CHAPTER XXII.

MR. MILL'S LOGIC[264].

The _History of the Inductive Sciences_ was published in 1837, and

the _Philosophy of the Inductive Sciences_ in 1840. In 1843 Mr. Mill

published his _System of Logic_, in which he states that without the

aid derived from the facts and ideas in my volumes, the corresponding

portion of his own would most probably not have been written, and

quotes parts of what I have said with commendation. He also, however,

dissents from me on several important and fundamental points, and

argues against what I have said thereon. I conceive that it may tend

to bring into a clearer light the doctrines which I have tried to

establish, and the truth of them, if I discuss some of the differences

between us, which I shall proceed to do[265].

Mr. Mill's work has had, for a work of its abstruse character, a

circulation so extensive, and admirers so numerous and so fervent, that

it needs no commendation of mine. But if my main concern at present

had not been with the points in which Mr. Mill _differs_ from me, I

should have had great pleasure in pointing out passages, of which there

are many, in which Mr. Mill appears to me to have been very happy in

promoting or in expressing philosophical truth.

There is one portion of his work indeed which tends to give it an

interest of a wider kind than belongs to that merely scientific truth

to which I purposely and resolutely confined my speculations in the

works to which I have referred. Mr. Mill has introduced into his work

a direct and extensive consideration of the modes of dealing with

moral and political as well as physical questions; and I have no doubt

that this part of his book has, for many of his readers, a more lively

interest than any other. Such a comprehensive scheme seems to give to

doctrines respecting science a value and a purpose which they cannot

have, so long as they are restricted to mere material sciences. I still

retain the opinion, however, upon which I formerly acted, that the

philosophy of science is to be extracted from the portions of science

which are universally allowed to be most certainly established, and

that those are the physical sciences. I am very far from saying, or

thinking, that there is no such thing as Moral and Political Science,

or that no method can be suggested for its promotion; but I think that

by attempting at present to include the Moral Sciences in the same

formulæ with the Physical, we open far more controversies than we

close; and that in the moral as in the physical sciences, the first

step towards showing how truth is to be discovered, is to study some

portion of it which is assented to so as to be beyond controversy.

1. _What is Induction?_--1. Confining myself, then, to the material

sciences, I shall proceed to offer my remarks on Induction with

especial reference to Mr. Mill's work. And in order that we may, as

I have said, proceed as intelligibly as possible, let us begin by

considering what we mean by _Induction_, as a mode of obtaining truth;

and let us note whether there is any difference between Mr. Mill and me

on this subject.

"For the purposes of the present inquiry," Mr. Mill says (i. 347[266]),

"Induction may be defined the operation of discovering and forming

general propositions:" meaning, as appears by the context, the

discovery of them from particular facts. He elsewhere (i. 370) terms

it "generalization from experience:" and again he speaks of it with

greater precision as the inference of a more general proposition from

less general ones.

2. Now to these definitions and descriptions I assent as far as they

go; though, as I shall have to remark, they appear to me to leave

unnoticed a feature which is very important, and which occurs in all

cases of Induction, so far as we are concerned with it. Science, then,

consists of general propositions, inferred from particular facts, or

from less general propositions, by Induction; and it is our object to

discern the nature and laws of _Induction_ in this sense. That the

propositions are general, or are more general than the facts from which

they are inferred, is an indispensable part of the notion of Induction,

and is essential to any discussion of the process, as the mode of

arriving at Science, that is, at a body of general truths.

3. I am obliged therefore to dissent from Mr. Mill when he includes, in

his notion of Induction, the process by which we arrive _at individual

facts_ from other facts _of the same order of particularity_.

Such inference is, at any rate, not Induction _alone_; if it be

Induction at all, it is Induction applied to an example.

For instance, it is a general law, obtained by Induction from

particular facts, that a body falling vertically downwards from rest,

describes spaces proportional to the squares of the times. But that a

particular body will fall through 16 feet in one second and 64 feet in

two seconds, is not an induction simply, it is a result obtained by

applying the inductive law to a particular case.

But further, such a process is often not induction _at all_. That a

ball striking another ball directly will communicate to it as much

momentum as the striking ball itself loses, is a law established

by induction: but if, from habit or practical skill, I make one

billiard-ball strike another, so as to produce the velocity which

I wish, without knowing or thinking of the general law, the term

_Induction_ cannot then be rightly applied. If I _know the law_ and

act upon it, I have in my mind both the general induction and its

particular application. But if I act by the ordinary billiard-player's

skill, without thinking of momentum or law, there is no Induction in

the case.

4. This distinction becomes of importance, in reference to Mr. Mill's

doctrine, because he has extended his use of the term _Induction_, not

only to the cases in which the general induction is consciously applied

to a particular instance; but to the cases in which the particular

instance is dealt with by means of experience, in that rude sense in

which _experience_ can be asserted of brutes; and in which, of course,

we can in no way imagine that the law is possessed or understood, as a

general proposition. He has thus, as I conceive, overlooked the broad

and essential difference between speculative knowledge and practical

action; and has introduced cases which are quite foreign to the idea

of science, alongside with cases from which we may hope to obtain some

views of the nature of science and the processes by which it must be

formed.

5. Thus (ii. 232) he says, "This inference of one particular fact from

another is a case of induction. It is of this sort of induction that

brutes are capable." And to the same purpose he had previously said (i.

251), "He [the burnt child who shuns the fire] is not generalizing:

he is inferring a particular from particulars. In the same way also,

brutes reason ... not only the burnt child, but the burnt dog, dreads

the fire."

6. This confusion, (for such it seems to me,) of knowledge with

practical tendencies, is expressed more in detail in other places. Thus

he says (i. 118), "I cannot dig the ground unless I have an idea of the

ground and of a spade, and of all the other things I am operating upon."

7. This appears to me to be a use of words which can only tend to

confuse our idea of knowledge by obliterating all that is distinctive

in _human_ knowledge. It seems to me quite false to say that I cannot

dig the ground, unless I have an idea of the ground and of my spade.

Are we to say that we cannot _walk_ the ground, unless we have an idea

of the ground, and of our feet, and of our shoes, and of the muscles of

our legs? Are we to say that a mole cannot dig the ground, unless he

has an idea of the ground and of the snout and paws with which he digs

it? Are we to say that a pholas cannot perforate a rock, unless he have

an idea of the rock, and of the acid with which he corrodes it?

8. This appears to me, as I have said, to be a line of speculation

which can lead to nothing but confusion. The knowledge concerning which

I wish to inquire is _human_ knowledge. And in order that I may have

any chance of success in the inquiry, I find it necessary to single

out that kind of knowledge which is especially and distinctively

human. Hence, I pass by, in this part of my investigation, all the

_knowledge_, if it is to be so called, which man has in no other way

than brutes have it;--all that merely shows itself in action. For

though action may be modified by habit, and habit by experience, in

animals as well as in men, such experience, so long as it retains

that merely practical form, is no part of the materials of science.

Knowledge in a _general_ form, is alone knowledge for that purpose;

and to _that_, therefore, I must confine my attention; at least till

I have made some progress in ascertaining its nature and laws, and am

thus prepared to compare such knowledge,--_human knowledge_ properly so

called,--with mere animal tendencies to action; or even with practical

skill which does not include, as for the most part practical skill does

not include, speculative knowledge.

9. And thus, I accept Mr. Mill's definition of Induction only in its

first and largest form; and reject, as useless and mischievous for our

purposes, his extension of the term to the practical influence which

experience of one fact exercises upon a creature dealing with similar

facts. Such influence cannot be resolved into _ideas_ and _induction_,

without, as I conceive, making all our subsequent investigation vague

and heterogeneous, indefinite and inconclusive. If we must speak of

animals as _learning_ from experience, we may at least abstain from

applying to them terms which imply that they learn, in the same way

in which men learn astronomy from the stars, and chemistry from the

effects of mixture and heat. And the same may be said of the language

which is to be used concerning what _men_ learn, when their _learning_

merely shows itself in action, and does not exist as a general thought.

_Induction_ must not be applied to such cases. _Induction_ must be

confined to cases where we have in our minds general propositions, in

order that the sciences, which are our most instructive examples of the

process we have to consider, may be, in any definite and proper sense,

_Inductive_ Sciences.

10. Perhaps some persons may be inclined to say that this difference

of opinion, as to the extent of meaning which is to be given to the

term _Induction_, is a question merely of words; a matter of definition

only. This is a mode in which men in our time often seem inclined to

dispose of philosophical questions; thus evading the task of forming

an opinion upon such questions, while they retain the air of looking

at the subject from a more comprehensive point of view. But as I have

elsewhere said, such questions of definition are never questions

of definition merely. A proposition is always implied along with

the definition; and the truth of the proposition depends upon the

settlement of the definition. This is the case in the present instance.

We are speaking of _Induction_, and we mean that kind of Induction

by which the sciences now existing among men have been constructed.

On this account it is, that we cannot include, in the meaning of the

term, mere practical tendencies or practical habits; for science is not

constructed of these. No accumulation of these would make up any of the

acknowledged sciences. The elements of such sciences are something of a

kind different from practical habits. The elements of such sciences are

principles which we _know_; truths which can be contemplated as being

_true_. Practical habits, practical skill, instincts and the like,

appear in action, and in action only. Such endowments or acquirements

show themselves when the occasion for action arrives, and then, show

themselves in the act; without being put, or being capable of being

put, in the form of truths contemplated by the intellect. But the

elements and materials of Science are necessary truths contemplated by

the intellect. It is by consisting of such elements and such materials,

that Science _is_ Science. Hence a use of the term _Induction_ which

requires us to obliterate this distinction, must make it impossible for

us to arrive at any consistent and intelligible view of the nature of

Science, and of the mental process by which Sciences come into being.

We must, for the purpose which Mr. Mill and I have in common, retain

his larger and more philosophical definition of Induction,--that it is

the inference of a more general proposition from less general ones.

11. Perhaps, again, some persons may say, that practical skill and

practical experience _lead_ to science, and may therefore be included

in the term _Induction_, which describes the formation of science. But

to this we reply, that these things lead to science as occasions only,

and do not form part of science; and that science begins then only

when we look at the facts in a general point of view. This distinction

is essential to the philosophy of science. The rope-dancer may, by

his performances, suggest, to himself or to others, properties of

the center of gravity; but this is so, because man has a tendency to

speculate and to think of general truths, as well as a tendency to

dance on a rope on special occasions, and to acquire skill in such

dancing by practice. The rope-dancer does not dance by Induction,

any more than the dancing dog does. To apply the terms Science and

Induction to such cases, carries us into the regions of metaphor;

as when we call birds of passage "wise meteorologists," or the bee

"a natural chemist, who turns the flower-dust into honey." This is

very well in poetry: but for our purposes we must avoid recognizing

these cases as really belonging to the sciences of meteorology and

chemistry,--as really cases of Induction. Induction for us is general

propositions, _contemplated as such_, derived from particulars.

Science may result _from_ experience and observation _by_ Induction;

but Induction is not therefore the same thing as experience and

observation. Induction is experience or observation _consciously_

looked at in a _general_ form. This consciousness and generality are

necessary parts of that knowledge which is science. And accordingly,

on the other hand, science cannot result from mere Instinct, as

distinguished from Reason; because Instinct by its nature is not

conscious and general, but operates blindly and unconsciously in

particular cases, the actor not seeing or thinking of the rule which he

obeys.

