; and the
consequent approach towards the notion of complete likeness itself allows
clas­si­fi­ca­tion to be carried higher. Moreover, clas­si­fi­ca­tion necessarily
advances pari passu with rationality—the clas­si­fi­ca­tion of things with the
clas­si­fi­ca­tion of relations . For things that belong to the same class are, by
implication, things of which the properties and modes of behaviour—the
co-existences and sequences—are more or less the same; and the
recognition of this sameness of co-existences and sequences is reasoning.
Whence it follows that the advance of clas­si­fi­ca­tion is necessarily
proportionate to the advance of gen­er­al­i­za­tions. Yet further, the notion of
likeness , both in things and relations, simultaneously evolves by one
process of culture the ideas of equality of things and equality of relations;
which are the respective bases of exact concrete reasoning and exact

abstract reasoning—Mathematics and Logic. And once more, this idea of
equality, in the very process of being formed, necessarily gives origin to
two series of relations—those of magnitude and those of number; from
which arise geometry and the calculus. Thus the process throughout is one
of perpetual subdivision and perpetual inter­com­mun­i­ca­tion of the divisions.
From the very first there has been that consensus of different kinds of
knowledge, {41} answering to the consensus of the intellectual faculties,
which, as already said, must exist among the sciences.
Let us now go on to observe how, out of the notions of equality and
number , as arrived at in the manner described, there gradually arose the
elements of quantitative prevision.
Equality, once having come to be definitely conceived, was recognizable
among other phenomena than those of magnitude. Being predicable of all
things producing in­dis­tin­guish­able impressions, there naturally grew up
ideas of equality in weights, sounds, colours, &c.; and, indeed, it can
scarcely be doubted that the occasional experience of equal weights,
sounds, and colours, had a share in developing the abstract conception of
equality—that the ideas of equality in sizes, relations, forces, resistances,
and sensible properties in general, were evolved during the same stage of
mental development. But however this may be, it is clear that as fast as the
notion of equality gained definiteness, so fast did that lowest kind of
quantitative prevision which is achieved without any instrumental aid,
become possible. The ability to estimate, however roughly, the amount of a
foreseen result, implies the conception that it will be equal to a certain
imagined quantity; and the correctness of the estimate will manifestly
depend on the precision which the perceptions of sensible equality have
reached. A savage with a piece of stone in his hand, and another piece lying
before him of greater bulk but of the same kind (sameness of kind being
inferred from the equality of the two in colour and texture) knows about
what effort he must put forth to raise this other piece; and he judges
accurately in proportion to the accuracy with which he perceives that the
one is twice, three times, four times, &c. as large as the other; that is—in
proportion to the precision of his ideas of equality and number. And here let

us not omit to notice that even in these vaguest of quantitative previsions,
the conception of equality of relations is also involved. For it is only in {42}
virtue of an undefined con­scious­ness that the relation between bulk and
weight in the one stone is equal to the relation between bulk and weight in
the other, that even the roughest approximation can be made.
But how came the transition from those uncertain perceptions of equality
which the unaided senses give, to the certain ones with which science
deals? It came by placing the things compared in juxtaposition. Equality
being asserted of things which give us in­dis­tin­guish­able impressions, and
no distinct comparison of impressions being possible unless they occur in
immediate succession, it results that exactness of equality is ascertainable in
proportion to the closeness of the compared things. Hence the fact that
when we wish to judge of two shades of colour whether they are alike or
not, we place them side by side; hence the fact that we cannot, with any
precision, say which of two allied sounds is the louder, or the higher in
pitch, unless we hear the one immediately after the other; hence the fact that
to estimate the ratio of weights, we take one in each hand, that we may
compare their pressures by rapidly alternating in thought from the one to
the other; hence the fact, that in a piece of music, we can continue to make
equal beats when the first beat has been given, but cannot ensure
commencing with the same length of beat on a future occasion; and hence,
lastly, the fact, that of all magnitudes, those of linear extension are those of
which the equality is most precisely ascertainable, and those to which, by
consequence, all others have to be reduced. For it is the peculiarity of linear
extension that it alone allows its magnitudes to be placed in absolute
juxtaposition, or, rather, in coincident position; it alone can test the equality
of two magnitudes by observing whether they will coalesce, as two equal
mathematical lines do, when placed between the same points; it alone can
test equality by trying whether it will become identity . Hence, then, the
fact, that all exact science is reducible, {43} by an ultimate analysis, to
results measured in equal units of linear extension.

Still it remains to be noticed in what manner this determination of
equality by comparison of linear magnitudes originated. Once more may we
perceive that surrounding natural objects supplied the needful lessons. From
the beginning there must have been a constant experience of like things
placed side by side—men standing and walking together; animals from the
same herd; fish from the same shoal. And the ceaseless repetition of these
experiences could not fail to suggest the observation, that the nearer
together any objects were, the more visible became any inequality between
them. Hence the obvious device of putting in apposition, things of which it
was desired to ascertain the relative magnitudes. Hence the idea of
measure . And here we suddenly come upon a group of facts which afford a
solid basis to the remainder of our argument; while they also furnish strong
evidence in support of the foregoing speculations. Those who look
sceptically on this attempted rehabilitation of early mental development,
and who think that the derivation of so many primary notions from organic
forms is somewhat strained, will perhaps see more probability in the
hypotheses which have been ventured, on discovering that all measures of
extension and force originated from the lengths and weights of organic
bodies, and all measures of time from the periodic phenomena of either
organic or inorganic bodies.
Thus, among linear measures, the cubit of the Hebrews was the length of
the forearm from the elbow to the end of the middle finger; and the smaller
scriptural dimensions are expressed in hand-breadths and spans . The
Egyptian cubit, which was similarly derived, was divided into digits, which
were finger-breadths ; and each finger-breadth was more definitely
expressed as being equal to four grains of barley placed breadthwise. Other
ancient measures were {44} the orgyia or stretch of the arms , the pace , and
the palm . So persistent has been the use of these natural units of length in
the East, that even now some Arabs mete out cloth by the forearm. So, too,
is it with European measures. The foot prevails as a dimension throughout
Europe, and has done so since the time of the Romans, by whom, also, it
was used: its lengths in different places varying not much more than men’s
feet vary. The heights of horses are still expressed in hands . The inch is the

length of the terminal joint of the thumb ; as is clearly shown in France,
where pouce means both thumb and inch. Then we have the inch divided
into three barley-corns . So completely, indeed, have these organic
dimensions served as the substrata of mensuration, that it is only by means
of them that we can form any estimate of some of the ancient distances. For
example, the length of a degree on the Earth’s surface, as determined by the
Arabian astronomers shortly after the death of Haroun-al-Raschid, was
fifty-six of their miles. We know nothing of their mile further than that it
was 4000 cubits; and whether these were sacred cubits or common cubits,
would remain doubtful, but that the length of the cubit is given as twenty-
seven inches, and each inch defined as the thickness of six barley-grains.
Thus one of the earliest measurements of a degree comes down to us in
barley-grains. Not only did organic lengths furnish those approximate
measures which satisfied men’s needs in ruder ages, but they furnished also
the standard measures required in later times. One instance occurs in our
own history. To remedy the irregularities then prevailing, Henry I.
commanded that the ulna, or ancient ell, which answers to the modern yard,
should be made of the exact length of his own arm .
Measures of weight had a kindred derivation. Seeds seem commonly to
have supplied the units. The original of the carat used for weighing in India
is a small bean . Our own systems, both troy and avoirdupois, are derived
{45} primarily from wheat-corns. Our smallest weight, the grain is a grain of
wheat . This is not a speculation; it is an his­tor­i­cal­ly-reg­is­tered fact. Henry
III. enacted that an ounce should be the weight of 640 dry grains of wheat
from the middle of the ear. And as all the other weights are multiples or
sub-multiples of this, it follows that the grain of wheat is the basis of our
scale. So natural is it to use organic bodies as weights, before artificial
weights have been established, or where they are not to be had, that in some
of the remoter parts of Ireland the people are said to be in the habit, even
now, of putting a man into the scales to serve as a measure for heavy
commodities.
Similarly with time. Astronomical periodicity, and the periodicity of
animal and vegetable life, are simultaneously used in the first stages of

progress for estimating epochs. The simplest unit of time, the day, nature
supplies ready made. The next simplest period, the moneth or month, is also
thrust upon men’s notice by the conspicuous changes constituting a
lunation. For larger divisions than these, the phenomena of the seasons, and
the chief events from time to time occurring, have been used by early and
uncivilized races. Among the Egyptians the rising of the Nile served as a
mark. The New Zealanders were found to begin their year from the
reappearance of the Pleiades above the sea. One of the uses ascribed to
birds, by the Greeks, was to indicate the seasons by their migrations.
Barrow describes the aboriginal Hottentot as expressing dates by the
number of moons before or after the ripening of one of his chief articles of
food. He further states that the Kaffir chronology is kept by the moon, and
is registered by notches on sticks—the death of a favourite chief, or the
gaining of a victory, serving for a new era. By which last fact, we are at
once reminded that in early history, events are commonly recorded as
occurring in certain reigns, and in certain years of certain reigns: a
proceeding which made a king’s reign {46} a rude measure of duration. And,
as further illustrating the tendency to divide time by natural phenomena and
natural events, it may be noticed that even by our own peasantry the
definite divisions of months and years are but little used; and that they
habitually refer to occurrences as “before sheep-shearing,” or “after
harvest,” or “about the time when the squire died.” It is manifest, therefore,
that the approximately equal periods perceived in Nature gave the first units
of measure for time; as did Nature’s approximately equal lengths and
weights give the first units of measure for space and force.
It remains only to observe, that measures of value were similarly derived.
Barter, in one form or other, is found among all but the very lowest human
races. It is obviously based upon the notion of equality of worth . And as it
gradually merges into trade by the introduction of some kind of currency,
we find that the measures of worth , constituting this currency, are organic
bodies; in some cases cowries , in others cocoa-nuts , in others cattle , in
others pigs ; among the American Indians peltry or skins , and in Iceland
dried fish .

Notions of exact equality and of measure having been reached, there
arose definite ideas of magnitudes as being multiples one of another;
whence the practice of measurement by direct apposition of a measure. The
determination of linear extensions by this process can scarcely be called
science, though it is a step towards it; but the determination of lengths of
time by an analogous process may be considered as one of the earliest
samples of quantitative prevision. For when it is first ascertained that the
moon completes the cycle of her changes in about thirty days—a fact
known to most uncivilized tribes that can count beyond the number of their
fingers—it is manifest that it becomes possible to say in what number of
days any specified phase of the moon will recur; and it is also manifest that
this prevision is effected by an apposition of two times, after the same
manner {47} that linear space is measured by the apposition of two lines. For
to express the moon’s period in days, is to say how many of these units of
measure are contained in the period to be measured—is to ascertain the
distance between two points in time by means of a scale of days , just as we
ascertain the distance between two points in space by a scale of feet or
inches; and in each case the scale coincides with the thing measured—
mentally in the one, visibly in the other. So that in this simplest, and
perhaps earliest case of quantitative prevision, the phenomena are not only
thrust daily upon men’s notice, but Nature is, as it were, perpetually
repeating that process of measurement by observing which the prevision is
effected.
This fact, that in very early stages of social progress it is known that the
moon goes through her changes in nearly thirty days, and that in rather
more than twelve moons the seasons return—this fact that chronological
astronomy assumes a certain scientific character even before geometry
does; while it is partly due to the circumstance that the astronomical
divisions, day, month, and year, are ready made for us, is partly due to the
further circumstances that agricultural and other operations were at first
regulated astronomically, and that from the supposed divine nature of the
heavenly bodies their motions determined the periodical religious festivals.
As instances of the one we have the observation of the Egyptians, that the

rising of the Nile corresponded with the heliacal rising of Sirius; the
directions given by Hesiod for reaping and ploughing, according to the
positions of the Pleiades; and his maxim that “fifty days after the turning of
the sun is a seasonable time for beginning a voyage.” As instances of the
other, we have the naming of the days after the sun, moon, and planets; the
early attempts among Eastern nations to regulate the calendar so that the
gods might not be offended by the displacement of their sacrifices; and the
fixing of the great annual festival of the Peruvians by the position of the
sun. {48} In all which facts we see that, at first, science was simply an
appliance of religion and industry.
After the discoveries that a lunation occupies nearly thirty days, and that
some twelve lunations occupy a year—discoveries which we may infer
were the earliest, from the fact that existing uncivilized races have made
them—we come to the first known astronomical records, which are those of
eclipses. The Chaldeans were able to predict these. “This they did,
probably,” says Dr. Whewell in his useful history, from which most of the
materials we are about to use will be drawn, “by means of their cycle of 223
months, or about eighteen years; for, at the end of this time, the eclipses of
the moon begin to return, at the same intervals and in the same order as at
the beginning.” Now this method of calculating eclipses by means of a
recurring cycle,—the Saros as they called it—is a more complex case of
prevision by means of coincidence of measures. For by what observations
must the Chaldeans have discovered this cycle? Obviously, as Delambre
infers, by inspecting their registers; by comparing the successive intervals;
by finding that some of the intervals were alike; by seeing that these equal
intervals were eighteen years apart; by discovering that all the intervals that
were eighteen years apart were equal; by ascertaining that the intervals
formed a series which repeated itself, so that if one of the cycles of intervals
were superposed on another the divisions would fit. And this being once
perceived, it became possible to use the cycle as a scale of time by which to
measure out future periods of recurrence. Seeing thus that the process of so
predicting eclipses, is in essence the same as that of predicting the moon’s
monthly changes by observing the number of days after which they repeat

—seeing that the two differ only in the extent and irregularity of the
intervals; it is not difficult to understand how such an amount of knowledge
should so early have been reached. And we shall be the less surprised on
remembering that the only things involved in these {49} previsions were
time and number ; and that the time was in a manner self-numbered.
Still, the ability to predict events recurring only after so long a period as
eighteen years, implies a considerable advance in civilization—a
considerable development of general knowledge; and we have now to
inquire what progress in other sciences accompanied, and was necessary to,
these astronomical previsions. In the first place, there must have been a
tolerably efficient system of calculation. Mere finger-counting, mere head-
reckoning, even with the aid of a decimal notation, could not have sufficed
for numbering the days in a year; much less the years, months, and days
between eclipses. Consequently there must have been a mode of registering
numbers; probably even a system of numerals. The earliest numerical
records, if we may judge by the practices of the less civilized races now
existing, were probably kept by notches cut on sticks, or strokes marked on
walls; much as public-house scores are kept now. And there is reason to
think that the first numerals used were simply groups of straight strokes, as
some of the still-extant Roman ones are; leading us to suspect that these
groups of strokes were used to represent groups of fingers, as the groups of
fingers had been used to represent groups of objects—a supposition
harmonizing with the aboriginal practice of picture writing. Be this so or
not, however, it is manifest that before the Chaldeans discovered their
Saros , they must have had both a set of written symbols serving for an
extensive numeration, and a familiarity with the simpler rules of arithmetic.
Not only must abstract mathematics have made some progress, but
concrete mathematics also. It is scarcely possible that the buildings
belonging to this era should have been laid out and erected without any
knowledge of geometry. At any rate, there must have existed that
elementary geometry which deals with direct {50} measurement—with the
apposition of lines; and it seems that only after the discovery of those

simple proceedings, by which right angles are drawn, and relative positions
fixed, could so regular an architecture be executed. In the case of the other
division of concrete mathematics—mechanics, we have definite evidence of
progress. We know that the lever and the inclined plane were employed
during this period: implying that there was a qualitative prevision of their
effects, if not a quantitative one. But we know more. We read of weights in
the earliest records; and we find weights in ruins of the highest antiquity.
Weights imply scales, of which we have also mention; and scales involve
the primary theorem of mechanics in its least complicated form—involve
not a qualitative but a quantitative prevision of mechanical effects. And here
we may notice how mechanics, in common with the other exact sciences,
took its rise from the simplest application of the idea of equality . For the
mechanical proposition which the scales involve, is, that if a lever with
equal arms, have equal weights suspended from them, the weights will
remain at equal altitudes. And we may further notice how, in this first step
of rational mechanics, we see illustrated the truth awhile since named, that
as magnitudes of linear extension are the only ones of which the equality is
exactly ascertainable, the equalities of other magnitudes have at the outset
to be determined by means of them. For the equality of the weights which
balance each other in scales, depends on the equality of the arms: we can
know that the weights are equal only by proving that the arms are equal.
And when by this means we have obtained a system of weights,—a set of
equal units of force and definite multiples of them, then does a science of
mechanics become possible. Whence, indeed, it follows, that rational
mechanics could not possibly have any other starting-point than the scales.
Let us further remember that during this same period {51} there was some
knowledge of chemistry. Sundry of the arts which we know to have been
carried on, were made possible only by a generalized experience of the
modes in which certain bodies affect each other under special conditions. In
metallurgy, which was extensively practised, this is abundantly illustrated.
And we even have evidence that in some cases the knowledge possessed
was, in a sense, quantitative. For, as we find by analysis that the hard alloy
of which the Egyptians made their cutting tools, was composed of copper

and tin in fixed proportions, there must have been an established prevision
that such an alloy was to be obtained only by mixing them in these
proportions. It is true, this was but a simple empirical generalization; but so
was the generalization respecting the recurrence of eclipses; so are the first
gen­er­al­i­za­tions of every science.
Respecting the simultaneous advance of the sciences during this early
epoch, it remains to point out that even the most complex of them must
have made some progress. For under what conditions only were the
foregoing developments possible? The conditions furnished by an
established and organized social system. A long continued registry of
eclipses; the building of palaces; the use of scales; the practice of
metallurgy—alike imply a settled and populous nation. The existence of
such a nation not only presupposes laws and some administration of justice,
which we know existed, but it presupposes successful laws—laws
conforming in some degree to the conditions of social stability—laws
enacted because it was found that the actions forbidden by them were
dangerous to the State. We do not by any means say that all, or even the
greater part, of the laws were of this nature; but we do say, that the
fundamental ones were. It cannot be denied that the laws affecting life and
property were such. It cannot be denied that, however little these were
enforced between class and class, they were to a considerable extent {52}
enforced between members of the same class. It can scarcely be questioned,
that the administration of them between members of the same class was
seen by rulers to be necessary for keeping society together. But supposition
aside, it is clear that the habitual recognition of these claims in their laws,
implied some prevision of social phenomena. That same idea of equality ,
which, as we have seen, underlies other science, underlies also morals and
sociology. The conception of justice, which is the primary one in morals;
and the administration of justice, which is the vital condition to social
existence; are impossible without the recognition of a certain likeness in
men’s claims, in virtue of their common humanity. Equity literally means
equalness ; and if it be admitted that there were even the vaguest ideas of
equity in these primitive eras, it must be admitted that there was some

appreciation of the equalness of men’s liberties to pursue the objects of life
—some appreciation, therefore, of the essential principle of national
equilibrium.
Thus in this initial stage of the positive sciences, before geometry had yet
done more than evolve a few empirical rules—before mechanics had passed
beyond its first theorem—before astronomy had advanced from its merely
chronological phase into the geometrical; the most involved of the sciences
had reached a certain degree of development—a development without
which no progress in other sciences was possible.
Only noting as we pass, how, thus early, we may see that the progress of
exact science was not only towards an increasing number of previsions, but
towards previsions more accurately quantitative—how, in astronomy, the
recurring period of the moon’s motions was by and by more correctly
ascertained to be two hundred and thirty-five lunations; how Callipus
further corrected this Metonic cycle, by leaving out a day at the end of
every seventy-six years; and how these successive advances implied a {53}
longer continued registry of observations, and the co-ordination of a greater
number of facts; let us go on to inquire how geometrical astronomy took its
rise. The first astronomical instrument was the gnomon. This was not only
early in use in the East, but it was found among the Mexicans; the sole
astronomical observations of the Peruvians were made by it; and we read
that 1100 B.C. , the Chinese observed that, at a certain place, the length of
the sun’s shadow, at the summer solstice, was to the height of the gnomon,
as one and a half to eight. Here again it is observable, both that the
instrument is found ready made, and that Nature is perpetually performing
the process of measurement. Any fixed, erect object—a column, a pole, the
angle of a building—serves for a gnomon; and it needs but to notice the
changing position of the shadow it daily throws, to make the first step in
geometrical astronomy. How small this first step was, may be seen in the
fact that the only things ascertained at the outset were the periods of the
summer and winter solstices, which corresponded with the least and
greatest lengths of the mid-day shadow; and to fix which, it was needful
merely to mark the point to which each day’s shadow reached. And now let

it not be overlooked that in the observing at what time during the next year
this extreme limit of the shadow was again reached, and in the inference
that the sun had then arrived at the same turning point in his annual course,
we have one of the simplest instances of that combined use of equal
magnitudes and equal relations , by which all exact science, all quantitative
prevision, is reached. For the relation observed was between the length of
the gnomon’s shadow and the sun’s position in the heavens; and the
inference drawn was that when, next year, the extremity of the shadow
came to the same point, he occupied the same place. That is, the ideas
involved were, the equality of the shadows, and the equality of the relations
between {54} shadow and sun in successive years. As in the case of the
scales, the equality of relations here recognized is of the simplest order. It is
not as those habitually dealt with in the higher kinds of scientific reasoning,
which answer to the general type—the relation between two and three
equals the relation between six and nine; but it follows the type—the
relation between two and three equals the relation between two and three: it
is a case of not simply equal relations, but coinciding relations. And here,
indeed, we may see beautifully illustrated how the idea of equal relations
takes its rise after the same manner that that of equal magnitudes does. As
already shown, the idea of equal magnitudes arose from the observed
coincidence of two lengths placed together; and in this case we have not
only two coincident lengths of shadows, but two coincident relations
between sun and shadows.
From the use of the gnomon there naturally grew up the conception of
angular measurements; and with the advance of geometrical conceptions
came the hemisphere of Berosus, the equinoctial armil, the solstitial armil,
and the quadrant of Ptolemy—all of them employing shadows as indices of
the sun’s position, but in combination with angular divisions. It is out of the
question for us here to trace these details of progress. It must suffice to
remark that in all of them we may see that notion of equality of relations of
a more complex kind, which is best illustrated in the astrolabe, an
instrument which consisted “of circular rims, moveable one within the
other, or about poles, and contained circles which were to be brought into

the position of the ecliptic, and of a plane passing through the sun and the
poles of the ecliptic”—an instrument, therefore, which represented, as by a
model, the relative positions of certain imaginary lines and planes in the
heavens; which was adjusted by putting these representative lines and
planes into parallelism with the celestial ones; and which depended for its
use on the perception that the relations among these {55} representative lines
and planes were equal to the relations among those represented. We might
go on to point out how the conception of the heavens as a revolving hollow
sphere, the explanation of the moon’s phases, and indeed all the successive
steps taken, involved this same mental process. But we must content
ourselves with referring to the theory of eccentrics and epicycles, as a
further marked illustration of it. As first suggested, and as proved by
Hipparchus to afford an explanation of the leading irregularities in the
celestial motions, this theory involved the perception that the progressions,
retrogressions, and variations of velocity seen in the heavenly bodies, might
be reconciled with their assumed uniform movements in circles, by
supposing that the earth was not in the centre of their orbits; or by
supposing that they revolved in circles whose centres revolved round the
earth; or by both. The discovery that this would account for the
appearances, was the discovery that in certain geometrical diagrams the
relations were such, that the uniform motion of points along curves
conditioned in specified ways, would, when looked at from a particular
position, present analogous irregularities; and the calculations of
Hipparchus involved the belief that the relations subsisting among these
geometrical curves were equal to the relations subsisting among the
celestial orbits.
Leaving here these details of astronomical progress, and the philosophy
of it, let us observe how the relatively concrete science of geometrical
astronomy, having been thus far helped forward by the development of
geometry in general, reacted upon geometry, caused it also to advance, and
was again assisted by it. Hipparchus, before making his solar and lunar
tables, had to discover rules for calculating the relations between the sides
and angles of triangles—trigonometry , a subdivision of pure mathematics.

Further, the reduction of the doctrine of the sphere to a quantitative form
needed for astronomical purposes, required the formation of a spherical
trigonometry , which {56} was also achieved by Hipparchus. Thus both
plane and spherical trigonometry, which are parts of the highly abstract and
simple science of extension, remained undeveloped until the less abstract
and more complex science of the celestial motions had need of them. The
fact admitted by M. Comte, that since Descartes the progress of the abstract
division of mathematics has been determined by that of the concrete
division, is paralleled by the still more significant fact that even thus early
the progress of mathematics was determined by that of astronomy. And
here, indeed, we see exemplified the truth, which the subsequent history of
science frequently illustrates, that before any more abstract division makes
a further advance, some more concrete division suggests the necessity for
that advance—presents the new order of questions to be solved. Before
astronomy put before Hipparchus the problem of solar tables, there was
nothing to raise the question of the relations between lines and angles: the
subject-matter of trigonometry had not been conceived.
Just incidentally noticing the circumstance that the epoch we are
describing witnessed the evolution of algebra, a comparatively abstract
division of mathematics, by the union of its less abstract divisions,
geometry and arithmetic (a fact proved by the earliest extant samples of
algebra, which are half algebraic, half geometric) we go on to observe that
during the era in which mathematics and astronomy were thus advancing,
rational mechanics made its second step; and something was done towards
giving a quantitative form to hydrostatics, optics, and acoustics. In each
case we shall see how the idea of equality underlies all quantitative
prevision; and in what simple forms this idea is first applied.
As already shown, the first theorem established in mechanics was, that
equal weights suspended from a lever with equal arms would remain in
equilibrium. Archimedes discovered that a lever with unequal arms was in
{57} equilibrium when one weight was to its arm as the other arm to its
weight; that is—when the numerical relation between one weight and its

arm was equal to the numerical relation between the other arm and its
weight.
The first advance made in hydrostatics, which we also owe to
Archimedes, was the discovery that fluids press equally in all directions;
and from this followed the solution of the problem of floating bodies;
namely, that they are in equilibrium when the upward and downward
pressures are equal .
In optics, again, the Greeks found that the angle of incidence is equal to
the angle of reflection; and their knowledge reached no further than to such
simple deductions from this as their geometry sufficed for. In acoustics they
ascertained the fact that three strings of equal lengths would yield the
octave, fifth and fourth, when strained by weights having certain definite
ratios; and they did not progress much beyond this. In the one of which
cases we see geometry used in elucidation of the laws of light; and in the
other, geometry and arithmetic made to measure certain phenomena of
sound.
While sundry sciences had thus reached the first stages of quantitative
prevision, others were progressing in qualitative prevision. It must suffice
just to note that some small gen­er­al­i­za­tions were made respecting
evaporation, and heat, and electricity, and magnetism, which, empirical as
they were, did not in that respect differ from the first gen­er­al­i­za­tions of
every science; that the Greek physicians had made advances in physiology
and pathology, which, considering the great imperfection of our present
knowledge, are by no means to be despised; that zoology had been so far
systematized by Aristotle, as, to some extent, enabled him from the
presence of certain organs to predict the presence of others; that in
Aristotle’s Politics , is shown progress towards a scientific conception of
social phenomena, and sundry previsions respecting {58} them; and that in
the state of the Greek societies, as well as in the writings of Greek
philosophers, we may recognize both an increasing clearness in the
conception of equity and some appreciation of the fact that social stability
depends on the maintenance of equitable relations. Space permitting, we
might dwell on the causes which retarded the development of some of the

sciences, as for example, chemistry; showing that relative complexity had
nothing to do with it—that the oxidation of a piece of iron is a simpler
phenomenon than the recurrence of eclipses, and the discovery of carbonic
acid less difficult than that of the precession of the equinoxes. The
relatively slow advance of chemical knowledge might be shown to be due,
partly to the fact that its phenomena were not daily thrust on men’s notice
as those of astronomy were; partly to the fact that Nature does not
habitually supply the means, and suggest the modes of investigation, as in
the sciences dealing with time, extension, and force; partly to the fact that
the great majority of the materials with which chemistry deals, instead of
being ready to hand, are made known only by the arts in their slow growth;
and partly to the fact that even when known, their chemical properties are
not self-exhibited, but have to be sought out by experiment.
Merely indicating these considerations, however, let us go on to
contemplate the progress and mutual influence of the sciences in modern
days; only parenthetically noticing how, on the revival of the scientific
spirit, the successive stages achieved exhibit the dominance of the law
hitherto traced—how the primary idea in dynamics, a uniform force, was
defined by Galileo to be a force which generates equal velocities in equal
successive times—how the uniform action of gravity was first
experimentally determined by showing that the time elapsing before a body
thrown up, stopped, was equal to the time it took to fall—how the first fact
in compound motion which Galileo {59} ascertained was, that a body
projected horizontally, will describe equal horizontal spaces in equal times,
compounded vertical spaces described which increase by equal increments
in equal times—how his discovery respecting the pendulum was, that its
oscillations occupy equal intervals of time whatever their lengths—how the
law which he established that in any machine the weights that balance each
other, are reciprocally as their virtual velocities implies that the relation of
one set of weights to their velocities equals the relation of the other set of
velocities to their weights;—and how thus his achievements consisted in
showing the equalities of certain magnitudes and relations, whose equalities
had not been previously recognized.

And now, but only now, physical astronomy became possible. The simple
laws of force had been disentangled from those of friction and atmospheric
resistance by which all their earthly manifestations are disguised.
Progressing knowledge of terrestrial physics had given a due insight into
these disturbing causes; and, by an effort of abstraction, it was perceived
that all motion would be uniform and rectilinear unless interfered with by
external forces. Geometry and mechanics having diverged from a common
root in men’s sensible experiences, and having, with occasional
inosculations, been separately developed, the one partly in connexion with
astronomy, the other solely by analyzing terrestrial movements, now join in
the investigations of Newton to create a true theory of the celestial motions.
And here, also, we have to notice the important fact that, in the very process
of being brought jointly to bear upon astronomical problems, they are
themselves raised to a higher phase of development. For it was in dealing
with the questions raised by celestial dynamics that the then incipient
infinitesimal calculus was unfolded by Newton and his continental
successors; and it was from inquiries into the mechanics of the solar system
that the general theorems of mechanics contained in the {60} Principia —
many of them of purely terrestrial application—took their rise. Thus, as in
the case of Hipparchus, the presentation of a new order of concrete facts to
be analyzed, led to the discovery of new abstract facts; and these abstract
facts then became instruments of access to endless groups of concrete facts
previously beyond quantitative treatment.
Meanwhile, physics had been carrying further that progress without
which, as just shown, rational mechanics could not be disentangled. In
hydrostatics, Stevinus had extended and applied the discovery of
Archimedes. Torricelli had proved atmospheric pressure, “by showing that
this pressure sustained different liquids at heights inversely proportional to
their densities;” and Pascal “established the necessary diminution of this
pressure at increasing heights in the atmosphere”: discoveries which in part
reduced this branch of science to a quantitative form. Something had been
done by Daniel Bernouilli towards the dynamics of fluids. The thermometer
had been invented; and sundry small gen­er­al­i­za­tions reached by it.

Huyghens and Newton had made considerable progress in optics; Newton
had approximately calculated the rate of transmission of sound; and the
continental mathematicians had ascertained some of the laws of sonorous
vibrations. Magnetism and electricity had been considerably advanced by
Gilbert. Chemistry had got as far as the mutual neutralization of acids and
alkalies. And Leonardo da Vinci had advanced in geology to the conclusion
that the deposition of animal remains in marine strata is the origin of fossils.
Our present purpose does not require that we should give particulars. Here
it only concerns us to illustrate the consensus subsisting in this stage of
growth, and afterwards. Let us look at a few cases.
The theoretic law of the velocity of sound deduced by Newton from
purely mechanical data, was found wrong by one-sixth. The error remained
unaccounted for until the {61} time of Laplace, who, suspecting that the heat
disengaged by the compression of the undulating strata of the air, gave
additional elasticity, and so produced the difference, made the needful
calculations and found he was right. Thus acoustics was arrested until
thermology overtook and aided it. When Boyle and Marriot had discovered
the relation between the densities of gases and the pressures they are subject
to; and when it thus became possible to calculate the rate of decreasing
density in the upper parts of the atmosphere; it also became possible to
make approximate tables of the atmospheric refraction of light. Thus optics,
and with it astronomy, advanced with barology. After the discovery of
atmospheric pressure had led to the invention of the air-pump by Otto
Guericke; and after it had become known that evaporation increases in
rapidity as atmospheric pressure decreases; it became possible for Leslie, by
evaporation in a vacuum, to produce the greatest cold known; and so to
extend our knowledge of thermology by showing that there is no zero
within reach of our researches. When Fourier had determined the laws of
conduction of heat, and when the Earth’s temperature had been found to
increase below the surface one degree in every forty yards, there were data
for inferring the past condition of our globe; the vast period it has taken to
cool down to its present state; and the immense age of the solar system—a
purely astronomical consideration. Chemistry having advanced sufficiently

to supply the needful materials, and a physiological experiment having
furnished the requisite hint, there came the discovery of galvanic electricity.
Galvanism reacting on chemistry disclosed the metallic bases of the alkalies
and earths, and inaugurated the electro-chemical theory; in the hands of
Oersted and Ampère it led to the laws of magnetic action; and by its aid
Faraday has detected significant facts relative to the constitution of light.
Brewster’s discoveries respecting double refraction and {62} dipolarization
proved the essential truth of the clas­si­fi­ca­tion of crystalline forms according
to the number of axes, by showing that the molecular constitution depends
on the axes. Now in these and in numerous other cases, the mutual
influence of the sciences has been quite independent of any supposed
hierarchical order. Often, too, their inter-actions are more complex than as
thus instanced—involve more sciences than two. One illustration of this
must suffice. We quote it in full from the History of the Inductive Sciences .
In Book XI., chap. II., on “The Progress of the Electrical Theory,” Dr.
Whewell writes:―
“Thus at that period, mathematics was behind experiment, and a problem was proposed, in which
theoretical numerical results were wanted for comparison with observation, but could not be
accurately obtained; as was the case in astronomy also, till the time of the approximate solution of the
problem of three bodies, and the consequent formation of the tables of the moon and planets, on the
theory of universal gravitation. After some time, electrical theory was relieved from this reproach,
mainly in consequence of the progress which astronomy had occasioned in pure mathematics. About
1801 there appeared in the Bulletin des Sciences , an exact solution of the problem of the distribution
of electric fluid on a spheroid, obtained by Biot, by the application of the peculiar methods which
Laplace had invented for the problem of the figure of the planets. And, in 1811, M. Poisson applied
Laplace’s artifices to the case of two spheres acting upon one another in contact, a case to which
many of Coulomb’s experiments were referrible; and the agreement of the results of theory and
observation, thus extricated from Coulomb’s numbers obtained above forty years previously, was
very striking and convincing.”
Not only do the sciences affect each other after this direct manner, but
they affect each other indirectly. Where there is no dependence, there is yet
analogy—likeness of relations ; and the discovery of the relations subsisting
among one set of phenomena, constantly suggests a search for similar
relations among another set. Thus the established fact that the force of
gravitation varies inversely as the square of the distance, being recognized
as a necessary characteristic of all influences proceeding from a centre,
raised the suspicion that heat and light follow the same law; which proved

to be the case—a suspicion and a {63} confirmation which were repeated in
respect to the electric and magnetic forces. Thus, again, the discovery of the
polarization of light led to experiments which ended in the discovery of the
polarization of heat—a discovery that could never have been made without
the antecedent one. Thus, too, the known refrangibility of light and heat
lately produced the inquiry whether sound also is not refrangible; which on
trial it turns out to be. In some cases, indeed, it is only by the aid of
conceptions derived from one class of phenomena that hypotheses
respecting other classes can be formed. The theory, at one time favoured,
that evaporation is a solution of water in air, assumed that the relation
between water and air is like the relation between water and a dissolved
solid; and could never have been conceived if relations like that between
salt and water had not been previously known. Similarly the received theory
of evaporation—that it is a diffusion of the particles of the evaporating fluid
in virtue of their atomic repulsion—could not have been entertained without
a foregoing experience of magnetic and electric repulsions. So complete in
recent days has become this consensus among the sciences, caused either
by the natural entanglement of their phenomena, or by analogies between
the relations of their phenomena, that scarcely any considerable discovery
concerning one order of facts now takes place, without shortly leading to
discoveries concerning other orders.
To produce a complete conception of this process of scientific evolution
it would be needful to go back to the beginning, and trace in detail the
growth of clas­si­fi­ca­tions and nomenclatures; and to show how, as
subsidiary to science, they have acted upon it while it has reacted upon
them. We can only now remark that, on the one hand, clas­si­fi­ca­tions and
nomenclatures have aided science by subdividing the subject-matter of
research, and giving fixity and diffusion to the truths disclosed; and that on
the other hand, they have caught from it that increasing {64} quan­ti­ta­tive­‐
ness, and that progress from considerations touching single phenomena to
considerations touching the relations among many phenomena, which we
have been describing. Of this last influence a few illustrations must be

given. In chemistry it is seen in the facts that the dividing of matter into the
four elements was ostensibly based on the single property of weight, that
the first truly chemical division into acid and alkaline bodies, grouped
together bodies which had not simply one property in common but in which
one property was constantly related to many others, and that the clas­si­fi­ca­‐
tion now current, places together in the groups supporters of combustion ,
metallic and non-metallic bases , acids , salts , &c., bodies which are often
quite unlike in sensible qualities, but which are like in the majority of their
relations to other bodies. In mineralogy again, the first clas­si­fi­ca­tions were
based on differences in aspect, texture, and other physical attributes.
Berzelius made two attempts at a clas­si­fi­ca­tion based solely on chemical
constitution. That now current recognizes, as far as possible, the relations
between physical and chemical characters. In botany the earliest classes
formed were trees , shrubs , and herbs : magnitude being the basis of
distinction. Dioscorides divided vegetables into aromatic , alimentary ,
medicinal , and vinous : a division of chemical character. Cæsalpinus
classified them by the seeds and seed-vessels, which he preferred because
of the relations found to subsist between the character of the fructification
and the general character of the other parts. While the “natural system”
since developed, carrying out the doctrine of Linnæus, that “the natural
orders must be formed by attention not to one or two, but to all the parts of
plants,” bases its divisions on like peculiarities which are found to be
constantly related to the greatest number of other like peculiarities. And
similarly in zoology, the successive clas­si­fi­ca­tions, from having been
originally determined by external and often {65} subordinate characters not
indicative of the essential nature, have been more and more determined by
those internal and fundamental differences, which have uniform relations to
the greatest number of other differences. Nor shall we be surprised at this
analogy between the modes of progress of positive science and clas­si­fi­ca­‐
tion, when we bear in mind that both proceed by making gen­er­al­i­za­tions;
that both enable us to make previsions, differing only in their precision; and
that while the one deals with equal properties, magnitudes, and relations,

the other deals with properties and relations which approximate towards
equality in various degrees.
Without further argument it will, we think, be admitted that the sciences
are none of them separately evolved—are none of them independent either
logically or historically; but that all of them have, in a greater or less
degree, required aid and reciprocated it. Indeed, it needs but to throw aside
hypotheses, and contemplate the mixed character of surrounding
phenomena, to see at once that these notions of division and succession in
the kinds of knowledge are simply scientific fictions: good, if regarded
merely as aids to study; bad, if regarded as representing realities in Nature.
No facts whatever are presented to our senses uncombined with other facts
—no facts whatever but are in some degree disguised by accompanying
facts: disguised in such a manner that all must be partially understood
before any one can be understood. If it be said, as by M. Comte, that
gravitating force should be treated of before other forces, seeing that all
things are subject to it, it may on like grounds be said that heat should be
first dealt with; seeing that thermal forces are everywhere in action. Nay
more, it may be urged that the ability of any portion of matter to manifest
visible gravitative phenomena depends on its state of aggregation, which is
determined by heat; that only by the aid of thermology can we explain those
apparent exceptions to {66} the gravitating tendency which are presented by
steam and smoke, and so establish its universality; and that, indeed, the very
existence of the Solar System in a solid form is just as much a question of
heat as it is one of gravitation. Take other cases:—All phenomena
recognized by the eyes, through which only are the data of exact science
ascertainable, are complicated with optical phenomena, and cannot be
exhaustively known until optical principles are known. The burning of a
candle cannot be explained without involving chemistry, mechanics,
thermology. Every wind that blows is determined by influences partly solar,
partly lunar, partly hygrometric; and implies considerations of fluid
equilibrium and physical geography. The direction, dip, and variations of
the magnetic needle, are facts half terrestrial, half celestial—are caused by
earthly forces which have cycles of change corresponding with

astronomical periods. The flowing of the gulf-stream and the annual
migration of icebergs towards the equator, involve in their explanation the
Earth’s rotation and spheroidal form, the laws of hydrostatics, the relative
densities of cold and warm water, and the doctrines of evaporation. It is no
doubt true, as M. Comte says, that “our position in the Solar System, and
the motions, form, size, and equilibrium of the mass of our world among
the planets, must be known before we can understand the phenomena going
on at its surface.” But, fatally for his hypothesis, it is also true that we must
understand a great part of the phenomena going on at its surface before we
can know its position, &c., in the Solar System. It is not simply that, as
already shown, those geometrical and mechanical principles by which
celestial appearances are explained, were first generalized from terrestrial
experiences; but it is that even the obtainment of correct data on which to
base astronomical gen­er­al­i­za­tions, implies advanced terrestrial physics.
Until after optics had made considerable advance, the Copernican {67}
system remained but a speculation. A single modern observation on a star
has to undergo a careful analysis by the combined aid of various sciences—
has to be digested by the organism of the sciences ; which have severally to
assimilate their respective parts of the observation, before the essential fact
it contains is available for the further development of astronomy. It has to
be corrected not only for nutation of the Earth’s axis and for precession of
the equinoxes, but for aberration and for refraction; and the formation of the
tables by which refraction is calculated, presupposes knowledge of the law
of decreasing density in the upper atmospheric strata, of the law of
decreasing temperature and the influence of this on the density, and of
hygrometric laws as also affecting density. So that, to get materials for
further advance, astronomy requires not only the indirect aid of the sciences
which have presided over the making of its improved instruments, but the
direct aid of an advanced optics, of barology, of thermology, of hygrometry;
and if we remember that these delicate observations are in some cases
registered electrically, and that they are further corrected for the “personal
equation”—the time elapsing between seeing and registering, which differs
with different observers—we may even add electricity and psychology. And

here, before leaving these illustrations, and especially this last one, let us
not omit to notice how well they exhibit that increasingly active consensus
of the sciences which characterizes their advancing development. Besides
finding that in these later times a discovery in one science commonly
causes progress in others; besides finding that a great part of the questions
with which modern science deals are so mixed as to require the co-
operation of many sciences for their solution; we find that, to make a single
good observation in the purest of the natural sciences, requires the
combined aid of half a dozen other sciences.
Perhaps the clearest comprehension of the interconnected {68} growth of
the sciences may be obtained by contemplating that of the arts, to which it
is strictly analogous, and with which it is bound up. Most intelligent
persons must have been occasionally struck with the numerous antecedents
pre-supposed by one of our processes of manufacture. Let him trace the
production of a printed cotton, and consider all that is implied by it. There
are the many successive improvements through which the power-looms
reached their present perfection; there is the steam-engine that drives them,
having its long history from Papin downwards; there are the lathes in which
its cylinder was bored, and the string of ancestral lathes from which those
lathes proceeded; there is the steam-hammer under which its crank shaft
was welded; there are the puddling furnaces, the blast-furnaces, the coal-
mines and the iron-mines needful for producing the raw material; there are
the slowly improved appliances by which the factory was built, and lighted,
and ventilated; there are the printing engine, and the dye-house, and the
colour-laboratory with its stock of materials from all parts of the world,
implying cochineal-culture, logwood-cutting, indigo-growing; there are the
implements used by the producers of cotton, the gins by which it is cleaned,
the elaborate machines by which it is spun; there are the vessels in which
cotton is imported, with the building-slips, the rope-yards, the sail-cloth
factories, the anchor-forges, needful for making them; and besides all these
directly necessary antecedents, each of them involving many others, there
are the institutions which have developed the requisite intelligence, the
printing and publishing arrangements which have spread the necessary

information, the social organization which has rendered possible such a
complex co-operation of agencies. Further analysis would show that the
many arts thus concerned in the economical production of a child’s frock,
have each been brought to its present efficiency by slow steps which the
other arts have aided; and that from the beginning this reciprocity has been
on {69} the increase. It needs but on the one hand to consider how
impossible it is for the savage, even with ore and coal ready, to produce so
simple a thing as an iron hatchet; and then to consider, on the other hand,
that it would have been impracticable among ourselves, even a century ago,
to raise the tubes of the Britannia bridge from lack of the hydraulic press; to
see how mutually dependent are the arts, and how all must advance that
each may advance. Well, the sciences are involved with each other in just
the same manner. They are, in fact, inextricably woven into this same
complex web of the arts; and are only conventionally independent of it.
Originally the two were one. How to fix the religious festivals; when to
sow; how to weigh commodities; and in what manner to measure ground;
were the purely practical questions out of which arose astronomy,
mechanics, geometry. Since then there has been a perpetual inosculation of
the sciences and the arts. Science has been supplying art with truer gen­er­al­i­‐
za­tions and more completely quantitative previsions. Art has been
supplying science with better materials, and more perfect instruments. And
all along the interdependence has been growing closer, not only between art
and science, but among the arts themselves, and among the sciences
themselves. How completely the analogy holds throughout, becomes yet
clearer when we recognize the fact that the sciences are arts to one
another . If, as occurs in almost every case, the fact to be analyzed by any
science, has first to be prepared—to be disentangled from disturbing facts
by the afore discovered methods of other sciences; the other sciences so
used, stand in the position of arts. If, in solving a dynamical problem, a
parallelogram is drawn, of which the sides and diagonal represent forces,
and by putting magnitudes of extension for magnitudes of force a
measurable relation is established between quantities not else to be dealt
with; it may be fairly said that geometry plays towards mechanics much the

same part that the fire of the founder plays towards the metal he is going to
cast. {70} If, in analyzing the phenomena of the coloured rings surrounding
the point of contact between two lenses, a Newton ascertains by calculation
the amount of certain interposed spaces, far too minute for actual
measurement; he employs the science of number for essentially the same
purpose as that for which the watchmaker employs tools. If, before
calculating the orbit of a comet from its observed position, the astronomer
has to separate all the errors of observation, it is manifest that the
refraction-tables, and logarithm-books, and formulæ, which he successively
uses, serve him much as retorts, and filters, and cupels serve the assayer
who wishes to separate the pure gold from all accompanying ingredients.
So close, indeed, is the relationship, that it is impossible to say where
science begins and art ends. All the instruments of the natural philosopher
are the products of art; the adjusting one of them for use is an art; there is
art in making an observation with one of them; it requires art properly to
treat the facts ascertained; nay, even the employing established gen­er­al­i­za­‐
tions to open the way to new gen­er­al­i­za­tions, may be considered as art. In
each of these cases previously organized knowledge becomes the
implement by which new knowledge is got at: and whether that previously
organized knowledge is embodied in a tangible apparatus or in a formula,
matters not in so far as its essential relation to the new knowledge is
concerned. If art is applied knowledge, then such portion of a scientific
investigation as consists of applied knowledge is art. Hence we may even
say that as soon as any prevision in science passes out of its originally
passive state, and is employed for reaching other previsions, it passes from
theory into practice—becomes science in action—becomes art. And after
contemplating these facts, we shall the more clearly perceive that as the
connexion of the arts with each other has been becoming more intimate; as
the help given by sciences to arts and by arts to sciences, has been age by
age increasing; so the interdependence of the sciences {71} themselves has
been ever growing greater, their relations more involved, their consensus
more active.

