In every act of my knowledge, there must be concerned the things

whereof I know, and thoughts of me who know: I must both passively

receive or have received impressions, and I must actively combine

them and reason on them. No apprehension of things is purely ideal:

no experience of external things is purely sensational. If they

be conceived as _things_, the mind must have been awakened to the

conviction of things by sensation: if they be _conceived_ as things,

the expressions of the senses must have been bound together by

conceptions. If we _think_ of any _thing_, we must recognize the

existence both of thoughts and of things. _The fundamental antithesis

of philosophy is an antithesis of inseparable elements._

10. Not only cannot these elements be separately exhibited, but they

cannot be separately conceived and described. The description of them

must always imply their relation; and the names by which they are

denoted will consequently always bear a relative significance. And thus

_the terms which denote the fundamental antithesis of philosophy cannot

be applied absolutely and exclusively in any case_. We may illustrate

this by a consideration of some of the common modes of expressing the

antithesis of which we speak. The terms Theory and Fact are often

emphatically used as opposed to each other: and they are rightly so

used. But yet it is impossible to say absolutely in any case, This is

a Fact and not a Theory; this is a Theory and not a Fact, meaning by

Theory, true Theory. Is it a fact or a theory that the stars appear

to revolve round the pole? Is it a fact or a theory that the earth is

a globe revolving round its axis? Is it a fact or a theory that the

earth revolves round the sun? Is it a fact or a theory that the sun

attracts the earth? Is it a fact or a theory that a loadstone attracts

a needle? In all these cases, some persons would answer one way and

some persons another. A person who has never watched the stars, and has

only seen them from time to time, considers their circular motion round

the pole as a theory, just as he considers the motion of the sun in the

ecliptic as a theory, or the apparent motion of the inferior planets

round the sun in the zodiac. A person who has compared the measures of

different parts of the earth, and who knows that these measures cannot

be conceived distinctly without supposing the earth a globe, considers

its globular form a fact, just as much as the square form of his

chamber. A person to whom the grounds of believing the earth to revolve

round its axis and round the sun, are as familiar as the grounds for

believing the movements of the mail-coaches in this country, conceives

the former events to be facts, just as steadily as the latter. And a

person who, believing the fact of the earth's annual motion, refers it

distinctly to its mechanical course, conceives the sun's attraction as

a fact, just as he conceives as a fact the action of the wind which

turns the sails of a mill. We see then, that in these cases we cannot

apply absolutely and exclusively either of the terms, Fact or Theory.

Theory and Fact are the elements which correspond to our Ideas and our

Senses. The Facts are facts so far as the Ideas have been combined with

the sensations and absorbed in them: the Theories are Theories so far

as the Ideas are kept distinct from the sensations, and so far as it is

considered as still a question whether they can be made to agree with

them. A true Theory is a fact, a Fact is a familiar theory.

In like manner, if we take the terms Reasoning and Observation; at

first sight they appear to be very distinct. Our observation of the

world without us, our reasonings in our own minds, appear to be clearly

separated and opposed. But yet we shall find that we cannot apply

these terms absolutely and exclusively. I see a book lying a few feet

from me: is this a matter of observation? At first, perhaps, we might

be inclined to say that it clearly is so. But yet, all of us, who

have paid any attention to the process of vision, and to the mode in

which we are enabled to judge of the distance of objects, and to judge

them to be distant objects at all, know that this judgment involves

inferences drawn from various sensations;--from the impressions on

our two eyes;--from our muscular sensations; and the like. These

inferences are of the nature of reasoning, as much as when we judge of

the distance of an object on the other side of a river by looking at

it from different points, and stepping the distance between them. Or

again: we observe the setting sun illuminate a gilded weathercock; but

this is as much a matter of reasoning as when we observe the phases of

the moon, and infer that she is illuminated by the sun. All observation

involves inferences, and inference is reasoning.

11. Even the simplest terms by which the antithesis is expressed cannot

be applied: ideas and sensations, thoughts and things, subject and

object, cannot in any case be applied absolutely and exclusively. Our

sensations require ideas to bind them together, namely, ideas of space,

time, number, and the like. If not so bound together, sensations do not

give us any apprehension of things or objects. All things, all objects,

must exist in space and in time--must be one or many. Now space, time,

number, are not sensations or things. They are something different

from, and opposed to sensations and things. We have termed them ideas.