12. A little further on I shall endeavour to show that not only a

general _thought_, but a general _word_ or phrase is a requisite

element in Induction. This doctrine, of course, still more decidedly

excludes the case of animals, and of mere practical knowledge in man.

A burnt child dreads the fire; but reason must be unfolded, before the

child learns to understand the words "fire will hurt you." The burnt

dog never thus learns to understand words. And this difference points

to an entirely different state of thought in the two cases: or rather,

to a difference between a state of rational thought on the one hand,

and of mere practical instinct on the other.

13. Besides this difference of speculative thought and practical

instinct which thus are, as appears to me, confounded in Mr. Mill's

philosophy, in such a way as tends to destroy all coherent views of

human knowledge, there is another set of cases to which Mr. Mill

applies the term _Induction_, and to which it appears to me to be

altogether inapplicable. He employs it to describe the mode in which

superstitious men, in ignorant ages, were led to the opinion that

striking natural events presaged or accompanied calamities. Thus he

says (i. 389), "The opinion so long prevalent that a comet or any

other unusual appearance in the heavenly regions was the precursor of

calamities to mankind, or at least to those who witnessed it; the

belief in the oracles of Delphi and Dodona; the reliance on astrology,

or on the weather-prophecies in almanacs; were doubtless inductions

supposed to be grounded on experience;" and he speaks of these

insufficient inductions being extinguished by the stronger inductions

subsequently obtained by scientific inquiry. And in like manner,

he says in another place (i. 367), "Let us now compare different

predictions: the first, that eclipses will occur whenever one planet

or satellite is so situated as to cast its shadow upon another: the

second, that they will occur whenever some great calamity is impending

over mankind."

14. Now I cannot see how anything but confusion can arise from

applying the term _Induction_ to superstitious fancies like those

here mentioned. They are not imperfect truths, but entire falsehoods.

Of that, Mr. Mill and I are agreed: how then can they exemplify the

progress towards truth? They were not collected from the facts by

seeking a law of their occurrence; but were suggested by an imagination

of the anger of superior powers shown by such deviations from the

ordinary course of nature. If we are to speak of _inductions_ to any

purpose, they must be such inductions as represent the facts, in some

degree at least. It is not meant, I presume, that these opinions are in

any degree true: to what purpose then are they adduced? If I were to

hold that my dreams predict or conform to the motions of the stars or

of the clouds, would this be an induction? It would be so, as much one

as those here so denominated: yet what but confusion could arise from

classing it among scientific truths? Mr. Mill himself has explained

(ii. 389) the way in which such delusions as the prophecies of

almanac-makers, and the like, obtain credence; namely, by the greater

effect which the positive instances produce on ordinary minds in

comparison with the negative, when the rule has once taken possession

of their thoughts. And this being, as he says, the recognized

explanation of such cases, why should we not leave them to their due

place, and not confound and perplex the whole of our investigation by

elevating them to the rank of "inductions"? The very condemnation of

such opinions is that they are not at all inductive. When we have made

any progress in our investigation of the nature of science, to attempt

to drive us back to the wearisome discussion of such elementary points

as these, is to make progress hopeless.

II. _Induction or Description?_--15. In the cases hitherto noticed, Mr.

Mill extends the term _Induction_, as I think, too widely, and applies

it to cases to which it is not rightly applicable. I have now to notice

a case of an opposite kind, in which he does not apply it where I do,

and condemns me for using it in such a case. I had spoken of Kepler's

discovery of the Law, that the planets move round the sun in ellipses,

as an example of Induction. The separate facts of any planet (Mars, for

instance,) being in certain places at certain times, are all included

in the general proposition which Kepler discovered, that Mars describes

an ellipse of a certain form and position. This appears to me a very

simple but a very distinct example of the operation of discovering

general propositions; general, that is, with reference to particular

facts; which operation Mr. Mill, as well as myself, says is Induction.

But Mr. Mill denies this operation in this case to be Induction at

all (i. 357). I should not have been prepared for this denial by the

previous parts of Mr. Mill's book, for he had said just before (i.

350), "such facts as the magnitudes of the bodies of the solar system,

their distances from each other, the figure of the earth and its

rotation ... are proved indirectly, by the aid of inductions founded

on other facts which we can more easily reach." If the figure of the

earth and its rotation are proved by Induction, it seems very strange,

and is to me quite incomprehensible, how the figure of the earth's

orbit and its revolution (and of course, of the figure of Mars's orbit

and his revolution in like manner,) are not also proved by Induction.

No, says Mr. Mill, Kepler, in putting together a number of places of

the planet into one figure, only performed an act of _description_.

"This descriptive operation," he adds (i. 359), "Mr. Whewell, by an

aptly chosen expression, has termed Colligation of Facts." He goes on

to commend my observations concerning this process, but says that,

according to the old and received meaning of the term, it is not

Induction at all.

16. Now I have already shown that Mr. Mill himself, a few pages

earlier, had applied the term _Induction_ to cases undistinguishable

from this in any essential circumstance. And even in this case, he

allows that Kepler did really perform an act of Induction (i. 358),

"namely, in concluding that, because the observed places of Mars were

correctly represented by points in an imaginary ellipse, therefore Mars

would continue to revolve in that same ellipse; and even in concluding

that the position of the planet during the time which had intervened

between the two observations must have coincided with the intermediate

points of the curve." Of course, in Kepler's Induction, of which I

speak, I include all this; all this is included in speaking of the

_orbit_ of Mars: a continuous line, a periodical motion, are implied

in the term _orbit_. I am unable to see what would remain of Kepler's

discovery, if we take from it these conditions. It would not only not

be an induction, but it would not be a description, for it would not

recognize that Mars moved in an orbit. Are particular positions to be

conceived as points in a curve, without thinking of the intermediate

positions as belonging to the same curve? If so, there is no law at

all, and the facts are not bound together by any intelligible tie.

In another place (ii. 209) Mr. Mill returns to his distinction of

Description and Induction; but without throwing any additional light

upon it, so far as I can see.

17. The only meaning which I can discover in this attempted distinction

of Description and Induction is, that when particular facts are bound

together by their relation in _space_, Mr. Mill calls the discovery

of the connexion _Description_, but when they are connected by other

general relations, as time, cause and the like, Mr. Mill terms the

discovery of the connexion _Induction_. And this way of making a

distinction, would fall in with the doctrine of other parts of Mr.

Mill's book, in which he ascribes very peculiar attributes to space

and its relations, in comparison with other Ideas, (as I should call

them). But I cannot see any ground for this distinction, of connexion

according to space and other connexions of facts.

To stand upon such a distinction, appears to me to be the way to miss

the general laws of the formation of science. For example: The ancients

discovered that the planets revolved in recurring periods, and thus

connected the observations of their motions according to the Idea of

_Time_. Kepler discovered that they revolved in ellipses, and thus

connected the observations according to the Idea of _Space_. Newton

discovered that they revolved in virtue of the Sun's attraction, and

thus connected the motions according to the Idea of _Force_. The first

and third of these discoveries are recognized on all hands as processes

of Induction. Why is the second to be called by a different name? or

what but confusion and perplexity can arise from refusing to class it

with the other two? It is, you say, Description. But such Description

is a kind of Induction, and must be spoken of as Induction, if we are

to speak of Induction as the process by which Science is formed: for

the three steps are all, the second in the same sense as the first

and third, in co-ordination with them, steps in the formation of

astronomical science.

18. But, says Mr. Mill (i. 363), "it is a fact surely that the planet

does describe an ellipse, and a fact which we could see if we had

adequate visual organs and a suitable position." To this I should

reply: "Let it be so; and it is a fact, surely, that the planet does

move periodically: it is a fact, surely, that the planet is attracted

by the sun. Still, therefore, the asserted distinction fails to find a

ground." Perhaps Mr. Mill would remind us that the elliptical form of

the orbit is a fact which we could see if we had adequate visual organs

and a suitable position: but that force is a thing which we cannot

see. But this distinction also will not bear handling. Can we not see

a tree blown down by a storm, or a rock blown up by gunpowder? Do we

not here see force:--see it, that is, by its effects, the only way in

which we need to see it in the case of a planet, for the purposes of

our argument? Are not such operations of force, Facts which may be the

objects of sense? and is not the operation of the sun's Force a Fact

of the same kind, just as much as the elliptical form of orbit which

results from the action? If the latter be "surely a Fact," the former

is a Fact no less surely.

19. In truth, as I have repeatedly had occasion to remark, all attempts

to frame an argument by the exclusive or emphatic appropriation of

the term _Fact_ to particular cases, are necessarily illusory and

inconclusive. There is no definite and stable distinction between Facts

and Theories; Facts and Laws; Facts and Inductions. Inductions, Laws,

Theories, which are true, _are_ Facts. Facts involve Inductions. It is

a fact that the moon is attracted by the earth, just as much as it is a

Fact that an apple falls from a tree. That the former fact is collected

by a more distinct and conscious Induction, does not make it the less

a Fact. That the orbit of Mars is a Fact--a true Description of the

path--does not make it the less a case of Induction.

20. There is another argument which Mr. Mill employs in order to

show that there is a difference between mere colligation which is

description, and induction in the more proper sense of the term. He

notices with commendation a remark which I had made (i. 364), that

at different stages of the progress of science the facts had been

successfully connected by means of very different conceptions, while

yet the later conceptions have not contradicted, but included, so far

as they were true, the earlier: thus the ancient Greek representation

of the motions of the planets by means of epicycles and eccentrics,

was to a certain degree of accuracy true, and is not negatived, though

superseded, by the modern representation of the planets as describing

ellipses round the sun. And he then reasons that this, which is thus

true of Descriptions, cannot be true of Inductions. He says (i. 367),

"Different descriptions therefore may be all true: but surely not

different explanations." He then notices the various explanations of

the motions of the planets--the ancient doctrine that they are moved

by an inherent virtue; the Cartesian doctrine that they are moved by

impulse and by vortices; the Newtonian doctrine that they are governed

by a central force; and he adds, "Can it be said of these, as was said

of the different descriptions, that they are all true as far as they

go? Is it not true that one only can be true in any degree, and that

the other two must be altogether false?"

21. And to this questioning, the history of science compels me to reply

very distinctly and positively, in the way which Mr. Mill appears to

think extravagant and absurd. I am obliged to say, Undoubtedly, all

these explanations _may_ be true and consistent with each other, and

would be so if each had been followed out so as to show in what manner

it could be made consistent with the facts. And this was, in reality,

in a great measure done[267]. The doctrine that the heavenly bodies

were moved by vortices was successively modified, so that it came to

coincide in its results with the doctrine of an inverse-quadratic

centripetal force, as I have remarked in the _History_[268]. When this

point was reached, the vortex was merely a machinery, well or ill

devised, for producing such a centripetal force, and therefore did not

contradict the doctrine of a centripetal force. Newton himself does

not appear to have been averse to explaining gravity by impulse. So

little is it true that if the one theory be true the other must be

false. The attempt to explain gravity by the impulse of streams of

particles flowing through the universe in all directions, which I have

mentioned in the _Philosophy_[269] so far from being inconsistent

with the Newtonian theory, that it is founded entirely upon it. And

even with regard to the doctrine, that the heavenly bodies move by

an inherent virtue; if this doctrine had been maintained in any such

way that it was brought to agree with the facts, the inherent virtue

must have had its laws determined; and then, it would have been found

that the virtue had a reference to the central body; and so, the

"inherent virtue" must have coincided in its effect with the Newtonian

force; and then, the two explanations would agree, except so far as

the word "inherent" was concerned. And if such a part of an earlier

theory as this word _inherent_ indicates, is found to be untenable,

it is of course rejected in the transition to later and more exact

theories, in Inductions of this kind, as well as in what Mr. Mill calls

Descriptions. There is therefore still no validity discoverable in the

distinction which Mr. Mill attempts to draw between "descriptions" like

Kepler's law of elliptical orbits, and other examples of induction.