In here ending our sketch of the Genesis of Science, we are conscious of
having done the subject but scant justice. Two difficulties have stood in our
way: one, the having to touch on so many points in such small space; the
other, the necessity of treating in serial arrangement a process which is not
serial. Nevertheless, we believe the evidence assigned suffices to
substantiate the leading propositions with which we set out. Inquiry into the
first stages of science confirms the conclusion drawn from analysis of
science as now existing, that it is not distinct from common knowledge, but
an outgrowth from it—an extension of perception by means of reason. That
more specific characteristic of scientific previsions, which was analytically
shown to distinguish them from the previsions of uncultured intelligence—
their quan­ti­ta­tive­ness—we also see to have been the characteristic alike of
the initial steps in science, and of all the steps succeeding them. The facts
and admissions cited in disproof of the assertion that the sciences follow
one another, both logically and historically, in the order of their decreasing
generality, have been enforced by the instances we have met with, showing
that a more general science as much owes its progress to the presentation of
new problems by a more special science, as the more special science owes
its progress to the solutions which the more general science is thus led to
attempt—instances, therefore, illustrating the position that scientific
advance is as much from the special to the general as from the general to
the special. Quite in harmony with this position we find to be the
admissions that the sciences are as branches of one trunk, and that they
were at first cultivated simultaneously. This harmony becomes the more
marked on finding, as we have done, not only that the sciences have a
common root, but that science in {72} general has a common root with
language, clas­si­fi­ca­tion, reasoning, art; that throughout civilization these
have advanced together, acting and reacting upon each other just as the
separate sciences have done; and that thus the development of intelligence
in all its divisions and sub-divisions has conformed to this same law which
we have shown that the sciences conform to. From all which we may
perceive that the sciences can with no greater propriety be arranged in a

succession, than language, clas­si­fi­ca­tion, reasoning, art, and science, can be
arranged in a succession; that, however needful a succession may be for the
convenience of books and catalogues, it must be recognized as merely a
convention; and that so far from its being the function of a philosophy of
the sciences to establish a hierarchy, it is its function to show that the linear
arrangements required for literary purposes, have none of them any basis
either in Nature or History.
There is one further remark we must not omit—a remark touching the
importance of the question that has been discussed. Topics of this abstract
nature are commonly slighted as of no practical moment; and, doubtless,
many will think it of little consequence what theory respecting the genesis
of science may be entertained. But the value of truths is often great, in
proportion as their generality is wide. And it must be so here. A correct
theory of the development of the sciences must have an important effect on
education; and, through education, on civilization. Much as we differ from
him in other respects, we agree with M. Comte in the belief that, rightly
conducted, the education of the individual must have a certain
correspondence with the evolution of the race. No one can contemplate the
facts we have cited in illustration of the early stages of science, without
recognizing the necessity of the processes through which those stages were
reached—a necessity which, in respect to the leading truths, may likewise
be traced in all after stages. This necessity, {73} originating in the very
nature of the phenomena to be analyzed and the faculties to be employed,
partially applies to the mind of the child as to that of the savage. We say
partially, because the correspondence is not special but general only. Were
the environment the same in both cases, the correspondence would be
complete. But though the surrounding material out of which science is to be
organized, is, in many cases, the same to the juvenile mind and the
aboriginal mind, it is not so throughout; as, for instance, in the case of
chemistry, the phenomena of which are accessible to the one but were
inaccessible to the other. Hence, in proportion as the environment differs,
the course of evolution must differ. After admitting exceptions, however,
there remains a substantial parallelism; and, if so, it is of moment to

ascertain what really has been the process of scientific evolution. The
establishment of an erroneous theory must be disastrous in its educational
results; while the establishment of a true one must be fertile in school-
reforms and consequent social benefits.

ENDNOTE TO THE GENESIS OF SCIENCE .

1 It is curious that the author of “The Plurality of Worlds,” with quite other aims, should have
persuaded himself into similar conclusions.

THE CLASSIFICATION OF THE SCIENCES.
[First published as a brochure in April 1864. The preface to the second edition, published in April
1869, I reproduce because of certain facts contained in it which are not without interest. ]

The first edition of this Essay is not yet out of print. But a proposal to
translate it into French having been made by Professor Réthoré, I have
decided to prepare a new edition free from the imperfections which
criticism and further thought have disclosed, rather than allow these
imperfections to be reproduced.
The occasion has almost tempted me into some amplification. Further
arguments against the clas­si­fi­ca­tion of M. Comte, and further arguments in
support of the clas­si­fi­ca­tion here set forth, have pleaded for utterance. But
reconsideration has convinced me that it is both needless and useless to say
more—needless because those who are not committed will think the case
sufficiently strong as it stands; and useless because to those who are
committed, additional reasons will seem as inadequate as the original ones.
[In the preface to the third edition, however, a reason is given for a change
of decision on this point at that time made (February 1871): the reason
being “the publication of several objections by Prof. Bain in his Logic.”]
This last conclusion is thrust on me by seeing how little M. Littré, the
leading expositor of M. Comte, is influenced by fundamental objections the
force of which he admits. After quoting one of these, he says, with a
candour equally {75} rare and admirable, that he has vainly searched M.
Comte’s works and his own mind for an answer. Nevertheless, he adds
—“j’ai réussi, je crois, à écarter l’attaque de M. Herbert Spencer, et à sauver
le fond par des sacrifices indispensables mais accessoires.” The sacrifices

are these. He abandons M. Comte’s division of Inorganic Science into
Celestial Physics and Terrestrial Physics—a division which, in M. Comte’s
scheme, takes precedence of all the rest; and he admits that neither logically
nor historically does Astronomy come before Physics, as M. Comte alleges.
After making these sacrifices, which most will think too lightly described as
“sacrifices indispensables mais accessoires,” M. Littré proceeds to
rehabilitate the Comtean clas­si­fi­ca­tion in a way which he considers
satisfactory, but which I do not understand. In short, the proof of these
incongruities affects his faith in the Positivist theory of the sciences, no
more than the faith of a Christian is affected by proof that the Gospels
contradict one another.
Here in England I have seen no attempt to meet the criticisms with which
M. Littré thus deals. There has been no reply to the allegation, based on
examples, that the several sciences do not develop in the order of their
decreasing generality; nor to the allegation, based on M. Comte’s own
admissions, that within each science the progress is not, as he says it is,
from the general to the special; nor to the allegation that the seeming
historical precedence of Astronomy over Physics in M. Comte’s pages, is
based on a verbal ambiguity—a mere sleight of words; nor to the allegation,
abundantly illustrated, that a progression in an order the reverse of that
asserted by M. Comte may be as well substantiated; nor to various minor
allegations equally irreconcileable with his scheme. I have met with nothing
more than iteration of the statement that the sciences do conform, logically
and historically, to the order in which M. Comte places them; regardless of
the assigned evidence that they do not .
Under these circumstances it is unnecessary for me to {76} say more; and
I think I am warranted in continuing to hold that the Comtean clas­si­fi­ca­tion
of the sciences is demonstrably untenable.

In an essay on “The Genesis of Science,” originally published in 1854, I
endeavoured to show that the Sciences cannot be rationally arranged in
serial order. Proof was given that neither the succession in which the

Sciences are placed by M. Comte (to a criticism of whose scheme the essay
was in part devoted), nor any other succession in which the Sciences can be
placed, represents either their logical dependence or their historical
dependence. To the question—How may their relations be rightly
expressed? I did not then attempt any answer. This question I propose now
to consider.
A true clas­si­fi­ca­tion includes in each class, those objects which have
more char­ac­ter­is­tics in common with one another, than any of them have in
common with any objects excluded from the class. Further, the char­ac­ter­is­‐
tics possessed in common by the colligated objects, and not possessed by
other objects, involve more numerous dependent char­ac­ter­is­tics. These are
two sides of the same definition. For things possessing the greatest number
of attributes in common, are things that possess in common those essential
attributes on which the rest depend; and, conversely, the possession in
common of the essential attributes, implies the possession in common of the
greatest number of attributes. Hence, either test may be used as convenience
dictates.
If, then, the Sciences admit of clas­si­fi­ca­tion at all, it must be by grouping
together the like and separating the unlike, as thus defined. Let us proceed
to do this.

The broadest natural division among the Sciences, is the division
between those which deal with the abstract relations {77} under which
phenomena are presented to us, and those which deal with the phenomena
themselves. Relations of whatever orders, are nearer akin to one another
than they are to any objects. Objects of whatever orders, are nearer akin to
one another than they are to any relations. Whether, as some hold, Space
and Time are nothing but forms of Thought2; or whether, as I hold myself,
they are forms of Things, that have generated forms of Thought through
organized and inherited experience of Things; it is equally true that Space
and Time are contrasted absolutely with the existences disclosed to us in
Space and Time; and hence the Sciences which deal exclusively with Space

and Time, are separated by the profoundest of all distinctions from the
Sciences which deal with the existences contained in Space and Time.
Space is the abstract of all relations of co-existence. Time is the abstract of
all relations of sequence. And dealing as they do entirely with relations of
co-existence and sequence, in their general or special forms, Logic and
Mathematics form a class of the Sciences more widely unlike the rest, than
any of the rest are from one another.
The Sciences which deal with existences themselves, instead of the blank
forms in which existences are presented to us, admit of a sub-division less
profound than the division above made, but more profound than any of the
divisions among the Sciences individually considered. They {78} fall into
two classes, having quite different aspects, aims, and methods. Every
phenomenon is more or less composite—is a manifestation of force under
several distinct modes. Hence result two objects of inquiry. We may study
the component modes of force separately; or we may study them as co-
operating to generate in this composite phenomenon. On the one hand,
neglecting all the incidents of particular cases, we may aim to educe the
laws of each mode of force, when it is uninterfered with. On the other hand,
the incidents of the particular case being given, we may seek to interpret the
entire phenomenon, as a product of the several forces simultaneously in
action. The truths reached through the first kind of inquiry, though concrete
inasmuch as they have actual existences for their subject-matters, are
abstract inasmuch as they refer to the modes of existence apart from one
another; while the truths reached by the second kind of inquiry are properly
concrete, inasmuch as they formulate the facts in their combined order, as
they occur in Nature.
The Sciences, then, in their main divisions, stand thus:―

SCIENCE is
that which treats of the forms in which phenomona are known to us:
A BSTRACT S CIENCE (Logic and Mathematics)
that which treats of the phenomena themselves:

in their elements: A BSTRACT -C ONCRETE S CIENCE
(Mechanics, Physics, Chemistry, etc.)
in their totalities: C ONCRETE S CIENCE (Astronomy, Geology,
Biology, Psychology, Sociology, etc.)
It is needful to define the words abstract and concrete as thus used;
since they are sometimes used with other {79} meanings. M. Comte divides
Science into abstract and concrete; but the divisions which he distinguishes
by these names are quite unlike those above made. Instead of regarding
some Sciences as wholly abstract, and others as wholly concrete, he regards
each Science as having an abstract part, and a concrete part. There is,
according to him, an abstract mathematics and a concrete mathematics—an
abstract biology and concrete biology. He says:—“Il faut distinguer, par
rapport à tous les ordres de phénomènes, deux genres de sciences
naturelles: les unes abstraites, générales, ont pour objet la découverte des
lois qui régissent les diverses classes de phénomènes, en considérant tous
les cas qu’on peut concevoir; les autres concrètes, particulières,
descriptives, et qu’on désigne quelquefois sous le nom de sciences
naturelles proprement dites, consistent dans l’application de ces lois a
l’histoire effective des différens êtres existans.” And to illustrate the
distinction, he names general physiology as abstract, and zoology and
botany as concrete. Here it is manifest that the words abstract and general
are used as synonymous. They have, however, different meanings; and
confusion results from not distinguishing their meanings. Abstractness
means detachment from the incidents of particular cases. Generality means
manifestation in numerous cases. On the one hand, the essential nature of
some phenomenon is considered, apart from disguising phenomena. On the
other hand, the frequency of the phenomenon, with or without disguising
phenomena, is the thing considered. Among the phenomena presented by
numbers, which are purely ideal, the two coincide; but excluding these, an
abstract truth is not realizable to perception in any case of which it is
asserted, whereas a general truth is realizable to perception in every case of
which it is asserted. Some illustrations will make the distinction clear. Thus

it is an abstract truth that the angle contained in a semi-circle is a right angle
—abstract in the sense that though it does not hold of {80} act­u­al­ly-con­‐
struct­ed semi-circles and angles, which are always inexact, it holds of the
ideal semi-circles and angles abstracted from real ones; but this is not a
general truth, either in the sense that it is commonly manifested in Nature,
or in the sense that it is a space-relation that comprehends many minor
space-relations: it is a quite special space-relation. Again, that the
momentum of a body causes it to move in a straight line at a uniform
velocity, is an ab­stract-con­crete truth—a truth abstracted from certain
experiences of concrete phenomena; but it is by no means a general truth:
so little generality has it, that no one fact in Nature displays it. Conversely,
surrounding things supply us with hosts of general truths that are not in the
least abstract. It is a general truth that the planets go round the Sun from
West to East—a truth which holds good in several hundred cases (including
the cases of the planetoids); but this truth is not at all abstract, since it is
perfectly realized as a concrete fact in every one of these cases. Every
vertebrate animal whatever, has a double nervous system; all birds and all
mammals are warm-blooded—these are general truths, but they are
concrete truths: that is to say, every vertebrate animal individually presents
an entire and unqualified manifestation of this duality of the nervous
system; every living bird exemplifies absolutely or completely the warm-
bloodedness of birds. What we here call, and rightly call, a general truth, is
simply a proposition which sums up a number of our actual experiences;
and not the expression of a truth drawn from our actual experiences, but
never presented to us in any of them. In other words, a general truth
colligates a number of particular truths; while an abstract truth colligates no
particular truths, but formulates a truth which certain phenomena all
involve, though it is actually seen in none of them.
Limiting the words to their proper meanings as thus defined, it becomes
manifest that the three classes of {81} Sciences above separated, are not dis­‐
tin­guish­able at all by differences in their degrees of generality. They are all
equally general; or rather they are all, considered as groups, universal.

Every object whatever presents at once the subject-matter for each of them.
In every fragment of substance we have simultaneously illustrated the
abstract truths of relation in Time and Space; the ab­stract-con­crete truths in
conformity with which the fragment manifests its several modes of force;
and the concrete truths resulting from the joint manifestation of these modes
of force, and which give to the fragment the characters by which it is known
as such or such. Thus these three classes of Sciences severally formulate
different, but co-extensive, classes of facts. Within each group there are
truths of greater and less generality: there are general abstract truths, and
special abstract truths; general ab­stract-con­crete truths, and special ab­stract-
con­crete truths; general concrete truths, and special concrete truths. But
while within each class there are groups and sub-groups and sub-sub-groups
which differ in their degrees of generality, the classes themselves differ only
in their degrees of abstractness.3

Let us pass to the sub-divisions of these classes. The first class is
separable into two parts—the one containing universal truths, the other non-
universal truths. Dealing {82} wholly with relations apart from related
things, Abstract Science considers first, that which is common to all
relations whatever; and, second, that which is common to each order of
relations. Besides the indefinite and variable connexions which exist among
phenomena, as occurring together in Space and Time, we find that there are
also definite and invariable connexions—that between each kind of
phenomenon and certain other kinds of phenomena, there exist uniform
relations. This is a universal abstract truth—that there is an unchanging
order, or fixity of law, in Space and Time. We come next to the several
kinds of unchanging order, which, taken together, form the subjects of the
{83} second division of Abstract Science. Of this second division, the most
general sub-division is that which deals with the natures of the connexions
in Space and Time, irrespective of the terms connected. The conditions
under which we may predicate a relation of coincidence or proximity in
Space and Time (or of non-coincidence or non-proximity) from the subject-

matter of Logic. Here the natures and amounts of the terms between which
the relations are {84} asserted (or denied) are of no moment: the propositions
of Logic are independent of any qualitative or quantitative specification of
the related things. The other sub-division has for its subject-matter, the
relations between terms which are specified quantitatively but not
qualitatively. The amounts of the related terms, irrespective of their natures,
are here dealt with; and Mathematics is a statement of the laws of quantity
considered apart from reality. Quantity considered apart from reality, is
occupancy of Space or Time; and occupancy of Space or Time is measured
by units of one or other order, but of which the ultimate ones are simply
separate places in con­scious­ness, either coexistent or sequent. Among units
that are unspecified in their natures (extensive, protensive, or intensive), but
are ideally endowed with existence considered apart from attributes, the
quantitative relations that arise, are those most general relations expressed
by numbers. Such relations fall into either of two orders, according as the
units are considered simply as capable of filling separate places in con­‐
scious­ness, or according as they are considered as filling places that are not
only separate, but equal. In the one case, we have that indefinite calculus by
which numbers of abstract existences, but not sums of abstract existence,
are predicable. In the other case, we have that definite calculus by which
both numbers of abstract existences and sums of abstract existence are
predicable. Next comes that division of Mathematics which deals with the
quantitative relations of magnitudes (or aggregates of units) considered as
coexistent, or as occupying Space—the division called Geometry. And then
we arrive at relations, the terms of which include both quantities of Time
and quantities of Space—those in which times are estimated by the units of
space traversed at a uniform velocity, and those in which equal units of time
being given, the spaces traversed with uniform or variable velocities are
estimated. {85} These Abstract Sciences, which are concerned exclusively
with relations and with the relations of relations, may be grouped as shown
in Table I.

TABLE I.

ABSTRACT SCIENCE.
Universal law of relation—an expression of the truth that uniformities of
connexion obtain among modes of Being, irrespective of any
specification of the natures of the uniformities of connexion.
Laws of relations
that are qualitative; or that are specified in their natures as relations of
coincidence or proximity in Time and Space, but not necessarily in
their terms the natures and amount of which are indifferent. (L OGIC. )4
that are quantitative (M ATHEMATICS )
negatively: the terms of the relations being def­i­nite­ly-re­lat­ed sets of
positions in space; and the facts predicated being the absences of
certain quantities. (Geometry of Position. 5)
positively: the terms being magnitudes composed of
units that are equal only as having independent existences.
(Indefinite Calculus. 6)
equal units
the equality of which is not defined as extensive, protensive,
or intensive (Definite Calculus )
when their numbers are completely specified (Arithmetic. )
when their numbers are specified only
in their relations (Algebra. )
in the relations of their relations. (Calculus of
Operations. )
the equality of which is that of extension
considered in their relations of coexistence. (Geometry. )
considered as traversed in Time

that is wholly indefinite. (Kinematics. )
that is divided into equal units (Geometry of Motion. 7)

Passing from the Sciences concerned with the ideal or unoccupied forms
of relations, and turning to the Sciences concerned with real relations, or the
relations among realities, we come first to those Sciences which treat of
realities, not as they are habitually manifested, but with realities as
manifested in their different modes, when these are artificially separated
from one another. While the Abstract Sciences are wholly ideal, relatively
to the Ab­stract-Con­crete and Concrete Sciences; the Ab­stract-Con­crete
Sciences are partially ideal, relatively to the Concrete Sciences. Just as
Logic and Mathematics generalize the laws of relation, qualitative and
quantitative, apart from related things; so, Mechanics, Physics, Chemistry
generalize the laws of relation which different modes of Matter and Motion
conform to, when severally disentangled from those actual phenomena in
which they are mutually modified. Just as the geometrician formulates the
properties of lines and surfaces, independently of the irregularities and
thicknesses of lines and surfaces as they really exist; so the physicist and
the chemist formulate the manifestations of each mode of force,
independently of the disturbances in its manifestations which other modes
of force cause in every actual case. In works on Mechanics, the laws of
motion are expressed without reference to friction and resistance of the
medium. Not what motion ever really is, but what it would be if retarding
forces were absent, is asserted. If afterwards any retarding force is taken
into account, then the effect of this retarding force is dealt with by itself:
neglecting the other retarding forces. Consider, again, the gen­er­al­i­za­tions of
the physicist respecting molecular motion. The law that light varies
inversely as the square of the distance, is absolutely true only when the
radiation {86} goes on from a point without dimensions, which it never does;
and it also assumes that the rays are perfectly straight, which they cannot be
unless the medium differs from all actual media in being perfectly
homogeneous. If the disturbing effects of changes of media are investigated,

the formulæ expressing the refractions take for granted that the new media
entered are homogeneous; which they never really are. Even when a
compound disturbance is allowed for, as when the refraction undergone by
light in traversing a medium of increasing density, like the atmosphere, is
calculated, the calculation still supposes conditions that are unnaturally
simple—it supposes that the atmosphere is not pervaded by heterogeneous
currents, which it always is. Similarly with the inquiries of the chemist. He
does not take his substances as Nature supplies them. Before he proceeds to
specify their respective properties, he purifies them—separates from each
all trace of every other. Before ascertaining the specific gravity of a gas, he
has to free this gas from the vapour of water, usually mixed with it. Before
describing the properties of a salt, he guards against any error that may arise
from the presence of an uncombined portion of the acid or base. And when
he alleges of any element that it has a certain atomic weight, and unites with
such and such equivalents of other elements, he does not mean that the
results thus expressed are exactly the results of any one experiment; but that
they are the results which, after averaging many trials, he concludes would
be realized if absolute purity could be obtained, and if the experiments
could be conducted without loss. His problem is to ascertain the laws of
combination of molecules, not as they are actually displayed, but as they
would be displayed in the absence of those minute interferences which
cannot be altogether avoided. Thus all Ab­stract-Con­crete Sciences have for
their object, analytical interpretation . In every case it is the aim to
decompose the phenomenon, and formulate its {87} components apart from
one another; or some two or three apart from the rest. Wherever, throughout
these Sciences, synthesis is employed, it is for the verification of analysis.8
The truths elaborated are severally asserted, not as truths exhibited by this
or that particular object; but as truths universally holding of Matter and
Motion in their more general or more special forms, considered apart from
particular objects, and particular places in space.
The sub-divisions of this group of Sciences, may be drawn on the same
principle as that on which the sub-divisions of the preceding group were
drawn. Phenomena, considered as more or less involved manifestations of

force, yield on analysis, certain laws of manifestation which are universal,
and other laws of manifestation, which, being dependent on conditions, are
not universal. Hence the Ab­stract-Con­crete Sciences are primarily divisible
into—the laws of force considered apart from its separate modes, and laws
of force considered under each of its separate modes. And this second
division of the Ab­stract-Con­crete group, is sub-divisible after a manner
essentially analogous. It is needless to occupy space by defining these
several {88} orders and genera of Sciences. Table II. will sufficiently explain
their relations.

TABLE II.

ABSTRACT-CONCRETE SCIENCE.
Universal laws of forces (tensions and pressures), as deducible from the
persistence of force: the theorems of resolution and composition of
forces.
Laws of forces as manifested by matter
in masses (M ECHANICS )
that are in equilibrium relatively to other masses
and are solid. (Statics. )
and are fluid. (Hydrostatics. )
that are not in equilibrium relatively to other masses
and are solid. (Dynamics. )
and are fluid. (Hydrodynamics. )
in molecules (M OLECULAR M ECHANICS )
when in equilibrium: (Molecular Statics )
giving statical properties of matter
general, as impenetrability or space-occupancy.
special, as the forms resulting from molecular equilibrium.
giving statico-dynamical properties of matter (cohesion,
elasticity, etc.)
when solid.
when liquid.
when gaseous.
when not in equilibrium: (Molecular Dynamics )
as resulting in a changed distribution of molecules

which alters their relative positions homogeneously
causing increase of volume (expansion, liquefaction,
evaporation).
causing decrease of volume (condensation, solidification,
contraction).
which alters their relative positions heterogeneously
(Chemistry )
producing new relations of molecules (new compounds).
producing new relations of forces (new affinities).
as resulting in a changed distribution of molecular motion,
which, by integration, generates sensible motion.
which, by disintegration, generates insensible motion, under
the forms of {Heat. Light. Electricity. Magnetism. }

We come now to the third great group. We have done with the Sciences
which are concerned only with the blank forms of relations under which
Being is manifested to us. We have left behind the Sciences which, dealing
with Being under its universal mode, and its several non-universal modes
regarded as independent, treat the terms of its relations as simple and
homogeneous; which they never are in Nature. There remain the Sciences
which, taking these modes of Being as they are habitually connected with
one another, have for the terms of their relations, those heterogeneous
combinations of forces that constitute actual phenomena. The subject-
matter of these Concrete-Sciences is the real, as contrasted with the wholly
or partially ideal. It is their aim, not to separate and generalize apart the
components of all phenomena, but to explain each phenomenon as a
product of these components. Their relations are not, like those of the
simplest Ab­stract-Con­crete Sciences, relations between one antecedent and
one consequent; nor are they, like those of the more involved Ab­stract-Con­‐
crete Sciences, relations between some few antecedents cut off in

imagination from all others, and some few consequents similarly cut off;
but they are relations each of which has for its terms a complete plexus of
antecedents and a complete plexus of consequents. This is manifest in the
least involved Concrete Sciences. The astronomer seeks to explain the Solar
System. He does not stop short after generalizing the laws of planetary
movement, such as planetary movement would be did only a single planet
exist; but he solves this ab­stract-con­crete problem, as a step towards solving
the concrete problem of the planetary movements as affecting one another.
In astronomical language, “the theory of the Moon” means an interpretation
of the Moon’s motions, not as determined simply by centripetal {89} and
centrifugal forces, but as perpetually modified by gravitation towards the
Earth’s equatorial protuberance, towards the Sun, and even towards Venus:
forces daily varying in their amounts and combinations. Nor does the
astronomer leave off when he has calculated what will be the position of a
given body at a given time, allowing for all perturbations; but he goes on to
consider the effects produced by reactions on the perturbing masses. And he
further goes on to consider how the mutual perturbations of the planets
cause, during a long period, increasing deviations from a mean state; and
then how compensating perturbations cause continuous decrease of the
deviations. That is, the goal towards which he ever strives, is a complete
explanation of these complex planetary motions in their totality. Similarly
with the geologist. He does not take for his problem only those irregularities
of the Earth’s crust that are worked by denudation; or only those which
igneous action causes. He does not seek simply to understand how
sedimentary strata were formed; or how faults were produced; or how
moraines originated; or how the beds of Alpine lakes were scooped out. But
taking into account all agencies co-operating in endless and ever-varying
combinations, he aims to interpret the entire structure of the Earth’s crust. If
he studies separately the actions of rain, rivers, glaciers, icebergs, tides,
waves, volcanoes, earthquakes, etc.; he does so that he may be better able to
comprehend their joint actions as factors in geological phenomena: the
object of his science being to generalize these phenomena in all their
intricate connexions, as parts of one whole. In like manner Biology is the

elaboration of a complete theory of Life, in each and all of its involved
manifestations. If different aspects of its phenomena are investigated apart
—if one observer busies himself in classing organisms, another in
dissecting them, another in ascertaining their chemical compositions,
another in studying functions, another in tracing laws of modification; they
are {90} all, consciously or un­con­scious­ly, helping to work out a solution of
vital phenomena in their entirety, both as displayed by individual organisms
and by organisms at large. Thus, in these Concrete Sciences, the object is
the converse of that which the Ab­stract-Con­crete Sciences propose to
themselves. In the one case we have analytical interpretation ; while in the
other case we have synthetical interpretation . Instead of synthesis being
used merely to verify analysis; analysis is here used only to aid synthesis.
Not to formulate the factors of phenomena is now the object; but to
formulate the phenomena resulting from these factors, under the various
conditions which the Universe presents.
This third class of Sciences, like the other classes, is divisible into the
universal and the non-universal. As there are truths which hold of all
phenomena in their elements; so there are truths which hold of all
phenomena in their totalities. As force has certain ultimate laws common to
its separate modes of manifestation, so in those combinations of its modes
which constitute actual phenomena, we find certain ultimate laws that are
conformed to in every case. These are the laws of the re-dis­tri­bu­tion of
force. Since we can become conscious of a phenomenon only by some
change wrought in us, every phenomenon necessarily implies re-dis­tri­bu­‐
tion of force—change in the arrangements of matter and motion. Alike in
molecular movements and the movements of masses, one great uniformity
may be traced. A decreasing quantity of motion, sensible or insensible,
always has for its concomitant an increasing aggregation of matter; and,
conversely, an increasing quantity of motion, sensible or insensible, has for
its concomitant a decreasing aggregation of matter. Give to the molecules of
any mass, more of that insensible motion which we call heat, and the parts
of the mass become somewhat less closely aggregated. Add a further
quantity of insensible motion, and the mass so far disintegrates as to

become {91} liquid. Add still more insensible motion, and the mass
disintegrates so completely as to become gas; which occupies a greater
space with every extra quantity of insensible motion given to it. On the
other hand, every loss of insensible motion by a mass, gaseous, liquid, or
solid, is accompanied by a progressing integration of the mass. Similarly
with sensible motions, be the bodies moved large or small. Augment the
velocities of the planets, and their orbits will enlarge—the Solar System
will occupy a wider space. Diminish their velocities, and their orbits will
lessen—the Solar System will contract, or become more integrated. And in
like manner we see that sensible motions given to bodies on the Earth’s
surface involve partial disintegrations of the bodies from the Earth; while
the loss of their motions are accompanied by their re-integration with the
Earth. In all changes we have either an integration of matter and
concomitant dissipation of motion; or an absorption of motion and
concomitant disintegration of matter. And where, as in living bodies, these
processes go on simultaneously, there is an integration of matter
proportioned to the dissipation of motion, and an absorption of motion
proportioned to the disintegration of matter. Such, then, are the universal
laws of that re-dis­tri­bu­tion of matter and motion everywhere going on—a
re-dis­tri­bu­tion which results in Evolution so long as the aggregation of
matter and dispersion of motion predominate; but which results in
Dissolution where there is a predominant aggregation of motion and
dispersion of matter. Hence we have a division of Concrete Science which
bears towards the other Concrete Sciences, a relation like that which the
Universal Law of Relation bears to Mathematics, and like that which
Universal Mechanics (composition and resolution of forces) bears to
Physics. We have a division of Concrete Science which generalizes those
concomitants of this re-dis­tri­bu­tion that hold good among all orders of
concrete objects—a division which explains why, along with a {92}
predominating integration of matter and dissipation of motion, there goes a
change from an indefinite, incoherent homogeneity, to a definite, coherent
heterogeneity; and why a reverse re-dis­tri­bu­tion of matter and motion, is

accompanied by a reverse structural change. Passing from this universal
Concrete Science, to the non-universal Concrete Sciences; we find that
these are primarily divisible into the science which deals with the re-dis­tri­‐
bu­tions of matter and motion among masses in space, consequent on their
mutual actions as wholes; and the science which deals with the re-dis­tri­bu­‐
tions of matter and motion consequent on the mutual actions of the parts of
each mass. And of these equally general Sciences, this last is re-divisible
into the Science which is limited to the concomitants of re-dis­tri­bu­tion
among the parts of each mass when regarded as independent, and the
Science which takes into account the molecular motion received by
radiation from other masses. But these sub-divisions, and their sub-sub-
divisions, will be best seen in the annexed Table III.

TABLE III.

CONCRETE SCIENCE.
Universal laws of the continuous re-dis­tri­bu­tion of Matter and Motion;
which results in Evolution where there is a predominant integration of
Matter and dissipation of Motion, and which results in Dissolution where
there is a predominant absorption of Motion and disintegration of Matter.
Laws of the redistributions of Matter and Motion actually going on
among the celestial bodies in their relations to one another as masses:
comprehending (A STRONOMY )
the dynamics of our solar system. (Planetary Astronomy. )
the dynamics of our stellar universe. (Sidereal Astronomy. )
among the molecules of any celestial mass; as caused by
the actions of these molecules on one another (A STROGENY )
resulting in the formation of compound molecules. (Solar
Mineralogy. )
resulting in molecular motions and genesis of radiant forces.9
resulting in movements of gases and liquids. (Solar
Meteorology. 10)
the actions of these molecules on one another, joined with the
actions on them of forces radiated by the molecules of other
masses: (G EOGENY )
as exhibited in the planets generally.
as exhibited in the Earth
causing composition and of decomposition of inorganic
matters. (Mineralogy. )
causing re-dis­tri­bu­tions of gases and liquids. (Meteorology. )
causing re-dis­tri­bu­tions of solids. (Geology. )

causing organic phenomena; which are (Biology )
those of structure (Morphology )
general.
special.
those of function
in their internal relations (Physiology )
general.
special.
in their external relations (Psychology )
general
special
separate.
combined. (Sociology. 11)

That these great groups of Sciences and their respective sub-groups, fulfil
the definition of a true clas­si­fi­ca­tion given at the outset, is, I think, tolerably
manifest. The subjects of inquiry included in each primary division, have
essential attributes in common with one another, which they have not in
common with any of the subjects contained in the other primary divisions;
and they have, by consequence, a greater number of attributes in which they
are severally like the subjects they are grouped with, and unlike the subjects
otherwise grouped. Between Sciences which deal with relations apart from
realities, and Sciences which deal with realities, the distinction is the widest
possible; since Being, in some or all of its attributes, is common to all
Sciences of the second class, and excluded from all Sciences of the first
class. And when we divide the Sciences which treat of realities, into those
which deal {93} with their component phenomena considered in ideal
separation and those which deal with their component phenomena as

actually united, we make a profounder distinction than can exist between
the Sciences which deal with one or other order of the components, or than
can exist between the Sciences which deal with one or other order of the
things composed. The three groups of Sciences may be briefly defined as—
laws of the forms ; laws of the factors ; laws of the products . When thus
defined, it becomes manifest that the groups are so radically unlike in their
natures, that there can be no transitions between them; and that any Science
belonging to one of the groups must be quite incongruous with the Sciences
belonging to either of the other groups, if transferred. How fundamental are
the differences between them, will be further seen on considering their
functions. The first, or abstract group, is instrumental with respect to both
the others; and the second, or ab­stract-con­crete group is instrumental with
respect to the third or concrete group. An endeavour to invert these
functions will at once show how essential is the difference of character. The
second and third groups supply subject-matter to the first, and the third
supplies subject-matter to the second; but none of the truths which
constitute the third group are of any use as solvents of the problems
presented by the second group; and none of the truths which the second
group formulates can act as solvents of problems contained in the first
group.
Concerning the sub-divisions of these great groups, little remains to be
added. That each of the groups, being co-extensive with all phenomena,
contains truths that are universal and others that are not universal, and that
these must be classed apart, is obvious. And that the sub-divisions of the
non-universal truths, are to be made according to their decreasing generality
in something like the manner shown in the Tables, is proved by the fact that
{94} when the descriptive words are read from the root to the extremity of
any branch, they form a definition of the Science constituting that branch.
That the minor divisions might be otherwise arranged, and that better
definitions of them might be given, is highly probable. They are here set
down merely for the purpose of showing how this method of clas­si­fi­ca­tion
works out.

I will only further remark that the relations of the Sciences as thus
represented, are still but imperfectly represented: their relations cannot be
truly shown on a plane, but only in space of three dimensions. The three
groups cannot rightly be put in linear order as they have here been. Since
the first stands related to the third, not only indirectly through the second,
but also directly—it is directly instrumental with respect to the third, and
the third supplies it directly with subject-matter. Their relations can thus
only be truly shown by branches diverging from a common root on different
sides, in such a way that each stands in juxta-position to the other two. And
only by a like mode of arrangement, can the relations among the sub-
divisions of each group be correctly represented.

The foregoing exposition, highly abstract as it is, will by some readers be
less readily followed than a more concrete one. With the view of carrying
conviction to such I will re-state the case in two ways: the first of them
adapted only to those who accept the doctrine of Evolution in its most
general form.
We set out with concentrating nebulous matter. Tracing the re-dis­tri­bu­‐
tions of this, as the rotating contracting spheroid leaves behind successive
annuli and as these severally form secondary rotating spheroids, we come at
length to planets in their early stages. Thus far we consider the phenomena
dealt with purely astronomical; and so long as our Earth, regarded as one of
these spheroids, {95} was made up of gaseous and molten matters only, it
presented no data for any more complex Concrete Science. In the lapse of
cosmical time a solid film forms, which, in the course of millions of years,
thickens, and, in the course of further millions of years, becomes cool
enough to permit the precipitation, first of various other gaseous
compounds, and finally of water. Presently, the varying exposure of
different parts of the spheroid to the Sun’s rays, begins to produce
appreciable effects; until at length there have arisen meteorological actions,
and consequent geological actions, such as those we now know: determined
partly by the Sun’s heat, partly by the still-retained internal heat of the

Earth, and partly by the action of the Moon on the ocean? How have we
reached these geological phenomena? When did the astronomical changes
end and the geological changes begin? It needs but to ask this question to
see that there is no real division between the two. Putting pre-conceptions
aside, we find nothing more than a group of phenomena continually
complicating under the influence of the same original factors; and we see
that our conventional division is defensible only on grounds of
convenience. Let us advance a stage. As the Earth’s surface continues to
cool, passing through all degrees of temperature by infinitesimal gradations,
the formation of more and more complex inorganic compounds becomes
possible. Later, its surface sinks to that heat at which the less complex
compounds of the kinds called organic can exist; and, finally, the formation
of the more complex organic compounds takes place. Chemists now show
us that these compounds may be built up synthetically in the laboratory—
each stage in ascending complexity making possible the next higher stage.
Hence it is inferable that, in the myriads of laboratories, endlessly
diversified in their materials and conditions, which the Earth’s surface
furnished during the myriads of years occupied in passing through these
stages of temperature, such successive {96} syntheses were effected; and that
the highly complex unstable substance out of which all organisms are
composed, was eventually formed in microscopic portions: from which, by
continuous integrations and dif­fer­entia­tions, the evolution of all organisms
has proceeded. Where then shall we draw the line between Geology and
Biology? The synthesis of this most complex compound, is but a
continuation of the syntheses by which all simpler compounds were formed.
The same primary factors have been co-operating with those secondary
factors, meteorologic and geologic, previously derived from them. Nowhere
do we find a break in the ever-complicating series; for there is a manifest
connexion between those movements which various complex compounds
undergo during their isomeric trans­for­ma­tions, and those changes of form
undergone by the protoplasm which we distinguish as living. Strongly
contrasted as they eventually become, biological phenomena are at their
root inseparable from geological phenomena—inseparable from the

aggregate of trans­for­ma­tions continually wrought in the matters forming the
Earth’s surface by the physical forces to which they are exposed. Further
stages I need not particularize. The gradual development out of the
biological group of phenomena, of the more specialized group we class as
psychological, needs no illustration. And when we come to the highest
psychological phenomena, it is clear that since aggregations of human
beings may be traced upwards from single wandering families to tribes and
nations of all sizes and complexities, we pass insensibly from the
phenomena of individual human action to those of corporate human action.
To resume, then, is it not manifest that in the group of sciences—
Astronomy, Geology, Biology, Psychology, Sociology, we have a natural
group that admits neither of disruption nor change of order? Here there is
both a genetic dependence, and a dependence of in­ter­pre­ta­tions. The
phenomena have arisen in this succession in cosmical {97} time; and
complete scientific interpretation of each group depends on scientific
interpretation of the preceding groups. No other science can be thrust in
anywhere without destroying the continuity. To insert Physics between
Astronomy and Geology, would be to make a break in the history of a
continuous series of changes; and a like break would be produced by
inserting Chemistry between Geology and Biology. It is true that Physics
and Chemistry are needful as interpreters of these successive assemblages
of facts; but it does not therefore follow that they are themselves to be
placed among these assemblages.
Concrete Science, made up of these five concrete sub-sciences, being
thus coherent within itself, and separated from all other science, there
comes the question—Is all other science similarly coherent within itself? or
is it traversed by some second division that is equally decided? It is thus
traversed. A statical or dynamical theorem, however simple, has always for
its subject-matter something that is conceived as extended, and as
displaying force or forces—as being a seat of resistance, or of tension, or of
both, and as capable of possessing more or less of vis viva . If we examine
the simplest proposition of Statics, we see that the conception of Force must
be joined with the conception of Space, before the proposition can be

framed in thought; and if we similarly examine the simplest proposition in
Dynamics, we see that Force, Space, and Time, are its essential elements.
The amounts of the terms are indifferent; and, by reduction of its terms
beyond the limits of perception, they are applied to molecules: Molar
Mechanics and Molecular Mechanics are continuous. From questions
concerning the relative motions of two or more molecules, Molecular
Mechanics passes to changes of aggregation among many molecules, to
changes in the amounts and kinds of the motions possessed by them as
members of an aggregate, and to changes of the motions transferred through
aggregates of them, as those constituting light. {98} Daily extending its
range of in­ter­pre­ta­tions, it is coming to deal even with the components of
each compound molecule on the same principles. And the unions and
disunions of such more or less compound molecules, which constitute the
phenomena of Chemistry, are also being conceived as resultant phenomena
of essentially kindred natures—the affinities of molecules for one another,
and their reactions in relation to light, heat, and other modes of force, being
regarded as consequent on the combinations of the various mech­an­i­cal­ly-
de­ter­mined motions of their various components. Without at all out-
running, however, this progress in the mechanical interpretation of
molecular phenomena, it suffices to point out that the indispensable
elements in any chemical conception are units occupying places in space,
and exerting forces on one another. This, then, is the common character of
all these sciences which we at present group under the names of Mechanics,
Physics, Chemistry. Leaving undiscussed the question whether it is possible
to conceive of force apart from extended somethings exerting it, we may
assert, as beyond dispute, that if the conception of force be expelled, no
science of Mechanics, Physics, or Chemistry remains. Made coherent, as
these sciences are, by this bond of union, it is impossible to thrust among
them any other science without breaking their continuity. We cannot place
Logic between Molar Mechanics and Molecular Mechanics. We cannot
place Mathematics between the group of propositions concerning the
behaviour of homogeneous molecules to one another, and the group of
propositions concerning the behaviour of heterogeneous molecules to one

another (which we call Chemistry). Clearly these two sciences lie outside
the coherent whole we have contemplated; separated from it in some radical
way.
By what are they radically separated? By the absence of the conception
of force through which alone we know objects as existing or acting.
However true it may be {99} that so long as Logic and Mathematics have
any terms at all, these must be capable of affecting con­scious­ness, and, by
implication, of exerting force; yet it is the distinctive trait of these sciences
that not only do their propositions make no reference to such force, but, as
far as possible, they deliberately ignore it. Instead of being, as in all the
other sciences, an element that is not only recognized but vital; in
Mathematics and Logic, force is an element that is not only not vital, but is
studiously not recognized. The terms in which Logic expresses its
propositions, are symbols that do not profess to represent things, properties,
or powers, of one kind more than another; and may equally well stand for
the attributes belonging to members of some connected series of ideal
curves which have never been drawn, as for so many real objects. And the
theorems of Geometry, so far from contemplating perceptible lines and
surfaces as elements in the truths enunciated, consider these truths as
becoming absolute only when such lines and surfaces become ideal—only
when the conception of something exercising force is extruded.