It may be said they are _relations_ of things, or of sensations. But

granting this form of expression, still a _relation_ is not a thing

or a sensation; and therefore we must still have another and opposite

element, along with our sensations. And yet, though we have thus these

two elements in every act of perception, we cannot designate any

portion of the act as absolutely and exclusively belonging to one of

the elements. Perception involves sensation, along with ideas of time,

space, and the like; or, if any one prefers the expression, involves

sensations along with the apprehension of relations. Perception is

sensation, along with such ideas as make sensation into an apprehension

of things or objects.

12. And as perception of objects implies ideas, as observation implies

reasoning; so, on the other hand, ideas cannot exist where sensation

has not been: reasoning cannot go on when there has not been previous

observation. This is evident from the necessary order of development

of the human faculties. Sensation necessarily exists from the first

moments of our existence, and is constantly at work. Observation

begins before we can suppose the existence of any reasoning which is

not involved in observation. Hence, at whatever period we consider

our ideas, we must consider them as having been already engaged in

connecting our sensations, and as modified by this employment. By being

so employed, our ideas are unfolded and defined, and such development

and definition cannot be separated from the ideas themselves. We

cannot conceive space without boundaries or forms; now forms involve

sensations. We cannot conceive time without events which mark the

course of time; but events involve sensations. We cannot conceive

number without conceiving things which are numbered; and things imply

sensations. And the forms, things, events, which are thus implied in

our ideas, having been the objects of sensation constantly in every

part of our life, have modified, unfolded and fixed our ideas, to

an extent which we cannot estimate, but which we must suppose to be

essential to the processes which at present go on in our minds. We

cannot say that objects create ideas; for to perceive objects we must

already have ideas. But we may say, that objects and the constant

perception of objects have so far modified our ideas, that we cannot,

even in thought, separate our ideas from the perception of objects.

We cannot say of any ideas, as of the idea of space, or time, or

number, that they are absolutely and exclusively ideas. We cannot

conceive what space, or time, or number would be in our minds, if we

had never perceived any thing or things in space or time. We cannot

conceive ourselves in such a condition as never to have perceived any

thing or things in space or time. But, on the other hand, just as

little can we conceive ourselves becoming acquainted with space and

time or numbers as objects of sensation. We cannot reason without

having the operations of our minds affected by previous sensations; but

we cannot conceive reasoning to be merely a series of sensations. In

order to be used in reasoning, sensation must become observation; and,

as we have seen, observation already involves reasoning. In order to

be connected by our ideas, sensations must be things or objects, and

things or objects already include ideas. And thus, as we have said,

none of the terms by which the fundamental antithesis is expressed can

be absolutely and exclusively applied.

13. I now proceed to make one or two remarks suggested by the views

which have thus been presented. And first I remark, that since, as

we have just seen, none of the terms which express the fundamental

antithesis can be applied absolutely and exclusively, the absolute

application of the antithesis in any particular case can never be a

conclusive or immoveable principle. This remark is the more necessary

to be borne in mind, as the terms of this antithesis are often used

in a vehement and peremptory manner. Thus we are often told that such

a thing is a _Fact_ and not a Theory, with all the emphasis which, in

speaking or writing, tone or italics or capitals can give. "We see from

what has been said, that when this is urged, before we can estimate the

truth, or the value of the assertion, we must ask to whom is it a fact?

what habits of thought, what previous information, what ideas does

it imply, to conceive the fact as a fact? Does not the apprehension

of the fact imply assumptions which may with equal justice be called

theory, and which are perhaps false theory? in which case, the fact is

no fact. Did not the ancients assert it as a fact, that the earth stood

still, and the stars moved? and can any fact have stronger apparent

evidence to justify persons in asserting it emphatically than this

had? These remarks are by no means urged in order to show that no fact

can be certainly known to be true; but only to show that no fact can

be certainly shown to be a fact merely by calling it a fact, however

emphatically. There is by no means any ground of general skepticism

with regard to truth involved in the doctrine of the necessary

combination of two elements in all our knowledge. On the contrary,

ideas are requisite to the essence, and things to the reality of our

knowledge in every case. The proportions of geometry and arithmetic are

examples of knowledge respecting our ideas of space and number, with

regard to which there is no room for doubt. The doctrines of astronomy

are examples of truths not less certain respecting the external world.