22. When Mr. Mill goes on to compare what he calls different

predictions--the first, the true explanation of eclipses by the shadows

which the planets and satellites cast upon one another, and the

other, the belief that they will occur whenever some great calamity

is impending over mankind, I must reply, as I have stated already,

(Art. 17), that to class such superstitions as the last with cases of

Induction, appears to me to confound all use of words, and to prevent,

as far as it goes, all profitable exercise of thought. What possible

advantage can result from comparing (as if they were alike) the

relation of two descriptions of a phenomenon, each to a certain extent

true, and therefore both consistent, with the relation of a scientific

truth to a false and baseless superstition?

23. But I may make another remark on this example, so strangely

introduced. If, under the influence of fear and superstition, men

may make such mistakes with regard to laws of nature, as to imagine

that eclipses portend calamities, are they quite secure from mistakes

in _description_? Do not the very persons who tell us how eclipses

predict disasters, also describe to us fiery swords seen in the air,

and armies fighting in the sky? So that even in this extreme case,

at the very limit of the rational exercise of human powers, there is

nothing to distinguish Description from Induction.

I shall now leave the reader to judge whether this feature in the

history of science,--that several views which appear at first quite

different are yet all true,--which Mr. Mill calls a curious and

interesting remark of mine, and which he allows to be "strikingly true"

of the Inductions which he calls _Descriptions_, (i. 364) is, as he

says, "unequivocally false" of other Inductions. And I shall confide

in having general assent with me, when I continue to speak of Kepler's

_Induction_ of the elliptical orbits.

I now proceed to another remark.

III. _In Discovery a new Conception is introduced._--

24. There is a difference between Mr. Mill and me in our view of the

essential elements of this Induction of Kepler, which affects all other

cases of Induction, and which is, I think, the most extensive and

important of the differences between us. I must therefore venture to

dwell upon it a little in detail.

I conceive that Kepler, in discovering the law of Mars's motion,

and in asserting that the planet moved in an ellipse, did this;--he

bound together particular observations of separate places of Mars

by the notion, or, as I have called it, the _conception_, of an

_ellipse_, which was supplied by his own mind. Other persons, and he

too, before he made this discovery, had present to their minds the

facts of such separate successive positions of the planet; but could

not bind them together rightly, because they did not apply to them

this conception of an _ellipse_. To supply this conception, required

a special preparation, and a special activity in the mind of the

discoverer. He, and others before him, tried other ways of connecting

the special facts, none of which fully succeeded. To discover such

a connexion, the mind must be conversant with certain relations of

space, and with certain kinds of figures. To discover the right figure

was a matter requiring research, invention, resource. To hit upon

the right conception is a difficult step; and when this step is once

made, the facts assume a different aspect from what they had before:

that done, they are seen in a new point of view; and the catching

this point of view, is a special mental operation, requiring special

endowments and habits of thought. Before this, the facts are seen as

detached, separate, lawless; afterwards, they are seen as connected,

simple, regular; as parts of one general fact, and thereby possessing

innumerable new relations before unseen. Kepler, then, I say, bound

together the facts by superinducing upon them the _conception_ of an

_ellipse_; and this was an essential element in his Induction.

25. And there is the same essential element in all Inductive

discoveries. In all cases, facts, before detached and lawless, are

bound together by a new thought. They are reduced to law, by being

seen in a new point of view. To catch this new point of view, is an

act of the mind, springing from its previous preparation and habits.

The facts, in other discoveries, are brought together according to

other relations, or, as I have called them, _Ideas_;--the Ideas of

Time, of Force, of Number, of Resemblance, of Elementary Composition,

of Polarity, and the like. But in all cases, the mind performs the

operation by an apprehension of some such relations; by singling out

the one true relation; by combining the apprehension of the true

relation with the facts; by applying to them the Conception of such a

relation.

26. In previous writings, I have not only stated this view generally,

but I have followed it into detail, exemplifying it in the greater part

of the History of the principal Inductive Sciences in succession. I

have pointed out what are the Conceptions which have been introduced in

every prominent discovery in those sciences; and have noted to which of

the above Ideas, or of the like Ideas, each belongs. The performance

of this task is the office of the greater part of my _Philosophy

of the Inductive Sciences_. For that work is, in reality, no less

historical than the _History_ which preceded it. The _History of the

Inductive Sciences_ is the history of the discoveries, mainly so far

as concerns the _Facts_ which were brought together to form sciences.

The _Philosophy_ is, in the first ten Books, the history of the _Ideas_

and _Conceptions_, by means of which the facts were connected, so as

to give rise to scientific truths. It would be easy for me to give a

long list of the Ideas and Conceptions thus brought into view, but

I may refer any reader who wishes to see such a list, to the Tables

of Contents of the _History_, and of the first ten Books of the

_Philosophy_.

27. That these Ideas and Conceptions are really distinct elements of

the scientific truths thus obtained, I conceive to be proved beyond

doubt, not only by considering that the discoveries never were made,

nor could be made, till the right Conception was obtained, and by

seeing how difficult it often was to obtain this element; but also, by

seeing that the Idea and the Conception itself, as distinct from the

Facts, was, in almost every science, the subject of long and obstinate

controversies;--controversies which turned upon the possible relations

of Ideas, much more than upon the actual relations of Facts. The first

ten Books of the _Philosophy_ to which I have referred, contain the

history of a great number of these controversies. These controversies

make up a large portion of the history of each science; a portion quite

as important as the study of the facts; and a portion, at every stage

of the science, quite as essential to the progress of truth. Men, in

seeking and obtaining scientific knowledge, have always shown that they

found the formation of right conceptions in their own minds to be an

essential part of the process.

28. Moreover, the presence of a Conception of the mind as a special

element of the inductive process, and as the tie by which the

particular facts are bound together, is further indicated, by there

being some special new _term_ or _phrase_ introduced in every

induction; or at least some term or phrase thenceforth steadily

applied to the facts, which had not been applied to them before; as

when Kepler asserted that Mars moved round the sun in an _elliptical

orbit_, or when Newton asserted that the planets _gravitate_ towards

the sun; these new terms, _elliptical orbit_, and _gravitate_, mark

the new conceptions on which the inductions depend. I have in the

_Philosophy_[270] further illustrated this application of "technical

terms," that is, fixed and settled terms, in every inductive discovery;

and have spoken of their use in enabling men to proceed from each such

discovery to other discoveries more general. But I notice these terms

here, for the purpose of showing the existence of a conception in the

discoverer's mind, corresponding to the term thus introduced; which

conception, the term is intended to convey to the minds of those to

whom the discovery is communicated.

29. But this element of discovery,--right conceptions supplied by

the mind in order to bind the facts together,--Mr. Mill denies to be

an element at all. He says, of Kepler's discovery of the elliptical

orbit (i. 363), "It superadded nothing to the particular facts

which it served to bind together;" yet he adds, "except indeed the

knowledge that a resemblance existed between the planetary orbit

and other ellipses;" that is, except the knowledge that it _was_ an

ellipse;--precisely the circumstance in which the discovery consisted.

Kepler, he says, "asserted as a fact that the planet moved in an

ellipse. But this fact, which Kepler did not add to, but found in the

motion of the planet ... was the very fact, the separate parts of

which had been separately observed; it was the sum of the different

observations."

30. That the fact of the elliptical motion was not merely the _sum_ of

the different observations, is plain from this, that other persons, and

Kepler himself before his discovery, did not find it by adding together

the observations. The fact of the elliptical orbit was not the sum of

the observations _merely_; it was the sum of the observations, _seen

under a new point of view_, which point of view Kepler's mind supplied.

Kepler found it in the facts, because it was there, no doubt, for one

reason; but also, for another, because he had, in his mind, those

relations of thought which enabled him to find it. We may illustrate

this by a familiar analogy. We too find the law in Kepler's book; but

if we did not understand Latin, we should not find it there. We must

learn Latin in order to find the law in the book. In like manner, a

discoverer must know the language of science, as well as look at the

book of nature, in order to find scientific truth. All the discussions

and controversies respecting Ideas and Conceptions of which I have

spoken, may be looked upon as discussions and controversies respecting

the grammar of the language in which nature speaks to the scientific

mind. Man is the _Interpreter_ of Nature; not the Spectator merely,

but the Interpreter. The study of the language, as well as the mere

sight of the characters, is requisite in order that we may read the

inscriptions which are written on the face of the world. And this

study of the language of nature, that is, of the necessary coherencies

and derivations of the relations of phenomena, is to be pursued by

examining Ideas, as well as mere phenomena;--by tracing the formation

of Conceptions, as well as the accumulation of Facts. And this is what

I have tried to do in the books already referred to.

31. Mr. Mill has not noticed, in any considerable degree, what I have

said of the formation of the Conceptions which enter into the various

sciences; but he has, in general terms, denied that the Conception is

anything different from the facts themselves. "If," he says (i. 301),

"the facts are rightly classed under the conceptions, it is because

there is in the facts themselves, something of which the conception

is a copy." But it is a copy which cannot be made by a person without

peculiar endowments; just as a person cannot copy an ill-written

inscription, so as to make it convey sense, unless he understand the

language. "Conceptions," Mr. Mill says (ii. 217), "do not develope

themselves from within, but are impressed from without." But what comes

from without is not enough: they must have both origins, or they cannot

make knowledge. "The conception," he says again (ii. 221), "is not

furnished _by_ the mind till it has been furnished _to_ the mind." But

it is furnished to the mind by its own activity, operating according to

its own laws. No doubt, the conception may be formed, and in cases of

discovery, must be formed, by the suggestion and excitement which the

facts themselves produce; and must be so moulded as to agree with the

facts. But this does not make it superfluous to examine, out of what

_materials_ such conceptions are formed, and _how_ they are capable of

being moulded so as to express laws of nature; especially, when we see

how large a share this part of discovery--the examination how our ideas

can be modified so as to agree with nature,--holds, in the history of

science.

32. I have already (Art. 28) given, as evidence that the conception

enters as an element in every induction, the constant introduction

in such cases, of a new fixed term or phrase. Mr. Mill (ii. 282)

notices this introduction of a new phrase in such cases as important,

though he does not appear willing to allow that it is necessary. Yet

the necessity of the conception at least, appears to result from the

considerations which he puts forward. "What darkness," he says, "would

have been spread over geometrical demonstration, if wherever the word

_circle_ is used, the definition of a circle was inserted instead of

it." "If we want to make a particular combination of ideas permanent

in the mind, there is nothing which clenches it like a name specially

devoted to express it." In my view, the new conception is the _nail_

which connects the previous notions, and the name, as Mr. Mill says,

_clenches_ the junction.