Let me now make a second re-statement, not implying acceptance of the
doctrine of Evolution, but exhibiting with a clearness almost if not quite as
great, these fundamental distinctions.
The concrete sciences, taken together or separately, contemplate as their
subject-matters, aggregates —either the entire aggregate of sensible
existences, or some secondary aggregate separable from this entire
aggregate, or some tertiary aggregate separable from this, and so on.
Sidereal Astronomy occupies itself with the totality of visible masses
distributed through space; which it deals with as made up of identifiable
individuals occupying specified places, and severally standing towards one

another, towards sub-groups, and towards the entire group, in defined ways.
Planetary Astronomy, cutting out of this all-including aggregate that {100}
relatively minute part constituting the Solar System, deals with this as a
whole—observes, measures, and calculates the sizes, shapes, distances,
motions, of its primary, secondary, and tertiary members; and, taking for its
larger inquiries the mutual actions of all these members as parts of a
coordinated assemblage, takes for its smaller inquiries the actions of each
member considered as an individual, having a set of intrinsic activities that
are modified by a set of extrinsic activities. Restricting itself to one of these
aggregates, which admits of close examination, Geology (using this word in
its comprehensive meaning) gives an account of terrestrial actions and
terrestrial structures, past and present; and, taking for its narrower problems
local formations and the agencies to which they are due, takes for its larger
problems the serial trans­for­ma­tions undergone by the entire Earth. The
geologist being occupied with this cosmically small, but otherwise vast,
aggregate, the biologist occupies himself with small aggregates formed out
of parts of the Earth’s superficial substance, and treats each of these as a
coordinated whole in its structures and functions; or, when he treats of any
particular organ, considers this as a whole made up of parts held in a sub-
coordination that refers to the coordination of the entire organism. To the
psychologist he leaves those specialized aggregates of functions which
adjust the actions of organisms to the complex activities surrounding them:
doing this, not simply because they are a stage higher in speciality, but
because they are the counterparts of those aggregated states of con­scious­‐
ness dealt with by the science of Subjective Psychology, which stands
entirely apart from all other sciences. Finally, the sociologist considers each
tribe and nation as an aggregate presenting multitudinous phenomena,
simultaneous and successive, that are held together as parts of one
combination. Thus, in every case, a concrete science deals with a real
aggregate (or a plurality of real aggregates); and it includes as its {101}
subject-matter whatever is to be known of this aggregate in respect of its
size, shape, motions, density, texture, general arrangement of parts, minute

structure, chemical composition, temperature, etc., together with all the
multitudinous changes, material and dynamical, gone through by it from the
time it begins to exist as an aggregate to the time it ceases to exist as an
aggregate.
No ab­stract-con­crete science makes the remotest attempt to do anything
of this sort. Taken together, the ab­stract-con­crete sciences give an account
of the various kinds of properties which aggregates display; and each ab­‐
stract-con­crete science concerns itself with a certain order of these
properties. By this, the properties common to all aggregates are studied and
formulated; by that, the properties of aggregates having special forms,
special states of aggregation, etc.; and by others, the properties of particular
components of aggregates when dissociated from other components. But by
all these sciences the aggregate, considered as an individual object, is tacitly
ignored; and a property, or a connected set of properties, exclusively
occupies attention. It matters not to Mechanics whether the moving mass it
considers is a planet or a molecule, a dead stick thrown into the river or the
living dog that leaps after it: in any case the curve described by the moving
mass conforms to the same laws. Similarly when the physicist takes for his
subject the relation between the changing bulk of matter and the changing
quantity of molecular motion it contains. Dealing with the subject generally,
he leaves out of consideration the kind of matter; and dealing with the
subject specially in relation to this or that kind of matter, he ignores the
attributes of size and form: save in the still more special cases where the
effect on form is considered, and even then size is ignored. So, too, is it
with the chemist. A substance he is investigating, never thought of by him
as distinguished in extension or amount, is not even required to be
perceptible. A portion of carbon on {102} which he is experimenting, may or
may not have been visible under its forms of diamond or graphite or
charcoal—this is indifferent. He traces it through various disguises and
various combinations—now as united with oxygen to form an invisible gas;
now as hidden with other elements in such more complex compounds as
ether, and sugar, and oil. By sulphuric acid or other agent he precipitates it
from these as a coherent cinder, or as a diffused impalpable powder; and

again, by applying heat, forces it to disclose itself as an element of animal
tissue. Evidently, while thus ascertaining the affinities and atomic
equivalence of carbon, the chemist has nothing to do with any aggregate.
He deals with carbon in the abstract, as something considered apart from
quantity, form, appearance, or temporary state of combination; and
conceives it as the possessor of powers or properties, whence the special
phenomena he describes result: the ascertaining of all these powers or
properties being his sole aim.
Finally, the Abstract Sciences ignore alike aggregates and the powers
which aggregates or their components possess; and occupy themselves with
relations —either with the relations among aggregates, or among their parts,
or the relations among aggregates and properties, or the relations among
properties, or the relations among relations. The same logical formula
applies equally well, whether its terms are men and their deaths, crystals
and their planes of cleavage, or plants and their seeds. And how entirely
Mathematics concerns itself with relations, we see on remembering that it
has just the same expression for the characters of an infinitesimal triangle,
as for those of the triangle which has Sirius for its apex and the diameter of
the Earth’s orbit for its base.
I cannot see how these definitions of these groups of sciences can be
questioned. It is undeniable that every Concrete Science gives an account of
an aggregate or of aggregates, inorganic, organic, or super-organic (a
society); {103} and that, not concerning itself with properties of this or that
order, it concerns itself with the co-ordination of the assembled properties
of all orders. It seems to me no less certain that an Ab­stract-Con­crete
Science gives an account of some order of properties, general or special; not
caring about the other traits of an aggregate displaying them, and not
recognizing aggregates at all further than is implied by discussion of the
particular order of properties. And I think it is equally clear that an Abstract
Science, freeing its propositions, so far as the nature of thought permits,
from aggregates and properties, occupies itself with relations of co-
existence and sequence, as disentangled from all particular forms of being
and action. If then these three groups of sciences are, respectively, accounts

of aggregates , accounts of properties , accounts of relations , it is manifest
that the divisions between them are not simply perfectly clear, but that the
chasms between them are absolute.

Here, perhaps more clearly than before, will be seen the untenability of
the clas­si­fi­ca­tion made by M. Comte. Already, after setting forth in a
general way these fundamental distinctions, I have pointed out the
incongruities that arise when the sciences, conceived as Abstract, Ab­stract-
Con­crete, and Concrete, are arranged in the order proposed by him. Such
incongruities become still more conspicuous if for these general names of
the groups we substitute the definitions given above. The series will then
stand thus:―
M ATHEMATICS . . . An account of relations (including, under Mechanics,
an account of properties ).
A STRONOMY . . . An account of aggregates .
P HYSICS . . . An account of properties .
C HEMISTRY . . . An account of properties .
B IOLOGY . . . An account of aggregates .
S OCIOLOGY . . . An account of aggregates .
That those who espouse opposite views see clearly the {104} defects in the
propositions of their opponents and not those in their own, is a trite remark
that holds in philosophical discussions as in all others: the parable of the
mote and the beam applies as well to men’s appreciations of one another’s
opinions as to their appreciations of one another’s natures. Possibly to my
positivist friends I exemplify this truth,—just as they exemplify it to me.
Those uncommitted to either view must decide where the mote exists and
where the beam. Meanwhile it is clear that one or other of the two views is
essentially erroneous; and that no qualifications can bring them into
harmony. Either the sciences admit of no such grouping as that which I

have described, or they admit of no such serial order as that given by M.
Comte.

P OSTSCRIPT R EPLYING TO C RITICISMS.
Among objections made to any doctrine, those which come from avowed
supporters of an adverse doctrine must be considered, other things equal, as
of less weight than those which come from men uncommitted to an adverse
doctrine, or but partially committed to it. The element of prepossession,
distinctly present in the one case and in the other case mainly or quite
absent, is a well-recognized cause of difference in the values of the
judgments: supposing the judgments to be otherwise fairly comparable.
Hence, when it is needful to bring the replies within a restricted space, a fit
course is that of dealing rather with independent criticisms than with
criticisms which are really indirect arguments for an opposite view,
previously espoused.
For this reason I propose here to confine myself substantially, though not
absolutely, to the demurrers entered against the foregoing clas­si­fi­ca­tion by
Prof. Bain, in his recent work on Logic. Before dealing with the more {105}
important of these, let me clear the ground by disposing of the less
important.

Incidentally, while commenting on the view I take respecting the position
of Logic, Prof. Bain points out that this, which is the most abstract of the
sciences, owes much to Psychology, which I place among the Concrete
Sciences; and he alleges an incongruity between this fact and my statement
that the Concrete Sciences are not instrumental in disclosing the truths of
the Abstract Sciences. Subsequently he re-raises this apparent anomaly
when saying―
“Nor is it possible to justify the placing of Psychology wholly among Concrete Sciences. It is a
highly analytic science, as Mr. Spencer thoroughly knows.”
For a full reply, given by implication, I must refer Prof. Bain to § 56 of The
Principles of Psychology , where I have contended that “while, under its

objective aspect, Psychology is to be classed as one of the Concrete
Sciences which successively decrease in scope as they increase in
speciality; under its subjective aspect, Psychology is a totally unique
science, independent of, and antithetically opposed to, all other sciences
whatever.” A pure idealist will not, I suppose, recognize this distinction; but
to every one else it must, I should think, be obvious that the science of
subjective existences is the correlative of all the sciences of objective
existences; and is as absolutely marked off from them as subject is from
object. Objective Psychology, which I class among the Concrete Sciences,
is purely synthetic, so long as it is limited, like the other sciences, to
objective data; though great aid in the interpretation of these data is derived
from the observed correspondence between the phenomena of Objective
Psychology as presented in other beings and the phenomena of Subjective
Psychology as presented in one’s own con­scious­ness. Now it is Subjective
Psychology only which is analytic, and which affords aid in the {106}
development of Logic. This being explained, the apparent incongruity
disappears.
A difficulty raised respecting the manner in which I have expressed the
nature of Mathematics, may next be dealt with. Prof. Bain writes:―
“In the first place, objection may be taken to his language, in discussing the extreme Abstract
Sciences, when he speaks of the empty forms therein considered. To call Space and Time empty
forms, must mean that they can be thought of without any concrete embodiment whatsoever; that one
can think of Time, as a pure abstraction, without having in one’s mind any concrete succession. Now,
this doctrine is in the last degree questionable.”
I quite agree with Prof. Bain that “this doctrine is in the last degree
questionable;” but I do not admit that this doctrine is implied by the
definition of Abstract Science which I have given. I speak of Space and
Time as they are dealt with by mathematicians, and as it is alone possible
for pure Mathematics to deal with them. While Mathematics habitually uses
in its points, lines, and surfaces, certain existences, it habitually deals with
these as representing points, lines, and surfaces that are ideal; and its
conclusions are true only on condition that it does this . Points having
dimensions, lines having breadths, planes having thicknesses, are negatived
by its definitions. Using, though it does, material representatives of

extension, linear, superficial, or solid, Geometry deliberately ignores their
materiality; and attends only to the truths of relation they present. Holding
with Prof. Bain, as I do, that our con­scious­ness of Space is disclosed by our
experiences of Matter—arguing, as I have done in The Principles of
Psychology , that it is a consolidated aggregate of all relations of co-
existence that have been severally presented by Matter; I nevertheless
contend that it is possible to dissociate these relations from Matter to the
extent required for formulating them as abstract truths. I contend, too, that
this separation is of the kind habitually made in other cases; as, for instance,
when the general laws of motion are formulated (as M. Comte’s system,
among {107} others, formulates them) in such way as to ignore all properties
of the bodies dealt with save their powers of taking up, and retaining, and
giving out, quantities of motion; though these powers are inconceivable
apart from the attribute of extension, which is intentionally disregarded.
Taking other of Prof. Bain’s objections, not in the order in which they
stand but in the order in which they may be most conveniently dealt with, I
quote as follows:―
“The law of the radiation of light (the inverse square of the distance) is said by Mr. Spencer to be
Ab­stract-Con­crete, while the disturbing changes in the medium are not to be mentioned except in a
Concrete Science of Optics. We need not remark that such a separate handling is unknown to
science.”
It is perfectly true that “such a separate handling is unknown to science.”
But, unfortunately for the objection, it is also perfectly true that no such
separate handling is proposed by me, or is implied by my clas­si­fi­ca­tion.
How Prof. Bain can have so missed the meaning of the word “concrete,” as
I have used it, I do not understand. After pointing out that “no one ever
drew the line,” between the Ab­stract-Con­crete and the Concrete Sciences,
“as I have done it,” he alleges an anomaly which exists only supposing that
I have drawn it where it is ordinarily drawn. He appears inadvertently to
have carried with him M. Comte’s conception of Optics as a Concrete
Science, and, importing it into my clas­si­fi­ca­tion, debits me with the
incongruity. If he will re-read the definition of the Ab­stract-Con­crete
Sciences, or study their sub-divisions as shown in Table II., he will, I think,
see that the most special laws of the redistribution of light, equally with its

most general laws, are included. And if he will pass to the definition and the
tabulation of the Concrete Sciences, he will, I think, see no less clearly that
Optics cannot be included among them.
Prof. Bain considers that I am not justified in classing Chemistry as an
Ab­stract-Con­crete Science, and excluding from it all consideration of the
crude forms of the various {108} substances dealt with; and he enforces his
dissent by saying that chemists habitually describe the ores and impure
mixtures in which the elements, etc., are naturally found. Undoubtedly
chemists do this. But do they therefore intend to include an account of the
ores of a substance, as a part of the science which formulates its molecular
constitution and the constitutions of all the definite compounds it enters
into? I shall be very much surprised if I find that they do. Chemists
habitually prefix to their works a division treating of Molecular Physics; but
they do not therefore claim Molecular Physics as a part of Chemistry. If
they similarly prefix to the chemistry of each substance an outline of its
mineralogy, I do not think they therefore mean to assert that the last belongs
to the first. Chemistry proper, embraces nothing beyond an account of the
constitutions and modes of action and combining proportions of substances
that are taken as absolutely pure; and its truths no more recognize impure
substances than the truths of Geometry recognize crooked lines.
Immediately after, in criticizing the fundamental distinction I have made
between Chemistry and Biology, as Ab­stract-Con­crete and Concrete
respectively, Prof. Bain says:―
“But the objects of Chemistry and the objects of Biology are equally concrete, so far as they go;
the simple bodies of chemistry, and their several compounds, are viewed by the Chemist as concrete
wholes, and are described by him, not with reference to one factor, but to all their factors.”
Issue is here raised in a form convenient for elucidation of the general
question. It is true that, for purposes of identification , a chemist gives an
account of all the sensible characters of a substance. He sets down its
crystalline form, its specific gravity, its power of refracting light, its
behaviour as magnetic or diamagnetic. But does he thereby include these
phenomena as part of the Science of Chemistry? It seems to me that the
relation between the weight {109} of any portion of matter and its bulk,

which is ascertained on measuring its specific gravity, is a physical and not
a chemical fact. I think, too, that the physicist will claim, as part of his
science, all investigations touching the refraction of light: be the substance
producing this refraction what it may. And the circumstance that the
chemist may test the magnetic or diamagnetic property of a body, as a
means of ascertaining what it is, or as a means of helping other chemists to
determine whether they have got before them the same body, will neither be
held by the chemist, nor allowed by the physicist, to imply a transfer of
magnetic phenomena from the domain of the one to that of the other. In
brief, though the chemist, in his account of an element or a compound, may
refer to certain physical traits associated with its molecular constitution and
affinities, he does not by so doing change these into chemical traits.
Whatever chemists may put into their books, Chemistry, considered as a
science, includes only the phenomena of molecular structures and changes
—of compositions and decompositions.12 I contend, then, that Chemistry
does not give an account of anything as a concrete whole, in the same way
that Biology gives an account of an organism as a concrete whole. This will
become even more manifest on observing the character of {110} the
biological account. All the attributes of an organism are comprehended,
from the most general to the most special—from its conspicuous structural
traits to its hidden and faint ones; from its outer actions that thrust
themselves on the attention, to the minutest sub-divisions of its
multitudinous internal functions; from its character as a germ, through the
many changes of size, form, organization, and habit, it goes through until
death; from the physical characters of it as a whole, to the physical
characters of its microscopic cells, and vessels, and fibres; from the
chemical characters of its substance in general to the chemical characters of
each tissue and each secretion—all these, with many others. And not only
so, but there is comprehended as the ideal goal of the science, the
consensus of all these phenomena in their co-existences and successions, as
constituting a coherent individualized group definitely combined in space
and in time. It is this recognition of individuality in its subject-matter, that
gives its concreteness to Biology, as to every other Concrete Science. As

Astronomy deals with bodies that have their several proper names, or (as
with the smaller stars) are registered by their positions, and considers each
of them as a distinct individual—as Geology, while dimly perceiving in the
Moon and nearest planets other groups of geological phenomena (which it
would deal with as independent wholes, did not distance forbid), occupies
itself with that individualized group presented by the Earth; so Biology
treats either of an individual distinguished from all others, or of parts or
products belonging to such an individual, or of structural or functional traits
common to many such individuals that have been observed, and supposed
to be common to others that are like them in most or all of their attributes.
Every biological truth connotes a specifically individualized object, or a
number of specifically individualized objects of the same kind, or numbers
of different kinds that are severally specific. See, then, the contrast. {111}
The truths of the Ab­stract-Con­crete Sciences do not imply specific
individuality. Neither Molar Physics, nor Molecular Physics, nor Chemistry,
concerns itself with this. The laws of motion are expressed without any
reference whatever to the sizes or shapes of the moving masses; which may
be taken indifferently to be suns or atoms. The relations between
contraction and the escape of molecular motion, and between expansion and
the absorption of molecular motion, are expressed in their general forms
without reference to the kind of matter; and, if the degree of either that
occurs in a particular kind of matter is formulated, no note is taken of the
quantity of that matter, much less of its individuality. Similarly with
Chemistry. When it inquires into the atomic weight, the molecular structure,
the atomicity, the combining proportions, etc., of a substance, it is
indifferent whether a grain or a ton be thought of—the conception of
amount is absolutely irrelevant. And so with more special attributes.
Sulphur, considered chemically, is not sulphur under its crystalline form, or
under its allotropic viscid form, or as a liquid, or as a gas; but it is sulphur
considered apart from those attributes of quantity, and shape, and state, that
give individuality.
Prof. Bain objects to the division I have drawn between the Concrete
Science of Astronomy and that Ab­stract-Con­crete Science which deals with

the mutually-modified motions of hypothetical masses in space, as “not a
little arbitrary.” He says:―
“We can suppose a science to confine itself solely to the ‘factors,’ or the separated elements, and
never, on any occasion, to combine two into a composite third. This position is intelligible, and
possibly defensible. For example, in Astronomy, the Law of Persistence of Motion in a straight line
might be discussed in pure ideal separation; and so, the Law of Gravity might be discussed in equally
pure separation—both under the Ab­stract-Con­crete department of Mechanics. It might then be
reserved to a concrete department to unite these in the explanation of a projectile or of a planet.
Such, however, is not Mr. Spencer’s boundary line. He allows Theoretical Mechanics to make this
particular combination, and to arrive at the laws of {112} planetary movement, in the case of a single
planet . What he does not allow is, to proceed to the case of two planets, mutually disturbing one
another, or a planet and a satellite, commonly called the ‘problem of the Three Bodies.’”
If I held what Prof. Bain supposes me to hold, my position would be an
absurd one; but he misapprehends me. The mis­app­re­hen­sion results in part
from his having here, as before, used the word “concrete” with the Comtean
meaning, as though it were my meaning; and in part from the inadequacy of
my explanation. I did not in the least mean to imply that the Ab­stract-Con­‐
crete Science of Mechanics, when dealing with the motions of bodies in
space, is limited to the interpretation of planetary movement such as it
would be did only a single planet exist. It never occurred to me that my
words might be so construed. Ab­stract-Con­crete problems admit, in fact, of
being complicated indefinitely, without going in the least beyond the
definition. I do not draw the line, as Prof. Bain alleges, between the
combination of two factors and the combination of three, or between the
combination of any number and any greater number. I draw the line
between the science which deals with the theory of the factors, taken singly
and in combinations of two, three, four, or more, and the science which,
giving to these factors the values derived from observations of actual
objects, uses the theory to explain actual phenomena .
It is true that, in these departments of science, no radical distinction is
consistently recognized between theory and the applications of theory. As
Prof. Bain says:―
“Newton, in the First Book of the Principia, took up the problem of the Three Bodies, as applied to
the Moon, and worked it to exhaustion. So writers on Theoretical Mechanics continue to include the
Three Bodies, Precession, and the Tides.”
But, supreme though the authority of Newton may be as a mathematician
and astronomer, and weighty as are the names of Laplace and Herschel,

who in their works have similarly mingled theorems and the explanations
yielded by them, it does not seem to me that these facts go for much; {113}
unless it can be shown that these writers intended thus to enunciate the
views at which they had arrived respecting the clas­si­fi­ca­tion of the sciences.
Such a union as that presented in their works, adopted merely for the sake
of convenience, is, in fact, the indication of incomplete development; and
has been paralleled in simpler sciences which have afterwards outgrown it.
Two conclusive illustrations are at hand. The name Geometry, utterly
inapplicable by its meaning to the science as it now exists, was applicable
in that first stage during which its few truths were taught in preparation for
land-measuring and the setting-out of buildings; but, at a comparatively
early date, these comparatively simple truths became separated from their
applications, and were embodied by the Greek geometers into systems of
theory.13 A like purification is now taking place in another division of the
science. In the Géométrie Descriptive of Monge, theorems were mixed with
their applications to projection and plan-drawing. But, since his time, the
science and the art have been segregating; and Descriptive Geometry, or, as
it may be better termed, the Geometry of Position, is now recognized by
mathematicians as a far-reaching system of truths, parts of which are
already embodied in books that make no reference to derived methods
available by the architect or the engineer. To meet a coun­ter-il­lus­tra­tion that
will be cited, I may remark that though, in works on Algebra intended for
beginners, the theories of quantitative relations, as treated algebraically, are
accompanied by groups of problems to be solved, the subject-matters of
these problems are not thereby made parts of the Science of Algebra. To say
that they are, is to say that Algebra includes the conceptions of distances
and relative speeds and times, or of weights and bulks and {114} specific
gravities, or of areas ploughed and days and wages; since these, and endless
others, may be the terms of its equations. And just in the same way that
these concrete problems, solved by its aid, cannot be incorporated with the
Abstract Science of Algebra; so I contend that the concrete problems of
Astronomy, cannot be incorporated with that division of Ab­stract-Con­crete

Science which develops the theory of the inter-actions of free bodies that
attract one another.
On this point I find myself at issue, not only with Prof. Bain, but also
with Mr. Mill, who contends that:―
“There is an abstract science of astronomy, namely, the theory of gravitation, which would equally
agree with and explain the facts of a totally different solar system from the one of which our earth
forms a part. The actual facts of our own system, the dimensions, distances, velocities, temperatures,
physical constitution, etc., of the sun, earth, and planets, are properly the subject of a concrete
science, similar to natural history; but the concrete is more inseparably united to the abstract science
than in any other case, since the few celestial facts really accessible to us are nearly all required for
discovering and proving the law of gravitation as an universal property of bodies, and have therefore
an indispensable place in the abstract science as its fundamental data.”—Auguste Comte and
Positivism , p. 43.
In this explanation, Mr. Mill recognizes the fundamental distinction
between the Concrete Science of Astronomy, dealing with the bodies
actually distributed in space, and a science dealing with hypothetical bodies
hypothetically distributed in space. Nevertheless, he regards these sciences
as not separable; because the second derives from the first the data whence
the law of inter-action is derived. But the truth of this premiss, and the
legitimacy of this inference, may alike be questioned. The discovery of the
law of inter-action was not due primarily, but only secondarily, to
observation of the heavenly bodies. The conception of an inter-acting force
that varies inversely as the square of the distance, is an à priori conception
rationally deducible from mechanical and geometrical considerations.
Though unlike in derivation to the many empirical hypotheses of Kepler
respecting planetary orbits and planetary motions, yet it was {115} like the
successful among these in its relation to astronomical phenomena: it was
one of many possible hypotheses, which admitted of having their
consequences worked out and tested; and one which, on having its
implications compared with the results of observation, was found to explain
them. In short, the theory of gravitation grew out of experiences of
terrestrial phenomena; but the verification of it was reached through
experiences of celestial phenomena. Passing now from premiss to inference,
I do not see that, even were the alleged parentage substantiated, it would
necessitate the supposed inseparability; any more than the descent of

Geometry from land-measuring necessitates a persistent union of the two.
In the case of Algebra, as above indicated, the disclosed laws of quantitative
relations hold throughout multitudinous orders of phenomena that are
extremely heterogeneous; and this makes conspicuous the distinction
between the theory and its applications. Here the laws of quantitative
relations among masses, distances, velocities, and momenta, being applied
mainly (though not exclusively) to the concrete cases presented by
Astronomy, the distinction between the theory and its applications is less
conspicuous. But, intrinsically, it is as great in the one case as in the other.
How great it is, we shall see on taking an analogy. This is a living man,
of whom we may know little more than that he is a visible, tangible person;
or of whom we may know enough to form a voluminous biography. Again,
this book tells of a fictitious hero, who, like the heroes of old romance, may
be an impersonated virtue or vice, or, like a modern hero, one of mixed
nature, whose various motives and consequent actions are elaborated into a
semblance of reality. But no accuracy and completeness of the picture
makes this fictitious personage an actual personage, or brings him any
nearer to one. Nor does any meagreness in our knowledge of a real man
reduce him any nearer to the imaginary being of a novel. To the {116} last,
the division between fiction and biography remains an impassable gulf. So,
too, remains the division between the Science dealing with the inter-actions
of hypothetical bodies in space, and the Science dealing with the inter-
actions of existing bodies in space. We may elaborate the first to any degree
whatever by the introduction of three, four, or any greater number of factors
under any number of assumed conditions, until we symbolize a solar
system; but to the last an account of our symbolic solar system is as far
from an account of the actual solar system as fiction is from biography.
Even more obvious, if it be possible, does the radical character of this
distinction become, on observing that from the simplest proposition of
General Mechanics we may pass to the most complex proposition of
Celestial Mechanics, without a break. We take a body moving at a uniform
velocity, and commence with the proposition that it will continue so to
move for ever. Next, we state the law of its accelerated motion in the same

line, when subject to a uniform force. We further complicate the proposition
by supposing the force to increase in consequence of approach towards an
attracting body; and we may formulate a series of laws of acceleration,
resulting from so many assumed laws of increasing attraction (of which the
law of gravitation is one). Another factor may now be added by supposing
the body to have motion in a direction other than that of the attracting body;
and we may determine, according to the ratios of the supposed forces,
whether its course will be hyperbolic, parabolic, elliptical, or circular—we
may begin with this hypothetical additional force as infinitesimal, and
formulate the varying results as it is little by little increased. The problem is
complicated a degree more by taking into account the effects of a third
force, acting in some other direction; and beginning with an infinitesimal
amount of this force we may reach any amount. Similarly, by introducing
factor after factor, {117} each at first insensible in proportion to the rest, we
arrive, through an infinity of gradations, at a combination of any
complexity.
Thus, then, the Science which deals with the inter-action of hypothetical
bodies in space, is absolutely continuous with General Mechanics. We have
already seen that it is absolutely discontinuous with that account of the
heavenly bodies which has been called Astronomy from the beginning.
When these facts are recognized, it seems to me that there cannot remain a
doubt respecting its true place in a clas­si­fi­ca­tion of the Sciences.

ENDNOTES TO THE CLASSIFICATION OF THE SCIENCES. .

2 I have been charged with misrepresenting Kant and mis­un­der­stand­ing him, because I have
used the expression “forms of Thought” instead of “forms of Intuition.” Elsewhere I have shown
that my argument against him remains equally valid when the phrase “forms of Intuition” is
used. Here I may in the first place add that I did but follow some Kantists in saying “forms of
Thought,” and I may add in the second place that the objection is superficial and quite irrelevant
to the issue. Thought when broadly used as antithetical to Things includes Intuition: it
comprehends in this sense all that is subjective as distinguished from all that is objective, and in
so doing comprehends Intuition. Nor is this all. There cannot be Intuition without Thought:
every act of intuition implies an act of classing without which the thing intuited is not known as
such or such; and every act of classing is an act of thought.

3 Some propositions laid down by M. Littré, in his book—Auguste Comte et la Philosophie
Positive (published in 1863), may fitly be dealt with here. In the candid and courteous reply he
makes to my strictures on the Comtean clas­si­fi­ca­tion in “The Genesis of Science,” he
endeavours to clear up some of the inconsistencies I pointed out; and he does this by drawing a
distinction between objective generality and subjective generality. He says—“qu’il existe deux
ordres de généralité, l’une objective et dans les choses, l’autre subjective, abstraite et dans
l’esprit.” This sentence, in which M. Littré makes subjective generality synonymous with
abstractness, led me at first to conclude that he had in view the same distinction as that which I
have above explained between generality and abstractness. On re-reading the paragraph,
however, I found this was not the case. In a previous sentence he says—“La biologie a passé de
la considération des organes à celles des tissus, plus généraux que les organes, et de la
considération des tissus à celle des éléments anatomiques, plus généraux que les tissus. Mais
cette généralité croissante est subjective non objective, abstraite non concrète.” Here it is
manifest that abstract and concrete, are used in senses analogous to those in which they are used
by M. Comte; who, as we have seen, regards general physiology as abstract and zoology and
botany as concrete. And it is further manifest that the word abstract, as thus used, is not used in
its proper sense. For, as above shown, no such facts as those of anatomical structure can be
abstract facts; but can only be more or less general facts. Nor do I understand M. Littré’s point
of view when he regards these more general facts of anatomical structure, as subjectively
general and not objectively general. The structural phenomena presented by any tissue, such as
mucous membrane, are more general than the phenomena presented by any of the organs which
mucous membrane goes to form, simply in the sense that the phenomena peculiar to the
membrane are repeated in a greater number of instances than the phenomena peculiar to any
organ into the composition of which the membrane enters. And, similarly, such facts as have
been established respecting the anatomical elements of tissues, are more general than the facts
established respecting any particular tissue, in the sense that they are facts which the various
parts of organized bodies exhibit in a greater number of cases—they are objectively more

general; and they can be called subjectively more general only in the sense that the conception
corresponds with the phenomena.
Let me endeavour to clear up this point:—There is, as M. Littré truly says, a decreasing
generality that is objective. If we omit the phenomena of Dissolution, which are changes from
the special to the general, all changes which matter undergoes are from the general to the special
—are changes involving a decreasing generality in the united groups of attributes. This is the
progress of things . The progress of thought , is not only in the same direction, but also in the
opposite direction. The investigation of Nature discloses an increasing number of specialities;
but it simultaneously discloses more and more the generalities within which these specialities
fall. Take a case. Zoology, while it goes on multiplying the number of its species, and getting a
more complete knowledge of each species (decreasing generality); also goes on discovering the
common characters by which species are united into larger groups (increasing generality). Both
these are subjective processes; and in this case, both orders of truth reached are concrete—
formulate the phenomena as actually manifested. The truth that mammals of all kinds have
seven cervical vertebræ (I believe there is one exception) is a generalization—a general relation
in thought answering to a general relation in things. As the existence of seven cervical vertebræ
in each mammal is a concrete fact, the statement of it is a concrete truth, and the statement
colligating such truths is not made other than concrete by holding of case after case.
M. Littré, recognizing the necessity for some modification of the hierarchy of the Sciences, as
enunciated by M. Comte, still regards it as substantially true; and for proof of its validity, he
appeals mainly to the essential constitutions of the Sciences. It is unnecessary for me here to
meet, in detail, the arguments by which he supports the proposition, that the essential
constitutions of the Sciences, justify the order in which M. Comte places them. It will suffice to
refer to the foregoing pages, and to the pages which are to follow, as containing the definitions
of those fundamental char­ac­ter­is­tics which demand the grouping of the Sciences in the way I
have pointed out. As already shown, and as will be shown still more clearly by and bye, the
radical differences of constitution among the Sciences, necessitate the colligation of them into
the three classes—Abstract, Ab­stract-Con­crete, and Concrete. How irreconcilable is M. Comte’s
clas­si­fi­ca­tion with these groups, will be at once apparent on inspection. It stands thus:―
Mathematics (including rational Mechanics), . . . partly Abstract, partly Ab­stract-Con­crete.
Astronomy . . . Concrete.
Physics . . . Ab­stract-Con­crete.
Chemistry . . . Ab­stract-Con­crete.
Biology . . . Concrete.
Sociology . . . Concrete.
4 This definition includes the laws of relations called necessary, but not those of relations
called contingent. These last, in which the probability of an inferred connexion varies with the
number of times such connexion has occurred in experience, are rightly dealt with
mathematically.

5 Here, by way of explanation of the term neg­at­ive­ly-quan­ti­ta­tive, it will suffice to instance
the proposition that certain three lines will meet in a point, as a neg­at­ive­ly-quan­ti­ta­tive

proposition; since it asserts the absence of any quantity of space between their intersections.
Similarly, the assertion that certain three points will always fall in a straight line, is neg­at­ive­ly-
quan­ti­ta­tive; since the conception of a straight line implies the negation of any lateral quantity,
or deviation.

6 Lest the meaning of this division should not be understood, it may be well to name, in
illustration, the estimates of the statistician. Calculations respecting population, crime, disease,
etc., have results which are correct only numerically, and not in respect of the totalities of being
or action represented by the numbers.
7 Perhaps it will be asked—how can there be a Geometry of Motion into which the
conception of Force does not enter? The reply is, that the time-relations and space-re­la­tions of
Motion may be considered apart from those of Force, in the same way that the space-re­la­tions of
Matter may be considered apart from Matter.
8 I am indebted to Prof. Frankland for reminding me of an objection that may be made to this
statement. The production of new compounds by synthesis, has of late become an important
branch of chemistry. According to certain known laws of composition, complex substances,
which never before existed, are formed, and fulfil anticipations both as to their general
properties and as to the proportions of their constituents—as proved by analysis. Here it may be
said with truth, that analysis is used to verify synthesis. Nevertheless, the exception to the above
statement is apparent only,—not real. In so far as the production of new compounds is carried
on merely for the obtainment of such new compounds, it is not Science but Art—the application
of pre-established knowledge to the achievement of ends. The proceeding is a part of Science,
only in so far as it is a means to the better interpretation of the order of Nature. And how does it
aid the interpretation? It does it only by verifying the pre-established conclusions respecting the
laws of molecular combination; or by serving further to explain them. That is to say, these
syntheses, considered on their scientific side, have simply the purpose of forwarding the
analysis of the laws of chemical combination .

9 This must not be supposed to mean chem­i­cal­ly-pro­duced forces. The molecular motion here
referred to as dissipated in radiations, is the equivalent of that sensible motion lost during the
integration of the mass of molecules, consequent on their mutual gravitation.

10 Embracing the interpretation of such phenomena as the solar spots, the faculæ and the
coronal flames.

11 Want of space prevents anything beyond the briefest indication of these subdivisions.

12 Perhaps some will say that such incidental phenomena as those of the heat and light
evolved during chemical changes, are to be included among chemical phenomena. I think,
however, the physicist will hold that all phenomena of re-distributed molecular motion, no
matter how arising, come within the range of Physics. But whatever difficulty there may be in
drawing the line between Physics and Chemistry (and, as I have incidentally pointed out in The
Principles of Psychology , § 55, the two are closely linked by the phenomena of allotropy and
isomerism), applies equally to the Comtean clas­si­fi­ca­tion, or to any other. And I may further

point out that no obstacle hence arises to the clas­si­fi­ca­tion I am defending. Physics and
Chemistry being both grouped by me as Ab­stract-Con­crete Sciences, no difficulty in
satisfactorily dividing them in the least affects the sa­tis­fac­tor­i­ness of the division of the great
group to which they both belong, from the other two great groups.

13 It may be said that the mingling of problems and theorems in Euclid is not quite consistent
with this statement; and it is true that we have, in this mingling, a trace of the earlier form of the
science. But it is to be remarked that these problems are all purely abstract, and, further, that
each of them admits of being expressed as a theorem.

REASONS FOR DISSENTING FROM THE PHILOSOPHY
OF M. COMTE.
[Originally published in April 1864 as an appendix to the foregoing essay. ]

While the preceding pages were passing through the press, there
appeared in the Revue des Deux Mondes for February 15th, 1864, an article
on a late work of mine—First Principles . To M. Auguste Laugel, the writer
of the article, I am much indebted for the careful exposition he has made of
some of the leading views set forth in that work; and for the catholic and
sympathetic spirit in which he has dealt with them. In one respect, however,
M. Laugel conveys to his readers an erroneous impression—an impression
doubtless derived from what appears to him adequate evidence, and
doubtless expressed in perfect sincerity. M. Laugel describes me as being,
in part, a follower of M. Comte. After describing the influence of M. Comte
as traceable in the works of some other English writers, naming especially
Mr. Mill and Mr. Buckle, he goes on to say that this influence, though not
avowed, is easily recognizable in the work he is about to make known; and
in several places throughout his review, there are remarks having the same
implication. I greatly regret having to take exception to anything said by a
critic so candid and so able. But the Revue des Deux Mondes {119}
circulates widely in England, as well as elsewhere; and finding that there
exists in some minds, both here and in America, an impression similar to
that entertained by M. Laugel—an impression likely to be confirmed by his
statement—it appears to me needful to meet it.

Two causes of quite different kinds, have conspired to diffuse the
erroneous belief that M. Comte is an accepted exponent of scientific
opinion. His bitterest foes and his closest friends, have un­con­scious­ly
joined in propagating it. On the one hand, M. Comte having designated by
the term “Positive Philosophy” all that de­fi­nite­ly-es­tab­lished knowledge
which men of science have been gradually organizing into a coherent body
of doctrine; and having habitually placed this in opposition to the
incoherent body of doctrine defended by theologians; it has become the
habit of the theological party to think of the antagonist scientific party,
under the title of “positivists.” And thus, from the habit of calling them
“positivists,” there has grown up the assumption that they call themselves
“positivists,” and that they are disciples of M. Comte. On the other hand,
those who have accepted M. Comte’s system, and believe it to be the
philosophy of the future, have naturally been prone to see everywhere the
signs of its progress; and wherever they have found opinions in harmony
with it, have ascribed these opinions to the influence of its originator. It is
always the tendency of discipleship to magnify the effects of the master’s
teachings; and to credit the master with all the doctrines he teaches. In the
minds of his followers, M. Comte’s name is associated with scientific
thinking, which, in many cases, they first understood from his exposition of
it. Influenced as they inevitably are by this association of ideas, they are
reminded of M. Comte wherever they meet with thinking which
corresponds, in some marked way, to M. Comte’s description of scientific
thinking; and hence are apt to imagine him as introducing into other minds,
the {120} conceptions which he introduced into their minds. Such
impressions are, however, in most cases quite unwarranted. That M. Comte
has given a general exposition of the doctrine and method elaborated by
Science, is true. But it is not true that the holders of this doctrine and
followers of this method, are disciples of M. Comte. Neither their modes of
inquiry nor their views concerning human knowledge in its nature and
limits, are appreciably different from what they were before. If they are
“positivists,” it is in the sense that all men of science have been more or less
consistently “positivists;” and the applicability of M. Comte’s title to them,

no more makes them his disciples, than does its applicability to men of
science who lived and died before M. Comte wrote, make these his
disciples. M. Comte himself by no means claims that which some of his
adherents are apt, by implication, to claim for him. He says:—“Il y a, sans
doute, beaucoup d’analogie entre ma philosophie positive et ce que les
savans anglais entendent, depuis Newton surtout, par philosophie
naturelle ;” (see Avertissement ) and further on he indicates the “grand
mouvement imprimé à l’esprit humain, il y a deux siècles, par l’action
combinée des préceptes de Bacon, des conceptions de Descartes, et des
découvertes de Galilée, comme le moment où l’esprit de la philosophie
positive a commencé à se prononcer dans le monde.” That is to say, the
general mode of thought and way of interpreting phenomena, which M.
Comte calls “Positive Philosophy,” he recognizes as having been growing
for two centuries; as having reached, when he wrote, a marked
development; and as being the heritage of all men of science.
That which M. Comte proposed to do, was to give scientific thought and
method a more definite embodiment and organization; and to apply it to the
interpretation of classes of phenomena not previously dealt with in a
scientific manner. The conception was a great one; and the endeavour to
work it out was worthy of sympathy and {121} applause. Some such
conception was entertained by Bacon. He, too, aimed at the organization of
the sciences; he, too, held that “Physics is the mother of all the sciences;”
he, too, held that the sciences can be advanced only by combining them,
and saw the nature of the required combination; he, too, held that moral and
civil philosophy could not flourish when separated from their roots in
natural philosophy; and thus he, too, had some idea of a social science
growing out of physical science. But the state of knowledge in his day
prevented any advance beyond the general conception: indeed, it was
marvellous that he should have advanced so far. Instead of a vague,
undefined conception, M. Comte has presented the world with a defined
and highly-elaborated conception. In working out this conception he has
shown remarkable breadth of view, great originality, immense fertility of
thought, unusual powers of generalization. Considered apart from the

question of its truth, his system of Positive Philosophy is a vast
achievement. But after according to M. Comte high admiration for his
conception, for his effort to realize it, and for the faculty he has shown in
the effort to realize it, there remains the inquiry—Has he succeeded? A
thinker who re-organizes the scientific method and knowledge of his age,
and whose re-organization is accepted by his successors, may rightly be
said to have such successors for his disciples. But successors who accept
this method and knowledge of his age, minus his re-organization, are
certainly not his disciples. How then stands the case with M. Comte? There
are some few who receive his doctrines with but little reservation; and these
are his disciples truly so called. There are others who regard with approval
certain of his leading doctrines, but not the rest: these we may distinguish as
partial adherents. There are others who reject all his distinctive doctrines;
and these must be classed as his antagonists. The members of this class
stand substantially in the same position as they would {122} have done had
he not written. Declining his re-organization of scientific doctrine, they
possess this scientific doctrine in its pre-existing state, as the common
heritage bequeathed by the past to the present; and their adhesion to this
scientific doctrine in no sense implicates them with M. Comte. In this class
stand the great body of men of science. And in this class I stand myself.

Coming thus to the personal part of the question, let me first specify
those great general principles on which M. Comte is at one with preceding
thinkers; and on which I am at one with M. Comte.
All knowledge is from experience, holds M. Comte; and this I also hold
—hold it, indeed, in a wider sense than M. Comte; since, not only do I
believe that all the ideas acquired by individuals, and consequently all the
ideas transmitted by past generations, are thus derived; but I also contend
that the very faculties by which they are acquired, are the products of
accumulated and organized experiences received by ancestral races of
beings (see Principles of Psychology ). But the doctrine that all knowledge
is from experience, is not originated by M. Comte; nor is it claimed by him.