14. I remark further, that since in every act of knowledge, observation

or perception, both the elements of the fundamental antithesis are

involved, and involved in a manner inseparable even in our conceptions,

it must always be possible to derive one of these elements from the

other, if we are satisfied to accept, as proof of such derivation,

that one always co-exists with and implies the other. Thus an

opponent may say, that our ideas of space, time, and number, are

derived from our sensations or perceptions, because we never were

in a condition in which we had the ideas of space and time, and had

not sensations or perceptions. But then, we may reply to this, that

we no sooner perceive objects than we perceive them as existing in

space and time, and therefore the ideas of space and time are not

derived from the perceptions. In the same manner, an opponent may

say, that all knowledge which is involved in our reasonings is the

result of experience; for instance, our knowledge of geometry. For

every geometrical principle is presented to us by experience as true;

beginning with the simplest, from which all others are derived by

processes of exact reasoning. But to this we reply, that experience

cannot be the origin of such knowledge; for though experience shows

that such principles are true, it cannot show that they _must be_ true,

which we also know. We never have seen, as a matter of observation,

two straight lines inclosing a space; but we venture to say further,

without the smallest hesitation, that we never shall see it; and if any

one were to tell us that, according to his experience, such a form was

often seen, we should only suppose that he did not know what he was

talking of. No number of acts of experience can add to the certainty

of our knowledge in this respect; which shows that our knowledge is

not made up of acts of experience. We cannot test such knowledge by

experience; for if we were to try to do so, we must first know that the

lines with which we make the trial _are_ straight; and we have no test

of straightness better than this, that two such lines cannot inclose a

space. Since then, experience can neither destroy, add to, nor test our

axiomatic knowledge, such knowledge cannot be derived from experience.

Since no one act of experience can affect our knowledge, no numbers of

acts of experience can make it.

15. To this a reply has been offered, that it is a characteristic

property of geometric forms that the ideas of them exactly resemble the

sensations; so that these ideas are as fit subjects of experimentation

as the realities themselves; and that by such experimentation we learn

the truth of the axioms of geometry. I might very reasonably ask those

who use this language to explain how a particular class of ideas can

be said to resemble sensations; how, if they do, we can know it to be

so; how we can prove this resemblance to belong to geometrical ideas

and sensations; and how it comes to be an especial characteristic of

those. But I will put the argument in another way. Experiment can only

show what is, not what must be. If experimentation on ideas shows what

must be, it is different from what is commonly called experience.

I may add, that not only the mere use of our senses cannot show that

the axioms of geometry _must be_ true, but that, without the light

of our ideas, it cannot even show that they _are_ true. If we had a

segment of a circle a mile long and an inch wide, we should have two

lines inclosing a space; but we could not, by seeing or touching any

part of either of them, discover that it was a bent line.

16. That mathematical truths are not derived from experience is perhaps

still more evident, if greater evidence be possible, in the case of

numbers. We assert that 7 and 8 are 15. We find it so, if we try with

counters, or in any other way. But we do not, on that account, say that

the knowledge is derived from experience. We refer to our conceptions

of seven, of eight, and of addition, and as soon as we possess these

conceptions distinctly, we see that the sum must be fifteen. We cannot

be said to make a trial, for we should not believe the apparent result

of the trial if it were different. If any one were to say that the

multiplication table is a table of the results of experience, we should

know that he could not be able to go along with us in our researches

into the foundations of human knowledge; nor, indeed, to pursue with

success any speculations on the subject.

17. Attempts have also been made to explain the origin of axiomatic

truths by referring them to the association of ideas. But this is

one of the cases in which the word _association_ has been applied so

widely and loosely, that no sense can be attached to it. Those who

have written with any degree of distinctness on the subject, have

truly taught, that the habitual association of the ideas leads us to

believe a connexion of the things: but they have never told us that

this association gave us the power of forming the ideas. Association

may determine belief, but it cannot determine the possibility of our

conceptions. The African king did not believe that water could become

solid, because he had never seen it in that state. But that accident

did not make it impossible to conceive it so, any more than it is

impossible for us to conceive frozen quicksilver, or melted diamond,

or liquefied air; which we may never have seen, but have no difficulty

in conceiving. If there were a tropical philosopher really incapable

of conceiving water solidified, he must have been brought into that

mental condition by abstruse speculations on the necessary relations of

solidity and fluidity, not by the association of ideas.