33. I have above (Art. 30) referred to the difficulty of getting

hold of the right conception, as a proof that induction is not a

mere juxtaposition of facts. Mr. Mill does not dispute that it is

often difficult to hit upon the right conception. He says (i. 360),

"that a conception of the mind is introduced, is indeed most certain,

and Mr. Whewell has rightly stated elsewhere, that to hit upon the

right conception is often a far more difficult, and more meritorious

achievement, than to prove its applicability when obtained. But," he

adds, "a conception implies and corresponds to something conceived; and

although the conception itself is not in the facts, but in our mind, it

must be a conception of something which really is in the facts." But to

this I reply, that its being really in the facts, does not help us at

all towards knowledge, if we cannot see it there. As the poet says,

It is the mind that sees: the outward eyes

Present the object, but the mind descries.

And this is true of the sight which produces knowledge, as well as of

the sight which produces pleasure and pain, which is referred to in the

Tale.

34. Mr. Mill puts his view, as opposed to mine, in various ways, but,

as will easily be understood, the answers which I have to offer are

in all cases nearly to the same effect. Thus, he says (ii. 216), "the

tardy development of several of the physical sciences, for example,

of Optics, Electricity, Magnetism, and the higher generalizations of

Chemistry, Mr. Whewell ascribes to the fact that mankind had not yet

possessed themselves of the idea of Polarity, that is, of opposite

properties in opposite directions. But what was there to suggest such

an idea, until by a separate examination of several of these different

branches of knowledge it was shown that the facts of each of them did

present, in some instances at least, the curious phenomena of opposite

properties in opposite directions?" But on this I observe, that these

facts did not, nor do yet, present this conception to ordinary minds.

The opposition of properties, and even the opposition of directions,

which are thus apprehended by profound cultivators of science, are

of an abstruse and recondite kind; and to conceive any one kind of

polarity in its proper generality, is a process which few persons

hitherto appear to have mastered; still less, have men in general

come to conceive of them all as modifications of a general notion of

Polarity. The description which I have given of Polarity in general,

"opposite properties in opposite directions," is of itself a very

imperfect account of the manner in which corresponding antitheses are

involved in the portions of science into which Polar relations enter.

In excuse of its imperfection, I may say, that I believe it is the

first attempt to define Polarity in general; but yet, the conception

of Polarity has certainly been strongly and effectively present in the

minds of many of the sagacious men who have discovered and unravelled

polar phenomena. They attempted to convey this conception, each in his

own subject, sometimes by various and peculiar expressions, sometimes

by imaginary mechanism by which the antithetical results were produced;

their mode of expressing themselves being often defective or imperfect,

often containing what was superfluous; and their meaning was commonly

very imperfectly apprehended by most of their hearers and readers.

But still, the conception was there, gradually working itself into

clearness and distinctness, and in the mean time, directing their

experiments, and forming an essential element of their discoveries. So

far would it be from a sufficient statement of the case to say, that

they conceived polarity because they saw it;--that they saw it as soon

as it came into view;--and that they described it as they saw it.

35. The way in which such conceptions acquire clearness and

distinctness is often by means of Discussions of Definitions. To define

well a thought which already enters into trains of discovery, is often

a difficult matter. The business of such definition is a part of the

business of discovery. These, and other remarks connected with these,

which I had made in the _Philosophy_, Mr. Mill has quoted and adopted

(ii. 242). They appear to me to point very distinctly to the doctrine

to which he refuses his assent,--that there is a special process in the

mind, in addition to the mere observation of facts, which is necessary

at every step in the progress of knowledge. The Conception must be

_formed_ before it can be _defined_. The Definition gives the last

stamp of distinctness to the Conception; and enables us to express, in

a compact and lucid form, the new scientific propositions into which

the new Conception enters.

36. Since Mr. Mill assents to so much of what has been said in the

_Philosophy_, with regard to the process of scientific discovery, how,

it may be asked, would he express these doctrines so as to exclude that

which he thinks erroneous? If he objects to our saying that when we

obtain a new inductive truth, we connect phenomena by applying to them

a new Conception which fits them, in what terms would he describe the

process? If he will not agree to say, that in order to discover the law

of the facts, we must find an appropriate Conception, what language

would he use instead of this? This is a natural question; and the

answer cannot fail to throw light on the relation in which his views

and mine stand to each other.

Mr. Mill would say, I believe, that when we obtain a new inductive law

of facts, we find something in which the facts _resemble each other_;

and that the business of making such discoveries is the business of

discovering such resemblances. Thus, he says (of me,) (ii. 211),

"his Colligation of Facts by means of appropriate Conceptions, is

but the ordinary process of finding by a comparison of phenomena, in

what consists their agreement or resemblance." And the Methods of

experimental Inquiry which he gives (i. 450, &c.), proceed upon the

supposition that the business of discovery may be thus more properly

described.

37. There is no doubt that when we discover a law of nature by

induction, we find some point in which all the particular facts agree.

All the orbits of the planets agree in being ellipses, as Kepler

discovered; all falling bodies agree in being acted on by a uniform

force, as Galileo discovered; all refracted rays agree in having

the sines of incidence and refraction in a constant ratio, as Snell

discovered; all the bodies in the universe agree in attracting each

other, as Newton discovered; all chemical compounds agree in being

constituted of elements in definite proportions, as Dalton discovered.

But it appears to me a most scanty, vague, and incomplete account of

these steps in science, to say that the authors of them discovered

something in which the facts in each case agreed. The point in which

the cases agree, is of the most diverse kind in the different cases--in

some, a relation of space, in others, the action of a force, in others,

the mode of composition of a substance;--and the point of agreement,

visible to the discoverer alone, does not come even into his sight,

till after the facts have been connected by thoughts of his own, and

regarded in points of view in which he, by his mental acts, places

them. It would seem to me not much more inappropriate to say, that an

officer, who disciplines his men till they move together at the word of

command, does so by finding something in which they agree. If the power

of consentaneous motion did not exist in the individuals, he could not

create it: but that power being there, he finds it and uses it. Of

course I am aware that the parallel of the two cases is not exact; but

in the one case, as in the other, that in which the particular things

are found to agree, is something formed in the mind of him who brings

the agreement into view.

IV. _Mr. Mill's Four Methods of Inquiry._--38. Mr. Mill has not only

thus described the business of scientific discovery; he has also given

rules for it, founded on this description. It may be expected that we

should bestow some attention upon the methods of inquiry which he thus

proposes. I presume that they are regarded by his admirers as among the

most valuable parts of his book; as certainly they cannot fail to be,

if they describe methods of scientific inquiry in such a manner as to

be of use to the inquirer.

Mr. Mill enjoins four methods of experimental inquiry, which he calls

_the Method of Agreement_, _the Method of Difference_, _the Method

of Residues_, and _the Method of Concomitant Variations_[271]. They

are all described by formulæ of this kind:--Let there be, in the

observed facts, combinations of antecedents, _ABC_, _BC_, _ADE_, &c.

and combinations of corresponding consequents, _abc_, _bc_, _ade_, &c.;

and let the object of inquiry be, the consequence of some cause _A_, or

the cause of some consequence _a_. The Method of Agreement teaches us,

that when we find by experiment such facts as _abc_ the consequent of

_ABC_, and _ade_ the consequent of _ADE_, then _a_ is the consequent of

_A_. The Method of Difference teaches us that when we find such facts

as _abc_ the consequent of _ABC_, and _bc_ the consequent of _BC_, then

_a_ is the consequent of _A_. The Method of Residues teaches us, that

if _abc_ be the consequent of _ABC_, and if we have already ascertained

that the effect of _A_ is _a_, and the effect of _B_ is _b_, then we

may infer that the effect of _C_ is _c_. The Method of Concomitant

Variations teaches us, that if a phenomenon _a_ varies according as

another phenomenon _A_ varies, there is some connexion of causation

direct or indirect, between _A_ and _a_.

39. Upon these methods, the obvious thing to remark is, that they take

for granted the very thing which is most difficult to discover, the

reduction of the phenomena to formulæ such as are here presented to

us. When we have any set of complex facts offered to us; for instance,

those which were offered in the cases of discovery which I have

mentioned,--the facts of the planetary paths, of falling bodies, of

refracted rays, of cosmical motions, of chemical analysis; and when, in

any of these cases, we would discover the law of nature which governs

them, or, if any one chooses so to term it, the feature in which all

the cases agree, where are we to look for our _A_, _B_, _C_ and _a_,

_b_, _c_? Nature does not present to us the cases in this form; and

how are we to reduce them to this form? You say, _when_ we find the

combination of _ABC_ with _abc_ and _ABD_ with _abd_, then we may

draw our inference. Granted: but when and where are we to find such

combinations? Even now that the discoveries are made, who will point

out to us what are the _A_, _B_, _C_ and _a_, _b_, _c_ elements of the

cases which have just been enumerated? Who will tell us which of the

methods of inquiry those historically real and successful inquiries

exemplify? Who will carry these formulæ through the history of the

sciences, as they have really grown up; and show us that these four

methods have been operative in their formation; or that any light is

thrown upon the steps of their progress by reference to these formulæ?

40. Mr. Mill's four methods have a great resemblance to Bacon's

"Prerogatives of Instances;" for example, the Method of Agreement to

the _Instantiæ Ostensivæ_; the Method of Differences to the _Instantiæ

Absentiæ in Proximo_, and the _Instantiæ Crucis_; the Method of

Concomitant Variations to the _Instantiæ Migrantes_. And with regard to

the value of such methods, I believe all study of science will convince

us more and more of the wisdom of the remarks which Sir John Herschel

has made upon them[272].

"It has always appeared to us, we must confess, that the help which

the classification of instances under their different titles of

prerogative, affords to inductions, however just such classification

may be in itself, is yet more apparent than real. The force of the

instance must be felt in the mind before it can be referred to

its place in the system; and before it can be either referred or

appreciated it must be known; and when it _is_ appreciated, we are

ready enough to weave our web of induction, without greatly troubling

ourselves whence it derives the weight we acknowledge it to have in our

decisions.... No doubt such instances as these are highly instructive;

but the difficulty in physics is to find such, not to perceive their

force when found."

V. _His Examples._--41. If Mr. Mill's four methods had been applied by

him in his book to a large body of conspicuous and undoubted examples

of discovery, well selected and well analysed, extending along the

whole history of science, we should have been better able to estimate

the value of these methods. Mr. Mill has certainly offered a number

of examples of his methods; but I hope I may say, without offence,

that they appear to me to be wanting in the conditions which I have

mentioned. As I have to justify myself for rejecting Mr. Mill's

criticism of doctrines which I have put forward, and examples which I

have adduced, I may, I trust, be allowed to offer some critical remarks

in return, bearing upon the examples which he has given, in order to

illustrate his doctrines and precepts.