He himself says—“Tous les bons esprits répètent, depuis Bacon, qu’il n’y a
de connaissances réelles que celles qui reposent sur des faits observés.” And
the elaboration and definite establishment of this doctrine, has been the
special characteristic of the English school of Psychology. Nor am I aware
that M. Comte, accepting this doctrine, has done anything to make it more
certain, or give it greater definiteness. Indeed it was impossible for him to
do so; since he repudiates that part of mental science by which alone this
doctrine can be proved.
It is a further belief of M. Comte, that all knowledge is phenomenal or
relative; and in this belief I entirely agree. But no one alleges that the
relativity of all knowledge was first enunciated by M. Comte. Among others
who have {123} more or less consistently held this truth, Sir William
Hamilton enumerates, Protagoras, Aristotle, St. Augustin, Boethius,
Averroes, Albertus Magnus, Gerson, Leo Hebræus, Melancthon, Scaliger,
Francis Piccolomini, Giordano Bruno, Campanella, Bacon, Spinoza,
Newton, Kant. And Sir William Hamilton, in his “Philosophy of the
Unconditioned,” first published in 1829, has given a scientific
demonstration of this belief. Receiving it in common with other thinkers,
from preceding thinkers, M. Comte has not, to my knowledge, advanced
this belief. Nor indeed could he advance it, for the reason already given—
he denies the possibility of that analysis of thought which discloses the
relativity of all cognition.
M. Comte reprobates the interpretation of different classes of phenomena
by assigning metaphysical entities as their causes; and I coincide in the
opinion that the assumption of such separate entities, though convenient, if
not indeed necessary, for purposes of thought, is, scientifically considered,
illegitimate. This opinion is, in fact, a corollary from the last; and must
stand or fall with it. But like the last it has been held with more or less
consistency for generations. M. Comte himself quotes Newton’s favorite
saying—“O! Physics, beware of Metaphysics!” Neither to this doctrine, any
more than to the preceding doctrines, has M. Comte given a firmer basis.
He has simply reasserted it; and it was out of the question for him to do
more. In this case, as in the others, his denial of subjective psychology

debarred him from proving that these metaphysical entities are mere
symbolic conceptions which do not admit of verification.
Lastly, M. Comte believes in invariable natural laws—absolute
uniformities of relation among phenomena. But very many before him have
believed in them too. Long familiar even beyond the bounds of the
scientific world, the proposition that there is an unchanging order in things,
has, within the scientific world, held, for generations, the {124} position of
an established postulate: by some men of science recognized only as
holding of inorganic phenomena; but recognized by other men of science,
as universal. And M. Comte, accepting this doctrine from the past, has left it
substantially as it was. Though he has asserted new uniformities, I do not
think scientific men will admit that he has so demonstrated them, as to
make the induction more certain; nor has he deductively established the
doctrine, by showing that uniformity of relation is a necessary corollary
from the persistence of force, as may readily be shown.
These, then, are the pre-established general truths with which M. Comte
sets out—truths which cannot be regarded as distinctive of his philosophy.
“But why,” it will perhaps be asked, “is it needful to point out this; seeing
that no instructed reader supposes these truths to be peculiar to M. Comte?”
I reply that though no disciple of M. Comte would deliberately claim them
for him; and though no theological antagonist at all familiar with science
and philosophy, supposes M. Comte to be the first propounder of them; yet
there is so strong a tendency to associate any doctrines with the name of a
conspicuous recent exponent of them, that false impressions are produced,
even in spite of better knowledge. Of the need for making this reclamation,
definite proof is at hand. In the No. of the Revue des Deux Mondes named
at the commencement, may be found, on p. 936, the words—“Toute
religion, comme toute philosophie, a la prétention de donner une
explication de l’univers. La philosophie qui s’appelle positive se distingue
de toutes les philosophies et de toutes les religions en ce qu’elle a renoncé à
cette ambition de l’esprit humain;” and the remainder of the paragraph is
devoted to explaining the doctrine of the relativity of knowledge. The next
paragraph begins—“Tout imbu de ces idées, que nous exposons sans les

discuter pour le moment, M. Spencer divise, etc.” Now this is one of those
collocations of ideas {125} which tends to create, or to strengthen, the
erroneous impression I would dissipate. I do not for a moment suppose that
M. Laugel intended to say that these ideas which he describes as ideas of
the “Positive Philosophy,” are peculiarly the ideas of M. Comte. But little as
he probably intended it, his expressions suggest this conception. In the
minds of both disciples and antagonists, “the Positive Philosophy” means
the philosophy of M. Comte; and to be imbued with the ideas of “the
Positive Philosophy” means to be imbued with the ideas of M. Comte—to
have received these ideas from M. Comte. After what has been said above, I
need scarcely repeat that the conception thus inadvertently suggested, is a
wrong one. M. Comte’s brief enunciations of these general truths, gave me
no clearer apprehensions of them than I had before. Such clarifications of
ideas on these ultimate questions, as I can trace to any particular teacher, I
owe to Sir William Hamilton.

From the principles which M. Comte held in common with many
preceding and contemporary thinkers, let us pass now to the principles that
are distinctive of his system. Just as entirely as I agree with M. Comte on
those cardinal doctrines which we jointly inherit; so entirely do I disagree
with him on those cardinal doctrines which he propounds, and which
determine the organization of his philosophy. The best way of showing this
will be to compare, side by side, the―
Propositions held by M. Comte. Propositions which I hold.

“. . . chacune de nos con­cep­tions prin­‐ The progress of our conceptions, and of each branch of
ci­pales, chaque branche de nos con­nais­‐ knowledge, is from be­gin­ning to end intrinsically alike.
sances, passe suc­ces­sive­ment par trois There are not three methods of phi­lo­so­phiz­ing radically
états théoriques différens: l’état opposed; but one method of phi­los­o­phiz­ing which
théologique, ou fictif; l’état remains, in essence, the same. At first, and to the last, the
métaphysique, ou abstrait; l’état conceived causal agencies of phenomena, have a degree
scientifique, ou positif. En d’autres of generality corresponding {126} to the width of the gen­‐
termes, l’esprit humain, par sa nature, er­al­i­za­tions which experiences have determined; and they
emploie successivement dans chacune de change just as gradually as experiences accumulate. The
ses recherches trois méthodes de integration of causal agencies, originally thought of as
philosopher, dont le caractère est es­sen­‐

tiel­le­ment différent et même mul­ti­tud­i­nous and local, but finally believed to be one
radicalement opposé: d’abord la méthode and universal, is a process which involves the passing
théologique, ensuite la méthode méta­‐ through all intermediate steps between these extremes;
phys­ique, et enfin la méthode positive.” and any appearance of stages can be but superficial.
Cours de Philosophie Positive , 1830, Supposed concrete and individual causal agencies,
Vol. i. p. 3. coalesce in the mind as fast as groups of phenomena are
assimilated, or seen to be similarly caused. Along with
their coalescence, comes a greater extension of their
individualities, and a concomitant loss of distinctness in
their individualities. Gradually, by continuance of such
coalescences, causal agencies become, in thought,
diffused and indefinite. And eventually, without any
change in the nature of the process, there is reached the
con­scious­ness of a universal causal agency, which cannot
be conceived.14
“Le système théologique est parvenu à As the progress of thought is one, so is the end one.
la plus haute perfection dont il soit There are not three possible terminal conceptions; but
susceptible, quand il a substitué l’action only a single terminal conception. When the theological
providentielle d’un être unique au jeu idea of the providential action of one being, is developed
varié des nombreuses divinités to its ultimate form, by the absorption of all independent
indépendantes qui avaient été imaginées secondary agencies, it becomes the conception of a being
primitivement. De même, le dernier immanent in all phenomena; and the reduction of it to
terme du système metaphysique consiste this {127} state, implies the fading-away, in thought, of all
à concevoir, au lieu des différentes those anthropomorphic attributes by which the aboriginal
entités particulières, une seule grande idea was distinguished. The alleged last term of the
entité générale, la nature , envisagée metaphysical system—the conception of a single great
comme la source unique de tous les general entity, nature , as the source of all phenomena—
phénomènes. Pareillement, la perfection is a conception identical with the previous one: the con­‐
du système positif, vers laquelle il tend scious­ness of a single source which, in coming to be
sans cesse, quoiqu’il soit très-probable regarded as universal, ceases to be regarded as
qu’il ne doive jamais l’atteindre, serait conceivable, differs in nothing but name from the con­‐
de pouvoir se représenter tous les divers scious­ness of one being, manifested in all phenomena.
phénomènes observables comme des cas And similarly, that which is described as the ideal state of
particuliers d’un seul fait général, tel que science—the power to represent all observable
celui de la gravitation, par exemple.” p. phenomena as particular cases of a single general fact,
5. implies the postulating of some ultimate existence of
which this single fact is alleged; and the postulating of
this ultimate existence, involves a state of con­scious­ness
in­dis­tin­guish­able from the other two.

“. . . la perfection du système positif, Though along with the extension of gen­er­al­i­za­tions,
vers laquelle il tend sans cesse, quoiqu’il and concomitant integration of conceived causal
soit très-probable, qu’il ne doive jamais agencies, the conceptions of causal agencies grow more
l’atteindre, serait de pouvoir se indefinite; and though as they gradually coalesce into a
représenter tous les divers phénomènes universal causal agency, they cease to be representable in
observables comme des cas particuliers thought, and are no longer supposed to be
d’un seul fait general, p. 5. . . . . . comprehensible; yet the con­scious­ness of cause remains
considérant comme absolument as dominant to the last as it was at first; and can never be

inaccessible, et vide de sens pour nous la got rid of. The con­scious­ness of cause can be abolished
recherche de ce qu’on appelle les only by abolishing con­scious­ness itself.15 (First
causes , soit premières, soit finales.” p. Principles , § 26.) {128}
14.

“Ce n’est pas aux lecteurs de cet Ideas do not govern and overthrow the world: the
ouvrage que je croirai jamais devoir world is governed or overthrown by feelings, to which
prouver que les idées gouvernent et ideas serve only as guides. The social mechanism does
bouleversent le monde, ou, en d’autres not rest finally on opinions; but almost wholly on
termes, que tout le mécanisme social character. Not intellectual anarchy, but moral
repose finalement sur des opinions. Ils antagonism, is the cause of political crises. All social
savent surtout que la grande crise phenomena are produced by the totality of human
politique et morale des sociétés actuelles emotions and beliefs; of which the emotions are mainly
tient, en dernière analyse, à l’anarchie pre-determined, while the beliefs are mainly post-
intellectuelle.” p. 48.16 determined. Men’s desires are chiefly inherited; but their
beliefs are chiefly acquired, and depend on surrounding
conditions; and the most important surrounding
conditions depend on the social state which the prevalent
desires have produced. The social state at any time
existing, is the resultant of all the ambitions, self-
interests, fears, reverences, indignations, sympathies,
etc., of ancestral citizens and existing citizens. The ideas
current in this social state, must, on the average, be
congruous with the feelings of citizens; and therefore, on
the average, with the social state these feelings have
produced. Ideas wholly foreign to this social state {129}
cannot be evolved, and if introduced from without,
cannot get accepted—or, if accepted, die out when the
temporary phase of feeling which caused their
acceptance, ends. Hence, though advanced ideas when
once established, act on society and aid its further
advance; yet the establishment of such ideas depends on
the fitness of the society for receiving them. Practically,
the popular character and the social state, determine what
ideas shall be current; instead of the current ideas
determining the social state and the character. The
modification of men’s moral natures, caused by the
continuous discipline of social life, which adapts them
more and more to social relations, is therefore the chief
proximate cause of social progress. (Social Statics , chap.
xxx.)

“. . . je ne dois pas négliger d’indiquer The order in which the gen­er­al­i­za­tions of science are
d’avance, comme une propriété established, is determined by the frequency and
essentielle de l’échelle encyclopédique impressiveness with which different classes of relations
que je vais proposer, sa conformité are repeated in conscious experience; and this depends,
générale avec l’ensemble de l’histoire partly on the directness with which personal welfare is
scientifique; en ce sens, que, malgré la affected ; partly on the con­spic­u­ous­ness of one or both

simultanéité réelle et continue du the phenomena between which a relation is to be
développement des différentes sciences, perceived ; partly on the absolute frequency with which
celles qui seront classées comme the relations occur ; partly on their relative frequency of
antérieures seront, en effet, plus occurrence ; partly on their degree of simplicity ; and
anciennes et constamment plus avancées partly on their degree of abstractness . (First Principles ,
que celles présentées comme 1st ed., § 36; or otherwise see “Essay on Laws in
postérieures.” p. 84. . . . . . . . . “Cet ordre General and the Order of their Discovery .”)
est déterminé par le degré de simplicité,
ou, ce qui revient au même, par le degré
de généralité des phénomènes.” p. 87.
“En résultat définitif, la The sciences as arranged in this succession specified
mathématique, l’astronomie, la physique, by M. Comte, do not logically conform to the natural and
la chimie, la physiologie, et la physique invariable hierarchy of phenomena; and {130} there is no
sociale; telle est la formule serial order whatever in which they can be placed, which
encyclopédique qui, parmi le très-grand represents either their logical dependence or the
nombre de clas­si­fi­ca­tions que dependence of phenomena. (See Genesis of Science , and
comportent les six sciences foregoing Essay.)
fondamentales, est seule logiquement
conforme à la hiérarchie naturelle et
invariable des phénomènes.”17 p. 115.

“On conçoit, en effet, que l’étude The historical development of the sciences has not
rationelle de chaque science taken place in this serial order; nor in any other serial
fondamentale exigeant la culture order. There is no “true filiation of the sciences.” From
préalable de toutes celles qui la the beginning, the abstract sciences, the ab­stract-con­crete
précèdent dans notre hiérarchie sciences, and the concrete sciences, have progressed
encyclopédique, n’a pu faire de progrès together: the first solving problems which the second and
réels et prendre son véritable caractère, third presented, and growing only by the solution of the
qu’ après un grand développement des problems; and the second similarly growing by joining
sciences antérieures relatives à des the first in solving the problems of the third. All along
phénomènes plus généraux, plus there has been a continuous action and reaction between
abstraits, moins compliqués, et the three great classes of sciences—an advance from
indépendans des autres. C’est done dans concrete facts to abstract facts, and then an application of
cet ordre que la progression, quoique such abstract facts to the analysis of new orders of
simultanée, a dû avoir lieu.” p. 100. concrete facts. (See Genesis of Science .)

Such then are the organizing principles of M. Comte’s philosophy and
my reasons for rejecting them. Leaving out of his “Exposition ” those pre-
established general {131} doctrines which are the common property of
modern thinkers; these are the general doctrines which remain—these are
the doctrines which fundamentally distinguish his system. From every one
of them I dissent. To each proposition I oppose either a widely-different
proposition, or a direct negation; and I not only do it now, but have done it
from the time when I became acquainted with his writings. The rejection of

his cardinal principles should, I think, alone suffice; but there are sundry
other views of his, some of them largely characterizing his system, which I
equally reject. Let us glance at them.
How organic beings have originated, This inquiry, I believe, admits of answer, and will be
is an inquiry which M. Comte deprecates answered. That division of Biology which concerns itself
as a useless speculation: asserting, as he with the origin of species, I hold to be the supreme
does, that species are immutable. division, to which all others are subsidiary. For on the
verdict of Biology on this matter, must wholly depend
our conception of human nature, past, present, and
future; our theory of the mind; and our theory of society.

M. Comte contends that of what is I have very emphatically expressed my belief in a
commonly known as mental science, all subjective science of the mind, by writing a Principles of
that most important part which consists Psychology , one half of which is subjective.
of the subjective analysis of our ideas, is
an impossibility.

M. Comte’s ideal of society is one in That form of society towards which we is are
which government developed to the progressing, I hold to be one in which government will
greatest extent—in which class-functions be reduced to the smallest amount possible, and freedom
are far more under conscious public increased to the greatest amount possible—one in which
regulation than now—in which human nature will have become so moulded by social
hierarchical organization with discipline into fitness for the social state, that it will need
unquestioned authority shall guide little external restraint, but will be self-restrained—one in
everything—in which the individual life which the citizen will tolerate no interference with his
shall be subordinated in the greatest freedom, save that which maintains the equal freedom of
degree to the social life. others—one in which the spontaneous {132} co-operation
which has developed our industrial system, and is now
developing it with increasing rapidity, will produce
agencies for the discharge of nearly all social functions,
and will leave to the primary governmental agency
nothing beyond the function of maintaining those
conditions to free action, which make such spontaneous
co-operation possible—one in which individual life will
thus be pushed to the greatest extent consistent with
social life; and in which social life will have no other end
than to maintain the completest sphere for individual life.

M. Comte, not including in his I conceive, on the other hand, that the object of
philosophy the con­scious­ness of a cause religious sentiment will ever continue to be, that which it
manifested to us in all phenomena, and has ever been—the unknown source of things. While the
yet holding that there must be a religion, forms under which men are conscious of the unknown
which must have an object, takes for his source of things, may fade away, the substance of the
object—Humanity. “This Collective Life con­scious­ness is permanent. Beginning with causal
(of Society) is in Comte’s system the agents conceived as imperfectly known; progressing to
Être Suprême ; the only one we can causal agents conceived as less known and less

know therefore the only one we can knowable; and coming at last to a universal causal agent
worship.” posited as not to be known at all; the religious sentiment
must ever continue to occupy itself with this universal
causal agent. Having in the course of evolution come to
have for its object of contemplation the Infinite
Unknowable, the religious sentiment can never again
(unless by retrogression) take a Finite Knowable, like
Humanity, for its object of contemplation.
Here, then, are sundry other points, all of them important, and the last
two supremely important, on which I am diametrically opposed to M.
Comte; and did space permit, I could add many others. Radically differing
from him as I thus do, in everything distinctive of his philosophy; and
having invariably expressed my dissent, {133} publicly and privately, from
the time I became acquainted with his writings; it may be imagined that I
have been not a little startled to find myself classed as one of the same
school. That any who are acquainted with my writings, should suppose I
have any general sympathy with M. Comte, save that implied by preferring
proved facts to superstitions, astonishes me.
It is true that, disagreeing with M. Comte, though I do, in all those
fundamental views that are peculiar to him, I agree with him in sundry
minor views. The doctrine that the education of the individual should
accord in mode and arrangement with the education of mankind, considered
historically, I have cited from him; and have endeavoured to enforce it. I
entirely concur in his opinion that there requires a new order of scientific
men, whose function shall be that of co-ordinating the results arrived at by
the rest. To him, I believe, I am indebted for the conception of a social
consensus ; and when the time comes for dealing with this conception, I
shall state my indebtedness. And I also adopt his word, Sociology. There
are, I believe, in the part of his writings which I have read, various
incidental thoughts of great depth and value; and I doubt not that were I to
read more of his writings, I should find others.18 It is very probable, too,
that I have said (as I am told I have) some things which M. Comte had
already said. It would be difficult, I believe, to find two men who had no
opinions in common. And it would be extremely strange if two men,
starting from the same general doctrines established by modern science,

should traverse some of the same fields of inquiry, without their lines of
thought having any points of intersection. But {134} none of these minor
agreements can be of much weight in comparison with the fundamental
disagreements above specified. Leaving out of view that general
community which we both have with the scientific thought of the age, the
differences between us are essential, while the correspondences are non-
essential. And I venture to think that kinship must be determined by
essentials, and not by non-essentials.19

Joined with the ambiguous use of the phrase “Positive Philosophy,”
which has led to a classing with M. Comte of many men who either ignore
or reject his distinctive principles, there has been one special circumstance
that has tended to originate and maintain this classing in my own case. The
assumption of some relationship between M. Comte and myself, was
unavoidably raised by the title of my first book—Social Statics . When that
book was published, I was unaware that this title had been before used: had
I known the fact, I should certainly have adopted an alternative title which I
had in view.20 If, however, instead of {135} the title, the work itself be
considered, its irrelation to the philosophy of M. Comte becomes
abundantly manifest. There is decisive testimony on this point. In the North
British Review for August, 1851, a reviewer of Social Statics says―
“The title of this work, however, is a complete misnomer. According to all analogy, the phrase
“Social Statics” should be used only in some such sense as that in which, as we have already
explained, it is used by Comte, namely as designating a branch of inquiry whose end it is to ascertain
the laws of social equilibrium or order, as distinct ideally from those of social movement or progress.
Of this Mr. Spencer does not seem to have had the slightest notion, but to have chosen the name for
his work only as a means of indicating vaguely that it proposed to treat of social concerns in a
scientific manner.”—p. 321.
Respecting M. Comte’s application of the words statics and dynamics to
social phenomena, now that I know what it is, I will only say that while I
perfectly understand how, by a defensible extension of their mathematical
meanings, the one may be used to indicate social functions in balance , and
the other social functions out of balance , I am quite at a loss to understand
how the phenomena of structure can be included in the one any more than

in the other. But the two things which here concern me, are, first, to point
out that I had not “the slightest notion” of giving Social Statics the meaning
which M. Comte gave it; and, second, to explain the meaning which I did
give it. The units of any aggregate of matter, are in equilibrium when they
severally act and re-act on one another on all sides with equal forces. A state
of change among them implies that there are forces exercised by some that
are not counterbalanced by like forces exercised by others; and a state of
rest implies the absence of such un­coun­ter­bal­anced {136} forces—implies, if
the units are homogeneous, equal distances among them—implies a
maintenance of their respective spheres of molecular motion. Similarly
among the units of a society, the fundamental condition to equilibrium, is,
that the restraining forces which the units exercise on each other, shall be
balanced. If the spheres of action of some units are diminished by extension
of the spheres of action of others, there necessarily results an unbalanced
force which tends to produce political change in the relations of individuals;
and the tendency to change can cease, only when individuals cease to
aggress on each other’s spheres of action—only when there is maintained
that law of equal freedom, which it was the purpose of Social Statics to
enforce in all its consequences. Besides this totally-unlike conception of
what constitutes Social Statics, the work to which I applied that title, is
fundamentally at variance with M. Comte’s teachings in almost everything.
So far from alleging, as M. Comte does, that society is to be re-organized
by philosophy; it alleges that society is to be re-organized only by the
accumulated effects of habit on character. Its aim is not the increase of
authoritative control over citizens, but the decrease of it. A more
pronounced individualism, instead of a more pronounced nationalism, is its
ideal. So profoundly is my political creed at variance with the creed of M.
Comte, that, unless I am misinformed, it has been instanced by a leading
English disciple of M. Comte as the creed to which he has the greatest
aversion. One point of coincidence, however, is recognizable. The analogy
between an individual organism and a social organism, which was held by
Plato and by Hobbes, is asserted in Social Statics, as it is in the Sociology
of M. Comte. Very rightly, M. Comte has made this analogy the cardinal

idea of this division of his philosophy. In Social Statics , the aim of which is
essentially ethical, this analogy is pointed out incidentally, to enforce
certain ethical considerations; and is there obviously suggested partly by the
definition of life which {137} Coleridge derived from Schelling, and partly
by the gen­er­al­i­za­tions of physiologists there referred to (chap. xxx. §§. 12,
13, 16). Excepting this incidental agreement, however, the contents of
Social Statics are so entirely antagonistic to the philosophy of M. Comte,
that, but for the title, the work would never, I think, have raised the
remembrance of him—unless, indeed, by the association of opposites.21
And now let me point out that which really has exercised a profound
influence over my course of thought. The truth which Harvey’s
embryological inquiries first dimly indicated, which was afterwards more
clearly perceived by Wolff, and which was put into a definite shape by Von
Baer—the truth that all organic development is a change from a state of
homogeneity to a state of heterogeneity—this it is from which very many of
the conclusions which I now hold, have indirectly resulted. In Social
Statics , there is everywhere manifested a dominant belief in the evolution
of man and of society. There is also manifested the belief that this evolution
is in both cases determined by the incidence of conditions—the actions of
circumstances. And there is further, in the sections already referred to, a
recognition of the fact that organic and social evolutions, conform to the
same law. Falling amid beliefs in evolutions of various orders, everywhere
determined by natural causes (beliefs {138} again displayed in the Theory of
Population and in the Principles of Psychology ); the formula of Von Baer
set up a process of organization. The extension of it to other kinds of
phenomena than those of individual and social bodies, is traceable through
successive stages. It may be seen in the last paragraph of an essay on “The
Philosophy of Style,” published in October, 1852; again in an essay on
“Manners and Fashion,” published in April, 1854; and then, in a
comparatively advanced form, in an essay on “Progress: its Law and
Cause,” published in April, 1857. Afterwards, there came the recognition of
the need for modifying Von Baer’s formula by including the trait of

increasing definiteness; next the inquiry into those general laws of force
from which this universal transformation necessarily results; next the
deduction of these from the ultimate law of the persistence of force; next
the perception that there is everywhere a process of Dissolution
complementary to that of Evolution; and, finally, the determination of the
conditions (specified in the foregoing essay) under which Evolution and
Dissolution respectively occur. The filiation of these results is, I think,
tolerably manifest. The process has been one of continuous development,
set up by the addition of Von Baer’s law to a number of ideas that were in
harmony with it. And I am not conscious of any other influences by which
the process has been affected.
It is possible, however, that there may have been influences of which I
am not conscious; and my opposition to M. Comte’s system may have been
one of them. The presentation of antagonistic thoughts, often produces
greater definiteness and development of one’s own thoughts. It is probable
that the doctrines set forth in the essay on “The Genesis of Science,” might
never have been reached, had not my dissent from M. Comte’s conception,
led me to work them out; and but for this, I might not have arrived at the
clas­si­fi­ca­tion of the sciences exhibited in the foregoing essay. Possibly there
are other cases in which the stimulus of {139} repugnance to M. Comte’s
views, may have aided in elaborating my own views; though I cannot call to
mind any other cases.
Let it by no means be supposed from all I have said, that I do not regard
M. Comte’s speculations as of value. True or untrue, his system as a whole,
has doubtless produced important and salutary revolutions of thought in
many minds; and will doubtless do so in many more. Doubtless, too, not a
few of those who dissent from his general views, have been healthfully
stimulated by consideration of them. The presentation of scientific
knowledge and method as a whole, whether rightly or wrongly co-
ordinated, cannot have failed greatly to widen the conceptions of most of
his readers. And he has done especial service by familiarizing men with the
idea of a social science, based on the other sciences. Beyond which benefits
resulting from the general character and scope of his philosophy, I believe

that there are scattered through his pages many large ideas that are valuable
not only as stimuli, but for their actual truth.
It has been by no means an agreeable task to make these personal
explanations; but it has seemed to me a task not to be avoided. Differing so
profoundly as I do from M. Comte on all fundamental doctrines, save those
which we inherit in common from the past; it has become needful to
dissipate the impression that I agree with him—needful to show that a large
part of what is currently known as “positive philosophy,” is not “positive
philosophy” in the sense of being peculiarly M. Comte’s philosophy; and to
show that beyond that portion of the so-called “positive philosophy” which
is not peculiar to him, I dissent from it.
And now at the close, as at the outset, let me express my great regret that
these explanations should have been called forth by the statements of a
critic who has treated me so liberally. Nothing will, I fear, prevent the
foregoing pages from appearing like a very ungracious response to M.
Laugel’s sym­pa­thet­i­cal­ly-writ­ten review. I can only hope that the gravity of
the question at issue, in so far as it {140} concerns myself, may be taken in
mitigation, if not as a sufficient apology.
N OTE .
The preceding pages originally formed the second portion of a pamphlet
entitled The Classification of the Sciences: to which are added
Reasons for dissenting from the Philosophy of M. Comte, which
was first published in 1864. For some time past this pamphlet has
been included in the third volume of my Essays, &c., and has
been no longer accessible in a separate form. There has recently
been diffused afresh, the misconception which originally led me to
exhibit my entire rejection of those views of M. Comte, which
essentially distinguish his system from other systems; and the
motives which then prompted me to publish the reasons for this
rejection, now prompt me to put them within the reach of all who
care to inquire about the matter. The Appendix, presenting an

outline of the leading propositions of the Synthetic Philosophy,
will further aid the reader in forming a correct judgment .
Oct. 7, 1884.
A PPENDIX A.
Some fourteen or more years ago, an American friend requested me, with
a view to a certain use which he named, to furnish him with a succinct
statement of the cardinal principles developed in the successive works I had
published and in those I was intending to publish. This statement I here
reproduce. Having been written solely for an expository purpose, and
without thought of M. Comte and his system, it will serve better than a
statement now drawn up since it is not open to the suspicion of being
adapted to the occasion.22
“1. Throughout the universe in general and in detail, there is an unceasing redistribution of matter
and motion.
“2. This redistribution constitutes evolution where there is a {141} predominant integration of
matter and dissipation of motion, and constitutes dissolution where there is a predominant absorption
of motion and disintegration of matter.
“3. Evolution is simple when the process of integration, or the formation of a coherent aggregate,
proceeds uncomplicated by other processes.
“4. Evolution is compound when, along with this primary change from an incoherent to a coherent
state, there go on secondary changes due to differences in the circumstances of the different parts of
the aggregate.
“5. These secondary changes constitute a transformation of the homogeneous into the
heterogeneous—a transformation which, like the first, is exhibited in the universe as a whole and in
all (or nearly all) its details: in the aggregate of stars and nebulae; in the planetary system; in the
earth as an inorganic mass; in each organism, vegetal or animal (Von Baer’s law); in the aggregate of
organisms throughout geologic time; in the mind; in society; in all products of social activity.
“6. The process of integration, acting locally as well as generally, combines with the process of dif­‐
fer­en­ti­at­ion to render this change not simply from homogeneity to heterogeneity, but from an
indefinite homogeneity to a definite heterogeneity; and this trait of increasing definiteness, which
accompanies the trait of increasing heterogeneity, is, like it, exhibited in the totality of things and in
all its divisions and sub-divisions down to the minutest.
“7. Along with this redistribution of the matter composing any evolving aggregate, there goes on a
redistribution of the retained motion of its components in relation to one another: this also becomes,
step by step, more definitely heterogeneous.
“8. In the absence of a homogeneity that is infinite and absolute, that redistribution of which
evolution is one phase, is inevitable. The causes which necessitate it are these:―
“9. The instability of the homogeneous, which is consequent upon the different exposures of the
different parts of any limited aggregate to incident forces. The trans­for­ma­tions hence resulting are
complicated by―

“10. The multiplication of effects. Every mass and part of a mass on which a force falls, sub-
divides and differentiates that force, which thereupon proceeds to work a variety of changes; and
each of these becomes the parent of sim­i­lar­ly-mul­ti­ply­ing changes: the multiplication of them
becoming greater in proportion as the aggregate becomes more heterogeneous. And these two causes
of increasing dif­fer­entia­tions are furthered by―
“11. Segregation, which is a process tending ever to separate unlike units and to bring together like
units—so serving continually to sharpen, or make definite, dif­fer­entia­tions otherwise caused.
“12. Equilibration is the final result of these trans­for­ma­tions which an evolving aggregate
undergoes. The changes go on until there is reached an equilibrium between the forces which all parts
of the aggregate are exposed to and the forces these parts oppose to them. Equilibration may pass
through a transition stage of balanced motions (as in a planetary system) or of {142} balanced
functions (as in a living body) on the way to ultimate equilibrium; but the state of rest in inorganic
bodies, or death in organic bodies, is the necessary limit of the changes constituting evolution.
“13. Dissolution is the counter-change which sooner or later every evolved aggregate undergoes.
Remaining exposed to surrounding forces that are unequilibrated, each aggregate is ever liable to be
dissipated by the increase, gradual or sudden, of its contained motion; and its dissipation, quickly
undergone by bodies lately animate and slowly undergone by inanimate masses, remains to be
undergone at an indefinitely remote period by each planetary and stellar mass, which, since an
indefinitely distant period in the past, has been slowly evolving: the cycle of its trans­for­ma­tions being
thus completed.
“14. This rhythm of evolution and dissolution, completing itself during short periods in small
aggregates, and in the vast aggregates distributed through space completing itself in periods which
are immeasurable by human thought, is, so far as we can see, universal and eternal—each alternating
phase of the process predominating now in this region of space and now in that, as local conditions
determine.
“15. All these phenomena, from their great features down to their minutest details, are necessary
results of the persistence of force, under its forms of matter and motion. Given these as distributed
through space, and their quantities being unchangeable, either by increase or decrease, there
inevitably result the continuous redistributions dis­tin­guish­able as evolution and dissolution, as well
as all those special traits above enumerated.
“16. That which persists unchanging in quantity but ever changing in form, under these sensible
appearances which the universe presents to us, transcends human knowledge and conception—is an
unknown and unknowable power, which we are obliged to recognize as without limit in space and
without beginning or end in time.”
These successive paragraphs set forth in the most abstract way, that
process of transformation going on throughout the Cosmos as a whole, and
in each larger or smaller portion of it. In First Principles the statements
contained in these paragraphs are elaborated, explained, and illustrated; and
in subsequent volumes of the series, the purpose has been to interpret the
several great groups of phenomena, Astronomical, Geological (both
postponed), Biological, Psychological, Sociological, and Ethical, in
conformity with these general laws of Evolution which First Principles
enunciates.

If it can be shown that any one of the above propositions has been
adopted from, or has been suggested by, the {143} Positive Philosophy, there
will be evidence that the Synthetic Philosophy is to that extent indebted to
it. Or if there can be quoted any expressed conviction of M. Comte, that the
factors producing changes of all kinds, inorganic and organic, co-operate
everywhere throughout the Cosmos in the same general way, and
everywhere work metamorphoses having the same essential traits, a much
more decided indebtedness may reasonably be supposed.
So far as I know it, however, the Positive Philosophy contains none of
the special ideas above enumerated, nor any of the more general ideas they
involve.
A PPENDIX B.
On pp. 119 and 120, I have pointed out that the followers of M. Comte,
swayed by the spirit of discipleship, habitually ascribe to him a great deal
which was the common inheritance of the scientific world before he wrote,
and to which he himself laid no claim. Kindred remarks have since been
made by others, both in England and in France—the one by Mr. Mill, and
the other by M. Fouillée. Mr. Mill says:―
“The foundation of M. Comte’s philosophy is thus in no way peculiar to him, but the general
property of the age, however far as yet from being universally accepted even by thoughtful minds.
The philosophy called Positive is not a recent invention of M. Comte, but a simple adherence to the
traditions of all the great scientific minds whose discoveries have made the human race what it is. M.
Comte has never presented it in any other light. But he has made the doctrine his own by his manner
of treating it.”—Auguste Comte and Positivism , pp. 8, 9.
In his Histoire de la Philosophie , 1875, M. Alfred Fouillée writes:―
“Saint-Simon voulut successivement organiser la société à l’aide de la science (prétention d’où
sortit le positivisme) puis à l’aide de l’industrie, et enfin à l’aide d’une religion nouvelle, capable de
‘forcer chacun de ses membres à suivre le précepte de l’amour du prochain.’”—p. 428.
“Les doctrines sociales de Saint-Simon, jointes au naturalisme de Cabanis et de Broussais,
donnèrent naissance au ‘positivisme’ d’Auguste Comte. {144} Ce dernier, comme Saint-Simon, voit
dans la science sociale ou ‘sociologie’ le terme et le but de toutes les recherches scientifiques.”—p.
422.
“A cette méthode Auguste Comte ajouta des vues historiques, qu’il croyait entièrement originales,
sur les trois états par où passe nécessairement selon lui la connaissance humaine: état théologique,
état métaphysique, et état scientifique. Le germe de cette théorie était déjà dans Turgot.”—p. 424.

“En somme, Auguste Comte a eu le mérite d’insister sur les méthodes qui conviennent aux
sciences de la nature; mais il faut avouer que ces méthodes étaient connues bien avant lui.”—p. 425.

ENDNOTES TO REASONS FOR DISSENTING FROM COMTE.

14 A clear illustration of this process, is furnished by the recent mental integration of Heat,
Light, Electricity, etc., as modes of molecular motion. If we go a step back, we see that the
modern conception of Electricity, resulted from the integration in con­scious­ness, of the two
forms of it involved in the galvanic battery and in the electric-machine. And going back to a still
earlier stage, we see how the conception of statical electricity, arose by the coalescence in
thought, of the pre­vious­ly-se­pa­rate forces manifested in rubbed amber, in rubbed glass, and in
lightning. With such illustrations before him, no one can, I think, doubt that the process has been
the same from the beginning.

15 Possibly it will be said that M. Comte himself admits that what he calls the perfection of
the positive system, will probably never be reached; and that what he condemns is the inquiry
into the natures of causes and not the general recognition of cause. To the first of these
allegations I reply that, as I understand M. Comte, the obstacle to the perfect realization of the
positive philosophy is the impossibility of carrying generalization so far as to reduce all
particular facts to cases of one general fact—not the impossibility of excluding the con­scious­‐
ness of cause. And to the second allegation I reply that the essential principle of his philosophy
is an avowed ignoring of cause altogether. For if it is not, what becomes of his alleged
distinction between the perfection of the positive system and the perfection of the metaphysical
system ? And here let me point out that, by affirming exactly the opposite to that which M.
Comte thus affirms, I am excluded from the positive school. If his own definition of positivism
is to be taken, then, as I hold that what he defines as positivism is an absolute impossibility, it is
clear that I cannot be what he calls a positivist.

16 A friendly critic alleges that M. Comte is not fairly represented by this quotation, and that
he is blamed by his biographer, M. Littré, for his too-great insistance on feeling as a motor of
humanity. If in his “Positive Politics,” which I presume is here referred to, M. Comte abandons
his original position, so much the better. But I am here dealing with what is known as “the
Positive Philosophy;” and that the passage above quoted does not misrepresent it, is proved by
the fact that this doctrine is re-asserted at the commencement of the Sociology.
17 In 1885, during a controversy with one of M. Comte’s English disciples, I was blamed for
speaking “of Comte as making six sciences,” and was told that “in all Comte’s works, except the
first, he makes seven sciences.” As I was dealing with The Positive Philosophy, I thought I
could not do better than give the foregoing extract from the Cours de Philosophie Positive ; and
it did not occur to me that I was called upon to see whether, in any of his later voluminous
works, M. Comte had made a different statement. My opponent, however, enlarged on this
“blunder,” as he politely called it: apparently oblivious of the fact that if it was a blunder on my
part to speak of Comte as recognizing six sciences when in his later days he recognized seven, it

was a much more serious blunder on the part of Comte himself to have long overlooked the
seventh.

18 M. Comte’s “Exposition” I read in the original in 1852; and in two or three other places
have referred to the original to get his exact words. The Inorganic Physics, and the first chapter
of the Biology, I read in Miss Martineau’s condensed translation, when it appeared. The rest of
M. Comte’s views I know only through Mr. Lewes’s outline, and through incidental references.

19 In his work, Auguste Comte et la Philosophie Positive (1863), M. Littré defending the
Comtean clas­si­fi­ca­tion of the sciences from the criticism I made upon it in the “Genesis of
Science,” deals with me wholly as an antagonist. The chapter he devotes to his reply, opens by
placing me in direct opposition to the English adherents of Comte, named in the preceding
chapter.

20 I believed at the time, and have never doubted until now, that the choice of this title was
absolutely independent of its previous use by M. Comte. While writing these pages, I have
found reason to think the contrary. On referring to Social Statics , to see what were my views of
social evolution in 1850, when M. Comte was to me but a name, I met with the following
sentence:—“Social philosophy may be aptly divided (as political economy has been) into statics
and dynamics” (ch. xxx. § 1). This I remembered to be a reference to a division which I had
seen in the Political Economy of Mr. Mill. But why had I not mentioned Mr. Mill’s name? On
referring to the first edition of his work, I found, at the opening of Book iv., this sentence:
—“The three preceding parts include as detailed a view as the limits of this treatise permit, of
what, by a happy generalization of a mathematical phrase, has been called the Statics of the
subject.” Here was the solution of the question. The division had not been made by Mr. Mill, but
by some writer (on Political Economy I supposed) who was not named by him; and whom I did
not know. It is now manifest, however, that while I supposed I was giving a more extended use
to this division, I was but returning to the original use which Mr. Mill had limited to his special
topic. Another thing is, I think, tolerably manifest. As I evidently wished to point out my
obligation to some unknown political economist, whose division I thought I was extending, I
should have named him had I known who he was. And in that case should not have put this
extension of the division as though it were new.

21 Let me add that the conception developed in Social Statics , dates back to a series of letters
on the “Proper Sphere of Government,” published in the Nonconformist newspaper in the latter
half of 1842, and republished as a pamphlet in 1843. In these letters will be found, along with
many crude ideas, the same belief in the conformity of social phenomena to unvariable laws; the
same belief in human progression as determined by such laws; the same belief in the moral
modification of men as caused by social discipline; the same belief in the tendency of social
arrangements “of themselves to assume a condition of stable equilibrium;” the same repudiation
of state-control over various departments of social life; the same limitation of state-action to the
maintenance of equitable relations among citizens. The writing of Social Statics arose from a
dissatisfaction with the basis on which the doctrines set forth in those letters were placed: the
second half of that work is an elaboration of these doctrines; and the first half a statement of the
principles from which they are deducible.

22 Published many years since in America, this statement was republished in England eight
years since. See Athenæum for July 22nd, 1882.

ON LAWS IN GENERAL, AND THE ORDER OF THEIR
DISCOVERY.
[The following was contained in the first edition of First Principles. I omitted it from the re-organized
second edition, because it did not form an essential part of the new structure. As it is
referred to in the foregoing pages, and as its general argument is germane to the contents
of those pages, I have thought well to insert it here. Moreover, though I hope eventually to
incorporate it in that division of the Principles of Sociology which treats of Intellectual
Progress, yet as it must be long before it can thus re-appear in its permanent place, and as,
should I not get so far in the execution of my undertaking, it may never thus re-appear at
all, it seems proper to make it more accessible than it is at present. The first and last
sections, which served to link it into the argument of the work to which it originally
belonged, are omitted. The rest has been carefully revised, and in some parts considerably
altered. ]

The recognition of Law being the recognition of uniformity of relations
among phenomena, it follows that the order in which different groups of
phenomena are reduced to law, must depend on the frequency with which
the uniform relations they severally display are distinctly experienced. At
any given stage of progress, those {146} uniformities will be best known
with which men’s minds have been oftenest and most strongly impressed.
In proportion partly to the number of times a relation has been presented to
con­scious­ness (not merely to the senses), and in proportion partly to the
vividness with which the terms of the relation have been cognized, will be
the degree in which the constancy of connexion is perceived.
The succession in which relations are generalized being thus determined,
there result certain derivative principles to which this succession must more
immediately and obviously conform. The first is the directness with
which personal welfare is affected . While, among surrounding things, many

do not appreciably influence us in any way, some produce pleasures and
some pains, in various degrees; and manifestly, those things of which the
actions on the organism for good or evil are most decided, will, cæteris
paribus , be those of which the laws of action are earliest observed.
Second comes the con­spic­u­ous­ness of one or both phenomena between
which a relation is to be perceived . On every side are phenomena so
concealed as to be detected only by close observation; others not obtrusive
enough to attract notice; others which moderately solicit the attention;
others so imposing or vivid as to force themselves on con­scious­ness; and,
supposing conditions to be the same, these last will of course be among the
first to have their relations generalized. In the third place, we have
the absolute frequency with which the relations occur . There are
coexistences and sequences of all degrees of commonness, from those
which are ever present to those which are extremely rare; and manifestly,
the rare coexistences and sequences, as well as the sequences which are
very long in taking place, will not be reduced to law so soon as those which
are familiar and rapid. Fourthly has to be added the relative
frequency of occurrence . Many events and appearances are limited to
certain times or certain places, or both; {147} and, as a relation which does
not exist within the environment of an observer cannot be perceived by him,
however common it may be elsewhere or in another age, we have to take
account of the surrounding physical circumstances, as well as of the state of
society, of the arts, and of the sciences—all of which affect the frequency
with which certain groups of facts are observable. The fifth
corollary to be noticed is, that the succession in which different classes of
relations are reduced to law, depends in part on their simplicity . Phenomena
presenting great composition of causes or conditions, have their essential
relations so masked, that it requires accumulated experiences to impress
upon con­scious­ness the true connexions of antecedents and consequents
they involve. Hence, other things equal, the progress of generalization will
be from the simple to the complex; and this it is which M. Comte has
wrongly asserted to be the sole regulative principle of the progress.
Sixth comes the degree of concreteness, or absence of abstractness .

Concrete relations are the earliest acquisitions. Such analyses of them as
separate the essential connexions from their disguising accompaniments,
necessarily come later. The analyses of the connexions, always more or less
compound, into their elements then becomes possible. And so on
continually, until the highest and most abstract truths have been reached.
These, then, are the several derivative principles. The frequency and
vividness with which uniform relations are repeated in conscious
experience, determining the recognition of their uniformity, and this
frequency and vividness depending on the above conditions, it follows that
the order in which different classes of facts are generalized, must depend on
the extent to which the above conditions are fulfilled in each class. Let us
mark how the facts harmonize with this conclusion: taking first a few that
elucidate the general truth, and afterwards some that {148} exemplify the
special truths which we here see follow from it.