18. To return to the results of the nature of the Fundamental

Antithesis. As by assuming universal and indissoluble connexion of

ideas with perceptions, of knowledge with experience, as an evidence

of derivation, we may assert the former to be derived from the latter,

so might we, on the same ground, assert the latter to be derived from

the former. We see all forms in space; and we might hence assert all

forms to be mere modifications of our idea of space. We see all events

happen in time; and we might hence assert all events to be merely

limitations and boundary-marks of our idea of time. We conceive all

collections of things as two or three, or some other number: it might

hence be asserted that we have an original idea of number, which is

reflected in external things. In this case, as in the other, we are met

at once by the impossibility of this being a complete account of our

knowledge. Our ideas of space, of time, of number, however distinctly

reflected to us with limitations and modifications, must be reflected,

limited and modified by something different from themselves. We must

have visible or tangible forms to limit space, perceived events to mark

time, distinguishable objects to exemplify number. But still, in forms,

and events, and objects, we have a knowledge which they themselves

cannot give us. For we know, without attending to them, that whatever

they are, they will conform and must conform to the truths of geometry

and arithmetic. There is an ideal portion in all our knowledge of the

external world; and if we were resolved to reduce all our knowledge

to one of its two antithetical elements, we might say that all our

knowledge consists in the relation of our ideas. Wherever there is

necessary truth, there must be something more than sensation can

supply: and the necessary truths of geometry and arithmetic show us

that our knowledge of objects in space and time depends upon necessary

relations of ideas, whatever other element it may involve.

19. This remark may be carried much further than the domain of geometry

and arithmetic. Our knowledge of matter may at first sight appear

to be altogether derived from the senses. Yet we cannot derive from

the senses our knowledge of a truth which we accept as universally

certain;--namely, that we cannot by any process add to or diminish

the quantity of matter in the world. This truth neither is nor can be

derived from experience; for the experiments which we make to verify

it pre-suppose its truth. When the philosopher was asked what was

the weight of smoke, he bade the inquirer subtract the weight of

the ashes from the weight of the fuel. Every one who thinks clearly

of the changes which take place in matter, assents to the justice of

this reply: and this, not because any one had found by trial that such

was the weight of the smoke produced in combustion, but because the

weight lost was assumed to have gone into some other form of matter,

not to have been destroyed. When men began to use the balance in

chemical analysis, they did not prove by trial, but took for granted,

as self-evident, that the weight of the whole must be found in the

aggregate weight of the elements. Thus it is involved in the idea of

matter that its amount continues unchanged in all changes which take

place in its consistence. This is a necessary truth: and thus our

knowledge of matter, as collected from chemical experiments, is also

a modification of our idea of matter as the material of the world

incapable of addition or diminution.

20. A similar remark may be made with regard to the mechanical

properties of matter. Our knowledge of these is reduced, in our

reasonings, to principles which we call the laws of motion. These laws

of motion, as I have endeavoured to show[351], depend upon the idea

of Cause, and involve necessary truths, which are necessarily implied

in the idea of cause;--namely, that every change of motion must have

a cause--that the effect is measured by the cause;--that reaction

is equal and opposite to action. These principles are not derived

from experience. No one, I suppose, would derive from experience the

principle, that every event must have a cause. Every attempt to see

the traces of cause in the world assumes this principle. I do not say

that these principles are anterior to experience; for I have already,

I hope, shown, that neither of the two elements of our knowledge is,

or can be, anterior to the other. But the two elements are co-ordinate

in the development of the human mind; and the ideal element may be

said to be the origin of our knowledge with the more propriety of the

two, inasmuch as our knowledge is the relation of ideas. The other

element of knowledge, in which sensation is concerned, and which

embodies, limits, and defines the necessary truths which express the

relations of our ideas, may be properly termed experience; and I have,

in the discussion just quoted, endeavoured to show how the principles

concerning mechanical causation, which I have just stated, are, by

observation and experiment, limited and defined, so that they become

the laws of motion. And thus we see that such knowledge is derived

from ideas, in a sense quite as general and rigorous, to say the least,

as that in which it is derived from experience.