42. The first remark which I have to make is, that a large proportion

of his examples (i. 480, &c.) is taken from one favourite author;

who, however great his merit may be, is too recent a writer to have

had his discoveries confirmed by the corresponding investigations and

searching criticisms of other labourers in the same field, and placed

in their proper and permanent relation to established truths; these

alleged discoveries being, at the same time, principally such as deal

with the most complex and slippery portions of science, the laws of

vital action. Thus Mr. Mill has adduced, as examples of discoveries,

Prof. Liebig's doctrine--that death is produced by certain metallic

poisons through their forming indecomposable compounds; that the effect

of respiration upon the blood consists in the conversion of peroxide

of iron into protoxide--that the antiseptic power of salt arises from

its attraction for moisture--that chemical action is contagious; and

others. Now supposing that we have no doubt of the truth of these

discoveries, we must still observe that they cannot wisely be cited,

in order to exemplify the nature of the progress of knowledge, till

they have been verified by other chemists, and worked into their places

in the general scheme of chemistry; especially, since it is tolerably

certain that in the process of verification, they will be modified and

more precisely defined. Nor can I think it judicious to take so large

a proportion of our examples from a region of science in which, of all

parts of our material knowledge, the conceptions both of ordinary

persons, and even of men of science themselves, are most loose and

obscure, and the genuine principles most contested; which is the case

in physiology. It would be easy, I think, to point out the vague and

indeterminate character of many of the expressions in which the above

examples are propounded, as well as their doubtful position in the

scale of chemical generalization; but I have said enough to show why I

cannot give much weight to these, as cardinal examples of the method

of discovery; and therefore I shall not examine in detail how far they

support Mr. Mill's methods of inquiry.

43. Mr. Liebig supplies the first and the majority of Mr. Mill's

examples in chapter IX. of his Book on Induction. The second is

an example for which Mr. Mill states himself to be indebted to

Mr. Alexander Bain; the law established being this, that (i. 487)

electricity cannot exist in one body without the simultaneous

excitement of the opposite electricity in some neighbouring body, which

Mr. Mill also confirms by reference to Mr. Faraday's experiments on

voltaic wires.

I confess I am quite at a loss to understand what there is in the

doctrine here ascribed to Mr. Bain which was not known to the

electricians who, from the time of Franklin, explained the phenomena of

the Leyden vial. I may observe also that the mention of an "electrified

atmosphere" implies a hypothesis long obsolete. The essential point in

all those explanations was, that each electricity produced by induction

the opposite electricity in neighbouring bodies, as I have tried to

make apparent in the _History_[273]. Faraday has, more recently,

illustrated this universal co-existence of opposite electricities with

his usual felicity.

But the conjunction of this fact with voltaic phenomena, implies a

non-recognition of some of the simplest doctrines of the subject.

"Since," it is said (i. 488), "common or machine electricity, and

voltaic electricity may be considered for the present purpose to be

identical, Faraday wished to know, &c." I think Mr. Faraday would be

much astonished to learn that he considered electricity in equilibrium,

and electricity in the form of a voltaic current, to be, for any

purpose, identical. Nor do I conceive that he would assent to the

expression in the next page, that "from the nature of a voltaic charge,

the two opposite currents necessary to the existence of each other are

both accommodated in one wire." Mr. Faraday has, as it appears to me,

studiously avoided assenting to this hypothesis.

44. The next example is the one already so copiously dwelt upon by Sir

John Herschel, Dr. Wells's researches on the production of Dew. I have

already said[274] that "this investigation, although it has sometimes

been praised as an original discovery, was in fact only resolving the

phenomenon into principles already discovered namely, the doctrine of a

_constituent temperature_ of vapour, the different conducting power of

different bodies, and the like. And this agrees in substance with what

Mr. Mill says (i. 497); that the discovery, when made, was corroborated

by deduction from the known laws of aqueous vapour, of conduction, and

the like. Dr. Wells's researches on Dew tended much in this country

to draw attention to the general principles of Atmology; and we may

see, in this and in other examples which Mr. Mill adduces, that the

explanation of special phenomena by means of general principles,

already established, has, for common minds, a greater charm, and

is more complacently dwelt on, than the discovery of the general

principles themselves.

45. The next example, (i. 502) is given in order to illustrate the

Method of Residues, and is the discovery by M. Arago that a disk

of copper affects the vibrations of the magnetic needle. But this

apparently detached fact affords little instruction compared with the

singularly sagacious researches by which Mr. Faraday discovered the

cause of this effect to reside in the voltaic currents which the motion

of the magnetic needle developed in the copper. I have spoken of this

discovery in the _History_[275]. Mr. Mill however is quoting Sir John

Herschel in thus illustrating the Method of Residues. He rightly gives

the Perturbations of the Planets and Satellites as better examples of

the method[276].

46. In the next chapter (c. x.) Mr. Mill speaks of Plurality of causes

and of the Intermixture of effects, and gives examples of such cases.

He here teaches (i. 517) that chemical synthesis and analysis, (as when

oxygen and hydrogen compose water, and when water is resolved into

oxygen and hydrogen,) is properly _transformation_, but that because we

find that the weight of the compound is equal to the sum of the weights

of the elements, we take up the notion of chemical _composition_. I

have endeavoured to show[277] that the maxim, that the sum of the

weights of the elements is equal to the weight of the compound, was,

historically, not _proved_ from experiment, but _assumed_ in the

reasonings upon experiments.

47. I have now made my remarks upon nearly all the examples which Mr.

Mill gives of scientific inquiry, so far as they consist of knowledge

which has really been obtained. I may mention, as points which

appear to me to interfere with the value of Mr. Mill's references to

examples, expressions which I cannot reconcile with just conceptions

of scientific truth; as when he says (i. 523), "some other force which

_impinges on_ the first force;" and very frequently indeed, of the

"tangential _force_," as co-ordinate with the centripetal force.

When he speaks (ii. 20, Note) of "the doctrine now universally received

that the earth is a great natural magnet with two poles," he does not

recognize the recent theory of Gauss, so remarkably coincident with a

vast body of facts[278]. Indeed in his statement, he rejects no less

the earlier views proposed by Halley, theorized by Euler, and confirmed

by Hansteen, which show that we are compelled to assume at least _four_

poles of terrestrial magnetism; which I had given an account of in the

first edition of the _History_.

There are several other cases which he puts, in which, the knowledge

spoken of not having been yet acquired, he tells us how he would

set about acquiring it; for instance, if the question were (i. 526)

whether mercury be a cure for a given disease; or whether the brain be

a voltaic pile (ii. 21); or whether the moon be inhabited (ii. 100);

or whether all crows are black (ii. 124); I confess that I have no

expectation of any advantage to philosophy from discussions of this

kind.

48. I will add also, that I do not think any light can be thrown upon

scientific methods, at present, by grouping along with such physical

inquiries as I have been speaking of, speculations concerning the

human mind, its qualities and operations. Thus he speaks (i. 508) of

human characters, as exemplifying the effect of plurality of causes;

of (i. 518) the phenomena of our mental nature, which are analogous to

chemical rather than to dynamical phenomena; of (i. 518) the reason why

susceptible persons are imaginative; to which I may add, the passage

where he says (i. 444), "let us take as an example of a phenomenon

which we have no means of fabricating artificially, a human mind."

These, and other like examples, occur in the part of his work in which

he is speaking of scientific inquiry in general, not in the Book on the

Logic of the Moral Sciences; and are, I think, examples more likely to

lead us astray than to help our progress, in discovering the laws of

Scientific Inquiry, in the ordinary sense of the term.

VI. _Mr. Mill against Hypothesis._--49. I will now pass from Mr. Mill's

methods, illustrated by such examples as those which I have been

considering, to the views respecting the conditions of Scientific

Induction to which I have been led, by such a survey as I could

make, of the whole history of the principal Inductive Sciences; and

especially, to those views to which Mr. Mill offers his objections[279].

Mr. Mill thinks that I have been too favourable to the employment

of hypotheses, as means of discovering scientific truth; and that

I have countenanced a laxness of method, in allowing hypotheses to

be established, merely in virtue of the accordance of their results

with the phenomena. I believe I should be as cautious as Mr. Mill, in

accepting mere hypothetical explanations of phenomena, in any case in

which we had the phenomena, and their relations, placed before both of

us in an equally clear light. I have not accepted the Undulatory theory

of Heat, though recommended by so many coincidences and analogies[280].

But I see some grave reasons for not giving any great weight to Mr.

Mill's admonitions;--reasons drawn from the language which he uses on

the subject, and which appears to me inconsistent with the conditions

of the cases to which he applies it. Thus, when he says (ii. 22) that

the condition of a hypothesis accounting for all the known phenomena

is "often fulfilled equally well by two conflicting hypotheses," I can

only say that I know of no such case in the history of Science, where

the phenomena are at all numerous and complicated; and that if such

a case were to occur, one of the hypotheses might always be resolved

into the other. When he says, that "this evidence (the agreement of the

results of the hypothesis with the phenomena) cannot be of the smallest

value, because we cannot have in the case of such an hypothesis the

assurance that if the hypothesis be false it must lead to results at

variance with the true facts," we must reply, with due submission, that

we have, in the case spoken of, the most complete evidence of this;

for any change in the hypothesis would make it incapable of accounting

for the facts. When he says that "if we give ourselves the license

of inventing the causes as well as their laws, a person of fertile

imagination might devise a hundred modes of accounting for any given

fact;" I reply, that the question is about accounting for a large and

complex series of facts, of which the laws have been ascertained: and

as a test of Mr. Mill's assertion, I would propose as a challenge to

any person of fertile imagination to devise any _one_ other hypothesis

to account for the perturbations of the moon, or the coloured fringes

of shadows, besides the hypothesis by which they have actually been

explained with such curious completeness. This challenge has been

repeatedly offered, but never in any degree accepted; and I entertain

no apprehension that Mr. Mill's supposition will ever be verified by

such a performance.

50. I see additional reason for mistrusting the precision of Mr. Mill's

views of that accordance of phenomena with the results of a hypothesis,

in several others of the expressions which he uses (ii. 23). He speaks

of a hypothesis being a "_plausible_ explanation of all or most of the

phenomena;" but the case which we have to consider is where it gives an

_exact_ representation of all the phenomena in which its results can be

traced. He speaks of its being certain that the laws of the phenomena

are "_in some measure analogous_" to those given by the hypothesis; the

case to be dealt with being, that they are in every way identical. He

speaks of this analogy being certain, from the fact that the hypothesis

can be "for a moment _tenable_;" as if any one had recommended a

hypothesis which is tenable only while a small part of the facts

are considered, when it is inconsistent with others which a fuller

examination of the case discloses. I have nothing to say, and have said

nothing, in favour of hypotheses which are _not_ tenable. He says there

are many such "_harmonies_ running through the laws of phenomena in

other respects radically distinct;" and he gives as an instance, the

laws of light and heat. I have never alleged such harmonies as grounds

of theory, unless they should amount to identities; and if they should

do this, I have no doubt that the most sober thinkers will suppose

the causes to be of the same kind in the two harmonizing instances.

If chlorine, iodine and brome, or sulphur and phosphorus, have, as

Mr. Mill says, analogous properties, I should call these substances

_analogous_: but I can see no temptation to frame an hypothesis that

they are _identical_ (which he seems to fear), so long as Chemistry

proves them distinct. But any hypothesis of an analogy in the

constitution of these elements (suppose, for instance, a resemblance

in their atomic form or composition) would seem to me to have a fair

claim to trial; and to be capable of being elevated from one degree of

probability to another by the number, variety, and exactitude of the

explanations of phenomena which it should furnish.

VII. _Against prediction of Facts._--51. These expressions of Mr.

Mill have reference to a way in which hypotheses may be corroborated,

in estimating the value of which, it appears that he and I differ.