The relations earliest known as uniformities, are those subsisting among
the common properties of matter—tangibility, visibility, cohesion, weight,
etc. We have no trace of a time when the resistance offered by an object was
regarded as caused by the will of the object; or when the pressure of a body
on the hand holding it, was ascribed to the agency of a living being. And
accordingly, these are the relations of which we are oftenest conscious:
being, as they are, objectively frequent, conspicuous, simple, concrete, and
of immediate personal concern.
Similarly with the ordinary phenomena of motion. The fall of a mass on
the withdrawal of its support, is a sequence which directly affects bodily
welfare, is conspicuous, simple, concrete, and very often repeated. Hence it
is one of the uniformities recognized before the dawn of tradition. We know
of no era when ordinary movements due to terrestrial gravitation were
attributed to volition. Only when the relation is obscured, as where the
withdrawal of a support is not obvious, or, as in the case of an aërolite,
where the antecedent of the descent is unperceived, do we find the
conception of personal agency. On the other hand, motions of

intrinsically the same order as that of a falling stone—those of the heavenly
bodies—long remain ungeneralized; and until their uniformity is seen, and
indeed for a long time after, are construed as results of will. This difference
is clearly not dependent on comparative complexity or abstractness, since
the motion of a planet in an ellipse of slight eccentricity, is as simple and
concrete a phenomenon as the motion of a projected arrow in an ellipse of
extreme eccentricity in­dis­tin­guish­able from a parabola. But the antecedents
are not conspicuous; the sequences are of long duration; and they are not
often repeated. And that these are the causes of their slow {149} reduction to
law, we see in the fact that they are severally generalized in the order of
their frequency and con­spic­u­ous­ness—the moon’s monthly cycle, the sun’s
annual change, the periods of the inferior planets, the periods of the
superior planets.
While astronomical sequences were still ascribed to volition, certain
terrestrial sequences of a different kind, but some of them equally without
complication, were interpreted in like manner. The solidification of water at
a low temperature, is a phenomenon that is simple, concrete, and of much
personal concern. But it is neither so frequent as those which we see are
earliest generalized, nor is the presence of the antecedent so manifest.
Though in all but tropical climates, mid-winter displays the relation
between cold and freezing with tolerable constancy; yet, during the spring
and autumn, the occasional appearance of ice in the mornings has no very
obvious connexion with coldness of the weather. Sensation being so
inaccurate a measure, it is not possible for the savage to experience the
definite relation between a temperature of 32° and the congealing of water;
and hence the long continued belief in personal agency. Similarly, but still
more clearly, with the winds. The absence of regularity and the incon­spic­u­‐
ous­ness of the antecedents, allowed the mythological explanation to survive
for a great period.
During the era in which the uniformity of many quite simple inorganic
relations was still unrecognized, certain organic relations, intrinsically very
complex and special, were generalized. The constant coexistence of feathers
and a beak, of four legs with an internal bony framework, are facts which

were, and are, familiar to every savage. Did a savage find a bird with teeth,
or a mammal clothed with feathers, he would be as much surprised as an
instructed naturalist. Now these uniformities of organic structure thus early
perceived, are of exactly the same kind as those more numerous ones later
established by biology. The constant {150} coexistence of mammary glands
with two occipital condyles to the skull, of vertebræ with teeth lodged in
sockets, of frontal horns with the habit of rumination, are gen­er­al­i­za­tions as
purely empirical as those known to the aboriginal hunter. The botanist
cannot in the least understand the complex relation between papilionaceous
flowers and seeds borne in flattened pods: he knows these and like
connexions simply in the same way that the barbarian knows the
connexions between particular leaves and particular kinds of wood. But the
fact that sundry of the uniform relations which chiefly make up the organic
sciences, were very early recognized, is due to the high degrees of vividness
and frequency with which they were presented to con­scious­ness. Though
the connexion between the sounds characteristic of a certain bird, and the
possession of edible flesh, is extremely involved, yet the two terms of the
relation are conspicuous, often recur in experience, and a knowledge of
their connexion has a direct bearing on personal welfare. Meanwhile
innumerable relations of the same order, which are displayed with even
greater frequency by surrounding plants and animals, remain for thousands
of years unrecognized, if they are unobtrusive or of no apparent moment.
When, passing from this primitive stage to a more advanced stage, we
trace the discovery of those less familiar uniformities which mainly
constitute what is distinguished as Science, we find the succession in which
knowledge of them is reached, to be still determined in the same manner.
This will become obvious on contemplating separately the influence of each
derivative condition.

How relations that have immediate bearings on the maintenance of life,
are, other things equal, fixed in the mind before those which have no
immediate bearings, the history of Science abundantly illustrates. The

habits of existing uncivilized races, who fix times by moons and barter so
many of one article for so many of another, show {151} us that conceptions
of equality and number, which are the germs of mathematical science, were
developed under the immediate pressure of personal wants; and it can
scarcely be doubted that those laws of numerical relations which are
embodied in the rules of arithmetic, were first brought to light through the
practice of mercantile exchange. Similarly with geometry. The derivation of
the word shows us that it originally included only certain methods of
partitioning ground and laying out buildings. The properties of the scales
and the lever, involving the first principle in mechanics, were early
generalized under the stimulus of commercial and architectural needs. To
fix the times of religious festivals and agricultural operations, were the
motives which led to the establishment of the simpler astronomic periods.
Such small knowledge of chemical relations as was involved in ancient
metallurgy, was manifestly obtained in seeking how to improve tools and
weapons. In the alchemy of later times, we see how greatly an intense hope
of private benefit contributed to the disclosure of a certain class of
uniformities. Nor is our own age barren of illustrations. “Here,” says
Humboldt, when in Guiana, “as in many parts in Europe, the sciences are
thought worthy to occupy the mind, only so far as they confer some
immediate and practical benefit on society.” “How is it possible to believe,”
said a missionary to him, “that you have left your country to come to be
devoured by mosquitoes on this river, and to measure lands that are not
your own?” Our coasts furnish like instances. Every sea-side naturalist
knows how great is the contempt with which fishermen regard the
collection of objects for the microscope or aquarium. Their incredulity as to
the possible value of such things is so great, that they can scarcely be
induced even by bribes to preserve the refuse of their nets. Nay, we need not
go for evidence beyond daily table-talk. The demand for “practical
science”—for a knowledge that can be brought to bear on the business of
{152} life—joined to the ridicule commonly vented on scientific pursuits
having no obvious uses, suffice to show that the order in which laws are

discovered greatly depends on the directness with which knowledge of
them affects our welfare.
That, when all other conditions are the same, obtrusive relations will be
generalized before unobtrusive ones, is so nearly a truism that examples
appear almost superfluous. If it be admitted that by the aboriginal man, as
by the child, the co-existent properties of large surrounding objects are
noticed before those of minute objects, and that the external relations which
bodies present are generalized before their internal relations, it must be
admitted that in subsequent stages of progress, the comparative con­spic­u­‐
ous­ness of relations has greatly affected the order in which they were
recognized as uniform. Hence it happened that after the establishment of
those very manifest sequences constituting a lunation, and those less
manifest ones marking a year, and those still less manifest ones marking the
planetary periods, astronomy occupied itself with such inconspicuous
sequences as those displayed in the repeating cycle of lunar eclipses, and
those which suggested the theory of epicycles and eccentrics; while modern
astronomy deals with still more inconspicuous sequences, some of which,
as the planetary rotations, are nevertheless the simplest which the heavens
present. In physics, the early use of canoes implied an empirical knowledge
of certain hydrostatic relations that are intrinsically more complex than
sundry static relations not empirically known; but these hydrostatic
relations were thrust upon observation. Or, if we compare the solution of
the problem of specific gravity by Archimedes with the discovery of
atmospheric pressure by Torricelli (the two involving mechanical relations
of the same class), we perceive that the much earlier occurrence of the first
than the last was determined, neither by a difference in their bearings on
personal welfare, nor by a difference in the frequency with {153} which
illustrations of them came under observation, nor by relative simplicity; but
by the greater obtrusiveness of the connexion between antecedent and
consequent in the one case than in the other. Among miscellaneous
illustrations, it may be pointed out that the connexions between lightning
and thunder, and between rain and clouds, were recognized long before
others of the same order, simply because they thrust themselves on the

attention. Or the long-delayed discovery of the microscopic forms of life,
with all the phenomena they present, may be named as very clearly showing
how certain groups of relations not ordinarily perceptible, though in other
respects like long-familiar relations, have to wait until changed conditions
render them perceptible. But, without further details, it needs only to
consider the inquiries which now occupy the electrician, the chemist, the
physiologist, to see that science has advanced, and is advancing, from the
more conspicuous phenomena to the less conspicuous ones.
How the degree of absolute frequency of a relation affects the recognition
of its uniformity, we see in contrasting certain biological facts. The
connexion between death and bodily injury, constantly displayed not only in
men but in all inferior creatures, came to be recognized as an instance of
natural causation while yet deaths from diseases or from some of them
continued to be thought supernatural. Among diseases themselves, it is
observable that unusual ones were regarded as of demoniacal origin during
ages when the more frequent were ascribed to ordinary causes: a truth
paralleled among our own peasantry, who by the use of charms show a
lingering superstition with respect to rare disorders, which they do not show
with respect to common ones, such as colds. Passing to physical
illustrations, we may note that within the historic period whirlpools were
accounted for by the agency of water-spirits; but we do not find that within
the same period the disappearance of water on exposure either to the sun or
to artificial heat was {154} interpreted in an analogous way: though a more
marvellous occurrence, and a more complex one, its great frequency led to
the early recognition of it as a natural uniformity. Rainbows and comets do
not differ much in con­spic­u­ous­ness, and a rainbow is intrinsically the more
involved phenomenon; but chiefly because of their far greater commonness,
rainbows were perceived to have a direct dependence on sun and rain while
yet comets were regarded as signs of divine wrath.
That races living inland must long have remained ignorant of the daily
and monthly sequences of the tides, and that tropical races could not early
have comprehended the phenomena of northern winters, are extreme
illustrations of the influence which relative frequency has on the

recognition of uniformities. Animals which, where they are indigenous, call
forth no surprise by their structures or habits, because these are so familiar,
when taken to countries where they have never been seen, are looked at
with an astonishment approaching to awe—are even thought supernatural: a
fact which will suggest numerous others that show how the localization of
phenomena shares in controlling the order in which they are reduced to law.
Not only however does their localization in space affect the progression, but
also their localization in time. Facts which are rarely if ever manifested in
one era, are rendered very frequent in another, simply through the changes
wrought by civilization. The lever, of which the properties are illustrated in
the use of sticks and weapons, is vaguely understood by every savage—on
applying it in a certain way he rightly anticipates certain effects; but the
wheel-and-axle, pulley, and screw, cannot have their powers either
empirically or rationally known till the advance of the arts has more or less
familiarized them. Through those various means of exploration which we
have inherited and added to, we have become acquainted with a vast range
of chemical relations that were relatively {155} non-existent to the primitive
man. To highly-developed industries we owe both the substances and the
appliances that have disclosed to us countless uniformities which our
ancestors had no opportunity of seeing. These and like instances, show that
the accumulated materials, and processes, and products, which characterize
the environments of complex societies, greatly increase the accessibility of
various classes of relations; and by thus multiplying the experiences of
them, or making them relatively frequent, facilitate the generalization of
them. Moreover, various classes of phenomena presented by society itself,
as for instance those which political economy formulates, become relatively
frequent, and therefore recognizable, in advanced social states; while in less
advanced ones they are either too rarely displayed to have their relations
perceived, or, as in the least advanced ones, are not displayed at all.
That, where no other circumstances interfere, the order in which different
uniformities are established varies as their complexity, is manifest. The
geometry of straight lines was understood before the geometry of curved
lines; the properties of the circle before the properties of the ellipse,

parabola, and hyperbola; and the equations of curves of single curvature
were ascertained before those of curves of double curvature. Plane
trigonometry comes in order of time and simplicity before spherical
trigonometry; and the mensuration of plane surfaces and solids before the
mensuration of curved surfaces and solids. Similarly with mechanics: the
laws of simple motion were generalized before those of compound motion;
and those of rectilinear motion before those of curvilinear motion. The
properties of equal-armed levers or scales, were understood before those of
levers with unequal arms; and the law of the inclined plane was formulated
earlier than that of the screw, which involves it. In chemistry the progress
has been from the simple inorganic compounds to the more involved or
organic compounds. And where, as in the higher sciences, the conditions of
the exploration are {156} more complicated, we still may trace relative
complexity as determining the order of discovery where other things are
equal.
The progression from concrete relations to abstract relations, and from
the less abstract to the more abstract, is equally obvious. Numeration, which
in its primary form concerned itself only with groups of actual objects,
came earlier than simple arithmetic; the rules of which deal with numbers
apart from objects. Arithmetic, limited in its sphere to concrete numerical
relations, is alike earlier and less abstract than Algebra, which deals with
the relations of these relations. And in like manner, the Calculus of
Operations comes after Algebra, both in order of evolution and in order of
abstractness. In Mechanics, the more concrete relations of forces exhibited
in the lever, inclined plane, etc., were understood before the more abstract
relations expressed in the laws of resolution and composition of forces; and
later than the three abstract laws of motion as formulated by Newton came
the still more abstract law of inertia. Similarly with Physics and Chemistry,
there has been an advance from truths entangled in all the specialities of
particular facts and particular classes of facts, to truths disentangled from
the disguising incidents under which they are manifested—to truths of a
higher abstractness.

Brief and rude as is this sketch of a mental development which has been
long and complicated, I venture to think it shows inductively what was
deductively inferred, that the order in which separate groups of uniformities
are recognized, depends not on one circumstance but on several
circumstances. The various classes of relations are generalized in a certain
succession, not solely because of one particular kind of difference in their
natures; but also because they are variously placed in time and in space,
variously open to observation, and variously related to our own
constitutions: our perception of them being influenced by all these
conditions in endless combinations. The comparative degrees {157} of
importance, of obtrusiveness, of absolute frequency, of relative frequency,
of simplicity, of concreteness, are every one of them factors; and from their
unions in proportions that are never twice alike, there results a highly
complex process of mental evolution. But while it is thus manifest that the
proximate causes of the succession in which relations are reduced to law,
are numerous and involved; it is also manifest that there is one ultimate
cause to which these proximate causes are subordinate. As the several
circumstances that determine the early or late recognition of uniformities
are circumstances that determine the number and strength of the
impressions which these uniformities make on the mind, it follows that the
progression conforms to a certain fundamental principle of psychology. We
see a posteriori , what we concluded à priori , that the order in which
relations are generalized, depends on the frequency and impressiveness
with which they are repeated in conscious experience.

Having roughly analyzed the progress of the past, let us take advantage
of the light thus thrown on the present, and consider what is implied
respecting the future.
Note, first, that the likelihood of the universality of Law has been ever
growing greater. Out of the countless coexistences and sequences with
which mankind are environed, they have been continually transferring some
from the group whose order was supposed to be arbitrary, to the group

whose order is known to be uniform. And manifestly, as fast as the relations
which are unreduced to law become fewer, the probability that among them
there are some which do not conform to law, becomes less. To put the
argument numerically—It is clear that when out of surrounding phenomena
a hundred of several kinds have been found to occur in constant
connexions, there arises a slight presumption that all phenomena occur in
constant connexions. When uniformity has been established in a thousand
cases, more varied {158} in their kinds, the presumption gains strength. And
when the known cases of uniformity amount to millions, including many of
each variety, it becomes an ordinary induction that uniformity exists
everywhere.
Silently and insensibly their experiences have been pressing men on
towards the conclusion thus drawn. Not out of a conscious regard for these
reasons, but from a habit of thought which these reasons formulate and
justify, all minds have been advancing towards a belief in the constancy of
surrounding coexistences and sequences. Familiarity with concrete
uniformities has generated the abstract conception of uniformity—the idea
of Law ; and this idea has been in successive generations slowly gaining
fixity and clearness. Especially has it been thus among those whose
knowledge of natural phenomena is the most extensive—men of science.
The mathematician, the physicist, the astronomer, the chemist, severally
acquainted with the vast accumulations of uniformities established by their
predecessors, and themselves daily adding new ones as well as verifying the
old, acquire a far stronger faith in law than is ordinarily possessed. With
them this faith, ceasing to be merely passive, becomes an active stimulus to
inquiry. Wherever there exist phenomena of which the dependence is not
yet ascertained, these most cultivated intellects, impelled by the conviction
that here too there is some invariable connexion, proceed to observe,
compare, and experiment; and when they discover the law to which the
phenomena conform, as they eventually do, their general belief in the
universality of law is further strengthened. So overwhelming is the
evidence, and such the effect of this discipline, that to the advanced student

of Nature, the proposition that there are lawless phenomena has become not
only incredible but almost inconceivable.
This habitual recognition of law which already distinguishes modern
thought from ancient thought, must spread among men at large. The
fulfilment of fresh predictions that are made possible by every new step,
and the further {159} command gained over Nature’s forces, prove to the
uninitiated the validity of scientific gen­er­al­i­za­tions and the doctrine they
illustrate. Widening education is daily diffusing among the mass of men that
knowledge of these gen­er­al­i­za­tions which has been hitherto confined to the
few. And as fast as this diffusion goes on, the belief of the scientific must
become the belief of the world at large.

That law is universal, will become an irresistible conclusion when it is
perceived that the progress in the discovery of laws itself conforms to law ;
and when this perception makes it clear why certain groups of phenomena
have been reduced to law, while other groups are still unreduced. When it is
seen that the order in which uniformities are recognized, must depend on
the frequency and vividness with which they are repeated in conscious
experience; when it is seen that, as a matter of fact, the most common,
important, conspicuous, concrete, and simple, uniformities were the earliest
recognized, because they were experienced oftenest and most distinctly; it
will by implication be seen that long after the great mass of phenomena
have been generalized, there must remain phenomena which, from their
rareness, or unobtrusiveness, or seeming unimportance, or complexity, or
abstractness, are still ungeneralized. Thus will be furnished a
solution to a difficulty sometimes raised. When it is asked why the
universality of law is not already fully established, there will be the answer
that the directions in which it is not yet established are those in which its
establishment must necessarily be latest. That state of things which is
inferable beforehand, is just the state which we find to exist. If such
coexistences and sequences as those of Biology and Sociology are not yet
reduced to law, the presumption is, not that they are irreducible to law, but

that their laws elude our present means of exploration. Having long ago
proved uniformity throughout all the lower classes of relations, and having
been step by step proving {160} uniformity throughout classes of relations
successively higher and higher, if we have not yet succeeded with the
highest classes, it may be fairly concluded that our powers are at fault,
rather than that the uniformity does not exist. And unless we make the
absurd assumption that the process of generalization, now going on with
unexampled rapidity, has reached its limit, and will suddenly cease, we
must infer that ultimately mankind will discover a constant order even
among the most involved and obscure phenomena.

THE VALUATION OF EVIDENCE.
[First published in The Leader for June 25, 1853. ]

With Spirit-rappings and Table-movings still the rage, and with the belief
in Spontaneous Combustion still unextinguished, it seems desirable that
something should be said in justification of that general scepticism with
which the philosophical meet the alleged wonders that periodically turn the
heads of the nation. Nothing less than a bulky octavo would be needed to
contain all that might be written on the matter; and unfortunately such an
octavo, when written, would be little read by those most requiring it. A brief
hint or two, however, may find listeners among them.
“I tell you I saw it myself,” is the so-thought conclusive assertion with
which many a controversy is abruptly ended. Commonly those who make
this assertion think that after it nothing remains to be urged; and they are
astonished at the un­reason­able­ness of those who still withhold their belief.
Though they reject many tales of witchcraft, many ghost stories whose
marvels were attested by eye-witnesses—though they have repeatedly seen
stage-conjurors seem to do things which they do not believe were really
done—though they have heard of the Automaton Chess-player and the
Invisible Girl, and have perhaps seen explanations of the modes in which
the public were deluded by {162} them—though in all these cases they know
that the facts were other than the spectators supposed them to be; yet they
cannot imagine that their own perceptions have been vitiated by influences
like those which vitiated the perceptions of others. Or, to put the thing more

charitably and perhaps more truly, they forget that such vitiations are
constantly occurring.
To observe correctly, though commonly thought very easy, every man of
science knows to be difficult. Our faculties are liable to report falsely from
two opposite causes—the presence of hypothesis, and the absence of
hypothesis. To the dangers arising from one or other of these, every
observation we make is exposed; and between the two it is hard to see any
fact quite truly. A few illustrations of the extreme distortions arising from
the one cause, and the extreme inaccuracy consequent on the other, will
justify this seeming paradox.
Nearly every one is familiar with the myth prevalent on our sea-coasts,
respecting the Barnacle Goose. The popular belief was, and indeed is still in
some places, that the fruits on branches which hang into the sea become
changed into shell-covered creatures called barnacles, found incrusting
these submerged branches; and further, that these barnacles are in process
of time transformed into the birds known as barnacle geese. This belief was
not confined to the vulgar; it was received among naturalists. Nor was it
with them simply an adopted rumour. It was based on observations which
were recorded and approved by the highest scientific authorities, and
published with their countenance. In a paper contained in the Philosophical
Transactions , Sir Robert Moray says:—“In every shell that I opened . . .
there appeared nothing wanting, as to the external parts, for making up a
perfect sea-fowl; the little bill like that of a goose, the eyes marked, the
head, neck, breast, wings, tail, and feet formed, the feathers everywhere
perfectly shaped and blackish coloured, and the feet like those of other {163}
waterfowl, to my best remembrance.” Now this myth respecting the
barnacle goose has been exploded for some century and a half. To a modern
zoologist who examines one of these cirrhipeds, as the barnacles are called,
it seems scarcely credible that it could ever have been thought a chick; and
what Sir Robert Moray could have taken for “head, neck, breast, wings, tail,
feet, and feathers,” he cannot imagine. Under the influence of a pre-
conception, here is a man of education describing as “a perfect sea-fowl”

what is now known to be a modified crustacean—a creature belonging to a
remote part of the animal kingdom.
A still more remarkable instance of perverted observation exists in an old
book entitled Metamorphosis Naturalis , &c., published at Middleburgh in
1662. This work, in which is attempted for the first time a detailed account
of in­sect-trans­for­ma­tions, contains numerous illustrative plates, in which
are represented the various stages of evolution—larva, pupa, and imago.
Those who have any knowledge of Entomology will recollect that the
chrysalises of all our common butterflies exhibit at the anterior end a
number of pointed projections, producing an irregular outline. Have they
ever observed in this outline a resemblance to a man’s face? For myself, I
can say that though in early days I kept brood after brood of butterfly larvæ
through all their changes, I never perceived any such likeness; nor can I see
it now. Nevertheless, in the plates of this Metamorphosis Naturalis , each
chrysalis has its projections so modified as to represent a burlesque human
head—the respective species having different profiles given them. Whether
the author was a believer in metempsychosis, and thought he saw in the
chrysalis a disguised humanity; or whether, swayed by the false analogy
which Butler makes so much of, between the change from chrysalis to
butterfly and that from mortality to immortality, he considered the chrysalis
as typical of man; does not appear. Here, however, is the fact, that
influenced by some {164} pre-conception or other, he has made his drawings
quite different from the actual forms. It is not that he simply thinks this
resemblance exists—it is not that he merely says he can see it; but his
preconception so possesses him as to swerve his pencil, and make him
produce representations laughably unlike the realities.
These, which are extreme cases of distorted perceptions, differ only in
degree from the distorted perceptions of daily life; and so strong is the
distorting influence that even the man of science cannot escape its effects.
Every microscopist knows that if they have conflicting theories respecting
its nature, two observers shall look through the same instrument at the same
object, and give quite different descriptions of its appearance.

From the dangers of hypothesis let us now turn to the dangers of no
hypothesis. Little recognized as is the fact, it is nevertheless true that we
cannot make the commonest observation correctly without beforehand
having some notion of what we are to observe. You are asked to listen to a
faint sound, and you find that without a pre-conception of the kind of sound
you are to hear, you cannot hear it. Provided that it is not strong, an unusual
flavour in your food may pass quite unperceived, unless some one draws
attention to it, when you taste it distinctly. After knowing him for years, you
shall suddenly discover that your friend’s nose is slightly awry, and wonder
that you never remarked it before. Still more striking becomes this inability
when the facts to be observed are complex. Of a hundred people who listen
to the dying vibrations of a church bell, almost all fail to perceive the
harmonics, and assert the sound to be simple. Scarcely any one who has not
practised drawing, sees, when in the street, that all the horizontal lines in
the walls, windows, shutters, roofs, seem to converge to one point in the
distance: a fact which, after a few lessons in perspective, becomes visible
enough.
Perhaps I cannot more clearly illustrate this necessity for {165} hypothesis
as a condition to accurate perception, than by narrating a portion of my own
experience relative to the colours of shadows.
Indian ink was the pigment which, during boyhood, I invariably used for
shading. Ask any one who has received no culture in art, or who has given
no thought to it, of what colour a shadow is, and the unhesitating reply will
be—black. This is uniformly the creed of the uninitiated; and in this creed I
undoubtingly remained till about eighteen. Happening, at that age, to come
much in contact with an amateur artist, I was told, to my great surprise, that
shadows are not black but of a neutral tint. This, to me, novel doctrine, I
strenuously resisted. I have a pretty distinct recollection of denying it point
blank, and quoting all my experience in support of the denial. I remember,
too, that the controversy lasted over a considerable period; and that it was
only after my friend had repeatedly drawn my attention to instances in
Nature, that I finally gave in. Though I must previously have seen myriads
of shadows, yet in consequence of the fact that very generally the tint

approaches to black, I had been unable, in the absence of hypothesis, to
perceive that in many cases it is distinctly not black.
I continued to hold this amended doctrine for some years. It is true that
from time to time I observed that the tone of the neutral tint varied
considerably in different shadows; but still the divergencies were not such
as to shake my faith in the dogma. By-and-bye, however, in a popular work
on Optics, I met with the statement that the colour of a shadow is always
the complement of the colour of the light casting it. Not seeing the
wherefore of this alleged law, which seemed moreover to conflict with my
established belief, I was led to study the matter as a question of causation.
Why are shadows coloured? and what determines the colour? were the
queries that suggested themselves. In seeking answers, it soon became
manifest {166} that as a space in shadow is a space from which the direct
light alone is excluded, and into which the indirect light (namely, that
reflected by surrounding objects, by the clouds and by the sky) continues to
fall, the colour of a shadow must partake of the colour of everything that
can either radiate or reflect light into it. Hence, the colour of a shadow must
be the average colour of the diffused light; and must vary, as that varies,
with the colours of all surrounding things. Thus was at once explained the
inconstancy I had already noticed; and I presently recognized in Nature that
which the theory implies—namely, that a shadow may have any colour
whatever, according to circumstances. Under a clear sky, and with no trees,
hedges, houses, or other objects at hand, shadows are of a pure blue. During
a red sunset, mixture of the yellow light from the upper part of the western
sky with the blue light from the eastern sky, produces green shadows. Go
near to a gas-lamp on a moonlight night, and a pencil-case placed at right
angles to a piece of paper will be found to cast a purple-blue shadow and a
yellow-grey shadow, produced by the gas and the moon respectively. And
there are conditions it would take too long here to describe, under which
two parts of the same shadow are differently coloured. All which facts
became obvious to me as soon as I knew that they must exist.
Here, then, respecting certain simple phenomena that are hourly visible,
are three successive convictions; each of them based on years of

observation; each of them held with unhesitating confidence; and yet only
one—as I now believe—true. But for the help of an hypothesis, I should
probably have remained in the common belief that shadows are black. And
but for the help of another hypothesis, I should probably have remained in
the half-true belief that they are neutral tint.
Is it not clear, therefore, that to observe correctly is by no means easy?
On the one hand, a pre-conception, makes {167} us liable to see things not
quite as they are, but as we think them. On the other hand, in the absence of
a pre-conception, we are liable to pass over much that we ought to see. Yet
we must have either a pre-conception or no pre-conception. Evidently, then,
all our observations, save those guided by true theories already reached, are
in danger of either distortion or incompleteness.
It remains but to remark, that if our observations are imperfect in cases
like the foregoing, where the things seen are persistent, and may be again
and again looked at or continuously contemplated; how much more
imperfect must they be where the things seen are complex processes,
changes, or actions, each presenting successive phases, which, if not truly
observed at the moments they severally occur, can never be truly observed
at all! Here the chances of error become immensely multiplied. And when,
in addition, there exists some moral excitement,—when, as in these Spirit-
rapping and Table-turning experiments, the intellect is partially paralysed
by fear or wonder correct observation becomes next to an impossibility.

WHAT IS ELECTRICITY?
[First published in The Reader for November 19, 1864. ]

Probably few, if any, competent physicists have, of late years, used the
term “electric fluid” in any other than a conventional sense. When
distinguishing electricity into the two kinds, “positive” and “negative,” or
“vitreous” and “resinous,” they have used the ideas suggested by these
names merely as convenient symbols, and not as representatives of different
entities. And, now that heat and light are proved to be modes of motion, it
has become obvious that all the allied manifestations of force must be
modes of motion.
What is the particular mode of motion which constitutes electricity, thus
becomes the question. That it is some kind of molecular vibration, different
from the molecular vibrations which luminous bodies give off, is, I
presume, taken for granted by all who bring to the consideration of the
matter a knowledge of recent discoveries. Beyond those simple oscillations
of molecules from which light and heat result, may we not suspect that
there will, in some cases, arise compound oscillations? Let us consider
whether the conditions under which electricity arises are not such as to
generate compound oscillations; and whether the phenomena of electricity
are not such as must result from compound oscillations.
The universal antecedent to the production of electricity {169} is the
immediate or mediate contact of heterogeneous substances—substances that
are heterogeneous either in their molecular constitutions, or in their
molecular states. If, then, electricity is some mode of molecular motion, and

if, whenever it is produced, the contact of substances having unlike
molecules or molecules in unlike states, is the antecedent, there seems
thrust upon us the conclusion that electricity results from some mutual
action of molecules whose motions are unlike.
What must be that mutual action of molecules having unlike motions,
which, as we see, is the universal antecedent of electrical disturbance? The
answer to this question does not seem difficult to reach, if we take the
simplest case—the case of con­tact-elec­tri­city. When two pieces of metal of
the same kind, and at the same temperature, are applied to one another,
there is no electrical excitation; but, if the metals applied to one another be
of different kinds, there is a genesis of electricity. This, which has been
regarded as an anomalous fact—a fact so anomalous that it has been much
disputed because apparently at variance with every hypothesis—is a fact to
which an interpretation is at once supplied by the hypothesis that electricity
results from the mutual disturbances of unlike molecular motions. For if, on
the one hand, we have homogeneous metals in contact, their respective
molecules, oscillating synchronously, will give and take any forces which
they impress on one another without producing oscillations of new orders.
But if, on the other hand, the molecules of the one mass have periods of
oscillation different from those of the other mass, their mutual impacts will
not agree with the period of oscillation of either, but will generate a new
rhythm, differing from, and much slower than, that of either. The
production of what are called “beats” in acoustics, will best illustrate this. It
is a familiar fact that two strings vibrating at different rates, from time to
time concur in sending off aërial waves in the {170} same direction at the
same instant: that then, their vibrations getting more and more out of
correspondence, they send off their aërial waves in the same direction at
exactly intermediate instants; and presently, coming once more into
correspondence, they again generate coinciding waves. So that when their
periods of vibration differ but little, and when consequently it takes an
appreciable time to complete their alternations of agreement and
disagreement, there results an audible alternation in the sound—a
succession of pulses of louder and feebler sound. In other words, besides

the primary, simple, and rapid series of waves, constituting the two sounds
themselves, there is a series of slow compound waves, resulting from their
repeated conflicts and concurrences. Now if, instead of the two strings
communicating their vibrations to the air, each communicated its vibrations
to the other, we should have just the same alternation of concurrent and
conflicting pulses. And if each of the two strings was combined with an
aggregate of others like itself, in such way that it communicated to its
neighbours both its normal and its abnormal vibrations, it is clear that
through each aggregate of strings there would be propagated one of these
compound waves of oscillation, in addition to their simple rapid
oscillations. This illustration will, I think, make it manifest that when a
mass of molecules which have a certain period of vibration, is placed in
contact with a mass of molecules which have another period of vibration,
there must result an alternation of coincidences and antagonisms in the
molecular motions, such as will make the molecules alternately increase
and decrease one another’s motions. There will be instants at which they are
moving in the same direction, and intervening instants at which they are
moving in opposite directions; whence will arise periods of greatest and
least deviations from their ordinary motions. And these greatest and least
deviations, being communicated to neighbouring molecules, and passed on
by them {171} to the next, will result in waves of perturbation propagated
throughout each mass.
Let us now ask what will be the mutual relations of these waves. Action
and reaction being equal and opposite, it must happen that whatever effect a
molecule of the mass A produces upon an adjacent molecule of the mass B,
must be accompanied by an equivalent reverse effect upon itself. If a
molecule of the mass A is at any instant moving in such way as to impress
on a molecule of the mass B an additional momentum in any given
direction, then the momentum of the molecule of A, in that direction, will
be diminished to an equal amount. That is to say, to any wave of increased
motion propagated through the molecules of B, there must be a reactive
wave of decreased motion propagated in the opposite direction through the
molecules of A. See, then, the two significant facts. Any addition of

motion, which at one of these alternate periods is given by the molecules of
A to the molecules of B, must be propagated through the molecules of B in
a direction away from A; and simultaneously there must be a subtraction
from the motion of the molecules of A, which will be propagated through
them in a direction away from B. To every wave of excess sent through the
one mass, there will be a corresponding wave of defect sent through the
other; and these positive and negative waves will be exactly coincident in
their times, and exactly equal in their amounts. Whence it follows that if
these waves, proceeding from the surface of contact through the two masses
in contrary directions, are brought into relation, they will neutralize each
other. Action and reaction being equal and opposite, these plus and minus
molecular motions will cancel if they are added together; and there will be a
restoration of equilibrium.
These positive and negative waves of perturbation will travel through the
two masses of molecules with great facility. It is now an established truth
that molecules {172} absorb, in the increase of their own vibrations, those
rhythmical impulses or waves which have periodic times the same as their
own; but that they cannot thus absorb successive impulses that have
periodic times different from their own. Hence these differential
undulations, being very long undulations in comparison with those of the
molecules themselves, will readily pass through the masses of molecules, or
be conducted by them. Further observe that, if the two masses of molecules
continue joined, these positive and negative differential waves travelling
away from the surface of contact in opposite directions, and severally
arriving at the outer surfaces of the two masses, will be reflected from
these; and, travelling back again toward the surface of contact, will there
meet and neutralize one another. Hence no current will be produced along a
wire joining the outer surfaces of the masses; since neutralization will be
more readily effected by this return of the waves through the masses
themselves. But, though no external current arises, the masses will continue
in what we call opposite electric states; as a delicate electrometer shows
that they do. And further, if they are parted, the positive and negative waves
which have the instant before been propagated through them respectively,

remaining unneutralized, the masses will display their opposite electric
states in a more conspicuous way. The residual positive and negative waves
will then neutralize each other along any conductor that is placed between
them, seeing that the plus waves communicated from the one mass to the
conductor, meeting with the minus waves communicated from the other,
and being mutually cancelled as they meet, the conductor will become a
line of least resistance to the waves of each mass.
Let us pass now to the allied phenomena of thermo-electricity. Suppose
these two masses of metal to be heated at their surfaces of contact: the
forms of the {173} masses being such that their surfaces of contact can be
considerably heated without their remoter parts being much heated. What
will happen? Prof. Tyndall has shown, in the cases of various gases and
liquids, that, other things equal, when molecules have given to them more
of the insensible motion which we call heat, there is no alteration in their
periods of oscillation, but an increase in the amplitudes of their oscillations:
the molecules make wider excursions in the same times. Assuming that it is
the same in solids, it will follow that, when the two metals are heated at
their surfaces of contact, the result will be the same as before in respect of
the natures and intervals of the differential waves. There will be a change,
however, in the strengths of these waves. For, if the two orders of molecules
have severally given to them increased quantities of motion, the
perturbations which they impress on each other will also be increased.
These stronger positive and negative waves of differential motion will, as
before, travel through either mass away from the surfaces of contact—that
is, toward the cold extremities of the masses. From these cold extremities
they will, as before, rebound toward the surfaces of contact; and, as before,
will tend thus to equilibriate each other. But they will meet with resistance
in thus travelling back. It is a well-ascertained fact that raising the
temperatures of metals decreases their conducting powers. Hence, if the two
cold ends of the masses be connected by some other mass whose molecules
can take on with facility these differential undulations—that is, if the two
ends be joined by a conductor, the positive and negative waves will meet
and neutralize one another along this conductor, instead of being reflected

back to the surfaces of contact. In other words, there will be established a
current along the wire joining the two cold ends of the metallic masses.
Carried a step further, this reasoning affords us an explanation of the
thermo-electric pile. If a number of {174} these bars of different metals, as
antimony and bismuth, are soldered together, end to end, in alternate order,
AB, AB, AB, etc., then, so long as they remain cold, there is no
manifestation of an electric current; or, if all the joints are equally heated,
there is no manifestation of an electric current beyond that which would
arise from any relative coolness of the two ends of the compound bar. But if
alternate joints are heated, an electric current is produced in a wire joining
the two ends of the compound bar—a current that is intense in proportion to
the number of pairs. What is the cause of this? Clearly, so long as all the
joints are of the same temperature, the differential waves propagated from
each joint toward the two adjacent joints will be equal and opposite to those
from the adjacent joints, and no disturbance will be shown. But if alternate
joints are heated, the positive and negative differential waves propagated
away from them will be stronger than those propagated from the other
joints. Hence, if the joint of bar A with bar B be heated, the other end of the
bar B, which is joined to A2, not being heated, will receive a stronger
differential wave than it sends back. In addition to the wave which its
molecules would otherwise induce in the molecules of A2, there is an effect
which it conducts from A1; and this extra impulse propagated to the other
end of B2 is added to the impulse which its heated molecules would
otherwise give to the molecules of A3; and so on throughout the series. The
waves being added together, become more violent, and the current through
the wire joining the extremities of the series, more intense.
This interpretation of the facts of thermo-electricity will probably be met
by the objection that there are, in some cases, thermo-electric currents
developed between masses of metal of the same kind, and even between
different parts of the same mass. It may be urged that, if unlikeness between
the rates of vibration of molecules in contact {175} is the cause of these
electric disturbances; then, heat ought not to produce any electric

disturbances when the molecules are of the same kind; since heat does not
change the periodic times of molecular vibrations. This objection, which
seems at first sight a serious one, introduces us to a confirmation. For where
the masses of molecules are homogeneous in all other respects, difference
of temperature does not generate any thermo-electric current. The junction
of hot with cold mercury sets up no electric excitement. In all cases where
thermo-electricity is generated between metals of the same kind, there is
evidence of heterogeneity in their molecular structures—either one has been
hammered and the other not, or one is annealed and the other unannealed.
And where the current is between different parts of the same mass, there are
differences in the crystalline states of the parts, or differences between the
ways in which the parts have cooled after being cast. That is to say, there is
proof that the molecules in the two masses, or in different parts of the same
mass, are in unlike relations to their neighbours—are in unlike states of
tension. Now, however true it may be that molecules of the same kind
vibrate at the same rate, whatever may be their temperature, it is obviously
true so long only as their motions are not modified by restraining forces. If
molecules of the same kind are in one mass arranged into that state which
constitutes crystallization, while in another mass they are not thus bound
together; or if in the one their molecular relations have been modified by
hammering, and in the other not; the differences in the restraints under
which they respectively vibrate will affect their rates of vibration. And if
their rates of vibration are rendered unequal, then the alleged cause of
electrical disturbance comes into existence.
To sum up, may it not be said that by some such action alone can the
phenomena of electricity be explained; {176} and that some such action must
inevitably arise under the conditions? On the one hand electricity, being a
mode of motion, implies the transformation of some preëxisting motion—
implies, also, a transformation such that there are two new kinds of motion
simultaneously generated, equal and opposite in their directions—implies,
further, that these differ in being plus and minus , and being therefore
capable of neutralizing each other. On the other hand, in the above cases,
molecular motion is the only source of motion that can be assigned; and this

molecular motion seems calculated, under the circumstances, to produce
effects like those witnessed. Molecules vibrating at different rates cannot be
brought in juxtaposition without affecting one another’s motions. They
must affect one another’s motions by periodically adding to, or deducting
from one another’s motions; and any excess of motion which those of the
one order receive, must be accompanied by an equivalent defect of motion
in those of the other order. When such molecules are units of aggregates
placed in contact, they must pass on these perturbations to their neighbours.
And so, from the surface of contact, there must be waves of excessive and
defective molecular motion, equal in their amounts, and opposite in their
directions—waves which must exactly compensate one another when
brought into relation.
I have here dealt only with electrical phenomena of the simplest kind.
Hereafter I may possibly endeavour to show how this hypothesis furnishes
in­ter­pre­ta­tions of other forms of Electricity.