21. I will take another example of this; although it is one less

familiar, and the consideration of it perhaps a little more difficult

and obscure. The objects which we find in the world, for instance,

minerals and plants, are of different kinds; and according to their

kinds, they are called by various names, by means of which we know

what we mean when we speak of them. The discrimination of these kinds

of objects, according to their different forms and other properties,

is the business of chemistry and botany. And this business of

discrimination, and of consequent classification, has been carried on

from the first periods of the development of the human mind, by an

industrious and comprehensive series of observations and experiments;

the only way in which any portion of the task could have been effected.

But as the foundation of all this labour, and as a necessary assumption

during every part of its progress, there has been in men's minds

the principle, that objects are so distinguishable by resemblances

and differences, that they may be named, and known by their names.

This principle is involved in the idea of a Name; and without it no

progress could have been made. The principle may be briefly stated

thus:--Intelligible Names of kinds are possible. If we suppose this

not to be so, language can no longer exist, nor could the business

of human life go on. If instead of having certain definite kinds of

minerals, gold, iron, copper and the like, of which the external forms

and characters are constantly connected with the same properties and

qualities, there were no connexion between the appearance and the

properties of the object;--if what seemed externally iron might turn

out to resemble lead in its hardness; and what seemed to be gold during

many trials, might at the next trial be found to be like copper; not

only all the uses of these minerals would fail, but they would not be

distinguishable kinds of things, and the names would be unmeaning. And

if this entire uncertainty as to kind and properties prevailed for all

objects, the world would no longer be a world to which language was

applicable. To man, thus unable to distinguish objects into kinds, and

call them by names, all knowledge would be impossible, and all definite

apprehension of external objects would fade away into an inconceivable

confusion. In the very apprehension of objects as intelligibly sorted,

there is involved a principle which springs within us, contemporaneous,

in its efficacy, with our first intelligent perception of the kinds

of things of which the world consists. We assume, as a necessary

basis of our knowledge, that things are of definite kinds; and the aim

of chemistry, botany, and other sciences is to find marks of these

kinds; and along with these, to learn their definitely-distinguished

properties. Even here, therefore, where so large a portion of our

knowledge comes from experience and observation, we cannot proceed

without a necessary truth derived from our ideas, as our fundamental

principle of knowledge.

22. What the marks are, which distinguish the constant differences of

kinds of things (definite marks, selected from among many unessential

appearances), and what their definite properties are, when they

are so distinguished, are parts of our knowledge to be learnt from

observation, by various processes; for instance, among others, by

chemical analysis. We find the differences of bodies, as shown by such

analysis, to be of this nature:--that there are various elementary

bodies, which, combining in different definite proportions, form kinds

of bodies definitely different. But, in arriving at this conclusion,

we introduce a new idea, that of Elementary Composition, which is not

extracted from the phenomena, but supplied by the mind, and introduced

in order to make the phenomena intelligible. That this notion of

elementary composition is not supplied by the chemical phenomena of

combustion, mixture, &c. as merely an observed fact, we see from this;

that men had in ancient times performed many experiments in which

elementary composition was concerned, and had not seen the fact. It

never was truly seen till modern times; and when seen, it gave a new

aspect to the whole body of known facts. This idea of elementary

composition, then, is supplied by the mind, in order to make the

facts of chemical analysis and synthesis intelligible _as_ analysis

and synthesis. And this idea being so supplied, there enters into our

knowledge along with it a corresponding necessary principle;--That the

elementary composition of a body determines its kind and properties.

This is, I say, a principle assumed, as a consequence of the idea of

composition, not a result of experience; for when bodies have been

divided into their kinds, we take for granted that the analysis of a

single specimen may serve to determine the analysis of all bodies of

the same kind: and without this assumption, chemical knowledge with

regard to the kinds of bodies would not be possible. It has been said

that we take only one experiment to determine the composition of any

particular kind of body, because we have a thousand experiments to

determine that bodies of the same kind have the same composition. But

this is not so. Our belief in the principle that bodies of the same

kind have the same composition is not established by experiments,

but is assumed as a necessary consequence of the ideas of Kind and of

Composition. If, in our experiments, we found that bodies supposed

to be of the same kind had not the same composition, we should not

at all doubt of the principle just stated, but conclude at once that

the bodies were _not_ of the same kind;--that the marks by which the

kinds are distinguished had been wrongly stated. This is what has very

frequently happened in the course of the investigations of chemists and

mineralogists. And thus we have it, not as an experiential fact, but

as a necessary principle of chemical philosophy, that the Elementary

Composition of a body determines its Kind and Properties.