"It seems to be thought," he says (ii. 23), "that an hypothesis of

the sort in question is entitled to a more favourable reception, if,

besides accounting for the facts previously known, it has led to the

anticipation and prediction of others which experience afterwards

verified." And he adds, "Such predictions and their fulfilment are

indeed well calculated to strike the ignorant vulgar;" but it is

strange, he says, that any considerable stress should be laid upon such

a coincidence by scientific thinkers. However strange it may seem to

him, there is no doubt that the most scientific thinkers, far more than

the ignorant vulgar, have allowed the coincidence of results predicted

by theory with fact afterwards observed, to produce the strongest

effects upon their conviction; and that all the best-established

theories have obtained their permanent place in general acceptance

in virtue of such coincidences, more than of any other evidence. It

was not the ignorant vulgar alone, who were struck by the return of

Halley's comet, as an evidence of the Newtonian theory. Nor was it the

ignorant vulgar, who were struck with those facts which did so much

strike men of science, as curiously felicitous proofs of the undulatory

theory of light,--the production of darkness by two luminous rays

interfering in a special manner; the refraction of a single ray of

light into a conical pencil; and other complex yet precise results,

predicted by the theory and verified by experiment. It must, one would

think, strike all persons in proportion to their thoughtfulness, that

when Nature thus does our bidding, she acknowledges that we have learnt

her true language. If we can predict new facts which we have not seen,

as well as explain those which we have seen, it must be because our

explanation is not a mere formula of observed facts, but a truth of a

deeper kind. Mr. Mill says, "If the laws of the propagation of light

agree with those of the vibrations of an elastic fluid in so many

respects as is necessary to make the hypothesis a plausible explanation

of all or most of the phenomena known at the time, it is nothing

strange that they should accord with each other in one respect more."

Nothing strange, if the theory be true; but quite unaccountable,

if it be not. If I copy a long series of letters of which the last

half-dozen are concealed, and if I guess those aright, as is found to

be the case when they are afterwards uncovered, this must be because

I have made out the import of the inscription. To say, that because I

have copied all that I could see, it is nothing strange that I should

guess those which I cannot see, would be absurd, without supposing such

a ground for guessing. The notion that the discovery of the laws and

causes of phenomena is a loose haphazard sort of guessing, which gives

"plausible" explanations, accidental coincidences, casual "harmonies,"

laws, "in some measure analogous" to the true ones, suppositions

"tenable" for a time, appears to me to be a misapprehension of the

whole nature of science; as it certainly is inapplicable to the case to

which it is principally applied by Mr. Mill.

52. There is another kind of evidence of theories, very closely

approaching to the verification of untried predictions, and to which,

apparently, Mr. Mill does not attach much importance, since he has

borrowed the term by which I have described it, _Consilience_, but

has applied it in a different manner (ii. 530, 563, 590). I have

spoken, in the _Philosophy_[281], of the _Consilience of Inductions_,

as one of the _Tests of Hypotheses_, and have exemplified it by many

instances; for example, the theory of universal gravitation, obtained

by induction from the motions of the planets, was found to explain

also that peculiar motion of the spheroidal earth which produces the

Precession of the Equinoxes. This, I have said, was a striking and

surprising coincidence which gave the theory a stamp of truth beyond

the power of ingenuity to counterfeit. I may compare such occurrences

to a case of interpreting an unknown character, in which two different

inscriptions, deciphered by different persons, had given the same

alphabet. We should, in such a case, believe with great confidence

that the alphabet was the true one; and I will add, that I believe the

history of science offers no example in which a theory supported by

such consiliences, had been afterwards proved to be false.

53. Mr. Mill accepts (ii. 21) a rule of M. Comte's, that we may apply

hypotheses, provided they are capable of being afterwards verified as

facts. I have a much higher respect for Mr. Mill's opinion than for

M. Comte's[282]; but I do not think that this rule will be found of

any value. It appears to me to be tainted with the vice which I have

already noted, of throwing the whole burthen of explanation upon the

unexplained word _fact_--unexplained in any permanent and definite

opposition to theory. As I have said, the Newtonian theory _is_ a

fact. Every true theory is a fact. Nor does the distinction become

more clear by Mr. Mill's examples. "The vortices of Descartes would

have been," he says, "a perfectly legitimate hypothesis, if it had

been possible by any mode of explanation which we could entertain

the hope of possessing, to bring the question whether such vortices

exist or not, within the reach of our observing faculties." But this

was possible, and was done. The free passage of comets through the

spaces in which these vortices should have been, convinced men that

these vortices did not exist. In like manner Mr. Mill rejects the

hypothesis of a luminiferous ether, "because it can neither be seen,

heard, smelt, tasted, or touched." It is a strange complaint to make of

the vehicle of light, that it cannot be heard, smelt, or tasted. Its

vibrations _can_ be seen. The fringes of shadows for instance, show its

vibrations, just as the visible lines of waves near the shore show the

undulations of the sea. Whether this can be touched, that is, whether

it resists motion, is hardly yet clear. I am far from saying there are

not difficulties on this point, with regard to _all_ theories which

suppose a _medium_. But there are no more difficulties of this kind in

the undulatory theory of light, than there are in Fourier's theory of

heat, which M. Comte adopts as a model of scientific investigation; or

in the theory of voltaic _currents_, about which Mr. Mill appears to

have no doubt; or of electric _atmospheres_, which, though generally

obsolete, Mr. Mill appears to favour; for though it had been said that

we _feel_ such atmospheres, no one had said that they have the other

attributes of matter.

VIII. _Newton's Vera Causa._--54. Mr. Mill conceives (ii. 17) that his

own rule concerning hypotheses coincides with Newton's Rule, that the

cause assumed must be a _vera causa_. But he allows that "Mr. Whewell

... has had little difficulty in showing that his (Newton's) conception

was neither precise nor consistent with itself." He also allows that

"Mr. Whewell is clearly right in denying it to be necessary that the

cause assigned should be a cause already known; else how could we ever

become acquainted with new causes?" These points being agreed upon, I

think that a little further consideration will lead to the conviction

that Newton's Rule of philosophizing will best become a valuable guide,

if we understand it as asserting that when the explanation of two or

more different kinds of phenomena (as the revolutions of the planets,

the fall of a stone, and the precession of the equinoxes,) lead us to

_the same_ cause, such a coincidence gives a reality to the cause. We

have, in fact, in such a case, a Consilience of Inductions.

55. When Mr. Mill condemns me (ii. 24) (using, however, expressions of

civility which I gladly acknowledge,) for having recognized no mode of

Induction except that of trying hypothesis after hypothesis until one

is found which fits the phenomena, I must beg to remind the readers of

our works, that Mr. Mill himself allows (i. 363) that the process of

finding a conception which binds together observed facts "is tentative,

that it consists of a succession of guesses, many being rejected until

one at last occurs fit to be chosen." I must remind them also that I

have given a Section upon the _Tests of Hypotheses_, to which I have

just referred,--that I have given various methods of Induction, as

the _Method of Gradation_, the _Method of Natural Classification_,

the _Method of Curves_, the _Method of Means_, the _Method of Least

Squares_, the _Method of Residues_: all which I have illustrated by

conspicuous examples from the History of Science; besides which, I

conceive that what I have said of the Ideas belonging to each science,

and of the construction and explication of conceptions, will point

out in each case, in what region we are to look for the Inductive

Element in order to make new discoveries. I have already ventured to

say, elsewhere, that the methods which I have given, are as definite

and practical as any others which have been proposed, with the

great additional advantage of being the methods by which all great

discoveries in science have really been made.

IX. _Successive Generalizations._--56. There is one feature in the

construction of science which Mr. Mill notices, but to which he does

not ascribe, as I conceive, its due importance: I mean, that process by

which we not only ascend from particular facts to a general law, but

when this is done, ascend from the first general law to others more

general; and so on, proceeding to the highest point of generalization.

This character of the scientific process was first clearly pointed

out by Bacon, and is one of the most noticeable instances of his

philosophical sagacity. "There are," he says, "two ways, and can

be only two, of seeking and finding truth. The one from sense and

particulars, takes a flight to the most general axioms, and from these

principles and their truth, settled once for all, invents and judges of

intermediate axioms. The other method collects axioms from sense and

particulars, ascending _continuously and by degrees_, so that in the

end it arrives at the most general axioms:" meaning by _axioms_, laws

or principles. The structure of the most complete sciences consists

of several such steps,--_floors_, as Bacon calls them, of successive

generalization; and thus this structure may be exhibited as a kind

of scientific pyramid. I have constructed this pyramid in the case

of the science of Astronomy[283]: and I am gratified to find that

the illustrious Humboldt approves of the design, and speaks of it as

executed with complete success[284]. The capability of being exhibited

in this form of successive generalizations, arising from particulars

upward to some very general law, is the condition of all tolerably

perfect sciences; and the steps of the successive generalizations are

commonly the most important events in the history of the science.

57. Mr. Mill does not reject this process of generalization; but he

gives it no conspicuous place, making it only one of three modes of

reducing a law of causation into other laws. "There is," he says (i.

555), "the _subsumption_ of one law under another; ... the gathering up

of several laws into one more general law which includes them all. He

adds afterwards, that the general law is the _sum_ of the partial ones

(i. 557), an expression which appears to me inadequate, for reasons

which I have already stated. The general law is not the mere sum of

the particular laws. It is, as I have already said, their amount _in a

new point of view_. A new conception is introduced; thus, Newton did

not merely add together the laws of the motions of the moon and of the

planets, and of the satellites, and of the earth; he looked at them

altogether as the result of a universal force of mutual gravitation;

and therein consisted his generalization. And the like might be pointed

out in other cases.

58. I am the more led to speak of Mr. Mill as not having given due

importance to this process of successive generalization, by the way in

which he speaks in another place (ii. 525) of this doctrine of Bacon.

He conceives Bacon "to have been radically wrong when he enunciates,

as a universal rule, that induction should proceed from the lowest to

the middle principles, and from those to the highest, never reversing

that order, and consequently, leaving no room for the discovery of new

principles by way of deduction[285] at all."

59. I conceive that the Inductive Table of Astronomy, to which I have

already referred, shows that in that science,--the most complete which

has yet existed,--the history of the science has gone on, as to its

general movement, in accordance with the view which Bacon's sagacity

enjoined. The successive generalizations, _so far as they were true_,

were made by successive generations. I conceive also that the Inductive

Table of Optics shows the same thing; and this, without taking for

granted the truth of the Undulatory Theory; for with regard to all the

steps of the progress of the science, lower than that highest one,

there is, I conceive, no controversy.

60. Also, the Science of Mechanics, although Mr. Mill more especially

refers to it, as a case in which the highest generalizations (for

example the Laws of Motion) were those earliest ascertained with any

scientific exactness, will, I think, on a more careful examination of

its history, be found remarkably to confirm Bacon's view. For, in that

science, we have, in the first place, very conspicuous examples of the

vice of the method pursued by the ancients in flying to the highest

generalizations first; as when they made their false distinctions of

the laws of _natural_ and _violent_ motions, and of _terrestrial_

and _celestial_ motions. Many erroneous laws of motion were asserted

through neglect of facts or want of experiments. And when Galileo and

his school had in some measure succeeded in discovering some of the

true laws of the motions of terrestrial bodies, they did not at once

assert them as general: for they did not at all apply those laws to

the celestial motions. As I have remarked, all Kepler's speculations

respecting the causes of the motions of the planets, went upon the

supposition that the First Law of terrestrial Motion did not apply to

celestial bodies; but that, on the contrary, some continual force was

requisite to keep up, as well as to originate, the planetary motions.