P OSTSCRIPT (1873).—During the nine years which have elapsed since
the foregoing essay was published, I have found myself no nearer to such
allied in­ter­pre­ta­tions of other forms of Electricity. Though, from time to
time, I have recurred to the subject, in the hope of fulfilling the {177}
expectation raised by the closing sentence, yet no clue has encouraged me
to pursue the speculation. Only now, when republication of the essay in a
permanent form once more brings the question before me, does there occur
a thought which appears worth setting down.
The union of two different ideas, not before placed side by side, has
generated this thought. In the first number of the Principles of Biology ,
issued in January 1863, and dealing, among other “Data of Biology,” with
organic matter and the effects of forces upon it, I ventured to speculate
about the molecular actions concerned in organic changes, and, among
others, those by which light enables plants to take the carbon from carbonic
acid (§ 13). Pointing out that the ability of heat to decompose compound
molecules, is generally proportionate to the difference between the atomic

weights of their component elements, and assuming that components
having widely-unlike atomic weights, have widely-unlike motions, and are
therefore affected by widely-unlike undulations; the inference drawn was,
that in proportion as the rhythms of its components differ, a compound
molecule will be unstable in presence of strong etherial undulations acting
upon one component more than on the other or others: their movements
thus being rendered so incongruous that they can no longer hold together. It
was argued, further, that a tolerably-stable compound molecule may, if
exposed to strong etherial undulations especially disturbing one of its
components, be decomposed when in presence of some unlike molecule
having components whose times of oscillation differ less from those of this
disturbed component. And a parallel was drawn between the de-oxidation of
metals by carbon when exposed to the longer undulations in a furnace, and
the de-carbonization of carbonic acid by hydrogen, &c., when exposed to
the shorter undulations in a plant’s leaves. These ideas I recall chiefly for
the purpose of presenting clearly the conception of a compound molecule as
containing {178} diversely-moving components—components having
independent and unlike oscillations, in addition to the oscillation of the
whole molecule formed by them. The legitimacy of this conception may, I
suppose, be assumed. The beautiful experiments by which Prof. Tyndall has
proved that light decomposes the vapours of certain compounds, illustrates
this ability which the elements of a compound molecule have, severally to
take up etherial undulations corresponding to their own; and thus to have
their individual movements so increased as to cause disruption of the
compound molecule. This, at least, is the interpretation which Prof. Tyndall
puts on the facts; and I presume that he puts a kindred interpretation upon
the facts he has disclosed respecting the marvellous power possessed by
complex-moleculed vapours to absorb heat—the interpretation, namely, that
the thermal undulations are, in such vapours, taken up in augmenting the
movements within each molecule, rather than in augmenting the
movements of the molecules as wholes.
But now, assuming this to be a true conception of compound molecules
and the effects produced on them by etherial undulations, there presents

itself the question—What will be the effects produced by compound
molecules on one another? How will the elements of one compound
molecule have their rhythmical motions affected by proximity to the
elements of an unlike compound molecule? May we not suspect that effects
will be produced on one another, not only by the unlike molecules as
wholes, but also certain other, and par­tial­ly-in­de­pen­dent, effects by their
components on one another; and that there will so be generated some
specialized form of molecular motion? Throughout the speculation set forth
in the foregoing essay, the supposition is that the molecules are those of
juxtaposed metals—molecules which, whether absolutely simple or not, are
relatively simple; and these are regarded as producing on one another’s
movements perturbations of a relatively-simple kind, which admit of being
transferred from molecule {179} to molecule throughout each mass. In trying
to carry further this interpretation, it had not occurred to me until now, to
consider the perturbations produced on one another by compound
molecules: taking into consideration, not merely the capacity each has for
affecting the other as a whole, but the capacity which the constituents of
each individually have for affecting the individual constituents of the other.
If an individual constituent of a compound molecule can, by the successive
impacts of etherial undulations, have the amplitudes of its oscillations so
increased as to detach it; we can scarcely doubt that an individual
constituent of a compound molecule may affect an individual constituent of
an unlike compound molecule near it: their respective oscillations
perturbing one another apart from the perturbation produced on one another
by the compound molecules as wholes. And it seems inferable that the
secondary perturbation thus arising, will, like the primary perturbation, be
such that the action and reaction, equal and opposite in their amounts, will
produce equal and opposite deviations in the molecular movements. From
this there appear to be several corollaries.
If a compound molecule, having a slow rhythm as a whole in addition to
the more rapid rhythms of its members, has the power of taking up much of
that motion we call heat in the increase of its internal movements, and to a
corresponding degree takes up less in the increase of its movements as a

whole; then may we not infer that the like will hold when other kinds of
forces are brought to bear on it? May we not anticipate that when a mass of
compound molecules of one kind is made to act upon a mass of compound
molecules of another kind (say by friction), the molecular effects mutually
produced, partly in agitating the molecules as wholes, and partly in
agitating their components relatively to one another, will become less of the
first and more of the last, in proportion as the molecules progress in
compositeness?
A further implication suggests itself. While much of the {180} force
mutually exercised will thus go to increase the motion within each of the
compound molecules that immediately act on one another, it appears
inferable that relatively little of this intestinal motion will be communicated
to other molecules. The excesses of oscillation given to individual members
of a large cluster, will not be readily passed on to homologous members of
adjacent large clusters; since they must be relatively far apart. Whatever
motion is transferred, must be transferred by waves of the intervening
etherial medium; and the power of these must decrease rapidly as the
distance increases. Obviously such difficulty of transfer must, for this
reason, become great when the molecules become highly compounded.
At the same time will it not follow that such augmentations of movement
caused in individual members of a cluster, not being readily transmissible to
homologous members of adjacent clusters, will accumulate? The more
composite molecules become, the more possible will it be for individual
components of them to be violently affected by individual components of
different composite molecules near them—the more possible will it be for
their mutual perturbations to progressively increase?
And now let us consider how these inferences bear on the interpretation
of Statical Electricity—the form of Electricity most unlike the form above
dealt with.
The substances which exhibit most conspicuously the phenomena of
statical electricity are distinguished either by the chemical complexity of
their molecules, or else by the compositeness of their molecules produced
allotropically or isomerically, or else by both. The simple substances

electrically excited by friction, as carbon and sulphur, are those having
several allotropic states—those capable of forming multiple molecules. The
conchoidal fracture of the diamond and of roll-sulphur, suggest some
colloidal form of aggregation, regarded by Prof. Graham as a form in which
the molecules are united into {181} relatively-large groups.23 In such
compound inorganic substances as glass, we have, besides the chemical
complexity, this same conchoidal fracture which, along with other evidence,
shows glass to be a colloid; and the colloidal form of molecule is to be
similarly inferred as characterizing resin, amber, &c. That dry animal
substances, such as silk and hair, are formed of extremely-large molecules,
we have clear proof; since these, chemically complex in a high degree, also
have their components united in high multiples. It needs but to name the
fact that non-electric and conducting substances, such as the metals, acids,
water, &c., have relatively-simple molecules, to make it clear that the
capacity for developing statical electricity depends in some way upon the
presence of molecules of highly composite kinds. And there is even still
more conclusive proof than that yielded by the contrast between these
groups—the proof furnished by the fact that the same substance may be a
conductor or a non-conductor, according to its form of molecular
aggregation. Thus selenium when crystalline is a conductor, but when in
that allotropic state called amorphous, or non-crystalline, it is a good non-
conductor. That is, accepting Prof. Graham’s interpretation of these states,
when its molecules are arranged simply, it is a conductor, but when they are
compounded into large groups it is a non-conductor, and, by implication, an
electric.
So far, then, the à priori inference that a peculiar form of molecular
perturbation will result when two unlike substances, one of which or each
of which consists of {182} highly-compounded molecules, are made to act
on one another, is justified a posteriori . And now, instead of asking
generally what will happen, let us ask what may be inferred to happen in a
special case. A piece of glass is rubbed by silk. The large colloidal
molecules forming the surface of each, are made to disturb one another.

This is an inference about which there will, I suppose, be no dispute; since
it is that assumed in the now-established doctrine of the correlation of heat
and motion. Besides the effect which, as wholes the molecules mutually
produce, there is the effect produced on one another by certain of their
components. Such of these as have times of oscillation which differ, but not
very widely, generate mutual perturbations that are equal and opposite.
Could these perturbations be readily propagated away from the surface of
contact through either mass, the effect would quickly dissipate, as in the
case of metals; but, for the reason given above, these perturbations cannot
be transferred with ease to the homologous members of the compound
molecules behind. Hence the mechanical force of the friction, transformed
into the molecular movements of these superficial constituent molecules,
exists in them as intense mutual perturbations, which, unable to diffuse, are
limited to the surfaces, and, indeed, to those parts of the surfaces that have
acted on one another. In other words, the two surfaces become charged with
two equal and opposite molecular perturbations—perturbations which,
cancelling one another if the surfaces are kept in contact, cannot do this if
the surfaces are parted; but can then cancel one another only if a conductor
is interposed.
Let me briefly point out some apparent agreements between the
corollaries from this hypothesis, and the observed phenomena.
We have, first, an interpretation of the fact, otherwise seeming so
anomalous, that this form of electrical excitement is superficial . That there
should be a mode of {183} activity limited to the surface of a substance, is
difficult to understand in the absence of some conception of the kind
suggested.
We have an explanation of the truth, insisted on by Faraday, that there
can be no charge of one kind of electricity obtained, without a
corresponding charge of the opposite kind. For it is a necessary implication
of the hypothesis above set forth, that no molecular perturbation of the
nature described, can be produced, without there being simultaneously
produced a coun­ter-per­tur­ba­tion exactly equal to it.

May we not also say that some insight is afforded into the phenomena of
induction? In the cases thus far considered, the two surfaces electrified by
the mutual perturbations of their molecules, are supposed to be in contact.
Since, however, apparent contact is not actual contact, we must, even in this
case, assume that the mutual perturbation is effected through an intervening
stratum of ether. To interpret induction, then, we have first to conceive this
stratum of ether to be greatly increased in thickness; and then to ask what
will happen if the molecules of one surface, in this state of extreme internal
perturbation, act on the molecules of a surface near it. Whether the stratum
of ether is so thin as to be inappreciable to our senses, or whether it is wide
enough to be conspicuous, it must still happen that if through it the mutual
perturbations are conveyed in the one case, they will be conveyed in the
other; and hence a surface which is already the seat of these molecular
perturbations of one order, will induce perturbations of a counter order in
the molecules of an adjacent surface.
In additional justification of the hypothesis, I will only point out that
voltaic electricity seems to admit of a kindred interpretation. For any
molecular re-arrangement, such as occurs in a chemical decomposition and
recombination, implies that the movements of the {184} molecules
concerned are mutually perturbed; and their perturbations must conform to
the general law already described: the molecules must derange one
another’s motions in equal and opposite ways, and so must generate plus
and minus derangements that cancel when brought into relation.
Of course I suggest this view simply as one occurring to an outsider.
Unquestionably it presents difficulties; as, for instance, that no manifest
explanation is yielded by it of electric attractions and repulsions. And there
are doubtless objections not obvious to me that will at once strike those to
whom the facts are more familiar. The hypothesis must be regarded as
speculative; and as set down on the chance that it may be worth
consideration.

Since the foregoing postscript was put in type, I have received criticisms
upon it, oral and written, from several leading electricians and physicists;
and I have profited by them to amend parts of the exposition. While I have
remained without endorsements of the hypothesis, the objections raised
have not been such as to make clear its untenability.
On one point an addition seems needful to exclude a misconstruction apt
to arise. The description of the mutually-produced molecular perturbations,
opposite in their kinds, as resulting in waves that are propagated away from
the place of disturbance, and that cancel when brought into relation, is met
by the criticism that waves, proceeding in opposite directions and meeting,
do not mutually cancel, but, passing one another, proceed onwards. There
are, however, two respects in which the parallelism does not hold, between
the waves referred to and the waves I have described, which perhaps cannot
rightly be called waves. The waves referred to, as those on the surface of a
liquid, {185} are such that each consists of two opposite deviations from a
mean state. Each shows excess and defect. A series of them is a series of
plus and minus divergences; and if two such series meet one another, they
do not cancel. But there is no analogy between this case and a case in which
the whole effect propagated in one direction is a plus motion, and the whole
effect propagated in the opposite direction is a minus motion—that is, plus
and minus changes in other motions. These, if equal in amount, will cancel
when they meet. If one is a continual addition to motion in a certain
direction, and the other a corresponding subtraction from motion in that
direction, the two, when added together, must produce zero. From another
point of view the absence of parallelism between the two cases may be
equally well seen. Waves of the kinds instanced as not cancelling one
another, are waves produced by some force foreign to the medium
exhibiting them—an extrinsic force. Hence, proceeding from the place of
initiation, they are necessarily, considered in their totalities, positive in
whatever directions they travel; and hence, too, when conducted round so as
to meet, an exaggerated perturbation will result. But in the simplest of the
cases here dealt with (that of con­tact-elec­tric­ity) the perturbation is not of
extrinsic origin, but of intrinsic origin. There is no external activity at the

expense of which the quantity of motion in the disturbed matter is
positively increased. The activity, being such only as is internally
possessed, can generate no more motion than already exists; and therefore
whatever gain of motion arises anywhere in the molecules must be at the
cost of an equal loss elsewhere. Here perturbation cannot be a plus motion
in all directions from the place of initiation; but any plus motion
continually generated can result only from an equal and opposite minus
motion continually generated; and the mutual cancelling becomes a
corollary from the mutual genesis.
In the course of the discussions which I have had, the {186} following way
of presenting the argument has occurred to me.
1. Two homogeneous bodies are rubbed together and there results heat:
the interpretation being that the molar motion is transformed into molecular
motion. Here motion produces motion—the form only being changed.
2. Now of the two bodies one is replaced by a body unlike in nature to
the other, and they are again rubbed. Again a certain amount of heat is
produced: some of the molar motion is, as before, transformed into
molecular motion. But, at the same time, another part of the molar motion is
changed into—what? Surely not a fluid, a substance, a thing. It cannot be
that what in the first case produces a change of state , in the second case
produces an entity . And in the second case itself, it cannot be that while part
of the original motion becomes changed into another species of motion, part
of it becomes changed into a species of matter.
3. Must we not say, then, that if, when the two bodies rubbed are
homogeneous, sensible motion is transformed into insensible motion, when
they are heterogeneous, sensible motion must still be transformed into
insensible motion: such difference of nature as this insensible motion has,
being consequent on the difference of nature between the two kinds of
molecules acting on one another?
4. If, when the two masses are homogeneous, those molecules which
compose the two rubbed surfaces disturb one another, and increase one
another’s oscillations; then, when the two masses are heterogeneous, those

molecules forming the two rubbed surfaces must also disturb one another in
some way—increase one another’s agitations.
5. If, when the two sets of molecules are alike in kind, the mutual
disturbance is such that they simply increase the amplitudes of one
another’s oscillations, and do this because their times correspond; then,
must it not be {187} that when they are unlike in kind, the mutual
disturbance will involve a differential action consequent on the unlikeness
of their motions? Must not the discord of the oscillations produce a result
which cannot be produced when the oscillations are concordant—a
compound form of molecular motion?
6. If masses of relatively-simple molecules, placed in apposition and
made to act on one another, cause such effects; then must we not say that
effects of the same class, but of a different order, will be caused by the
mutual actions, not of the molecules as wholes, but of their constituents? If
the rubbed surfaces severally consist of highly-compounded molecules—
each containing, it may be, several hundreds of minor molecules, united
into a def­i­nite­ly-ar­ranged cluster; then, while the molecules as wholes affect
one another’s motions, must we not infer that the constituents of the one
class will affect the constituents of the other class in their motions? While
the molecules as wholes increase one another’s oscillations, or derange one
another’s oscillations, or both, the components of them cannot be so stably
arranged that members of the one group are wholly inoperative on members
of the other group. And if they are operative, then there must be a
compound form of molecular motion which arises when masses of highly-
compounded molecules of unlike kinds, are made to act on one another.
With this series of propositions and questions, I leave the suggestion to
its fate; merely remarking that, setting out with the principles of molecular
physics now accepted, it seems difficult to avoid the implication that some
actions of the kinds described take place, and that there result from them
some classes of phenomena—phenomena which, if not those we call
electrical, remain to be identified.

ENDNOTE TO WHAT IS ELECTRICITY? .

23 Though conchoidal fracture may not be conclusive proof of colloidality, yet colloidal
substances hard enough for fracture always display it. Respecting roll-sulphur I may say that
though in a few days after it is made, it changes from its original state to a state in which it
consists of minute crystals of another kind irregularly massed, yet there is reason for suspecting
that these have a matrix of amorphous sulphur. I learn from Dr. Frankland that, when sublimed,
sulphur aggregates partly into minute crystals and partly into an amorphous powder
distinguished by insolubility.

MILL versus HAMILTON—THE TEST OF TRUTH.
[First published in The Fortnightly Review for July 1865. ]

British speculation, to which, the chief initial ideas and established truths
of Modern Philosophy are due, is no longer dormant. By his System of
Logic , Mr. Mill probably did more than any other writer to re-awaken it.
And to the great service he thus rendered some twenty years ago, he now
adds by his Examination of Sir William Hamilton’s Philosophy —a work
which, taking the views of Sir William Hamilton as texts, reconsiders
sundry ultimate questions that still remain unsettled.
Among these questions is one of much importance which has already
been the subject of controversy between Mr. Mill and others; and this
question I propose to discuss afresh. Before doing so, however, it will be
desirable to glance at two cardinal doctrines of the Hamiltonian philosophy
from which Mr. Mill shows reasons for dissenting—desirable, because
comment on them will elucidate what is to follow.
In his fifth chapter, Mr. Mill points out that “what is rejected as
knowledge by Sir William Hamilton,” is “brought back by him under the
name of belief.” The quotations justify this description of Sir W. Hamilton’s
position, and warrant the assertion that the relativity of {189} knowledge was
held by him but nominally. His inconsistency may, I think, be traced to the
use of the word “belief” in two quite different senses. We commonly say we
“believe” a thing for which we can assign preponderating evidence, or
concerning which we have received some indefinable impression. We
believe that the next House of Commons will not abolish Church-rates; or

we believe that a person on whose face we look is good-natured. That is,
when we can give con­fes­sed­ly-in­ad­eq­ uate proofs or no proofs at all for the
things we think, we call them “beliefs.” And it is the peculiarity of these
beliefs, as contrasted with cognitions, that their connexions with antecedent
states of con­scious­ness may be easily severed, instead of being difficult to
sever. But, unhappily, the word “belief” is also applied to each of those
temporarily or permanently indissoluble connexions in con­scious­ness, for
the acceptance of which the only warrant is that it cannot be got rid of.
Saying that I feel a pain, or hear a sound, or see one line to be longer than
another, is saying that there has occurred in me a certain change of state;
and it is impossible for me to give a stronger evidence of this fact than that
it is present to my mind. Every argument, too, is resolvable into successive
affections of con­scious­ness which have no warrants beyond themselves.
When asked why I assert some mediately known truth, as that the three
angles of a triangle are equal to two right angles, I find that the proof may
be decomposed into steps, each of which is an immediate con­scious­ness
that certain two quantities or two relations are equal or unequal—a con­‐
scious­ness for which no further evidence is assignable than that it exists in
me. Nor, on finally getting down to some axiom underlying the whole
fabric of demonstration, can I say more than that it is a truth of which I am
immediately conscious. But now observe the confusion that has arisen. The
immense majority of truths which we accept as beyond doubt, and from
which our notion of unquestionable truth is abstracted, {190} have this other
trait in common—they are severally established by affiliation on deeper
truths. These two characters have become so associated, that one seems to
imply the other. For each truth of geometry we are able to assign some
wider truth in which it is involved; for that wider truth we are able, if
required, to assign some still wider; and so on. This being the general nature
of the demonstration by which exact knowledge is established, there has
arisen the illusion that knowledge so established is knowledge of higher
validity than that immediate knowledge which has nothing deeper to rest
on. The habit of asking for proof, and having proof given, in all these
multitudinous cases, has produced the implication that proof may be asked

for those ultimate dicta of con­scious­ness into which all proof is resolvable.
And then, because no proof of these can be given, there arises the vague
feeling that they are akin to other things of which no proof can be given—
that they are uncertain—that they have unsatisfactory bases. This feeling is
strengthened by the accompanying misuse of words. “Belief” having, as
above pointed out, become the name of an impression for which we can
give only a con­fes­sed­ly-in­ad­eq­ uate reason, or no reason at all; it happens
that when pushed hard respecting the warrant for any ultimate dictum of
con­scious­ness, we say, in the absence of all assignable reason, that we
believe it. Thus the two opposite poles of knowledge go under the same
name; and by the reverse connotations of this name, as used for the most
coherent and least coherent relations of thought, profound misconceptions
have been generated. Here, it seems to me, is the source of Sir William
Hamilton’s error. Classing as “beliefs” those direct, undecomposable dicta
of con­scious­ness which transcend proof, he asserts that these are of higher
authority than knowledge (meaning by knowledge that for which reasons
can be given); and in asserting this he is fully justified. But when he claims
equal authority for those affections of con­scious­ness which {191} go under
the same name of “beliefs,” but differ in being ex­treme­ly-in­di­rect affections
of con­scious­ness, or not definite affections of con­scious­ness at all, the claim
cannot be admitted. By his own showing, no positive cognition answering
to the word “infinite” exists; while, contrariwise, those cognitions which he
rightly holds to be above question, are not only positive, but have the
peculiarity that they cannot be suppressed. How, then, can the two be
grouped together as of like degrees of validity?
Nearly allied in nature to this, is another Hamiltonian doctrine, which Mr.
Mill effectively combats. I refer to the corollary respecting noumenal
existence which Sir William Hamilton draws from the law of the Excluded
Middle, or, as it might be more intelligibly called, the law of the Alternative
Necessity. A thing must either exist or not exist—must have a certain
attribute or not have it: there is no third possibility. This is a postulate of all
thought; and in so far as it is alleged of phenomenal existence, no one calls
it in question. But Sir William Hamilton, applying the formula beyond the

limits of thought, draws from it certain conclusions respecting things as
they are, apart from our con­scious­ness. He says, for example, that though
we cannot conceive Space as infinite or as finite, yet, “on the principle of
the Excluded Middle, one or other must be admitted.” This inference Mr.
Mill shows good reason for rejecting. His argument may be supplemented
by another, which at once suggests itself if from the words of Sir William
Hamilton’s propositions we pass to the thoughts for which they are
supposed to stand. When remembering a certain thing as in a certain place,
the place and the thing are mentally represented together; while to think of
the non-existence of the thing in that place, implies a con­scious­ness in
which the place is represented but not the thing. Similarly, if, instead of
thinking of an object as colourless, we think of it as having colour, the
change consists in the addition to the {192} concept of an element that was
before absent from it—the object cannot be thought of first as red and then
as not red, without one component of the thought being expelled from the
mind by another. The doctrine of the Excluded Middle, then, is simply a
generalization of the universal experience that some mental states are
directly destructive of other states. It formulates a certain ab­so­lute­ly-con­‐
stant law, that no positive mode of con­scious­ness can occur without
excluding a correlative negative mode; and that the negative mode cannot
occur without excluding the correlative positive mode: the antithesis of
positive and negative, being, indeed, merely an expression of this
experience. Hence it follows that if con­scious­ness is not in one of the two
modes, it must be in the other. But now, under what conditions only can this
law of con­scious­ness hold? It can hold only so long as there are positive
states of con­scious­ness which can exclude the negative states, and which
the negative states can in their turn exclude. If we are not concerned with
positive states of con­scious­ness at all, no such mutual exclusion takes place,
and the law of the Alternative Necessity does not apply. Here, then, is the
flaw in Sir William Hamilton’s proposition. That Space must be infinite or
finite, are alternatives of which we are not obliged to regard one as
necessary; seeing that we have no state of con­scious­ness answering to either
of these words as applied to the totality of Space, and therefore no

exclusion of two antagonist states of con­scious­ness by one another. Both
alternatives being unthinkable, the proposition should be put thus: Space is
either or is ; neither of which can be conceived, but one of
which must be true. In this, as in some other cases, Sir William Hamilton
continues to work out the forms of thought when they no longer contain any
substance; and, of course, reaches nothing more than verbal conclusions.
Ending here these comments on doctrines of Sir William {193} Hamilton,
which Mr. Mill rejects on grounds that will be generally recognized as
valid, let me now pass to a doctrine, partly held by Sir William Hamilton,
and held by others in ways variously qualified and variously extended—a
doctrine which, I think, may be successfully defended against Mr. Mill’s
attack.

In the fourth and fifth editions of his Logic , Mr. Mill treats, at
considerable length, the question—Is in­con­ceiv­abil­ity an evidence of
untruth?—replying to criticisms previously made on his reasons for
asserting that it is not. The chief answers which he there makes to these
criticisms, turn upon the interpretation of the word inconceivable . This
word he considers is used as the equivalent of the word unbelievable ; and,
translating it thus, readily disposes of sundry arguments brought against
him. Whether any others who have used these words in philosophical
discussion, have made them synonymous, I do not know; but that they are
so used in those reasonings of my own which Mr. Mill combats, I was not
conscious, and was surprised to find alleged. It is now manifest that I had
not adequately guarded myself against the misconstruction which is liable
to arise from the double meaning of the word belief —a word which, we
have seen, is used for the most coherent and the least coherent connexions
in con­scious­ness, because they have the common character that no reason is
assignable for them. Throughout the argument to which Mr. Mill replies, the
word is used by me only in the first of these senses. The “invariably existent
beliefs,” the “indestructible beliefs,” are the indissoluble connexions in con­‐
scious­ness—never the dissoluble ones. But unbelievable implies the

dissoluble ones. By association with the other and more general meaning of
the word belief , the word unbelievable suggests cases in which the
proposition admits of being represented in thought, though it may be with
difficulty; and in which, consequently, the coun­ter-pro­po­si­tion admits of
being {194} decomposed. To be quite sure of our ground, let us define and
illustrate the meanings of inconceivable and unbelievable. An
inconceivable proposition is one of which the terms cannot, by any effort,
be brought before con­scious­ness in that relation which the proposition
asserts between them—a proposition of which the subject and the predicate
offer an insurmountable resistance to union in thought. An unbelievable
proposition is one which admits of being framed in thought, but is so much
at variance with experience that its terms cannot be put in the alleged
relation without effort. Thus, it is unbelievable that a cannon-ball fired from
England should reach America; but it is not inconceivable. Conversely, it is
inconceivable that one side of a triangle is equal to the sum of the other two
sides—not simply unbelievable. The two sides cannot be represented in
con­scious­ness as becoming equal in their joint length to the third side,
without the rep­re­sen­ta­tion of a triangle being destroyed; and the concept of
a triangle cannot be framed without a simultaneous destruction of a concept
in which these magnitudes are represented as equal. That is to say, the
subject and predicate cannot be united in the same intuition—the
proposition is unthinkable. It is in this sense only that I have used the word
inconceivable; and only when rigorously restricted to this sense do I regard
the test of in­con­ceiv­able­ness as having any value.
I had concluded that when this explanation was made, Mr. Mill’s reasons
for dissent would be removed. Passages in his recently-published volume,
however, show that, even restricting the use of the word inconceivable to
the meaning here specified, he still denies that a proposition is proved to be
true by the in­con­ceiv­able­ness of its negation. To meet, within any moderate
compass, all the issues which have grown out of the controversy, is
difficult. Before passing to the essential question, however, I will endeavour
to clear the ground of certain minor questions.

Describing Sir William Hamilton’s doctrine respecting {195} the ultimate
facts of con­scious­ness, or those which are above proof, Mr. Mill writes:
“The only condition he requires is that we be not able to ‘reduce it [a fact
of this class] to a generalization from experience.’ This condition is realized
by its possessing the ‘character of necessity.’ ‘It must be impossible not to
think it. In fact, by its necessity alone can we recognize it as an original
datum of intelligence, and distinguish it from any mere result of
generalization and custom.’ In this Sir William Hamilton is at one with the
whole of his own section of the philosophical world; with Reid, with
Stewart, with Cousin, with Whewell, we may add, with Kant, and even with
Mr. Herbert Spencer. The test by which they all decide a belief to be a part
of our primitive con­scious­ness—an original intuition of the mind—is the
necessity of thinking it. Their proof that we must always, from the
beginning, have had the belief, is the impossibility of getting rid of it now.
This argument, applied to any of the disputed questions of philosophy, is
doubly illegitimate: neither the major nor the minor premise is admissible.
For in the first place, the very fact that the question is disputed, disproves
the alleged impossibility. Those against whom it is needful to defend the
belief which is affirmed to be necessary, are unmistakable examples that it
is not necessary . . . . These philosophers, therefore, and among them Sir
William Hamilton, mistake altogether the true conditions of psychological
investigation, when, instead of proving a belief to be an original fact of con­‐
scious­ness by showing that it could not have been acquired, they conclude
that it was not acquired, for the reason, often false, and never sufficiently
substantiated, that our con­scious­ness cannot get rid of it now.”
This rep­re­sen­ta­tion, in so far as it concerns my own views, has somewhat
puzzled me. Considering that I have avowed a general agreement with Mr.
Mill in the doctrine that all knowledge is from experience, and have
defended {196} the test of in­con­ceiv­able­ness on the very ground that it
expresses “the net result of our experiences up to the present time”
(Principles of Psychology , § 430)—considering that, so far from asserting
the distinction quoted from Sir William Hamilton, I have aimed to abolish

such distinction—considering that I have endeavoured to show how all our
conceptions, even down to those of Space and Time, are “acquired”—
considering that I have sought to interpret forms of thought (and by
implication all intuitions) as products of organized and inherited
experiences (Principles of Psychology , § 208); I am taken aback at finding
myself classed as in the above paragraph. Leaving the personal question,
however, let me pass to the assertion that the difference of opinion
respecting the test of necessity itself disproves the validity of the test. Two
issues are here involved. First, if a particular proposition is by some
accepted as a necessary belief, but by one or more denied to be a necessary
belief, is the validity of the test of necessity thereby disproved in respect of
that particular proposition? Second, if the validity of the test is disproved in
respect of that particular proposition, does it therefore follow that the test
cannot be depended on in other cases?—does it follow that there are no
beliefs universally accepted as necessary, and in respect of which the test of
necessity is valid? Each of these questions may, I think, be rightly answered
in the negative.
In alleging that if a belief is said by some to be necessary, but by others
to be not necessary, the test of necessity is thereby shown to be no test, Mr.
Mill tacitly assumes that all men have powers of introspection enabling
them in all cases to say what con­scious­ness testifies; whereas a great
proportion of men are incapable of correctly interpreting con­scious­ness in
any but its simplest modes, and even the remainder are liable to mistake for
dicta of con­scious­ness what prove on closer examination not to be its dicta.
Take the case of an arithmetical blunder. {197} A boy adds up a column of
figures, and brings out a wrong total. Again he does it and again errs. His
master asks him to go through the process aloud, and then hears him say
“35 and 9 are 46”—an error which he had repeated on each occasion. Now
without discussing the mental act through which we know that 35 and 9 are
44, and through which we recognize the necessity of this relation, it is clear
that the boy’s mis­in­ter­pre­ta­tion of con­scious­ness, leading him tacitly to
deny this necessity by asserting that “35 and 9 are 46,” cannot be held to
prove that the relation is not necessary. This, and kindred misjudgments

daily made by accountants, merely show that there is a liability to overlook
what are necessary connexions in our thoughts, and to assume as necessary
others which are not. In these and hosts of cases, men do not distinctly
translate into their equivalent states of con­scious­ness the words they use.
This negligence is with many so habitual, that they are unaware that they
have not clearly represented to themselves the propositions they assert; and
are then apt, quite sincerely though erroneously, to assert that they can think
things which it is really impossible to think.
But supposing it to be true that whenever a particular belief is alleged to
be necessary, the existence of some who profess themselves able to believe
otherwise, proves that this belief is not necessary; must it be therefore
admitted that the test of necessity is invalid? I think not. Men may mistake
for necessary, certain beliefs which are not necessary; and yet it may remain
true that there are necessary beliefs, and that the necessity of such beliefs is
our warrant for them. Were conclusions thus tested proved to be wrong in a
hundred cases, it would not follow that the test is an invalid one; any more
than it would follow from a hundred errors in the use of a logical formula,
that the logical formula is invalid. If from the premise that all horned
animals ruminate, it were inferred that the rhinoceros, being a horned
animal, ruminates; the error would {198} furnish no argument against the
worth of syllogisms in general—whatever their worth may be. Daily there
are thousands of erroneous deductions which, by those who draw them, are
supposed to be warranted by the data from which they draw them; but no
multiplication of such erroneous deductions is regarded as proving that
there are no deductions truly drawn, and that the drawing of deductions is
illegitimate. In these cases, as in the case to which they are here paralleled,
the only thing shown is the need for verification of data and criticism of the
acts of con­scious­ness.
“This argument,” says Mr. Mill, referring to the argument of necessity,
“applied to any of the disputed questions of philosophy, is doubly
illegitimate; . . . the very fact that the question is disputed, disproves the
alleged impossibility.” Besides the foregoing replies to this, there is another.
Granting that there have been appeals illegitimately made to this test—

granting that there are many questions too complex to be settled by it,
which men have nevertheless proposed to settle by it, and have
consequently got into controversy; it may yet be truly asserted that in
respect of all, or almost all, questions legitimately brought to judgment by
this test, there is no dispute about the answer. From the earliest times on
record down to our own, men have not changed their beliefs concerning the
truths of number. The axiom that if equals be added to unequals the sums
are unequal, was held by the Greeks no less than by ourselves, as a direct
verdict of con­scious­ness, from which there is no escape and no appeal.
Each of the propositions of Euclid appears to us absolutely beyond doubt as
it did to them. Each step in each demonstration we accept, as they accepted
it, because we immediately see that the alleged relation is as alleged, and
that it is impossible to conceive it otherwise.

But how are legitimate appeals to the test to be distinguished? The
answer is not difficult to find. Mr. Mill {199} cites the belief in the antipodes
as having been rejected by the Greeks because inconceivable, but as being
held by ourselves to be both conceivable and true. He has before given this
instance, and I have before objected to it (Principles of Psychology , § 428),
for the reason that the states of con­scious­ness involved in the judgment are
too complex to admit of any trustworthy verdict being given. An illustration
will show the difference between a legitimate appeal to the test and an

illegitimate appeal to it. A and B are two lines. How is it decided that they
are equal or not equal? No way is open but that of comparing the two
impressions they make on con­scious­ness. I know them to be unequal by an
immediate act, if the difference is great, or if, though only moderately
different, they are close together; and supposing the difference is but slight,
I decide the question by putting the lines in apposition when they are
movable, or by carrying a movable line from one to the other if they are
fixed. But in any case, I obtain in con­scious­ness the testimony that the
impression produced by the one line differs from that produced by the other.
Of this difference I can give no further evidence than that I am conscious of
it, and find it impossible, while contemplating the lines, to get rid of the
con­scious­ness. The proposition that the lines are unequal is a proposition of
which the negation is inconceivable. But now suppose it is asked whether B
and C are equal; or whether C and D are equal. No positive answer is
possible. Instead of its being {200} inconceivable that B is longer than C , or
equal to it, or shorter, it is conceivable that it is any one of the three. Here
an appeal to the direct verdict of con­scious­ness is illegitimate, because on
transferring the attention from B to C , or C to D , the changes in the other
elements of the impressions so entangle the elements to be compared, as to
prevent them from being put in apposition. If the question of relative length
is to be determined, it must be by rectification of the bent line; and this is
done through a series of steps, each one of which involves an immediate
judgment akin to that by which A and B are compared. Now as here, so in
other cases, it is only simple percepts or concepts respecting the relations of
which immediate con­scious­ness can satisfactorily testify; and as here, so in
other cases, it is by resolution into such simple percepts and concepts, that
true judgments respecting complex percepts and concepts are reached. That
things which are equal to the same thing are equal to one another, is a fact
which can be known by direct comparison of actual or ideal relations, and
can be known in no other way: the proposition is one of which the negation
is inconceivable, and is rightly asserted on that warrant. But that the square
of the hypothenuse of a right-angled triangle equals the sum of the squares
of the other two sides, cannot be known immediately by comparison of two

states of con­scious­ness. Here the truth can be reached only mediately,
through a series of simple judgments respecting the likenesses or
unlikenesses of certain relations: each of which judgments is essentially of
the same kind as that by which the above axiom is known, and has the same
warrant. Thus it becomes apparent that the fallacious result of the test of
necessity which Mr. Mill instances, is due to a misapplication of the test.
These preliminary explanations have served to make clear the question at
issue. Let us now pass to the essence of it.

Metaphysical reasoning is usually vitiated by some covert {201} petitio
principii . Either the thing to be proved or the thing to be disproved, is
tacitly assumed to be true in the course of the proof or disproof. It is thus
with the argument of Idealism. Though the conclusion reached is that Mind
and Ideas are the only existences; yet the steps by which this conclusion is
reached, take for granted that external objects have just the kind of
independent existence which is eventually denied. If that extension which
the Idealist contends is merely an affection of con­scious­ness, has nothing
out of con­scious­ness answering to it; then, in each of his propositions
concerning extension, the word should always mean an affection of con­‐
scious­ness and nothing more. But if wherever he speaks of distances and
dimensions we write ideas of distances and dimensions, his propositions are
reduced to nonsense. So, too, is it with Scepticism. The resolution of all
knowledge into “impressions” and “ideas,” is effected by an analysis which
assumes at every step an objective reality producing the impressions and the
subjective reality receiving them. The reasoning becomes impossible if the
existence of object and subject be not admitted at the outset. Agree with the
Sceptic’s doubt, and then propose to revise his argument so that it may
harmonize with his doubt. Of the two alternatives between which he halts,
assume, first, the reality of object and subject. His argument is practicable;
whether valid or not. Now assume that object and subject do not exist. He
cannot stir a step toward his conclusion—nay, he cannot even state his

conclusion; for the word “impression” cannot be translated into thought
without assuming a thing impressing and a thing impressed.
Though Empiricism, as at present understood, is not thus suicidal, it is
open to an analogous criticism on its method, similarly telling against the
validity of its inference. It proposes to account for our so-called necessary
beliefs, as well as all our other beliefs; and to do this without postulating
any one belief as necessary. Bringing {202} forward abundant evidence that
the connexions among our states of con­scious­ness are determined by our
experiences—that two experiences frequently recurring together in con­‐
scious­ness, become so coherent that one strongly suggests the other, and
that when their joint recurrence is perpetual and invariable, the connexion
between them becomes indissoluble; it argues that the indissolubility, so
produced, is all that we mean by necessity. And then it seeks to explain each
of our so-called necessary beliefs as thus originated. Now could pure
Empiricism reach this analysis and its subsequent synthesis without taking
any thing for granted, its arguments would be unobjectionable. But it cannot
do this. Examine its phraseology, and there arises the question, Experiences
of what ? Translate the word into thought, and it clearly involves something
more than states of mind and the connexions among them. For if it does not,
then the hypothesis is that states of mind are generated by the experiences
of states of mind; and if the inquiry be pursued, this ends with initial states
of mind which are not accounted for—the hypothesis fails. Evidently, there
is tacitly assumed something beyond the mind by which the “experiences”
are produced—something in which exist the objective relations to which the
subjective relations correspond—an external world. Refuse thus to explain
the word “experiences,” and the hypothesis becomes meaningless. But now,
having thus postulated an external reality as the indispensable foundation of
its reasonings, pure Empiricism can subsequently neither prove nor
disprove its postulate. An attempt to disprove it, or to give it any other
meaning than that originally involved, is suicidal; and an attempt to
establish it by inference is reasoning in a circle. What then are we to say of
this proposition on which Empiricism rests? Is it a necessary belief, or is it
not? If necessary, the hypothesis in its pure form is abandoned. If not

necessary—if not posited {203} à priori as absolutely certain—then the
hypothesis rests on an uncertainty; and the whole fabric of its argument is
unstable. More than this is true. Besides the insecurity implied by building
on a foundation that is confessedly not beyond question, there is the much
greater insecurity implied by raising proposition upon proposition of which
each is confessedly not beyond question. For to say that there are no
necessary truths, is to say that each successive inference is not necessarily
involved in its premises—is an empirical judgment—a judgment not
certainly true. Hence, applying rigorously its own doctrine, we find that
pure Empiricism, starting from an uncertainty and progressing through a
series of uncertainties, cannot claim much certainty for its conclusions.
Doubtless, it may be replied that any theory of human knowledge must
set out with assumptions—either permanent or provisional; and that the
validity of these assumptions is to be determined by the results reached
through them. But that such assumptions may be made legitimately, two
things are required. In the first place they must not be multiplied step after
step as occasion requires; otherwise the conclusion reached might as well
be assumed at once. And in the second place, the fact that they are
assumptions must not be lost sight of: the conclusions drawn must not be
put forward as though they have a certainty which the premises have not.
Now pure Empiricism, in common with other theories of knowledge, is
open to the criticism, that it neglects thus avowedly to recognize the nature
of those primary assumptions which it lays down as provisionally valid, if it
denies that they can be necessarily valid. And it is open to the further
criticism, that it goes on at every step in its argument making assumptions
which it neglects to specify as provisional; since they, too, cannot be known
as necessary. Until it has assigned some warrant for its original datum and
for each of its subsequent inferences, or else has {204} acknowledged them
all to be but hypothetical, it may be stopped either at the outset or at any
stage in its argument. Against every “because” and every “therefore,” an
opponent may enter a caveat, until he is told why it is asserted: contending,
as he may, that if this inference is not necessary he is not bound to accept it;

and that if it is necessary it must be openly declared to be necessary, and
some test must be assigned by which it is distinguished from propositions
that are not necessary.
These considerations will, I think, make it obvious that the first step in a
metaphysical argument, rightly carried on, must be an examination of
propositions for the purpose of ascertaining what character is common to
those which we call unquestionably true, and is implied by asserting their
unquestionable truth. Further, to carry on this inquiry legitimately, we must
restrict our analysis rigorously to states of con­scious­ness considered in their
relations to one another: wholly ignoring any thing beyond con­scious­ness to
which these states and their relations may be supposed to refer. For if,
before we have ascertained by comparing propositions what is the trait that
leads us to class some of them as certainly true, we avowedly or tacitly take
for granted the existence of something beyond con­scious­ness; then, a
particular proposition is assumed to be certainly true before we have
ascertained what is the distinctive character of the propositions which we
call certainly true, and the analysis is vitiated. If we cannot transcend con­‐
scious­ness—if, therefore, what we know as truth must be some mental
state, or some combination of mental states; it must be possible for us to say
in what way we distinguish this state or these states. The definition of truth
must be expressible in terms of con­scious­ness; and, indeed, cannot
otherwise be expressed if con­scious­ness cannot be transcended. Clearly,
then, the metaphysician’s first step must be to shut out from his
investigation every thing but what is subjective; not taking for granted the
{205} existence of any thing objective corresponding to his ideas, until he
has ascertained what property of his ideas it is which he predicates by
calling them true. Let us note the result if he does this.