23. How bodies differ in their elementary composition, experiment must

teach us, as we have already said, that experiment has taught us. But

as we have also said, whatever be the nature of this difference, kinds

must be definite, in order that language may be possible: and hence,

whatever be the terms in which we are taught by experiment to express

the elementary composition of bodies, the result must be conformable

to this principle, That the differences of elementary composition

are definite. The law to which we are led by experiment is, that the

elements of bodies continue in definite proportions according to

weight. Experiments add other laws; as for instance, that of multiple

proportions in different kinds of bodies composed of the same elements;

but of these we do not here speak.

24. We are thus led to see that in our knowledge of mechanics,

chemistry, and the like, there are involved certain necessary

principles, derived from our ideas, and not from experience. But to

this it may be objected, that the parts of our knowledge in which these

principles are involved has, in historical fact, all been acquired by

experience. The laws of motion, the doctrine of definite proportions,

and the like, have all become known by experiment and observation; and

so far from being seen as necessary truths, have been discovered by

long-continued labours and trials, and through innumerable vicissitudes

of confusion, error, and imperfect truth. This is perfectly true: but

does not at all disprove what has been said. Perception of external

objects and experience, experiment and observation are needed,

not only, as we have said, to supply the objective element of all

knowledge--to embody, limit, define, and modify our ideas; but this

intercourse with objects is also requisite to unfold and fix our ideas

themselves. As we have already said, ideas and facts can never be

separated. Our ideas cannot be exercised and developed in any other

form than in their combination with facts, and therefore the trials,

corrections, controversies, by which the matter of our knowledge is

collected, is also the only way in which the form of it can be rightly

fashioned. Experience is requisite to the clearness and distinctness of

our ideas, not because they are derived from experience, but because

they can only be exercised upon experience. And this consideration

sufficiently explains how it is that experiment and observation have

been the means, and the only means, by which men have been led to a

knowledge of the laws of nature. In reality, however, the necessary

principles which flow from our ideas, and which are the basis of such

knowledge, have not only been inevitably assumed in the course of such

investigations, but have been often expressly promulgated in words

by clear-minded philosophers, long before their true interpretation

was assigned by experiment. This has happened with regard to such

principles as those above mentioned; That every event must have a

cause; That reaction is equal and opposite to action; That the quantity

of matter in the world cannot be increased or diminished: and there

would be no difficulty in finding similar enunciations of the other

principles above mentioned;--That the kinds of things have definite

differences, and that these differences depend upon their elementary

composition. In general, however, it may be allowed, that the necessary

principles which are involved in those laws of nature of which we have

a knowledge become then only clearly known, when the laws of nature are

discovered which thus involve the necessary ideal element.

25. But since this is allowed, it may be further asked, how we are to

distinguish between the necessary principle which is derived from our

ideas, and the law of nature which is learnt by experience. And to this

we reply, that the necessary principle may be known by the condition

which we have already mentioned as belonging to such principles: ...

that it is impossible distinctly to conceive the contrary. We cannot

conceive an event without a cause, except we abandon all distinct idea

of cause; we cannot distinctly conceive two straight lines inclosing

space; and if we seem to conceive this, it is only because we conceive

indistinctly. We cannot conceive 5 and 3 making 7 or 9; if a person

were to say that he could conceive this, we should know that he was a

person of immature or rude or bewildered ideas, whose conceptions had

no distinctness. And thus we may take it as the mark of a necessary

truth, that we cannot conceive the contrary distinctly.