Nor did Descartes, though he enunciated the Laws of Motion with more

generality than his predecessors, (but not with exactness,) venture

to trust the planets to those laws; on the contrary, he invented his

machinery of Vortices in order to keep up the motions of the heavenly

bodies. Newton was the first who extended the laws of terrestrial

motion to the celestial spaces; and in doing so, he used all the laws

of the celestial motions which had previously been discovered by

more limited inductions. To these instances, I may add the gradual

generalization of the Third Law of motion by Huyghens, the Bernoullis,

and Herman, which I have described in the _History_[286] as preceding

that Period of Deduction, to which the succeeding narrative[287] is

appropriated. In Mechanics, then, we have a cardinal example of the

historically gradual and successive ascent of science from particulars

to the most general laws.

61. The Science of Hydrostatics may appear to offer a more favourable

example of the ascent to the most general laws, without going through

the intermediate particular laws; and it is true, with reference

to this science, as I have observed[288], that it does exhibit the

_peculiarity_ of our possessing the most general principles on which

the phenomena depend, and from which many cases of special facts are

explained by deduction; while other cases cannot be so explained,

from the want of principles intermediate between the highest and the

lowest. And I have assigned, as the reason of this peculiarity, that

the general principles of the Mechanics of Fluids were not obtained

with reference to the science itself, but by extension from the sister

science of the Mechanics of Solids. The two sciences are parts of the

same Inductive Pyramid; and having reached the summit of this Pyramid

on one side, we are tempted to descend on the other from the highest

generality to more narrow laws. Yet even in this science, the best

part of our knowledge is mainly composed of inductive laws, obtained

by inductive examination of particular classes of facts. The mere

mathematical investigations of the laws of waves, for instance, have

not led to any results so valuable as the experimental researches of

Bremontier, Emy, the Webers, and Mr. Scott Russell. And in like manner

in Acoustics, the Mechanics of Elastic Fluids[289], the deductions of

mathematicians made on general principles have not done so much for

our knowledge, as the cases of vibrations of plates and pipes examined

experimentally by Chladni, Savart, Mr. Wheatstone and Mr. Willis. We

see therefore, even in these sciences, no reason to slight the wisdom

which exhorts us to ascend from particulars to intermediate laws,

rather than to hope to deduce these latter better from the more general

laws obtained once for all.

62. Mr. Mill himself indeed, notwithstanding that he slights Bacon's

injunction to seek knowledge by proceeding from less general to more

general laws, has given a very good reason why this is commonly

necessary and wise. He says (ii. 526), "Before we attempt to explain

deductively, from more general laws, any new class of phenomena, it is

desirable to have gone as far as is practicable in ascertaining the

empirical laws of these phenomena; so as to compare the results of

deduction, not with one individual instance after another, but with

general propositions expressive of the points of agreement which have

been found among many instances. For," he adds with great justice,

"if Newton had been obliged to verify the theory of gravitation, not

by deducing from it Kepler's laws, but by deducing all the observed

planetary positions which had served Kepler to establish those laws,

the Newtonian theory would probably never have emerged from the state

of an hypothesis." To which we may add, that it is certain, from the

history of the subject, that in that case the hypothesis would never

have been framed at all.

X. _Mr. Mill's Hope from Deduction._--63. Mr. Mill expresses a hope

of the efficacy of Deduction, rather than Induction, in promoting

the future progress of Science; which hope, so far as the physical

sciences are concerned, appears to me at variance with all the lessons

of the history of those sciences. He says (i. 579), "that the advances

henceforth to be expected even in physical, and still more in mental

and social science, will be chiefly the result of deduction, is evident

from the general considerations already adduced:" these considerations

being, that the phenomena to be considered are very complex, and are

the result of many known causes, of which we have to disentangle the

results.

64. I cannot but take a very different view from this. I think that

any one, looking at the state of physical science, will see that there

are still a vast mass of cases, in which we do not at all know the

causes, at least, in their full generality; and that the knowledge of

new causes, and the generalization of the laws of those already known,

can only be obtained by new _inductive_ discoveries. Except by new

Inductions, equal, in their efficacy for grouping together phenomena

in new points of view, to any which have yet been performed in the

history of science, how are we to solve such questions as those which,

in the survey of what we already know, force themselves upon our minds?

Such as, to take only a few of the most obvious examples--What is the

nature of the connexion of heat and light? How does heat produce the

expansion, liquefaction and vaporization of bodies? What is the nature

of the connexion between the optical and the chemical properties of

light? What is the relation between optical, crystalline and chemical

polarity? What is the connexion between the atomic constitution and

the physical qualities of bodies? What is the tenable definition of a

mineral species? What is the true relation of the apparently different

types of vegetable life (monocotyledons, dicotyledons, and cryptogamous

plants)? What is the relation of the various types of animal life

(vertebrates, articulates, radiates, &c.)? What is the number, and

what are the distinctions of the Vital Powers? What is the internal

constitution of the earth? These, and many other questions of equal

interest, no one, I suppose, expects to see solved by deduction from

principles already known. But we can, in many of them, see good hope of

progress by a large use of induction; including, of course, copious and

careful experiments and observations.

65. With such questions before us, as have now been suggested, I

can see nothing but a most mischievous narrowing of the field and

enfeebling of the spirit of scientific exertion, in the doctrine that

"Deduction is the great scientific work of the present and of future

ages;" and that "A revolution is peaceably and progressively effecting

itself in philosophy the reverse of that to which Bacon has attached

his name." I trust, on the contrary, that we have many new laws of

nature still to discover; and that our race is destined to obtain a

sight of wider truths than any we yet discern, including, as cases, the

general laws we now know, and obtained from these known laws as they

must be, by Induction.

66. I can see, however, reasons for the comparatively greater favour

with which Mr. Mill looks upon Deduction, in the views to which he has

mainly directed his attention. The explanation of remarkable phenomena

by known laws of Nature, has, as I have already said, a greater charm

for many minds than the discovery of the laws themselves. In the case

of such explanations, the problem proposed is more definite, and the

solution more obviously complete. For the process of induction includes

a mysterious step, by which we pass from particulars to generals,

of which step the reason always seems to be inadequately rendered

by any words which we can use; and this step to most minds is not

demonstrative, as to few is it given to perform it on a great scale.

But the process of explanation of facts by known laws is deductive,

and has at every step a force like that of demonstration, producing

a feeling peculiarly gratifying to the clear intellects which are

most capable of following the process. We may often see instances in

which this admiration for deductive skill appears in an extravagant

measure; as when men compare Laplace with Newton. Nor should I think

it my business to argue against such a preference, unless it were

likely to leave us too well satisfied with what we know already, to

chill our hope of scientific progress, and to prevent our making any

further strenuous efforts to ascend, higher than we have yet done, the

mountain-chain which limits human knowledge.

67. But there is another reason which, I conceive, operates in leading

Mr. Mill to look to Deduction as the principal means of future progress

in knowledge, and which is a reason of considerable weight in the

subjects of research which, as I conceive, he mainly has in view. In

the study of our own minds and of the laws which govern the history of

society, I do not think that it is very likely that we shall hereafter

arrive at any wider principles than those of which we already possess

some considerable knowledge; and this, for a special reason; namely,

that our knowledge in such cases is not gathered by mere external

observation of a collection of external facts; but acquired by

attention to internal facts, our own emotions, thoughts, and springs of

action; facts are connected by ties existing in our own consciousness,

and not in mere observed juxtaposition, succession, or similitude.

How the character, for instance, is influenced by various causes, (an

example to which Mr. Mill repeatedly refers, ii. 518, &c.), is an

inquiry which may perhaps be best conducted by considering what we know

of the influence of education and habit, government and occupation,

hope and fear, vanity and pride, and the like, upon men's characters,

and by tracing the various effects of the intermixture of such

influences. Yet even here, there seems to be room for the discovery

of laws in the way of experimental inquiry: for instance, what share

race or family has in the formation of character; a question which can

hardly be solved to any purpose in any other way than by collecting

and classing instances. And in the same way, many of the principles

which regulate the material wealth of states, are obtained, if not

exclusively, at least most clearly and securely, by induction from

large surveys of facts. Still, however, I am quite ready to admit that

in Mental and Social Science, we are much less likely than in Physical

Science, to obtain new truths by any process which can be distinctively

termed _Induction_; and that in those sciences, what may be called

_Deductions_ from principles of thought and action of which we are

already conscious, or to which we assent when they are felicitously

picked out of our thoughts and put into words, must have a large share;

and I may add, that this observation of Mr. Mill appears to me to be

important, and, in its present connexion, new.

XI. _Fundamental opposition of our doctrines._--68. I have made nearly

all the remarks which I now think it of any consequence to make upon

Mr. Mill's _Logic_, so far as it bears upon the doctrines contained

in my _History_ and _Philosophy_. And yet there remains still

untouched one great question, involving probably the widest of all the

differences between him and me. I mean the question whether geometrical

axioms, (and, as similar in their evidence to these, _all_ axioms,) be

truths derived from experience, or be necessary truths in some deeper

sense. This is one of the fundamental questions of philosophy; and all

persons who take an interest in metaphysical discussions, know that the

two opposite opinions have been maintained with great zeal in all ages

of speculation. To me it appears that there are _two_ distinct elements

in our knowledge, Experience, without, and the Mind, within. Mr. Mill

derives all our knowledge from Experience _alone_. In a question thus

going to the root of all knowledge, the opposite arguments must needs

cut deep on both sides. Mr. Mill cannot deny that our knowledge of

geometrical axioms and the like, _seems_ to be _necessary_. I cannot

deny that our knowledge, axiomatic as well as other, _never is_

acquired _without experience_.

69. Perhaps ordinary readers may despair of following our reasonings,

when they find that they can only be made intelligible by supposing,

on the one hand, a person who thinks distinctly and yet has never seen

or felt any external object; and on the other hand, a person who is

transferred, as Mr. Mill supposes (ii. 117), to "distant parts of the

stellar regions where the phenomena may be entirely unlike those with

which we are acquainted," and where even the axiom, that every effect

must have a cause, does not hold good. Nor, in truth, do I think it

necessary here to spend many words on this subject. Probably, for those

who take an interest in this discussion, most of the arguments on each

side have already been put forwards with sufficient repetition. I have,

in an "Essay on the Fundamental Antithesis of Philosophy," and in some

accompanying "Remarks," printed[290] at the end of the second edition

of my _Philosophy_, given my reply to what has been said on this

subject, both by Mr. Mill, and by the author of a very able critique on

my _History_ and _Philosophy_ which appeared in the _Quarterly Review_

in 1841: and I will not here attempt to revive the general discussion.

70. Perhaps I may be allowed to notice, that in one part of Mr. Mill's

work where this subject is treated, there is the appearance of one of

the parties to the controversy pronouncing judgment in his own cause.

This indeed is a temptation which it is especially difficult for an

author to resist, who writes a treatise upon _Fallacies_, the subject

of Mr. Mill's fifth Book. In such a treatise, the writer has an easy

way of disposing of adverse opinions by classing them as "Fallacies,"

and putting them side by side with opinions universally acknowledged to

be false. In this way, Mr. Mill has dealt with several points which are

still, as I conceive, matters of controversy (ii. 357, &c.).