The words of a proposition are the signs of certain states of con­scious­‐
ness; and the thing alleged by a proposition is the connexion or
disconnexion of the states of con­scious­ness signified. When thinking is
carried on with precision—when the mental states which we call words, are

translated into the mental states they symbolize (which they very frequently
are not)—thinking a proposition consists in the occurrence together in con­‐
scious­ness of the subject and predicate. “The bird was brown,” is a
proposition which implies the union in thought of a particular attribute with
a group of other attributes. When the inquirer compares various
propositions thus rendered into states of con­scious­ness, he finds that they
differ very greatly in respect of the facility with which the states of con­‐
scious­ness are connected and disconnected. The mental state known as
brown may be united with those mental states which make up the figure
known as bird , without appreciable effort, or may be separated from them
without appreciable effort: the bird may easily be thought of as black, or
green, or yellow. Contrariwise, such an assertion as “The ice was hot,” is
one to which he finds much difficulty in making his mind respond. The
elements of the proposition cannot be put together in thought without great
resistance. Between those other states of con­scious­ness which the word ice
connotes, and the state of con­scious­ness named cold , there is an extremely
strong cohesion—a cohesion measured by the resistance to be overcome in
thinking of the ice as hot . Further, he finds that in many cases the states of
con­scious­ness grouped together cannot be separated at all. The idea of
pressure cannot be disconnected from the idea of something occupying
space. Motion cannot be thought {206} of without an object that moves being
at the same time thought of. And then, besides these connexions in con­‐
scious­ness which remain absolute under all circumstances, there are others
which remain absolute under special circumstances. Between the elements
of those more vivid states of con­scious­ness which the inquirer distinguishes
as perceptions, he finds that there is a temp­or­ar­i­ly-in­dis­sol­u­ble cohesion.
Though when there arises in him that comparatively faint state of con­‐
scious­ness which he calls the idea of a book, he can easily think of the book
as red, or brown, or green; yet when he has that much stronger con­scious­‐
ness which he calls seeing a book, he finds that so long as there continue
certain accompanying states of con­scious­ness which he calls the conditions
to perception, those several states of con­scious­ness which make up the
perception cannot be disunited—he cannot think of the book as red, or

green, or brown; but finds that, along with a certain figure, there absolutely
coheres a certain colour.
Still shutting himself up within these limits, let us suppose the inquirer to
ask himself what he thinks about these various degrees of cohesion among
his states of con­scious­ness—how he names them, and how he behaves
toward them. If there comes, no matter whence, the proposition—“The bird
was brown,” subject and predicate answering to these words spring up
together in con­scious­ness; and if there is no opposing proposition, he unites
the specified and implied attributes without effort, and believes the
proposition. If, however, the proposition is—“The bird was necessarily
brown,” he makes an experiment like those above described, and finding
that he can separate the attribute of brownness, and can think of the bird as
green or yellow, he does not admit that the bird was necessarily brown.
When such a proposition as “The ice was cold” arises in him, the elements
of the thought behave as before; and so long as no test is applied, the union
of the con­scious­ness of cold with the {207} accompanying states of con­‐
scious­ness, seems to be of the same nature as the union between those
answering to the words brown and bird . But should the proposition be
changed into—“The ice was necessarily cold,” quite a different result
happens from that which happened in the previous case. The ideas
answering to subject and predicate are here so coherent, that in the absence
of careful examination they might pass as inseparable, and the proposition
be accepted. But suppose the proposition is deliberately tested by trying
whether ice can be thought of as not cold. Great resistance is offered in con­‐
scious­ness to this. Still, by an effort, he can imagine water to have its
temperature of congelation higher than blood heat; and can so think of
congealed water as hot instead of cold. Now the extremely strong cohesion
of states of con­scious­ness, thus experimentally proved by the difficulty of
separating them, he finds to be what he calls a strong belief. Once more, in
response to the words—“Along with motion there is something that
moves,” he represents to himself a moving body; and, until he tries an
experiment upon it, he may suppose the elements of the rep­re­sen­ta­tion to be
united in the same way as those of the representations instanced above. But

supposing the proposition is modified into—“Along with motion there is
necessarily something that moves,” the response made in thought to these
words, discloses the fact that the states of con­scious­ness called up in this
case are indissolubly connected in the way alleged. He discovers this by
trying to conceive the negation of the proposition—by trying to think of
motion as not having along with it something that moves; and his inability
to conceive this negation is the obverse of his inability to tear asunder the
states of con­scious­ness which constitute the affirmation. Those propositions
which survive this strain, are the propositions he distinguishes as necessary.
Whether or not he means any thing else by this word, he evidently means
that in his con­scious­ness the connexions {208} they predicate are, so far as
he can ascertain, unalterable. The bare fact is that he submits to them
because he has no choice. They rule his thoughts whether he will or not.
Leaving out all questions concerning the origin of these connexions—all
theories concerning their significations, there remains in the inquirer the
con­scious­ness that certain of his states of con­scious­ness are so welded
together that all other links in the chain of con­scious­ness yield before these
give way.
Continuing rigorously to exclude everything beyond con­scious­ness, let
him now ask himself what he means by reasoning? what is the essential
nature of an argument? what is the peculiarity of a conclusion? Analysis
soon shows him that reasoning is the formation of a coherent series of states
of con­scious­ness. He has found that the thoughts expressed by propositions,
vary in the cohesions of their subjects and predicates; and he finds that at
every step in an argument, carefully carried on, he tests the strengths of all
the connexions asserted and implied. He considers whether the object
named really does belong to the class in which it is included—tries whether
he can think of it as not like the things it is said to be like. He considers
whether the attribute alleged is really possessed by all members of the class
—tries to think of some member of the class that has not the attribute—
And he admits the proposition only on finding, by this criticism, that there
is a greater degree of cohesion in thought between its elements, than
between the elements of the coun­ter-pro­po­si­tion. Thus testing the strength

of each link in the argument, he at length reaches the conclusion, which he
tests in the same way. If he accepts it, he does so because the argument has
established in him an indirect cohesion between states of con­scious­ness that
were not directly coherent, or not so coherent directly as the argument
makes them indirectly. But he accepts it only supposing that the connexion
between the two states of con­scious­ness {209} composing it, is not resisted
by some stronger counter-connexion. If there happens to be an opposing
argument, of which the component thoughts are felt, when tested, to be
more coherent; or if, in the absence of an opposing argument, there exists
an apposing conclusion, of which the elements have some direct cohesion
greater than that which the proffered argument indirectly gives; then the
conclusion reached by this argument is not admitted. Thus, a discussion in
con­scious­ness proves to be simply a trial of strength between different
connexions in con­scious­ness—a systematized struggle serving to determine
which are the least coherent states of con­scious­ness. And the result of the
struggle is, that the least coherent states of con­scious­ness separate, while
the most coherent remain together—form a proposition of which the
predicate persists in rising up in the mind along with its subject—constitute
one of the connexions in thought which is distinguished as something
known, or as something believed, according to its strength.
What corollary may the inquirer draw, or rather what corollary must he
draw, on pushing the analysis to its limit? If there are any indissoluble
connexions, he is compelled to accept them. If certain states of con­scious­‐
ness absolutely cohere in certain ways, he is obliged to think them in those
ways. The proposition is an identical one. To say that they are necessities of
thought is merely another way of saying that their elements cannot be torn
asunder. No reasoning can give to these absolute cohesions in thought any
better warrant; since all reasoning, being a process of testing cohesions, is
itself carried on by accepting the absolute cohesions; and can, in the last
resort, do nothing more than present some absolute cohesions in
justification of others—an act which unwarrantably assumes in the absolute
cohesions it offers, a greater value than is allowed to the absolute cohesions

it would justify. Here, then, the inquirer comes down to an {210} ultimate
mental uniformity—a universal law of his thinking. How completely his
thought is subordinated to this law, is shown by the fact that he cannot even
represent to himself the possibility of any other law. To suppose the
connexions among his states of con­scious­ness to be otherwise determined,
is to suppose a smaller force overcoming a greater—a proposition which
may be expressed in words but cannot be rendered into ideas. No matter
what he calls these indestructible relations, no matter what he supposes to
be their meanings, he is completely fettered by them. Their in­de­struc­ti­bil­i­ty
is the proof to him that his con­scious­ness is imprisoned within them; and
supposing any of them to be in some way destroyed, he perceives that in­de­‐
struc­ti­bil­ity would still be the distinctive character of the bounds that
remained—the test of those which he must continue to think.
These results the inquirer arrives at without assuming any other existence
than that of his own con­scious­ness. They postulate nothing about mind or
matter, subject or object. They leave wholly untouched the questions—what
does con­scious­ness imply? and how is thought generated? There is not
involved in the analysis any hypothesis respecting the origin of these
relations between thoughts—how there come to be feeble cohesions, strong
cohesions, and absolute cohesions. Whatever some of the terms used may
have seemed to connote, it will be found, on examining each step, that
nothing is essentially involved beyond states of mind and the connexions
among them, which are themselves other states of mind. Thus far, the
argument is not vitiated by any petitio principii .
Should the inquirer enter upon the question, How are these facts to be
explained? he must consider how any further investigation is to be
conducted, and what is the possible degree of validity of its conclusions.
Remembering that he cannot transcend con­scious­ness, he sees that anything
in the shape of an interpretation must be {211} subordinate to the laws of
con­scious­ness. Every hypothesis he entertains in trying to explain himself
to himself, being an hypothesis which can be dealt with by him only in
terms of his mental states, it follows that any process of explanation must

itself be carried on by testing the cohesions among mental states, and
accepting the absolute cohesions. His conclusions, therefore, reached only
by repeated recognitions of this test of absolute cohesion, can never have
any higher validity than this test. It matters not what name he gives to a
conclusion—whether he calls it a belief, a theory, a fact, or a truth. These
words can be themselves only names for certain relations among his states
of con­scious­ness. Any secondary meanings which he ascribes to them must
also be meanings expressed in terms of con­scious­ness, and therefore
subordinate to the laws of con­scious­ness. Hence he has no appeal from this
ultimate dictum; and seeing this, he sees that the only possible further
achievement is the reconciliation of the dicta of con­scious­ness with one
another—the bringing all other dicta of con­scious­ness into harmony with
this ultimate dictum.

Here, then, the inquirer discovers a warrant higher than that which any
argument can give, for asserting an objective existence. Mysterious as
seems the con­scious­ness of something which is yet out of con­scious­ness, he
finds that he alleges the reality of this something in virtue of the ultimate
law—he is obliged to think it. There is an indissoluble cohesion between
each of those vivid and definite states of con­scious­ness which he calls a
sensation, and an indefinable con­scious­ness which stands for a mode of
being beyond sensation, and separate from himself. When grasping his fork
and putting food into his mouth, he is wholly unable to expel from his mind
the notion of something which resists the force he is conscious of using; and
he cannot suppress the nascent thought of an independent existence keeping
apart his tongue and palate, and giving {212} him that sensation of taste
which he is unable to generate in con­scious­ness by his own activity. Though
self-criticism shows him that he cannot know what this is which lies outside
of him; and though he may infer that not being able to say what it is, it is a
fiction; he discovers that such self-criticism utterly fails to extinguish the
con­scious­ness of it as a reality. Any conclusion into which he argues
himself, that there is no objective existence connected with these subjective

states, proves to be a mere verbal conclusion to which his thoughts will not
respond. The relation survives every effort to destroy it—is proved by
experiment, repeated no matter how often, to be one of which the negation
is inconceivable; and therefore one having supreme authority. In vain he
endeavours to give it any greater authority by reasoning; for whichever of
the two alternatives he sets out with, leaves him at the end just where he
started. If, knowing nothing more than his own states of con­scious­ness, he
declines to acknowledge any thing beyond con­scious­ness until it is proved,
he may go on reasoning for ever without getting any further; since the
perpetual elaboration of states of con­scious­ness out of states of con­scious­‐
ness, can never produce anything more than states of con­scious­ness. If,
contrariwise, he postulates external existence, and considers it as merely
postulated, then the whole fabric of his argument, standing upon this
postulate, has no greater validity than the postulate gives it, minus the
possible invalidity of the argument itself. The case must not be confounded
with those cases in which an hypothesis, or provisional assumption, is
eventually proved true by its agreement with facts; for in these cases the
facts with which it is found to agree, are facts known in some other way
than through the hypothesis: a calculated eclipse of the moon serves as a
verification of the hypothesis of gravitation, because its occurrence is
observable without taking for granted the hypothesis of gravitation. But
when the external world {213} is postulated, and it is supposed that the
validity of the postulate may be shown by the explanation of mental
phenomena which it furnishes, the vice is, that the process of verification is
itself possible only by assuming the thing to be proved.
But now, recognizing the indissoluble cohesion between the con­scious­‐
ness of self and an unknown not-self , as constituting a dictum of con­scious­‐
ness which he is both compelled to accept and is justified by analysis in
accepting, it is competent for the inquirer to consider whether, setting out
with this dictum, he can base on it a satisfactory explanation of what he
calls knowledge. He finds such an explanation possible. The hypothesis that
the more or less coherent relations among his states of con­scious­ness, are
generated by experience of the more or less constant relations in something

beyond his con­scious­ness, furnishes him with solutions of numerous facts
of con­scious­ness: not, however, of all, if he assumes that this adjustment of
inner to outer relations has resulted from his own experiences alone.
Nevertheless, if he allows himself to suppose that this moulding of thoughts
into correspondence with things, has been going on through countless
preceding generations; and that the effects of experiences have been
inherited in the shape of modified organic structures; then he is able to
interpret all the phenomena. It becomes possible to understand how these
persistent cohesions among states of con­scious­ness, are themselves the
products of often-repeated experiences; and that even what are known as
“forms of thought,” are but the absolute internal uniformities generated by
infinite repetitions of absolute external uniformities. It becomes possible
also to understand how, in the course of organizing of these multiplying and
widening experiences, there may arise partially-wrong connexions in
thought, answering to limited converse with things; and that these
connexions in thought, temporarily taken for indissoluble ones, may
afterwards be made dissoluble by presentation {214} of external relations at
variance with them. But even when this occurs, it can afford no ground for
questioning the test of indissolubility; since the process by which some
connexion previously accepted as indissoluble, is broken, is simply the
establishment of some antagonistic connexion, which proves, on a trial of
strength, to be the stronger—which remains indissoluble when pitted
against the other, while the other gives way. And this leaves the test just
where it was; showing only that there is a liability to error as to what are
indissoluble connexions. From the very beginning, therefore, to the very
end of the explanation, even down to the criticism of its conclusions and the
discovery of its errors, the validity of this test must be postulated. Whence it
is manifest, as before said, that the whole business of explanation can be
nothing more than that of bringing all other dicta of con­scious­ness into
harmony with this ultimate dictum.

To the positive justification of a proposition, may be added that negative
justification which is derived from the untenability of the coun­ter-pro­po­si­‐
tion. When describing the attitude of pure Empiricism, some indications
that its coun­ter-pro­po­si­tion is untenable were given; but it will be well here
to state, more specifically, the fundamental objections to which it is open.
If the ultimate test of truth is not that here alleged, then what is the
ultimate test of truth? And if there is no ultimate test of truth, then what is
the warrant for accepting certain propositions and rejecting others? An
opponent who denies the validity of this test, may legitimately decline to
furnish any test himself, so long as he does not affirm any thing to be true;
but if he affirms some things to be true and others to be not true, his warrant
for doing so may fairly be demanded. Let us glance at the possible response
to the demand. If asked why he holds it to be unquestionably true that two
quantities which differ {215} in unequal degrees from a third quantity are
themselves unequal, two replies seem open to him: he may say that this is
an ultimate fact of con­scious­ness, or that it is an induction from personal
experiences. The reply that it is an ultimate fact of con­scious­ness, raises the
question, How is an ultimate fact of con­scious­ness distinguished? All
beliefs, all conclusions, all imaginations even, are facts of con­scious­ness;
and if some are to be accepted as beyond question because ultimate, while
others are not to be accepted as beyond question because not ultimate, there
comes the inevitable inquiry respecting the test of ultimacy. On the other
hand, the reply that this truth is known only by induction from personal
experiences, suggests the query—On what warrant are personal experiences
asserted? The testimony of experience is given only through memory; and
its worth depends wholly on the trustworthiness of memory. Is it, then, that
the trustworthiness of memory is less open to doubt than the immediate
con­scious­ness that two quantities must be unequal if they differ from a third
quantity in unequal degrees? This can scarcely be alleged. Memory is
notoriously uncertain. We sometimes suppose ourselves to have said things
which it turns out we did not say; and we often forget seeing things which it

is proved we did see. We speak of many passages of our lives as seeming
like dreams; and can vaguely imagine the whole past to be an illusion. We
can go much further toward conceiving that our recollections do not answer
to any actualities, than we can go toward conceiving the non-existence of
Space. But even supposing the deliverances of memory to be above
criticism, the most that can be said for the experiences to which memory
testifies, is that we are obliged to think we have had them—cannot conceive
the negation of the proposition that we have had them; and to say this is to
assign the warrant which is repudiated.
A further counter-criticism may be made. Throughout the argument of
pure Empiricism, it is tacitly assumed that {216} there may be a Philosophy
in which nothing is asserted but what is proved. It proposes to admit into
the coherent fabric of its conclusions, no conclusion that is incapable of
being established by evidence; and it thus takes for granted that not only
may all derivative truths be proved, but also that proof may be given of the
truths from which they are derived, down to the very deepest. The result of
thus refusing to recognize some fundamental unproved truth, is simply to
leave its fabric of conclusions without a base. The giving proof of any
special proposition, is the assimilation of it to some class of propositions
known to be true. If any doubt arises respecting the general proposition
which is cited in justification of this special proposition, the course is to
show that this general proposition is deducible from a proposition or
propositions of still greater generality; and if pressed for proof of each such
still more general proposition, the only resource is to repeat the process. Is
this process endless? If so, nothing can be proved—the whole series of
propositions depends on some unassignable proposition. Has the process an
end? If so, there must eventually be reached a widest proposition—one
which cannot be justified by showing that it is included by any wider—one
which cannot be proved. Or to put the argument otherwise: Every inference
depends on premises; every premise, if it admits of proof, depends on other
premises; and if the proof of the proof be continually demanded, it must
either end in an unproved premise, or in the acknowledgment that there
cannot be reached any premise on which the entire series of proofs depends.

Hence Philosophy, if it does not avowedly stand on some datum underlying
reason, must acknowledge that it has nothing on which to stand.

The expression of divergence from Mr. Mill on this fundamental
question, I have undertaken with reluctance, only on finding it needful, both
on personal and on general {217} grounds, that his statements and arguments
should be met. For two reasons, especially, I regret having thus to contend
against the doctrine of one whose agreement I should value more than that
of any other thinker. In the first place, the difference is, I believe, superficial
rather than substantial; for it is in the interests of the Ex­per­i­ence-Hy­poth­es­ is
that Mr. Mill opposes the alleged criterion of truth; while it is as
harmonizing with the Ex­per­i­ence-Hy­poth­es­ is, and reconciling it with all the
facts, that I defend this criterion. In the second place, this lengthened
exposition of a single point of difference, unaccompanied by an exposition
of the numerous points of concurrence, unavoidably produces an
appearance of dissent very far greater than that which exists. Mr. Mill,
however, whose unswerving allegiance to truth is on all occasions so
conspicuously displayed, will fully recognize the justification for this
utterance of disagreement on a matter of such profound importance,
philosophically considered; and will not require any apology for the entire
freedom with which I have criticised his views while seeking to substantiate
my own.

REPLIES TO CRITICISMS.
[First published in The Fortnightly Review for November and December 1873. ]

When made by a competent reader, an objection usually implies one of
two things. Either the statement to which he demurs is wholly or partially
untrue; or, if true, it is presented in such a way as to permit mis­app­re­hen­‐
sion. A need for some change or addition is in any case shown.
Not recognizing the errors alleged, but thinking rather that mis­app­re­hen­‐
sions cause the dissent of those who have attacked the me­ta­phys­i­co-the­o­lo­‐
gi­cal doctrines held by me, I propose here to meet, by explanations and
arguments, the chief objections urged: partly with the view of justifying
these doctrines, and partly with the view of guarding against the wrong in­‐
ter­pre­ta­tions which it appears are apt to be made.
The pages of a periodical intended for general reading may be thought
scarcely fitted for the treatment of these highly abstract questions. There is
now, however, so considerable a class interested in them, and they are so
deeply involved with the great changes of opinion in progress, that I have
ventured to hope for readers outside the circle of those who occupy
themselves with philosophy.
Of course the criticisms to be noticed I have selected, {219} either because
of their intrinsic force, or because they come from men whose positions or
reputations give them weight. To meet more than a few of my opponents is
out of the question.

Let me begin with a criticism contained in the sermon preached by the
Rev. Principal Caird before the British Association, on the occasion of its
meeting in Edinburgh, in August, 1871. Expressed with a courtesy which,
happily, is now less rare than of yore in theological controversy, Dr. Caird’s
objection might, I think, be admitted without involving essential change in
the conclusion demurred to; while it might be shown to tell with greater
force against the conclusions of thinkers classed as orthodox, Sir W.
Hamilton and Dean Mansel, than against my own. Describing this as set
forth by me, Dr. Caird says:―
“His thesis is that the provinces of science and religion are distinguished from each other as the
known from the unknown and unknowable. This thesis is maintained mainly on a critical
examination of the nature of human intelligence, in which the writer adopts and carries to its extreme
logical results the doctrine of the relativity of human knowledge which, propounded by Kant, has
been reproduced with special application to theology by a famous school of philosophers in this
country. From the very nature of human intelligence, it is attempted to be shown that it can only
know what is finite and relative, and that therefore the absolute and infinite the human mind is, by an
inherent and insuperable disability, debarred from knowing. . . . . May it not be asked, for one thing,
whether in the assertion, as the result of an examination of the human intellect, that it is incapable of
knowing what lies beyond the finite, there is not involved an obvious self-contradiction? The
examination of the mind can be conducted only by the mind, and if the instrument be, as is alleged,
limited and defective, the result of the inquiry must partake of that defectiveness. Again, does not the
knowledge of a limit imply already the power to transcend it? In affirming that human science is
incapable of crossing the bounds of the finite world, is it not a necessary presupposition that you who
so affirm have crossed these bounds?”
That this objection is one I am not disinclined to recognize, will be
inferred when I state that it is one I have myself raised. While preparing the
second edition of the {220} Principles of Psychology , I found, among my
memoranda, a note which still bore the wafers by which it had been
attached to the original manuscript (unless, indeed, it had been transferred
from the MS. of First Principles , which its allusion seems to imply). It was
this:―
“I may here remark in passing that the several reasonings, including the one above quoted, by
which Sir William Hamilton would demonstrate the pure relativity of our knowledge—reasonings
which clearly establish many important truths, and with which in the main I agree—are yet capable
of being turned against himself, when he definitely concludes that it is impossible for us to know the
absolute. For to positively assert that the absolute cannot be known, is in a certain sense to assert a
knowledge of it—is to know it as unknowable . To affirm that human intelligence is confined to the
conditioned, is to put an absolute limit to human intelligence, and implies absolute knowledge . It
seems to me that the ‘learned ignorance’ with which philosophy ends, must be carried a step further;

and instead of positively saying that the absolute is unknowable, we must say that we cannot tell
whether it is knowable or not.”
Why I omitted this note I cannot now remember. Possibly it was because
re-consideration disclosed a reply to the contained objection. For while it is
true that the intellect cannot prove its own competence, since it must
postulate its own competence in the course of the proof, and so beg the
question; yet it does not follow that it cannot prove its own incompetence
respecting questions of certain kinds. Its inability in respect of such
questions has two conceivable causes. It may be that the deliverances of
Reason in general are invalid, in which case the incompetence of Reason to
solve questions of a certain class is implied by its general incompetence; or
it may be that the deliverances of Reason, valid within a certain range,
themselves end in the conclusion that Reason is incapable beyond that
range. So that while there can be no proof of competence, because
competence is postulated in each step of the demonstration, there may be
proof of incompetence either (1) if the successive deliverances forming the
steps of the demonstration, by severally evolving contradictions, show their
un­trust­worth­i­ness, or (2) if, being trustworthy, {221} they lead to the result
that on certain questions Reason cannot give any deliverance.
Reason leads both inductively and deductively to the conclusion that the
sphere of Reason is limited. Inductively, this conclusion expresses the result
of countless futile attempts to transcend this sphere—attempts to understand
Matter, Motion, Space, Time, Force, in their ultimate natures—attempts
which, bringing us always to alternative impossibilities of thought, warrant
the inference that such attempts will continue to fail, as they have hitherto
failed. Deductively, this conclusion expresses the result of mental analysis,
which shows us that the product of thought is in all cases a relation,
identified as such or such; that the process of thought is the identification
and classing of relations; that therefore Being in itself, out of relation, is
unthinkable, as not admitting of being brought within the form of thought.
That is to say, deduction explains that failure of Reason established as an
induction from many experiments. And to call in question the ability of
Reason to give this verdict against itself in respect of these transcendent

problems, is to call in question its ability to draw valid conclusions from
premises; which is to assert a general incompetence necessarily inclusive of
the special incompetence.

Closely connected with the foregoing, is a criticism from Dr. Mansel, on
which I may here make some comments. In a note to his Philosophy of the
Conditioned p. 39, he says:―
“Mr. Herbert Spencer, in his work on First Principles , endeavours to press Sir W. Hamilton into
the service of Pantheism and Positivism together” [a somewhat strange assertion, by the way,
considering that I reject them both], “by adopting the negative portion only of his philosophy—in
which, in common with many other writers, he declares the absolute to be inconceivable by the mere
intellect,—and rejecting the positive portions, in which he most emphatically maintains that the
belief in a personal God is imperatively demanded by the facts of our moral and emotional con­‐
scious­ness. . . . . Sir W. Hamilton’s fundamental principle is, that con­scious­ness {222} must be
accepted entire, and that the moral and religious feelings, which are the primary source of our belief
in a personal God, are in no way invalidated by the merely negative inferences which have deluded
men into the assumption of an impersonal absolute. . . . . Mr. Spencer, on the other hand, takes these
negative inferences as the only basis of religion, and abandons Hamilton’s great principle of the
distinction between knowledge and belief.”
Putting these statements in the order most convenient for discussion, I
will deal first with the last of them. Instead of saying what he does, Dr.
Mansel should have said that I decline to follow Sir W. Hamilton in
confounding two distinct, and indeed radically-opposed, meanings of the
word belief . This word “is habitually applied to dicta of con­scious­ness for
which no proof can be assigned: both those which are unprovable because
they underlie all proof, and those which are unprovable because of the
absence of evidence.”24 In the pages of the Fortnightly Review for July,
1865, I exhibited this distinction as follows:―
“We commonly say we ‘believe’ a thing for which we can assign some preponderating evidence,
or concerning which we have received some indefinable impression. We believe that the next House
of Commons will not abolish Church-rates; or we believe that a person on whose face we look is
good-natured. That is, when we can give con­fes­sed­ly-in­ad­eq­ uate proofs, or no proofs at all, for the
things we think, we call them ‘beliefs.’ And it is the peculiarity of these beliefs, as contrasted with
cognitions, that their connexions with antecedent states of con­scious­ness may be easily severed,
instead of being difficult to sever. But unhappily, the word ‘belief’ is also applied to each of those
temporarily or permanently indissoluble connexions in con­scious­ness, for the acceptance of which
the only warrant is that it cannot be got rid of. Saying that I feel a pain, or hear a sound, or see one
line to be longer than another, is saying that there has occurred in me a certain change of state; and it
is impossible for me to give a stronger evidence of this fact than that it is present to my mind. . . . .
‘Belief’ having, as above pointed out, become the name of an impression for which we can give only

a con­fes­sed­ly-in­ad­eq­ uate reason, or no reason at all; it happens that when pushed hard respecting the
warrant for any ultimate dictum of con­scious­ness, we say, in the absence of all assignable reason, that
we believe it. Thus the two opposite poles of knowledge go under the same name; and by the reverse
connotations of this name, as used for the most coherent and least coherent relations of thought,
profound misconceptions have been generated.”
Now that the belief which the moral and religious {223} feelings are said
to yield of a personal God, is not one of the beliefs which are unprovable
because they underlie all proof, is obvious. It needs but to remember that in
works on Natural Theology, the existence of a personal God is inferred
from these moral and religious feelings, to show that it is not contained in
these feelings themselves, or joined with them as an inseparable intuition. It
is not a belief like the beliefs which I now have that this is daylight, and that
there is open space before me—beliefs which cannot be proved because
they are of equal simplicity with, and of no less certainty than, each step in
a demonstration. Were it a belief of this most certain kind, argument would
be superfluous: all races of men and every individual would have the belief
in an inexpugnable form. Hence it is manifest that, confusing the two very
different states of con­scious­ness called beliefs, Sir W. Hamilton ascribes to
the second a certainty that belongs only to the first.
Again, neither Sir W. Hamilton nor Dr. Mansel has enabled us to
distinguish those “facts of our moral and emotional con­scious­ness” which
imperatively demand the belief in a personal God, from those facts of our
(or of men’s) “moral and emotional con­scious­ness” which, in those having
them, imperatively demand beliefs that Sir W. Hamilton would regard as
untrue. A New Zealand chief, discovering his wife in an infidelity, killed the
man; the wife then killed herself that she might join her lover in the other
world; and the chief thereupon killed himself that he might go after them to
defeat this intention. These two acts of suicide furnish tolerably strong
evidence that these New Zealanders believed in another world to which,
they could go at will, and fulfil their desires as they did here. If they were
asked the justification for this belief, and if the arguments by which they
sought to establish it were not admitted, they might still fall back on
emotional {224} con­scious­ness as yielding them an unshakeable foundation
for it. I do not see why a Fiji Islander, adopting the Hamiltonian argument,

should not justify by it his conviction that after being buried alive, his life in
the other world, forthwith commencing at the age he has reached in this,
will similarly supply him with the joys of conquest and the gratifications of
cannibalism. That he has a conviction to this effect stronger than the
religious convictions current among civilized people, is proved by the fact
that he goes to be buried alive quite willingly. And as we may presume that
his conviction is not the outcome of a demonstration, it must be the
outcome of some state of feeling—some “emotional con­scious­ness.” Why,
then, should he not assign the “facts” of his “emotional con­scious­ness” as
“imperatively demanding” this belief? Manifestly, this principle that “con­‐
scious­ness must be accepted entire,” either obliges us to accept as true the
superstitions of all mankind, or else obliges us to say that the con­scious­ness
of a certain limited class of cultivated people is alone meant. If things are to
be believed simply because the facts of emotional con­scious­ness
imperatively demand the beliefs, I do not see why the actual existence of a
ghost in a house, is not inevitably implied by the intense fear of it that is
aroused in the child or the servant.
Lastly, and chiefly, I have to deal with Dr. Mansel’s statement that “Mr.
Spencer, on the other hand, takes these negative inferences as the only basis
of religion.” This statement is exactly the reverse of the truth; since I have
contended, against Hamilton and against him, that the con­scious­ness of that
which is manifested to us through phenomena is positive , and not negative ,
as they allege, and that this positive con­scious­ness supplies an
indestructible basis for the religious sentiment (First Principles , § 26).
Instead of giving here passages to show this, I may fitly quote the statement
and opinion of a {225} foreign theologian. M. le pasteur Grotz, of the
Reformed Church at Nismes, writes thus:―
“La science serait-elle done par nature ennemie de la religion? pour être religieux, faut-il proscrire
la science?—C’est la science, la science expérimentale qui va maintenant parler en faveur de la
religion; c’est elle qui, par la bouche de l’un des penseurs . . . de notre époque, M. Herbert Spencer,
va répondre à la fois à M. Vacherot et à M. Comte.”

“Ici, M. Spencer discute la théorie de l’inconditionné ; entendez par ce mot: Dieu. Le philosophie
écossais, Hamilton, et son disciple, M. Mansel, disent comme nos positivistes français: ‘Nous ne

pouvons affirmer l’existence positive de quoi que ce soit au delà des phénomènes.’ Seulement,
Hamilton et son disciple se séparent de nos compatriotes en faisant intervenir une ‘révélation
merveilleuse’ qui nous fait croire à l’existence de l’inconditionné, et grâce à cette révélation vraiment
merveilleuse, toute l’orthodoxie revient. Est-il vrai que nous ne puissions rien affirmer au delà des
phénomènes? M. Spencer déclare qu’il y a dans cette assertion une grave erreur. Le côté logique, dit-
il fort justement, n’est pas le seul; il y a aussi le côté psychologique, et, selon nous, il prouve que
l’existence positive de l’absolu est une donnée nécessaire de la conscience.”
“Là est la base de l’accord entre la religion et la science. Dans un chapitre . . . . intitulé
Réconciliation , M. Spencer etablit et développe cet accord sur son véritable terrain.”

“M. Spencer, en restant sur le terrain de la logique et de la psychologie, et sans recourir à une
intervention surnaturelle, a établi la legitimité, la nécessité et l’eternelle durée du sentiment religieux
et de la religion.”25
I turn next to what has been said by Dr. Shadworth H. Hodgson, in his
essay on “The Future of Metaphysic,” published in the Contemporary
Review for November, 1872. Remarking only, with respect to the
agreements he expresses in certain views of mine, that I value them as
coming from a thinker of subtlety and independence, I will confine myself
here to his disagreements. Dr. Hodgson, before giving his own view, briefly
describes and criticizes the views of Hegel and Comte, with both of whom
he partly agrees and partly disagrees, and then {226} proceeds to criticize the
view set forth by me. After a preliminary brief statement of my position, to
the wording of which I demur, he goes on to say:―
“In his First Principles , Part I, second ed., there is a chapter headed ‘Ultimate Scientific Ideas,’ in
which he enumerates six such ideas or groups of ideas, and attempts to show that they are entirely in­‐
com­pre­hen­sible. The six are:—1. Space and Time. 2. Matter. 3. Rest and Motion. 4. Force. 5.
Consciousness. 6. The Soul, or the Ego. Now to enter at length into all of these would be an
undertaking too large for the present occasion; but I will take the first of the six, and endeavour to
show in its case the entire untenability of Mr. Spencer’s view; and since the same arguments may be
employed against the rest, I shall be content that my case against them should be held to fail if my
case should fail in respect to Space and Time.”
I willingly join issue with Dr. Hodgson on these terms; and proceed to
examine, one by one, the several arguments he uses to show the invalidity
of my conclusions. Following his criticisms in the order he has chosen, I
begin with the sentence following that which I have just quoted. The first
part of it runs thus:—“The metaphysical view of Space and Time is, that
they are elements in all phenomena, whether the phenomena are
presentations or representations.”

Whether, by “the metaphysical view,” is here meant the view of Kant,
whether it means Dr. Hodgson’s own view, or whether the expression has a
more general meaning, I have simply to reply that the metaphysical view is
incorrect. Dealing with the Kantian version of this doctrine, that Space is a
form of intuition, I have pointed out that only with certain classes of
phenomena is Space united indissolubly; that Kant habitually considers
phenomena belonging to the visual and tactual groups, with which the con­‐
scious­ness of space is inseparably joined, and overlooks groups with which
it is not inseparably joined. Though in the adult, perception of sound has
certain space-implications, mostly, if not wholly, acquired by individual
experience; and though it would seem from the instructive experiments of
Mr. Spalding, that in creatures born with nervous systems much more
organized than our own are at birth, {227} there is some innate perception of
the side from which a sound comes; yet it is demonstrable that the space-
implications of sound are not originally given with the sensation as its form
of intuition. Bearing in mind the Kantian doctrine, that Space is the form of
sensuous intuitions not only as presented but also as represented , let us
examine critically our musical ideas. As I have elsewhere suggested to the
reader―
“Let him observe what happens when some melody takes possession of his imagination. Its tones
and cadences go on repeating themselves apart from any space-con­scious­ness—they are not
localized. He may or may not be reminded of the place where he heard them—this association is
incidental only. Having observed this, he will see that such space-implications as sounds have, are
learnt in the course of individual experience, and are not given with the sounds themselves. Indeed, if
we refer to the Kantian definition of form, we get a simple and conclusive proof of this. Kant says
form is ‘that which effects that the content of the phænomenon can be arranged under certain
relations.’ How then can the content of the phenomenon we call sound be arranged? Its parts can be
arranged in order of sequence—that is, in Time. But there is no possibility of arranging its parts in
order of coexistence—that is, in Space. And it is just the same with odour. Whoever thinks that sound
and odour have Space for their form of intuition, may convince himself to the contrary by trying to
find the right and left sides of a sound, or to imagine an odour turned the other way upwards.”—
Principles of Psychology , § 399.—Note.
As I thus dissent, not I think without good reason, from “the
metaphysical view of Space and Time” as “elements in all phenomena,” it
will naturally be expected that I dissent from the first criticism which Dr.
Hodgson proceeds to deduce from it. Dealing first with the arguments I
have used to show the in­comp­re­hens­i­bil­i­ty of Space and Time, if we

consider them as objective, and stating in other words the conclusion I
draw, that “as Space and Time cannot be either nonentities nor the attributes
of entities, we have no choice but to consider them as entities.” Dr.
Hodgson continues:―
“So far good. Secondly, he argues that they cannot be represented in thought as such real
existences, because ‘to be conceived at all, a thing must be conceived as having attributes.’ Now here
the metaphysical doctrine enables us to conceive them as real existences, and rebuts the argument for
{228} their in­con­ceiv­abil­ity; for the other element, the material element, the feeling or quality
occupying Space and Time stands in the place and performs the function of the required attributes,
composing together with the space and time which is occupied the empirical phenomena of
perception. So far as this argument of Mr. Spencer goes, then, we are entitled to say that his case for
the in­con­ceiv­abil­ity of Space and Time as real existences is not made out.”
Whether the fault is in me or not I cannot say, but I fail to see that my
argument is thus rebutted. On the contrary, it appears to me substantially
conceded. What kind of entity is that which can exist only when occupied
by something else? Dr. Hodgson’s own argument is a tacit assertion that
Space by itself cannot be conceived as an existence; and this is all that I
have alleged.
Dr. Hodgson deals next with the further argument, familiar to all readers,
which I have added as showing the insurmountable difficulty in the way of
conceiving Space and Time as objective entities; namely, that “all entities
which we actually know as such are limited. . . . But of Space and Time we
cannot assert either limitation, or the absence of limitation.” Without
quoting at length the reasons Dr. Hodgson gives for distinguishing between
Space as per ceived and Space as con ceived, it will suffice if I quote his
own statement of the result to which they bring him: “So that Space and
Time as perceived are not finite, but infinite, as conceived are not infinite,
but finite.”
Most readers will, I think, be startled by the assertion that conception is
less extensive in range than perception; but, without dwelling on this, I will
content myself by asking in what case Space is perceived as infinite? Surely
Dr. Hodgson does not mean to say that he can perceive the whole
surrounding Space at once—that the Space behind is united in perception
with the Space in front. Yet this is the necessary implication of his words.
Taking his statement less literally, however, and not dwelling on the fact

that in perception Space is habitually bounded by objects more or less
distant, let us test his {229} assertion under the most favourable conditions.
Supposing the eye directed upwards towards a clear sky; is not the space
then perceived, laterally limited? The visual area, restricted by the visual
apertures, cannot include in perception even 180° from side to side, and is
still more confined in a direction at right angles to this. Even in the third
direction, to which alone Dr. Hodgson evidently refers, it cannot properly
be said that it is infinite in perception. Look at a position in the sky a
thousand miles off. Now look at a position a million miles off. What is the
difference in perception? Nothing. How then can an infinite distance be
perceived when these immensely-unlike finite distances cannot be
perceived as differing from one another, or from an infinite distance? Dr.
Hodgson has used the wrong word. Instead of saying that Space as
perceived is infinite, he should have said that, in perception, Space is finite
in two dimensions, and becomes indefinite in the third when this becomes
great.
I now come to the paragraph beginning “Mr. Spencer then turns to the
second or subjective hypothesis, that of Kant.” This paragraph is somewhat
difficult to deal with, because in it my reasoning is criticized both from the
Kantian point of view and from Dr. Hodgson’s own point of view.
Dissenting from Kant’s view, Dr. Hodgson says, “I hold that both Space and
Time and Feeling, or the material element, are equally and alike subjective,
equally and alike objective.” As I cannot understand this, I am unable to
deal with those arguments against me which Dr. Hodgson bases upon it, and
must limit myself to that which he urges on behalf of Kant. He says:―
“But I think that Mr. Spencer’s rep­re­sen­ta­tion of Kant’s view is very incorrect; he seems to be
misled by the large term non-ego. Kant held that Space and Time were in their origin subjective, but
when applied to the non-ego resulted in phenomena, and were the formal element in those
phenomena, among which some were phenomena of the internal sense or ego, others of the external
sense or non-ego. The non-ego to which the forms of Space and Time did not apply and did not
belong, was the Ding-an-sich, not the {230} phenomenal non-ego. Hence the objective existence of
Space and Time in phenomena, but not in the Ding-an-sich, is a consistent and necessary
consequence of Kant’s view of their subjective origin.”
If I have misunderstood Kant, as thus alleged, then my comment must be
that I credited him with an hypothesis less objectionable than that which he

held. I supposed his view to be that Space, as a form of intuition belonging
to the ego , is imposed by it on the non-ego (by which I understood the
thing in itself) in the act of intuition. But now the Kantian doctrine is said to
be that Space, originating in the ego , when applied to the non-ego , results
in phenomena (the non-ego meant being, in that case, necessarily the Ding-
an-sich, or thing in itself); and that the phenomena so resulting become
objective existences along with the Space given to them by the subject. The
subject having imposed Space as a form on the primordial object, or thing
in itself, and so created phenomena, this Space thereupon becomes an
objective existence, independent of both the subject and the original thing
in itself! To Dr. Hodgson this may seem a more tenable position than that
which I ascribed to Kant; but to me it seems only a multiplication of in­con­‐
ceiv­abil­i­ties. I am content to leave it as it stands: not feeling my reasons for
rejecting the Kantian hypothesis much weakened.26
The remaining reply which Dr. Hodgson makes runs thus:―
“But Mr. Spencer has a second argument to prove this in­con­ceiv­abil­ity. It is this:—‘If Space and
Time are forms of thought, they can never be {231} thought of; since it is impossible for anything to
be at once the form of thought and the matter of thought.’ . . . . An instance will show the fallacy
best. Syllogism is usually held to be a form of thought. Would it be any argument for the in­con­ceiv­‐
abil­ity of syllogisms to say, they cannot be at once the form and the matter of thought? Can we not
syllogize about syllogism? Or, more plainly still,—no dog can bite himself, for it is impossible to be
at once the thing that bites and the thing that is bitten.”
Had Dr. Hodgson quoted the whole of the passage from which he takes
the above sentence; or had he considered it in conjunction with the Kantian
doctrine to which it refers (namely, that Space survives in con­scious­ness
when all contents are expelled, which implies that then Space is the thing
with which con­scious­ness is occupied, or the object of con­scious­ness), he
would have seen that his reply has none of the cogency he supposes. If,
taking his first illustration, he will ask himself whether it is possible to
“syllogize about syllogism,” when syllogism has no content whatever,
symbolic or other—has nonentity to serve for major, nonentity for minor,
and nonentity for conclusion; he will, I think, see that syllogism, considered
as surviving terms of every kind, cannot be syllogized about: the “pure
form” of reason (supposing it to be syllogism, which it is not) if absolutely
discharged of all it contains, cannot be represented in thought, and therefore

cannot be reasoned about. Following Dr. Hodgson to his second illustration,
I must express my surprise that a metaphysician of his acuteness should
have used it. For an illustration to have any value, the relation between the
terms of the analogous case {232} must have some parallelism to the relation
between the terms of the case with which it is compared. Does Dr. Hodgson
really think that the relation between a dog and the part of himself which he
bites, is like the relation between matter and form ? Suppose the dog bites
his tail. Now the dog, as biting, stands, according to Dr. Hodgson, for the
form as the containing mental faculty; and the tail, as bitten, stands for this
mental faculty as contained. Now suppose the dog loses his tail. Can the
faculty as containing and the faculty as contained be separated in the same
way? Does the mental form when deprived of all content, even itself
(granting that it can be its own content), continue to exist in the same way
that a dog continues to exist when he has lost his tail? Even had this
illustration been applicable, I should scarcely have expected Dr. Hodgson to
remain satisfied with it. I should have thought he would prefer to meet my
argument directly, rather than indirectly. Why has he not shown the
invalidity of the reasoning used in the Principles of Psychology (§ 399, 2nd
ed.)? Having there quoted the statement of Kant, that “Space and Time are
not merely forms of sensuous intuition, but intuitions themselves;” I have
written―
“If we inquire more closely, this ir­rec­on­cil­abil­ity becomes still clearer. Kant says:—‘That which in
the phænomenon corresponds to the sensation, I term its matter ; but that which effects that the
content of the phenomenon can be arranged under certain relations, I call its form .’ Carrying with us
this definition of form, as ‘that which effects that the content . . . . can be arranged under certain
relations,’ let us return to the case in which the intuition of Space is the intuition which occupies con­‐
scious­ness. Can the content of this intuition ‘be arranged under certain relations’ or not? It can be so
arranged, or rather, it is so arranged. Space cannot be thought of save as having parts, near and
remote, in this direction or the other. Hence, if that is the form of a thing ‘which effects that the
content . . . . can be arranged under certain relations,’ it follows that when the content of con­scious­‐
ness is the intuition of Space, which has ‘parts that can be arranged under certain relations,’ there
must be a form of that intuition. What is it? Kant does not tell us—does not appear to perceive that
there must be such a form; and could not have perceived this without abandoning his hypothesis that
the space-intuition is primordial.”
Now when Dr. Hodgson has shown me how that “which {233} effects that
the content . . . . can be arranged under certain relations,” may also be that

which effects its own arrangement under the same relations, I shall be ready
to surrender my position; but until then, no analogy drawn from the ability
of a dog to bite himself will weigh much with me.
Having, as he considers, disposed of the reasons given by me for
concluding that, considered in themselves, “Space and Time are wholly in­‐
com­pre­hen­sible” (he continually uses on my behalf the word
“inconceivable,” which, by its unfit connotations, gives a wrong aspect to
my position), Dr. Hodgson goes on to say:-
“Yet Mr. Spencer proceeds to use these inconceivable ideas as the basis of his philosophy. For
mark, it is Space and Time as we know them, the actual and phenomenal Space and Time, to which
all these in­con­ceiv­ab­ il­i­ties attach. Mr. Spencer’s result, ought, therefore, logically to be—Scepticism.
What is his actual result? Ontology. And how so? Why, instead of rejecting Space and Time as the
inconceivable things he has tried to demonstrate them to be, he substitutes for them an Unknowable,
a something which they really are, though we cannot know it, and rejects that, instead of them, from
knowledge.”
This statement has caused me no little astonishment. That having before
him the volume from which he quotes, so competent a reader should have
so completely missed the meaning of the passages (§ 26) already referred
to, in which I have contended against Hamilton and Mansel, makes me
almost despair of being understood by any ordinary reader. In that section I
have, in the first place, contended that the con­scious­ness of an Ultimate
Reality, though not capable of being made a thought, properly so called,
because not capable of being brought within limits, nevertheless remains as
a con­scious­ness that is positive : is not rendered negative by the negations
of limits. I have pointed out that―
“The error, (very naturally fallen into by philosophers intent on demonstrating the limits and
conditions of con­scious­ness), consists in assuming that con­scious­ness contains nothing but limits and
conditions; to the entire neglect of that which is limited and conditioned. It is forgotten that there is
something which alike forms the raw material of definite thought and remains after the definiteness
which thinking gave to it has been {234} destroyed”—something which “ever persists in us as the
body of a thought to which we can give no shape.”
This positive element of con­scious­ness it is which, “at once necessarily
indefinite and necessarily indestructible,” I regard as the con­scious­ness of
the Unknowable Reality. Yet Dr. Hodgson says “Mr. Spencer proceeds to
use these inconceivable ideas as the basis of his philosophy:” implying that
such basis consists of negations, instead of consisting of that which persists
notwithstanding the negation of limits . And then, beyond this perversion, or

almost inversion, of meaning, he conveys the notion that I take as the basis
of philosophy, the “inconceivable ideas” “or self-contradictory notions”
which result when we endeavour to comprehend Space and Time. He
speaks of me as proposing to evolve substance out of form, or rather, out of
the negations of forms—gives his readers no conception that the Power
manifested to us is that which I regard as the Unknowable, while what we
call Space and Time answer to the unknowable nexus of its manifestations.
And yet the chapter from which I quote, and still more the chapter which
follows it, makes this clear—as clear, at least, as I can make it by carefully-
worded statements and re-statements.