26. If it be asked what is the test of distinct conception (since it

is upon the distinctness of conception that the matter depends), we

may consider what answer we should give to this question if it were

asked with regard to the truths of geometry. If we doubted whether

anyone had these distinct conceptions which enable him to see the

necessary nature of geometrical truth, we should inquire if he could

understand the axioms as axioms, and could follow, as demonstrative,

the reasonings which are founded upon them. If this were so, we should

be ready to pronounce that he had distinct ideas of space, in the sense

now supposed. And the same answer may be given in any other case. That

reasoner has distinct conceptions of mechanical causes who can see

the axioms of mechanics as axioms, and can follow the demonstrations

derived from them as demonstrations. If it be said that the science,

as presented to him, may be erroneously constructed; that the axioms

may not be axioms, and therefore the demonstrations may be futile, we

still reply, that the same might be said with regard to geometry: and

yet that the possibility of this does not lead us to doubt either of

the truth or of the necessary nature of the propositions contained

in Euclid's Elements. We may add further, that although, no doubt,

the authors of elementary books maybe persons of confused minds, who

present as axioms what are not axiomatic truths; yet that in general,

what is presented as an axiom by a thoughtful man, though it may

include some false interpretation or application of our ideas, will

also generally include some principle which really is necessarily true,

and which would still be involved in the axiom, if it were corrected

so as to be true instead of false. And thus we still say, that if in

any department of science a man can conceive distinctly at all, there

are principles the contrary of which he cannot distinctly conceive, and

which are therefore necessary truths.

27. But on this it may be asked, whether truth can thus depend upon

the particular state of mind of the person who contemplates it; and

whether that can be a necessary truth which is not so to all men. And

to this we again reply, by referring to geometry and arithmetic. It

is plain that truths may be necessary truths which are not so to all

men, when we include men of confused and perplexed intellects; for to

such men it is not a necessary truth that two straight lines cannot

inclose a space, or that 14 and 17 are 31. It need not be wondered

at, therefore, if to such men it does not appear a necessary truth

that reaction is equal and opposite to action, or that the quantity of

matter in the world cannot be increased or diminished. And this view of

knowledge and truth does not make it depend upon the state of mind of

the student, any more than geometrical knowledge and geometrical truth,

by the confession of all, depend upon that state. We know that a man

cannot have any knowledge of geometry without so much of attention to

the matter of the science, and so much of care in the management of

his own thoughts, as is requisite to keep his ideas distinct and clear.

But we do not, on that account, think of maintaining that geometrical

truth depends merely upon the state of the student's mind. We conceive

that he knows it because it is true, not that it is true because he

knows it. We are not surprised that attention and care and repeated

thought should be requisite to the clear apprehension of truth. For

such care and such repetition are requisite to the distinctness and

clearness of our ideas: and yet the relations of these ideas, and

their consequences, are not produced by the efforts of attention or

repetition which we exert. They are in themselves something which

we may discover, but cannot make or change. The idea of space, for

instance, which is the basis of geometry, cannot give rise to any

doubtful propositions. What is inconsistent with the idea of space

cannot be truly obtained from our ideas by any efforts of thought or

curiosity; if we blunder into any conclusion inconsistent with the idea

of space, our knowledge, so far as this goes, is no knowledge: any more

than our observation of the external world would be knowledge, if, from

haste or inattention, or imperfection of sense, we were to mistake the

object which we see before us.

28. But further: not only has truth this reality, which makes it

independent of our mistakes, that it must be what is really consistent

with our ideas; but also, a further reality, to which the term

is more obviously applicable, arising from the principle already

explained, that ideas and perceptions are inseparable. For since,

when we contemplate our ideas, they have been frequently embodied and

exemplified in objects, and thus have been fixed and modified; and

since this compound aspect is that under which we constantly have

them before us, and free from which they cannot be exhibited; our

attempts to make our ideas clear and distinct will constantly lead us

to contemplate them as they are manifested in those external forms

in which they are involved. Thus in studying geometrical truth, we

shall be led to contemplate it as exhibited in visible and tangible

figures;--not as if these could be sources of truth, but as enabling

us more readily to compare the aspects which our ideas, applied to the

world of objects, may assume. And thus we have an additional indication

of the reality of geometrical truth, in the necessary possibility of

its being capable of being exhibited in a visible or tangible form. And

yet even this test by no means supersedes the necessity of distinct

ideas, in order to a knowledge of geometrical truth. For in the case

of the duplication of the cube by Hobbes, mentioned above, the diagram

which he drew made two points appear to coincide, which did not

really, and by the nature of our idea of space, coincide; and thus

confirmed him in his error.

_Thus the inseparable nature of the Fundamental Antithesis of Ideas and

Things gives reality to our knowledge, and makes objective reality a

corrective of our subjective imperfections in the pursuit of knowledge.