71. But undoubtedly, Mr. Mill has given his argument against my

opinions with great distinctness in another place (i. 319). In order

to show that it is merely habitual association which gives to an

experimental truth the character of a necessary truth, he quotes

the case of the laws of motion, which were really discovered from

experiment, but are now looked upon as the only conceivable laws; and

especially, what he conceives as "the _reductio ad absurdum_ of the

theory of inconceivableness," an opinion which I had ventured to throw

out, that if we could conceive the Composition of bodies distinctly,

we might be able to see that it is necessary that the modes of their

composition should be definite. I do not think that readers in general

will see anything absurd in the opinion, that the laws of Mechanics,

and even the laws of the Chemical Composition of bodies, may depend

upon principles as necessary as the properties of space and number; and

that this necessity, though not at all perceived by persons who have

only the ordinary obscure and confused notions on such subjects, may

be evident to a mind which has, by effort and discipline, rendered its

ideas of Mechanical Causation, Elementary Composition and Difference of

Kind, clear and precise. It may easily be, I conceive, that while such

necessary principles are perceived to be necessary only by a few minds

of highly cultivated insight, such principles as the axioms of Geometry

and Arithmetic may be perceived to be necessary by _all_ minds which

have any habit of abstract thought at all: and I conceive also, that

though these axioms are brought into distinct view by a certain degree

of intellectual cultivation, they may still be much better described

as conditions of experience, than as results of experience:--as laws

of the mind and of its activity, rather than as facts impressed upon a

mind merely passive.

XII. _Absurdities in Mr. Mill's Logic._--72. I will not pursue the

subject further: only, as the question has arisen respecting the

absurdities to which each of the opposite doctrines leads, I will point

out opinions connected with this subject, which Mr. Mill has stated in

various parts of his book.

He holds (i. 317) that it is merely from habit that we are unable to

conceive the _last point_ of space or the _last instant_ of time.

He holds (ii. 360) that it is strange that any one should rely upon

the _à priori_ evidence that space or extension is infinite, or that

nothing can be made of nothing. He holds (i. 304) that the first law

of _motion_ is _rigorously true_, but that the axioms respecting

the _lever_ are only _approximately_ true. He holds (ii. 110) that

there may be sidereal firmaments in which events succeed each other

at random, without obeying any laws of causation; although one might

suppose that even if space and cause are both to have their limits,

still they might terminate together: and then, even on this bold

supposition, we should no _where_ have a world in which events were

_casual_. He holds (ii. 111) that the axiom, that every event must

have a cause, is established by means of an "induction by simple

enumeration:" and in like manner, that the principles of number and

of geometry are proved by this method of simple enumeration alone. He

ascribes the proof (i. 162) of the axiom, "things which are equal to

the same are equal to each other," to the fact that this proposition

has been perpetually _found_ true and never false. He holds (i. 338)

that "In all propositions concerning numbers, a condition is implied,

without which none of them would be true; and that condition is an

assumption which _may be false_. _The condition is that_ 1 = 1."

73. Mr. Mill further holds (i. 309), that it is a characteristic

property of geometrical forms, that they are capable of being painted

in the imagination with a distinctness equal to reality:--that our

ideas of forms exactly resemble our sensations: which, it is implied,

is not the case with regard to any other class of our ideas;--that we

thus may have mental pictures of all possible combinations of lines

and angles, which are as fit subjects of geometrical experimentation

as the realities themselves. He says, that "we know that the imaginary

lines exactly resemble real ones;" and that we obtain this knowledge

respecting the characteristic property of the idea of space by

experience; though it does not appear _how_ we can compare our _ideas_

with the _realities_, since we know the realities only _by_ our ideas;

or why this property of their resemblance should be confined to _one

class_ of ideas alone.

74. I have now made such remarks as appear to me to be necessary, on

the most important parts of Mr. Mill's criticism of my _Philosophy_. I

hope I have avoided urging any thing in a contentious manner; as I have

certainly written with no desire of controversy, but only with a view

to offer to those who may be willing to receive it, some explanation of

portions of my previous writings. I have already said, that if this had

not have been my especial object, I could with pleasure have noted the

passages of Mr. Mill's _Logic_ which I admire, rather than the points

in which we differ. I will in a very few words refer to some of these

points, as the most agreeable way of taking leave of the dispute.

I say then that Mr. Mill appears to me especially instructive in

his discussion of the nature of the proof which is conveyed by the

syllogism; and that his doctrine, that the force of the syllogism

consists in an _inductive assertion, with an interpretation added

to it_, solves very happily the difficulties which baffle the

other theories of this subject. I think that this doctrine of his

is made still more instructive, by his excepting from it the cases

of Scriptural Theology and of Positive Law (i. 260), as cases in

which general propositions, not particular facts, are our original

data. I consider also that the recognition of _Kinds_ (i. 166) as

classes in which we have, not a finite but an _inexhaustible_ body of

resemblances among individuals, and as groups made by nature, not by

mere definition, is very valuable, as stopping the inroad to an endless

train of false philosophy. I conceive that he takes the right ground

in his answer to Hume's argument against miracles (ii. 183): and I

admire the acuteness with which he has criticized Laplace's tenets on

the Doctrine of Chances, and the candour with which he has, in the

second edition, acknowledged oversights on this subject made in the

first. I think that much, I may almost say all, which he says on the

subject of Language, is very philosophical; for instance, what he says

(ii. 238) of the way in which words acquire their meaning in common

use. I especially admire the acuteness and force with which he has

shown (ii. 255) how moral principles expressed in words degenerate into

formulas, and yet how the formula cannot be rejected without a moral

loss. This "perpetual oscillation in spiritual truths," as he happily

terms it, has never, I think, been noted in the same broad manner,

and is a subject of most instructive contemplation. And though I have

myself refrained from associating moral and political with physical

science in my study of the subject, I see a great deal which is full of

promise for the future progress of moral and political knowledge in Mr.

Mill's sixth Book, "On the Logic of the Moral and Political Sciences."

Even his arrangement of the various methods which have been or may

be followed in "the Social Science,"--"the Chemical or Experimental

Method," "the Geometrical or Abstract Method," "the Physical or

Concrete Deductive Method," "the Inverse Deductive or Historical

Method," though in some degree fanciful and forced, abounds with

valuable suggestions; and his estimate of "the interesting philosophy

of the Bentham school," the main example of "the geometrical method,"

is interesting and philosophical. On some future occasion, I may,

perhaps, venture into the region of which Mr. Mill has thus essayed

to map the highways: for it is from no despair either of the great

progress to be made in such truth as that here referred to, or of the

effect of philosophical method in arriving at such truth, that I have,

in what I have now written, confined myself to the less captivating but

more definite part of the subject.

FOOTNOTES:

[Footnote 264: [_A System of Logic, Ratiocinative and Inductive, being

a connected view of the Principles of Evidence, and of the Methods of

Scientific Investigation._ By John Stuart Mill.]]

[Footnote 265: These Remarks were published in 1849, under the title

_Of Induction, with especial reference to Mr. J. S. Mill's System of

Logic_.]

[Footnote 266: My references are throughout (except when otherwise

expressed) to the volume and the page of Mr. Mill's first edition of

his _Logic_.]

[Footnote 267: On this subject see an Essay _On the Transformation of

Hypotheses_, given in the Appendix.]

[Footnote 268: B. vii. c. iii. sect. 3.]

[Footnote 269: B. iii. c. ix. art. 7.]

[Footnote 270: B. i. c. iii.]

[Footnote 271: B. iii. c. viii.]

[Footnote 272: _Discourse_, Art. 192.]

[Footnote 273: B. xi. c. xi.]

[Footnote 274: _Phil._ b. xiii. c. ix. art. 7.]

[Footnote 275: B. xiii. c. viii.]

[Footnote 276: Given also in the _Phil. Ind. Sc._ b. xiii. c. vii.

sect. 17.]

[Footnote 277: _Ibid._ b. vi. c. iv.]

[Footnote 278: See _Hist. Ind. Sc._ b. xii. note D, in the second

edition.]

[Footnote 279: There are some points in my doctrines on the subject

of the Classificatory Sciences to which Mr. Mill objects, (ii. 314,

&c.), but there is nothing which I think it necessary to remark here,

except one point. After speaking of Classification of organized beings

in general, Mr. Mill notices (ii. 321) as an additional subject, the

arrangement of natural groups into a Natural Series; and he says, that

"all who have attempted a theory of natural arrangement, including

among the rest Mr. Whewell, have stopped short of this: all except M.

Comte." On this I have to observe, that I stopped short of, or rather

passed by, the doctrine of a Series of organized beings, because I

thought it bad and narrow philosophy: and that I sufficiently indicated

that I did this. In the _History_ (b. xvi. c. vi.) I have spoken of the

doctrine of Circular Progression propounded by Mr. Macleay, and have

said, "so far as this view _negatives_ a mere _linear_ progression in

nature, which would place each genus in contact with the preceding and

succeeding ones, and so far as it requires us to attend to the more

varied and ramified resemblances, there can be no doubt that it is

supported by the result of all the attempts to form natural systems."

And with regard to the difference between Cuvier and M. de Blainville,

to which Mr. Mill refers (ii. 321), I certainly cannot think that M.

Comte's suffrage can add any weight to the opinion of either of those

great naturalists.]

[Footnote 280: _Hist. Ind. Sc._ b. x. note (VA) in the second edition.]

[Footnote 281: B. xi. c. v. art. 11.]

[Footnote 282: I have given elsewhere (see last chapter) reasons why I

cannot assign to M. Comte's _Philosophie Positive_ any great value as a

contribution to the philosophy of science. In this judgment I conceive

that I am supported by the best philosophers of our time. M. Comte

owes, I think, much of the notice which has been given to him to his

including, as Mr. Mill does, the science of society and of human nature

in his scheme, and to his boldness in dealing with these. He appears

to have been received with deference as a mathematician: but Sir John

Herschel has shown that a supposed astronomical discovery of his is a

mere assumption. I conceive that I have shown that his representation

of the history of science is erroneous, both in its details and in its

generalities. His distinction of the three stages of sciences, the

theological, metaphysical, and positive, is not at all supported by the

facts of scientific history. Real discoveries always involve what he

calls _metaphysics_; and the doctrine of final causes in physiology,

the main element of science which can properly be called _theological_,

is retained at the end, as well as the beginning of the science, by all

except a peculiar school.]

[Footnote 283: I have also, in the same place, given the Inductive

Pyramid for the science of Optics. These Pyramids are necessarily

inverted in their form, in order that, in reading in the ordinary way,

we may proceed _to_ the vertex. _Phil. Ind. Sc._ b. xi. c. vi.]

[Footnote 284: _Cosmos_, vol. ii. note 35.]

[Footnote 285: The reader will probably recollect that as _Induction_

means the inference of general propositions from particular cases,

_Deduction_ means the inference by the application of general

propositions to particular cases, and by combining such applications;

as when from the most general principles of Geometry or of Mechanics,

we prove some less general theorem; for instance, the number of the

possible regular solids, or the principle of _vis viva_.]

[Footnote 286: B. vi. c. v.]

[Footnote 287: c. vi.]

[Footnote 288: _Hist._ b. vi. c. vi. sect. 13.]

[Footnote 289: _Hist. Ind. Sc._ b. viii.]

[Footnote 290: Reprinted in the Appendix to this volume.]