Philosophical systems, like theological ones, following the law of
evolution in general, severally become in course of time more rigid, while
becoming more complex and more definite; and they similarly become less
alterable—resist all compromise, and have to be replaced by the more
plastic systems that descend from them.
It is thus with pure Empiricism and pure Tran­scen­den­ta­lism. Down to the
present time disciples of Locke have continued to hold that all mental
phenomena are interpretable as results of accumulated individual
experiences; and, by criticism, have been led simply to elaborate their in­ter­‐
pre­ta­tions—ignoring the proofs of inadequacy. On the other hand, disciples
of Kant, {235} asserting this inadequacy, and led by perception of it to adopt
an antagonist theory, have persisted in defending that theory under a form
presenting fatal inconsistencies. And then, when there is offered a mode of
reconciliation, the spirit of no-compromise is displayed: each side
continuing to claim the whole truth. After it has been pointed out that all the
obstacles in the way of the experiential doctrine disappear if the effects of
ancestral experiences are joined with the effects of individual experiences,
the old form of the doctrine is still adhered to. And meanwhile Kantists
persist in asserting that the ego is born with intuitional forms which are
wholly independent of anything in the non-ego , after it has been shown that

the innateness of these intuitional forms may be so understood as to escape
the insurmountable difficulties of the hypothesis as originally expressed.
I am led to say this by reading the remarks concerning my own views,
made with an urbanity I hope to imitate, by Professor Max Müller, in a
lecture delivered at the Royal Institution in March, 1873.27 Before dealing
with the criticisms contained in this lecture, I must enter a demurrer against
that interpretation of my views by which Professor Max Müller makes it
appear that they are more allied to those of Kant than to those of Locke. He
says:―
“Whether the pre-historic genesis of these congenital dispositions or inherited necessities of
thought, as suggested by Mr. Herbert Spencer, be right or wrong, does not signify for the purpose
which Kant had in view. In admitting that there is something in our mind, which is not the result of
our own à posteriori experience, Mr. Herbert Spencer is a thorough Kantian, and we shall see that he
is a Kantian in other respects too. If it could be proved that nervous modifications, accumulated from
generation to generation, could result in nervous structures that are fixed in proportion as the outer
relations to which they answer are fixed, we, as followers of Kant, should only have to put in the
place of Kant’s intuitions of Space and Time ‘the constant space-re­la­tions expressed in definite
nervous structures, congenitally framed to act in definite ways, and incapable of acting in any other
{236} way.’ If Mr. Herbert Spencer had not misunderstood the exact meaning of what Kant calls the
intuitions of Space and Time, he would have perceived that, barring his theory of the pre-historic
origin of these intuitions, he was quite at one with Kant.”
On this passage let me remark, first, that the word “pre-historic,”
ordinarily employed only in respect to human history, is misleading when
applied to the history of Life in general; and his use of it leaves me in some
doubt whether Professor Max Müller has rightly conceived the hypothesis
he refers to.
My second comment is, that the description of me as “quite at one with
Kant,” “barring ” the “theory of the prehistoric origin of these intuitions,”
curiously implies that it is a matter of comparative indifference whether the
forms of thought are held to be naturally generated by intercourse between
the organism and its environing relations, during the evolution of the lowest
into the highest types, or whether such forms are held to be supernaturally
given to the human mind, and are independent both of environing relations
and of ancestral minds. But now, addressing myself to the essential point, I
must meet the statement that I have “misunderstood the exact meaning of
what Kant calls the intuitions of Space and Time,” by saying that I think

Professor Max Müller has overlooked certain passages which justify my
interpretation, and render his interpretation untenable. For Kant says “Space
is nothing else than the form of all phenomena of the external sense;”
further, he says that “Time is nothing but the form of our internal intuition;”
and, to repeat words I have used elsewhere, “He distinctly shuts out the
supposition that there are forms of the non-ego to which these forms of the
ego correspond, by saying that ‘Space is not a conception which has been
derived from outward experiences.’” Now so far from being in harmony
with, these statements are in direct contradiction to, the view which I hold;
and seem to me absolutely irreconcilable with it. How can it be said that,
“barring” a difference represented as trivial, I am {237} “quite at one with
Kant,” when I contend that these subjective forms of intuition are moulded
into correspondence with, and therefore derived from, some objective form
or nexus , and therefore dependent upon it; while the Kantian hypothesis is
that these subjective forms are not derived from the object, but pre-exist in
the subject—are imposed by the ego on the non-ego . It seems to me that
not only do Kant’s words, as above given, exclude the view which I hold,
but also that Kant could not consistently have held any such view. Rightly
recognizing, as he did, these forms of intuition as innate, he was, from his
stand-point, obliged to regard them as imposed on the matter of intuition in
the act of intuition. In the absence of the hypothesis that intelligence has
been evolved, it was not possible for him to regard these subjective forms
as having been derived from objective forms.
A disciple of Locke might, I think, say that the Evolution-view of our
con­scious­ness of Space and Time is essentially Lockian, with more truth
than Professor Max Müller can represent it as essentially Kantian. The
Evolution-view is completely experiential. It differs from the original view
of the ex­pe­rien­tial­ists by containing a great extension of that view. With the
relatively-small effects of individual experiences, it joins the relatively-vast
effects of the experiences of antecedent individuals. But the view of Kant is
avowedly and absolutely unexperiential. Surely this makes the
predominance of kinship manifest.

In Professor Max Müller’s replies to my criticisms on Kant, I cannot see
greater validity than in this affiliation to which I have demurred. One of his
arguments is that which Dr. Hodgson has used, and which I have already
answered; and I think that the others, when compared with the passages of
the Principles of Psychology which they concern, will not be found
adequate. I refer to them here {238} chiefly for the purpose of pointing out
that when he speaks of me as bringing “three arguments against Kant’s
view,” he understates the number. Let me close what I have to say on this
disputed question, by quoting the summary of reasons I have given for
rejecting the Kantian hypothesis:―
“Kant tells us that Space is the form of all external intuition; which is not true. He tells us that the
con­scious­ness of Space continues when the con­scious­ness of all things contained in it is suppressed;
which is also not true. From these alleged facts he infers that Space is an à priori form of intuition. I
say infers , because this conclusion is not presented in necessary union with the premises, in the same
way that the con­scious­ness of duality is necessarily presented along with the con­scious­ness of
inequality; but it is a conclusion voluntarily drawn for the purpose of explaining the alleged facts.
And then that we may accept this conclusion, which is not necessarily presented along with these
alleged facts which are not true, we are obliged to affirm several propositions which cannot be
rendered into thought. When Space is itself contemplated, we have to conceive it as at once the form
of intuition and the matter of intuition; which is impossible. We have to unite that which we are
conscious of as Space with that which we are conscious of as the ego , and contemplate the one as a
property of the other; which is impossible. We have at the same time to disunite that which we are
conscious of as Space, from that which we are conscious of as the non-ego, and contemplate the one
as separate from the other; which is also impossible. Further, this hypothesis that Space is “nothing
else” than a form of intuition belonging wholly to the ego , commits us to one of the two alternatives,
that the non-ego is formless or that its form produces absolutely no effect upon the ego ; both of
which alternatives involve us in impossibilities of thought.”—Prin. of Psy., § 399.

Objections of another, though allied, class have been made in a review of
the Principles of Psychology by Mr. H. Sidgwick—a critic whose remarks
on questions of mental philosophy always deserve respectful consideration.
Mr. Sidgwick’s chief aim is to show what he calls “the mazy
inconsistency of his [my] metaphysical results.” More specifically, he
expresses thus the proposition he seeks to justify—“His view of the subject
appears to have a fundamental incoherence, which shows itself in various
ways on the surface of his exposition, but of which the root lies {239} much
deeper, in his inability to harmonise different lines of thought.”

Before dealing with the reasons given for this judgment, let me say that,
in addition to the value which candid criticisms have as showing where
more explanation is needed, they are almost indispensable as revealing to a
writer incongruities he had not perceived. Especially where, as in this case,
the subject-matter has many aspects, and where the words supplied by our
language are so inadequate in number that, to avoid cumbrous
circumlocution, they have to be used in senses that vary according to the
context, it is extremely difficult to avoid imperfections of statement. But
while I acknowledge sundry such imperfections and the resulting
incongruities, I cannot see that these are, as Mr. Sidgwick says,
fundamental. Contrariwise, their superficiality seems to me proved by the
fact that they may be rectified without otherwise altering the expositions in
which they occur. Here is an instance.
Mr. Sidgwick points out that, when treating of the “Data of Psychology,”
I have said (in § 56) that, though we reach inferentially “the belief that mind
and nervous action are the subjective and objective faces of the same thing,
we remain utterly incapable of seeing, and even of imagining, how the two
are related” (I quote the passage more fully than he does). He then goes on
to show that in the “Special Synthesis,” where I have sketched the evolution
of Intelligence under its objective aspect, as displayed in the processes by
which beings of various grades adjust themselves to surrounding actions, I
“speak as if” we could see how con­scious­ness “naturally arises at a
particular stage” of nervous action. The chapter he here refers to is one
describing that “dif­fer­en­ti­at­ion of the psychical from the physical life”
which accompanies advancing organization, and more especially advancing
development of the nervous system. In it I have shown {240} that, while the
changes constituting physical life continue to be characterized by the
simultaneity with which all kinds of them go on throughout the organism,
the changes constituting psychical life, arising as the nervous system
develops, become gradually more distinguished by their seriality . And I
have said that as nervous integration advances, “there must result an
unbroken series of these changes—there must arise a con­scious­ness.” Now
I admit that here is an apparent inconsistency. I ought to have said that

“there must result an unbroken series of these changes,” which, taking place
in the nervous system of a highly-organized creature, gives coherence to its
conduct; and along with which we assume a con­scious­ness, because con­‐
scious­ness goes along with coherent conduct in ourselves. If Mr. Sidgwick
will substitute this statement for the statement as it stands, he will see that
the arguments and conclusions remain intact. A survey of the chapter as a
whole, proves that its aim is not in the least to explain how nervous
changes, considered as waves of molecular motion, become the feelings
constituting con­scious­ness; but that, contemplating the facts objectively in
living creatures at large, it points out the cardinal distinction between vital
actions in general, and those particular vital actions which, in a creature
displaying them, lead us to speak of it as intelligent. It is shown that the rise
of such actions becomes marked in proportion as the changes taking place
in the part called the nervous system, are made more and more distinctly
serial, by union in a supreme centre of co-ordination. The introduction of
the word con­scious­ness, arises in the effort to show what fundamental
character there is in these particular physiological changes which is parallel
to a fundamental character in the psychological changes.
Another instance of the way in which Mr. Sidgwick evolves an
incongruity which he considers fundamental, out of what I should have
thought he would see is a {241} defective expression, I will give in his own
words. Speaking of a certain view of mine, he says:―
“He tells us that ‘logic . . . contemplates in its propositions certain connexions predicated, which
are necessarily involved with certain other connexions given: regarding all these connexions as
existing in the non-ego —not, it may be, under the form in which we know them, but in some form.’
But in § 473, where Mr. Spencer illustrates by a diagram his ‘Transfigured Realism,’ the view seems
to be this: although we cannot say that the real non-ego resembles our notion of it in ‘its elements,
relations, or laws,’ we can say that ‘a change in the objective reality causes in the subjective state a
change exactly answering to it—so answering as to constitute a cognition of it .’ Here the ‘something
beyond con­scious­ness’ is no longer said to be unknown, as its effect in con­scious­ness ‘constitutes a
cognition of it.’”
This apparent inconsistency, marked by the italics, would not have
existed if, instead of “a cognition of it,” I had said, as I ought to have said,
“what we call a cognition of it”—that is, a relative cognition as
distinguished from an absolute cognition. In ordinary language we speak of

as cognitions, those connexions in thought which so guide us in our
dealings with things, that actual experience verifies ideal anticipation:
marking off, by opposed words, those connexions in thought which mis -
guide us. The difference between accepting a cognition as relatively true
and accepting it as absolutely true, will be clearly shown by an illustration.
There is no direct resemblance whatever between the sizes, forms, colours,
and arrangements, of the figures in an account-book, and the moneys or
goods, debts or credits, represented by them; and yet the forms and
arrangements of the written symbols, are such as answer in a perfectly-
exact way to stocks of various commodities and to various kinds of
transactions. Hence we say, figuratively, that the account-book will “tell us”
all about these stocks and transactions. Similarly, the diagram Mr. Sidgwick
refers to, suggests a way in which symbols, registered in us by objects, may
have forms and arrangements wholly unlike their objective causes and the
nexus among those causes, while yet they are so related as to guide us
correctly in our transactions {242} with those objective causes, and, in that
sense , constitute cognitions of them; though they no more constitute
cognitions in the absolute sense, than do the guiding symbols in the
account-book constitute cognitions of the things to which they refer. So
repeatedly is this view implied throughout the Principles of Psychology ,
that I am surprised to find a laxity of expression raising the suspicion that I
entertain any other.
To follow Mr. Sidgwick through sundry criticisms of like kind, which
may be similarly met, would take more space than I can here afford. I must
restrict myself now to the alleged “fundamental incoherence” of which he
thinks these inconsistencies are signs. I refer to that reconciliation of
Realism and Idealism considered by him as an impossible compromise. A
difficulty is habitually felt in accepting a coalition after long conflict.
Whoever has espoused one of two antagonist views, and, in defending it,
has gained a certain comprehension of the opposite view, becomes
accustomed to regard these as the only alternatives, and is puzzled by an
hypothesis which is at once both and neither. Yet, since it turns out in nearly
all cases that, of conflicting doctrines, each contains an element of truth,

and that controversy ends by combination of their respective half-truths,
there is a priori probability on the side of an hypothesis which qualifies
Realism by Idealism.
Mr. Sidgwick expresses his astonishment, or rather bespeaks that of his
readers, because, while I accept Idealistic criticisms, I nevertheless defend
the fundamental intuition of Common Sense; and, as he puts it, “fires his
[my] argument full in the face of Kant, Mill, and ‘metaphysicians’
generally.”
“He tells us that ‘metaphysicians’ illegitimately assume that ‘beliefs reached through complex
intellectual processes,’ are more valid than ‘beliefs reached through simple intellectual processes;’
that the common language they use refuses to express their hypotheses, and thus their reasoning
inevitably implies the common notions which they repudiate; that the belief of Realism has the
advantage of ‘priority,’ ‘simplicity,’ ‘distinctness.’ {243} But surely this prior, simple, distinctly
affirmed belief is that of what Mr. Spencer terms ‘crude Realism’, the belief that the non-ego is per
se extended, solid, even coloured (if not resonant and odorous). This is what common language
implies; and the argument by which Mr. Spencer proves the relativity of feelings and relations, still
more the subtle and complicated analysis by which he resolves our notion of extension into an
aggregate of feelings and transitions of feeling, lead us away from our original simple belief—that
(e.g. ) the green grass we see exists out of con­scious­ness as we see it—just as much as the reasonings
of Idealism, Scepticism, or Kantism.”
On the face of it the anomaly seems great; but I should have thought that
after reading the chapter on “Transfigured Realism,” a critic of Mr.
Sidgwick’s acuteness would have seen the solution of it. He has overlooked
an essential distinction. All which my argument implies is that the direct
intuition of Realism must be held of superior authority to the arguments of
Anti-Realism, where their deliverances cannot be reconciled . The one point
on which their deliverances cannot be reconciled, is the existence of an
objective reality. But while, against this intuition of Realism, I hold the
arguments of Anti-Realism to be powerless, because they cannot be carried
on without postulating that which they end by denying; yet, having
admitted objective existence as a necessary postulate, it is possible to make
valid criticisms upon all those judgments which Crude Realism joins with
this primordial judgment: it is possible to show that a transfigured
interpretation of properties and relations, is more tenable than the original
interpretation.

To elucidate the matter, let us take the most familiar case in which the
indirect judgments of Reason correct the direct judgments of Common
Sense. The direct judgment of Common Sense is that the Sun moves round
the Earth. In course of time, Reason, finding some facts at variance with
this, begins to doubt; and, eventually, hits upon an hypothesis which
explains the anomalies, but which denies this appar­ent­ly-cer­tain dictum of
Common Sense. What is the reconciliation? It consists in showing {244} to
Common Sense that the new interpretation equally well corresponds with
direct intuition, while it avoids all the difficulties. Common Sense is
reminded that the apparent motion of an object may be due either to its
actual motion or to the motion of the observer; and that there are terrestrial
experiences in which the observer thinks an object he looks at is moving,
when the motion is in himself. Extending the conception thus given, Reason
shows that if the Earth revolves on its axis, there will result that apparent
motion of the Sun which Common Sense interpreted into an actual motion
of the Sun; and the common-sense observer thereupon becomes able to
think of sunrise and sunset as due to his position as spectator on a vast
revolving globe. Now if the astronomer, setting out by recognizing these
celestial appearances, and proceeding to evolve the various anomalies
following from the common-sense interpretation of them, had drawn the
conclusion that there externally exist no Sun and no motion at all, he would
have done what Idealists do; and his arguments would have been equally
powerless against the intuition of Common Sense. But he does nothing of
the kind. He accepts the intuition of Common Sense respecting the reality
of the Sun and of the motion; but replaces the old interpretation of the
motion by a new interpretation reconcilable with all the facts.
Everyone must see that here, acceptance of the inexpugnable element in
the common-sense judgment, by no means involves acceptance of the
accompanying judgments; and I contend that the like discrimination must
be made in the case we are considering. It does not follow that while,
against the con­scious­ness which Crude Realism has of an objective reality,
the arguments of Anti-Realism are futile, they are therefore futile against
the conceptions which Crude Realism forms of the objective reality. If Anti-

Realism can show that, granting an objective reality, the interpretation of
Crude Realism contains insuperable {245} difficulties, the process is quite
legitimate. And, its primordial intuition remaining unshaken, Realism may,
on reconsideration, be enabled to frame a new conception which
harmonizes all the facts.
To show that there is not here the “mazy inconsistency” alleged, let us
take the case of sound as interpreted by Crude Realism, and as re-
interpreted by Transfigured Realism. Crude Realism assumes the sound
present in con­scious­ness to exist as such beyond con­scious­ness. Anti-
Realism proves the inadmissibility of this assumption in sundry ways (all of
which, however, set out by talking of sounding bodies beyond con­scious­‐
ness, just as Realism talks of them); and then Anti-Realism concludes that
we know of no existence save the sound as a mode of con­scious­ness: which
conclusion, and all kindred conclusions, I contend are vicious—first,
because all the words used connote an objective activity; second, because
the arguments are impossible without postulating at the outset an objective
activity; and third, because no one of the intuitions out of which the
arguments are built, is of equal validity with the single intuition of Realism
that an objective activity exists. But now the Transfigured Realism which
Mr. Sidgwick thinks “has all the serious incongruity of an intense
metaphysical dream,” neither affirms the untenable conception of Crude
Realism, nor, like Anti-Realism, draws unthinkable conclusions by suicidal
arguments; but, accepting that which is essential in Crude Realism, and
admitting the difficulties which Anti-Realism insists upon, reconciles
matters by a re-inter­pre­ta­tion analogous to that which an astronomer makes
of the solar motion. Continuing all along to recognize an objective activity
which Crude Realism calls sound, it shows that the answering sensation is
produced by a succession of separate impacts which, if made slowly, may
be separately identified, and which will, if progressively increased in
rapidity, produce tones higher and higher in pitch. It {246} shows by other
experiments that sounding bodies are in states of vibration, and that the
vibrations may be made visible. And it concludes that the objective activity

is not what it subjectively seems, but is proximately interpretable as a
succession of aërial waves. Thus Crude Realism is shown that while there
unquestionably exists an objective activity corresponding to the sensation
known as sound, yet the facts are not explicable on the original supposition
that this is like the sensation; while they are explicable by conceiving it as a
rhythmical mechanical action. Eventually this re-inter­pre­ta­tion, joined with
kindred re­in­ter­pre­ta­tions of other sensations, comes to be itself further
transfigured by analysis of its terms, and re-expression of them in terms of
molecular motion; but, however abstract the interpretation ultimately
reached, the objective activity continues to be postulated: the primordial
judgment of Crude Realism remains unchanged, though it has to change the
rest of its judgments.
In another part of his argument, however, Mr. Sidgwick implies that I
have no right to use those conceptions of objective existence by which this
compromise is effected. Quoting sundry passages to show that while I hold
the criticisms of the Idealist to be impossible without “tacitly or avowedly
postulating an unknown something beyond con­scious­ness,” I yet admit that
“our states of con­scious­ness are the only things we can know;” he goes on
to argue that I am radically inconsistent, because, in interpreting the
phenomena of con­scious­ness, I continually postulate, not an unknown
something, but a something of which I speak in ordinary terms, as though
its ascribed physical characters really exist as such, instead of being, as I
admit they are, synthetic states of my con­scious­ness. His objection, if I
understand it, is that for the purposes of Objective Psychology I apparently
profess to know Matter and Motion in the ordinary realistic way; while, as a
result of subjective analysis, I reach the conclusion that {247} it is impossible
to have that knowledge of objective existence which Realism supposes we
have. Doubtless there seems here to be what he calls “a fundamental
incoherence.” But I think it exists, not between my two expositions, but
between the two con­scious­nesses of subjective and objective existence,
which we cannot suppress and yet cannot put into definite forms. The
alleged incoherence I take to be but another name for the inscrutability of
the relation between subjective feeling and its objective correlate which is

not feeling—an inscrutability which meets us at the bottom of all our
analyses. An exposition of this inscrutability I have elsewhere summed up
thus:―
“See, then, our predicament. We can think of Matter only in terms of Mind. We can think of Mind
only in terms of Matter. When we have pushed our explorations of the first to the uttermost limit, we
are referred to the second for a final answer; and when we have got the final answer of the second,
we are referred back to the first for an interpretation of it. We find the value of x in terms of y ; then
we find the value of y in terms of x ; and so on we may continue for ever without coming nearer to a
solution.”—Prin. of Psy. § 272.
Carrying a little further this simile, will, I think, show where lies the
insuperable difficulty felt by Mr. Sidgwick. Taking x and y as the
subjective and objective activities, unknown in their natures and known
only as phenomenally manifested; and recognizing the fact that every state
of con­scious­ness implies, immediately or remotely, the action of object on
subject or subject on object, or both; we may say that every state of con­‐
scious­ness will be symbolized by some modification of xy —the
phenomenally-known product of the two unknown factors. In other words,
xy′ , x′y , x′y′ , x″y′ , x′y″ , &c., &c., will represent all perceptions and
thoughts. Suppose, now, that these are thoughts about the object; composing
some hypothesis respecting its characters as analyzed by physicists. Clearly,
all such thoughts, be they about shapes, resistances, momenta, molecules,
molecular motions, or what not, will contain forms of the subjective activity
x . Now let the thoughts {248} be concerning mental processes. It must
similarly happen that some mode of the unknown objective activity y , will
be in every case a component. Now suppose that the problem is the genesis
of mental phenomena; and that, in the course of the inquiry, bodily
organization and the functions of the nervous system are brought into the
explanation. It will happen, as before, that these, considered as objective,
have to be described and thought about in modes of xy . And when by the
actions of such a nervous system, conceived objectively in modes of xy ,
and acted upon by physical forces which are conceived in other modes of
xy , we endeavour to explain the genesis of sensations, perceptions, and
ideas, which we can think of only in other modes of xy, we find that all our
factors, and therefore all our in­ter­pre­ta­tions, contain the two unknown

terms, and that no interpretation is imaginable that will not contain the two
unknown terms.
What is the defence for this appar­ent­ly-circ­u­lar process? Simply that it is
a process of establishing congruity among our symbols. It is finding a mode
of so symbolizing the unknown activities, subjective and objective, and so
operating with our symbols, that all our acts may be rightly guided—
guided, that is, in such ways that we can anticipate, when, where, and in
what quantity some one of our symbols, or some combination of our
symbols, will be found. Mr. Sidgwick’s difficulty arises, I think, from
having insufficiently borne in mind the statements made at the outset, in
“The Data of Philosophy,” that such conceptions as “are vital, or cannot be
separated from the rest without mental dissolution, must be assumed as true
provisionally ;” that “there is no mode of establishing the validity of any
belief except that of showing its entire congruity with all other beliefs;” and
that “Philosophy, compelled to make those fundamental assumptions
without which thought is impossible, has to justify them by showing their
congruity with all other dicta of con­scious­ness.” In {249} pursuance of this
distinctly-avowed mode of procedure, I assume provisionally, an objective
activity and a subjective activity, and certain general forms and modes
(Space, Time, Matter, Motion, Force), which the subjective activity,
operated on by the objective activity, ascribes to it, and which I suppose to
correspond in some way to unknown forms and modes of the objective
activity. These provisional assumptions, having been carried out to all their
consequences, and these consequences proved to be congruous with one
another and with the original assumptions, these original assumptions are
justified. And if, finally, I assert, as I have repeatedly asserted, that the
terms in which I express my assumptions and carry on my operations are
but symbolic, and that all I have done is to show that by certain ways of
symbolizing, perfect harmony results—invariable agreement between the
symbols in which I frame my expectations, and the symbols which occur in
experience—I cannot be blamed for incoherence. On the contrary, it seems
to me that my method is the most coherent that can be devised. Lastly,
should it be said that this regarding of everything constituting experience

and thought as symbolic, has a very shadowy aspect; I reply that these
which I speak of as symbols, are real relatively to our con­scious­ness; and
are symbolic only in their relation to the Ultimate Reality.
That these explanations will make clear the coherence of views which
before seemed “fundamentally incoherent,” I feel by no means certain;
since, as I did not perceive the difficulties presented by the exposition as at
first made, I may similarly fail to perceive the difficulties in this
explanation. Originally, I had intended to complete the Principles of
Psychology by a division showing how the results reached in the preceding
divisions, physiological and psychological, analytic and synthetic,
subjective and objective, harmonize with one another, and are but different
aspects of the same aggregate of phenomena. But the work was already
{250} bulky; and I concluded that this division might be dispensed with,
because the congruities to be pointed out were sufficiently obvious. So little
was I conscious of the alleged “inability to harmonize different lines of
thought.” Mr. Sidgwick’s perplexities, however, show me that such an
exposition of concords is needful.

I have reserved to the last, one of the first objections made to the me­ta­‐
phys­i­co-the­o­lo­gi­cal doctrine set forth in First Principles , and implied in the
several volumes that have succeeded it. It was urged by an able
metaphysician, the Rev. James Martineau, in an essay entitled “Science,
Nescience, and Faith;” and, effective against my argument as it stands,
shows the need for some development of my argument. That Mr.
Martineau’s criticism may be understood, I must quote the passages it
concerns. Continuing the reasoning employed against Hamilton and
Mansel, to show that our con­scious­ness of that which transcends knowledge
is positive , and not, as they allege, negative , I have said:―
“Still more manifest will this truth become when it is observed that our conception of the Relative
itself disappears, if our conception of the Absolute is a pure negation. It is admitted, or rather it is
contended, by the writers I have quoted above, that contradictories can be known only in relation to
each other—that Equality, for instance, is unthinkable apart from its correlative Inequality; and that
thus the Relative can itself be conceived only by opposition to the Non-relative. It is also admitted, or
rather contended, that the con­scious­ness of a relation implies a con­scious­ness of both the related
members. If we are required to conceive the relation between the Relative and Non-relative without

being conscious of both, ‘we are in fact’ (to quote the words of Mr. Mansel differently applied)
‘required to compare that of which we are conscious with that of which we are not conscious; the
comparison itself being an act of con­scious­ness, and only possible through the con­scious­ness of both
its objects.’ What, then, becomes of the assertion that, ‘the Absolute is conceived merely by a
negation of conceivability,’ or as ‘the mere absence of the conditions under which con­scious­ness is
possible?’ If the Non-relative or Absolute, is present in thought only as a mere negation, then the
relation between it and the Relative becomes unthinkable, because one of the terms of the relation is
absent from con­scious­ness. {251} And if this relation is unthinkable, then is the Relative itself
unthinkable, for want of its antithesis: whence results the disappearance of all thought whatever.”—
First Principles , § 26.
On this argument Mr. Martineau comments as follows; first re-stating it
in other words:―
“Take away its antithetic term, and the relative, thrown into isolation, is set up as absolute, and
disappears from thought. It is indispensable therefore to uphold the Absolute in existence, as
condition of the relative sphere which constitutes our whole intellectual domain. Be it so: but when
saved on this plea,—to preserve the balance and interdependence of two co -relatives,—the
‘Absolute’ is absolute no more; it is reduced to a term of relation: it loses therefore its exile from
thought: its dis­qual­i­fi­ca­tion is cancelled: and the alleged nescience is discharged.
“So, the same law of thought which warrants the existence, dissolves the inscrutableness, of the
Absolute.”—Essays, Philosophical and Theological pp. 186–7.
I admit this to be a telling rejoinder; and one which can be met only when
the meanings of the words, as I have used them, are carefully discriminated,
and the implications of the doctrine fully traced out. We will begin by
clearing the ground of minor misconceptions.
First, let it be observed that though I have used the word Absolute as the
equivalent of Non-relative, because it is used in the passages quoted from
the writers I am contending against; yet I have myself chosen for the
purposes of my argument, the name Non-relative, and I do not necessarily
commit myself to any propositions respecting the Absolute, considered as
that which includes both Subject and Object. The Non-relative as spoken of
by me, is to be understood rather as the totality of Being minus that which
constitutes the individual con­scious­ness, present to us under forms of
Relation. Did I use the word in some Hegelian sense, as comprehensive of
that which thinks and that which is thought about, and did I propose to treat
of the order of things, not as phenomenally manifested but as noumenally
proceeding, the objection would be fatal. But the aim being simply to
formulate the order of things as present under relative forms, the antithetical
Non-relative here named as {252} implied by the conception of the Relative,

is that which, in any act of thought, is outside of and beyond it, rather than
that which is inclusive of it. Further, it should be observed that this Non-
relative, spoken of as a necessary complement to the Relative, is not spoken
of as a conception but as a con­scious­ness ; and I have in sundry passages
distinguished between those modes of con­scious­ness which, having limits,
and constituting thought proper, are subject to the laws of thought, and the
mode of con­scious­ness which persists when the removal of limits is carried
to the uttermost, and when distinct thought consequently ceases.
This opens the way to the reply here to be made to Mr. Martineau’s
criticism—namely, that while by the necessities of thought the Relative
implies a Non-relative; and while, to think of this antithesis completely,
requires that the Non-relative shall be made a conception proper; yet, for
the vague thought which is alone in this case possible, it suffices that the
Non-relative shall be present as a con­scious­ness which though undefined is
positive. Let us observe what necessarily happens when thought is
employed on this ultimate question.
In a preceding part of the argument criticized, I have, in various ways,
aimed to show that, alike when we analyze the product of thought and when
we analyze the process of thought, we are brought to the conclusion that
invariably “a thought involves relation , difference , likeness ;” and that even
from the very nature of Life itself, we may evolve the conclusion that
“thinking being relationing, no thought can ever express more than
relations.” What, now, must happen if thought, having this law, occupies
itself with the final mystery? Always implying terms in relation, thought
implies that both terms shall be more or less defined; and as fast as one of
them becomes indefinite, the relation also becomes indefinite, and thought
becomes indistinct. Take the {253} case of magnitudes. I think of an inch; I
think of a foot; and having tolerably-definite ideas of the two, I have a
tolerably-definite idea of the relation between them. I substitute for the foot
a mile; and being able to represent a mile much less definitely, I cannot so
definitely think of the relation between an inch and a mile—cannot
distinguish it in thought from the relation between an inch and two miles, as
clearly as I can distinguish in thought the relation between an inch and one

foot from the relation between an inch and two feet. And now if I endeavour
to think of the relation between an inch and the 240,000 miles from here to
the Moon, or the relation between an inch and the 93,000,000 miles from
here to the Sun, I find that while these distances, practically inconceivable,
have become little more than numbers to which I frame no answering ideas,
so, too, has the relation between an inch and either of them become
practically inconceivable. Evidently then this partial failure in the process
of forming thought-relations, which happens even with finite magnitudes
when one of them is immense, passes into complete failure when one of
them cannot be brought within any limits. The relation itself becomes
unrepresentable at the same time that one of its terms becomes
unrepresentable. Nevertheless, in this case it is to be observed that the
almost-blank form of relation preserves a certain qualitative character. It is
still dis­tin­guish­able as belonging to the con­scious­ness of extensions, not to
the con­scious­nesses of forces or durations; and in so far remains a vague­ly-
ident­i­fi­able relation. But now suppose we ask what happens when one term
of the relation has not simply magnitude having no known limits, and
duration of which neither beginning nor end is cognizable, but is also an
existence not to be defined? In other words, what must happen if one term
of the relation is not only quantitatively but also qualitatively
unrepresentable? Clearly in this case the {254} relation does not simply cease
to be thinkable except as a relation of a certain class, but it lapses
completely. When one of the terms becomes wholly unknowable, the law of
thought can no longer be conformed to; both because one term cannot be
present, and because relation itself cannot be framed. That is to say, the law
of thought that contradictories can be known only in relation to each other,
no longer holds when thought attempts to transcend the Relative; and yet,
when it attempts to transcend the Relative, it must make the attempt in
conformity with its law—must in some dim mode of con­scious­ness posit a
Non-relative, and, in some similarly dim mode of con­scious­ness, a relation
between it and the Relative. In brief then, to Mr. Martineau’s objection I
reply, that the insoluble difficulties he indicates arise here, as elsewhere,
when thought is applied to that which transcends the sphere of thought; and

that just as when we try to pass beyond phenomenal manifestations to the
Ultimate Reality manifested, we have to symbolize it out of such materials
as the phenomenal manifestations give us; so we have simultaneously to
symbolize the connexion between this Ultimate Reality and its
manifestations, as somehow allied to the connexions among the
phenomenal manifestations themselves. The truth Mr. Martineau’s criticism
adumbrates, is that the law of thought fails where the elements of thought
fail; and this is a conclusion quite conformable to the general view I defend.
Still holding the validity of my argument against Hamilton and Mansel, that
in pursuance of their own principle the Relative is not at all thinkable as
such , unless in contra­dis­tinc­tion to some existence posited, however
vaguely, as the other term of a relation, conceived however indefinitely; it is
consistent on my part to hold that in this effort which thought inevitably
makes to pass beyond its sphere, not only does the product of thought
become a dim symbol of a product, but the process of thought becomes a
dim {255} symbol of a process; and hence any predicament inferable from
the law of thought cannot be asserted.
I may fitly close this reply by a counter-criticism. To the direct defence of
a proposition, may be added the indirect defence which results from
showing the untenability of an alternative proposition. This criticism on the
doctrine of an Unknowable Existence manifested to us in phenomena, Mr.
Martineau makes in the interests of the doctrine held by him, that this
existence is, to a considerable degree, knowable. We are quite at one in
holding that there is an indestructible con­scious­ness of Power behind
Appearance; but whereas I contend that this Power cannot be brought
within the forms of thought, Mr. Martineau contends that there can be
consistently ascribed certain attributes of personality—not, indeed, human
char­ac­ter­is­tics so concrete as were ascribed in past times; but still, human
char­ac­ter­is­tics of the more abstract and higher class. His general doctrine is
this:—Regarding Matter as independently existing; regarding as also
independently existing, those primary qualities of Body “which are
inseparable from the very idea of Body, and may be evolved a priori from
the consideration of it as solid extension or extended solidity;” and saying

that to this class “belong Triple Dimension, Divisibility, In­com­pres­si­bil­i­ty;”
he goes on to assert that as these―
“cannot absent themselves from Body, they have a reality coeval with it, and belong eternally to the
material datum objective to God: and his mode of activity with regard to them must be similar to that
which alone we can think of his directing upon the relations of Space, viz. not Volitional, to cause
them, but Intellectual, to think them out. The Secondary Qualities, on the other hand, having no
logical tie to the Primary, but being appended to them as contingent facts, cannot be referred to any
deductive thought, but remain over as products of pure Inventive Reason and Determining Will. This
sphere of cognition, a posteriori to us,—where we cannot move a step alone but have submissively
to wait upon experience, is precisely the realm of Divine originality: and we are most sequacious
where He is most free. While on this Secondary field His Mind and ours are thus contrasted, they
meet in resemblance again upon the Primary: for the evolutions of deductive Reason there is but one
track possible to all intelligences; no {256} merum arbitrium can interchange the false and true, or
make more than one geometry, one scheme of pure Physics, for all worlds: and the Omnipotent
Architect Himself, in realizing the Kosmical conception, in shaping the orbits out of immensity and
determining seasons out of eternity, could but follow the laws of curvature, measure, and
proportion.”—Essays, Philosophical and Theological , pp. 163–4.
Before the major criticism which I propose to make on this hypothesis,
let me make a minor one. Not only of space-re­la­tions, but also of primary
physical properties, Mr. Martineau asserts the necessity: not a necessity to
our minds simply, but an ontological necessity. What is true for human
thought, is, in respect of these, true absolutely: “the laws of curvature,
measure, and proportion,” as we know them, are unchangeable even by
Divine power; as are also the Divisibility and In­com­pres­si­bil­ity of Matter.
But if, in these cases, Mr. Martineau holds that a necessity in thought
implies an answering necessity in things, why does he refrain from saying
the like in other cases? Why, if he tacitly asserts it in respect of space-re­la­‐
tions and the statical attributes of Body, does he not also assert it in respect
of the dynamical attributes of Body? The laws conformed to by that mode
of force now distinguished as “energy,” are as much necessary to our
thought as are the laws of space-re­la­tions. The axioms of Mechanics lie on
the same plane with the axioms of pure Mathematics. Now if Mr. Martineau
admits this—if he admits, as he must, the corollary that there can be no
such manifestation of energy as that displayed in the motion of a planet,
save at the expense of equivalent energy which pre-existed—if he draws the
further necessary corollary that the direction of a motion cannot be changed
by any action, without an equal reaction in an opposite direction on

something acting—if he bears in mind that this holds not only of all visible
motions, celestial and terrestrial, but that those activities of Body which
affect us as secondary properties, are also known only through other forms
of {257} energy, which are equivalents of mechanical energy and conform to
these same laws—and if, lastly, he infers that none of these derivative
energies can have given to them their characters and directions, save by pre-
existing forces, statical and dynamical, conditioned in special ways; what
becomes of that “realm of Divine originality” which Mr. Martineau
describes as remaining within the realm of necessity? Consistently carried
out, his argument implies a un­i­vers­al­ly-in­ev­i­ta­ble order, in which volition
can have no such place as that he alleges.
Not pushing Mr. Martineau’s reasoning to this conclusion, so entirely at
variance with the one he draws, but accepting his statement just as it stands,
let us consider the solution it offers us. We are left by it without any
explanation of Space and Time; we are not helped in conceiving the origin
of Matter; and there is afforded us no idea how Matter came to have its
primary attributes. All these are tacitly assumed to exist uncreated. Creative
activity is represented as under the restrictions imposed by mathematical
necessities, and as having for datum (mark the word) a substance which, in
respect of certain characters, defies modification. But surely this is not an
interpretation of the mystery of things. The mystery is simply relegated to a
remoter region, respecting which no inquiry is to be made. But the inquiry
must be made. After every such solution there arises afresh the question—
what is the origin and nature of that which imposes these limits on creative
power? what is the primary God which dominates over this secondary God?
For, clearly, if the “Omnipotent Architect himself” (to use Mr. Martineau’s
somewhat inconsistent name) is powerless to change the “material datum
objective” to him, and powerless to change the conditions under which it
exists, and under which he works, there is obviously implied a power to
which he is subject. So that in Mr. Martineau’s doctrine also, there is an
Ultimate {258} Unknowable; and it differs from the doctrine he opposes,

only by intercalating a partially Knowable between this and the wholly
Knowable.
Finding, as explained above, that this interpretation is not consistent with
itself; and finding, as just shown, that it leaves the essential mystery
unsolved; I do not see that it has an advantage over the doctrine of the
Unknowable in its unqualified shape. There cannot, I think, be more than
temporary rest in a proximate solution which takes for its basis the
ultimately insoluble. Just as thought cannot be prevented from passing
beyond Appearance, and trying to conceive the Cause behind; so, following
out the interpretation Mr. Martineau offers, thought cannot be prevented
from asking what Cause it is which restricts the Cause he assigns. And if we
must admit that the question under this eventual form cannot be answered,
may we not as well confess that the question under its immediate form
cannot be answered? Is it not better candidly to acknowledge the
incompetence of our intelligence, rather than to persist in calling that an
explanation which does but disguise the inexplicable? Whatever answer
each may give to this question, he cannot rightly blame those who, finding
in themselves an indestructible con­scious­ness of an ultimate Cause, whence
proceed alike what we call the Material Universe and what we call Mind,
refrain from affirming anything respecting it; because they find it as
inscrutable in nature as it is inconceivable in extent and duration.

P OSTSCRIPT .—With the concluding paragraph of the foregoing article, I
had hoped to end, for a long time, all controversial writing; and, if the
article had been published entire in the November number of the
Fortnightly , as originally intended, the need for any addition would not
have been pressing. But while it was in the printer’s {259} hands, two
criticisms, more elaborate than those dealt with above, made their
appearance; and now that the postponed publication of this latter half of the
article affords the opportunity, I cannot, without risking mis­in­ter­pre­ta­tions,
leave these criticisms unnoticed.
Especially do I feel called upon by courtesy to make some response to
one who, in the Quarterly Review for October, 1873, has dealt with me in a

spirit which, though largely antagonistic, is not wholly unsympathetic; and
who manifestly aims to estimate justly the views he opposes. In the space at
my disposal, I cannot of course follow him through all the objections he has
urged. I must content myself with brief comments on the two propositions
he undertakes to establish. His enunciation of these runs thus:―
“We would especially direct attention to two points, to both of which we are confident objections
may be made; and although Mr. Spencer has himself doubtless considered such objections (and they
may well have struck many of his readers also), we nevertheless do not observe that he has anywhere
noticed or provided for them.
“The two points we so select are:―
“(1) That his system involves the denial of all truth.
“(2) That it is radically and necessarily opposed to all sound principles of morals. ”
On this passage, ending in these two startling assertions, let me first
remark that I am wholly without this con­scious­ness the reviewer ascribes to
me. Remembering that I have expended some little labour in developing
what I conceive to be a system of truths, I am surprised by the supposition
that “the denial of all truth” is an implication which I am “doubtless” aware
may be alleged against this system. Remembering, too, that by its
programme this system is shown to close with two volumes on The
Principles of Morality , the statement that it is “necessarily opposed to all
sound principles of morals,” naturally astonishes me; and still more the
statement that I am doubtless conscious it may be so regarded. Saying thus
much by way of repudiating that latent scepticism {260} attributed to me by
the reviewer, I proceed to consider what he says in proof of these
propositions.
On those seeming incongruities of Transfigured Realism commented on
by him, I need say no more than I have already said in reply to Mr.
Sidgwick; by whom also they have been alleged. I will limit myself to the
corollary he draws from the doctrine of the Relativity of Knowledge, as
held by me. Rightly pointing out that I hold this in common with “Messrs.
Mill, Lewes, Bain, and Huxley;” but not adding, as he should have done,
that I hold it in common with Hamilton, Mansel, and the long list of
predecessors through whom Hamilton traced it; the reviewer proceeds to
infer from this doctrine of relativity that no absolute truth of any kind can
be asserted—not even the absolute truth of the doctrine of relativity itself.

And then he leaves it to be supposed by his readers, that this inference tells
especially against the system he is criticizing. If, however, the reviewer’s
inference is valid, this “denial of all truth” must be charged against the
doctrines of thinkers called orthodox, as well as against the doctrines of
those many philosophers, from Aristotle down to Kant, who have said the
same thing. But now I go further, and reply that against that form of the
doctrine of relativity held by me, this allegation cannot be made with the
same effect as it can against preceding forms of the doctrine. For I diverge
from other relativists in asserting that the existence of a non-relative is not
only a positive deliverance of con­scious­ness, but a deliverance transcending
in certainty all others whatever; and is one without which the doctrine of
relativity cannot be framed in thought. I have urged that “unless a real Non-
relative or Absolute be postulated, the Relative itself becomes absolute; and
so brings the argument to a contradiction;”28 and elsewhere I have
described this con­scious­ness of a Non-relative manifested to us through the
Relative as {261} “deeper than demonstration—deeper even than definite
cognition—deep as the very nature of mind;”29 which seems to me to be
saying as emphatically as possible that, while all other truths may be held as
relative, this truth must be held as absolute. Yet, strangely enough, though
contending thus against the pure relativists, and holding with the reviewer,
that “every asserter of such a [purely-relative] philosophy must be in the
position of a man who saws across the branch of a tree on which he actually
sits, at a point between himself and the trunk,”30 I am singled out by him as
though this were my own predicament! So far, then, from admitting that the
view I hold “involves the denial of all truth,” I assert that, having at the
outset posited the co-existence of subject and object as a deliverance of
con­scious­ness which precedes all reasoning;31 having subsequently shown,
analytically, that this postulate is in every way verified,32 and that in its
absence the proof of relativity is impossible; my view is distinguished by an
exactly-opposite trait.
The justification of his second proposition the reviewer commences by
saying that—“In the first place the process of Evolution, as understood by
Mr. Spencer, compels him to be at one with Mr. Darwin in his denial of the