But this objective exhibition of knowledge can by no means supersede a

complete development of the subjective condition, namely, distinctness

of ideas. And that there is a subjective condition, by no means makes

knowledge altogether subjective, and thus deprives it of reality;

because, as we have said, the subjective and the objective elements are

inseparably bound together in the fundamental antithesis._

29. It would be easy to apply these remarks to other cases, for

instance, to the case of the principle we have just mentioned, that

the differences of elementary composition of different kinds of bodies

must be definite. We have stated that this principle is necessarily

true;--that the contrary proposition cannot be distinctly conceived.

But by whom? Evidently, according to the preceding reasoning, by a

person who distinctly conceives Kinds, as marked by intelligible

names, and Composition, as determining the kinds of bodies. Persons

new to chemical and classificatory science may not possess these ideas

distinctly; or rather, cannot possess them distinctly; and therefore

cannot apprehend the impossibility of conceiving the opposite of

the above principle; just as the schoolboy cannot apprehend the

impossibility of the numbers in his multiplication table being other

than they are. But this inaptitude to conceive, in either case, does

not alter the necessary character of the truth: although, in one case,

the truth is obvious to all except schoolboys and the like, and the

other is probably not clear to any except those who have attentively

studied the philosophy of elementary compositions. At the same time,

this difference of apprehension of the truth in different persons does

not make the truth doubtful or dependent upon personal qualifications;

for in proportion as persons attain to distinct ideas, they will see

the truth; and cannot, with such ideas, see anything as truth which

is not truth. When the relations of elements in a compound become as

familiar to a person as the relations of factors in a multiplication

table, he will then see what are the necessary axioms of chemistry, as

he now sees the necessary axioms of arithmetic.

30. There is also one other remark which I will here make. In the

progress of science, both the elements of our knowledge are constantly

expanded and augmented. By the exercise of observation and experiment,

we have a perpetual accumulation of facts, the materials of knowledge,

the objective element. By thought and discussion, we have a perpetual

development of man's ideas going on: theories are framed, the materials

of knowledge are shaped into form; the subjective element is evolved;

and by the necessary coincidence of the objective and subjective

elements, the matter and the form, the theory and the facts, each of

these processes furthers and corrects the other: each element moulds

and unfolds the other. Now it follows, from this constant development

of the ideal portion of our knowledge, that we shall constantly be

brought in view of new Necessary Principles, the expression of the

conditions belonging to the Ideas which enter into our expanding

knowledge. These principles, at first dimly seen and hesitatingly

asserted, at last become clearly and plainly self-evident. Such is the

case with the principles which are the basis of the laws of motion.

Such may soon be the case with the principles which are the basis

of the philosophy of chemistry. Such may hereafter be the case with

the principles which are to be the basis of the philosophy of the

connected and related polarities of chemistry, electricity, galvanism,

magnetism. That knowledge is possible in these cases, we know; that

our knowledge may be reduced to principles, gradually more simple,

we also know; that we have reached the last stage of simplicity of

our principles, few cultivators of the subject will be disposed to

maintain; and that the additional steps which lead towards very simple

and general principles will also lead to principles which recommend

themselves by a kind of axiomatic character, those who judge from the

analogy of the past history of science will hardly doubt. That the

principles thus axiomatic in their form, do also express some relation

of our ideas, of which experiment and observation have given a true

and real interpretation, is the doctrine which I have here attempted

to establish and illustrate in the most clear and undoubted of the

existing sciences; and the evidence of this doctrine in those cases

seems to be unexceptionable, and to leave no room to doubt that such is

the universal type of the progress of science. Such a doctrine, as we

have now seen, is closely connected with the views here presented of

the nature of the Fundamental Antithesis of Philosophy, which I have

endeavoured to illustrate.

FOOTNOTES:

[Footnote 351: _Hist. Sc. Ind._ b. iii.]

APPENDIX F.

REMARKS ON A REVIEW OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.

_Trinity Lodge, April 11th, 1844._

MY DEAR HERSCHEL,

Being about to send you a copy of a paper on a philosophical question

just printed in the Transactions of our Cambridge Society, I am tempted

to add, as a private communication, a few Remarks on another aspect of

the same question. These Remarks I think I may properly address to you.

They will refer to an Article in the _Quarterly Review_ for June, 1841,

respecting my _History_ and _Philosophy_ of the Inductive Sciences; and

without assigning any other reason, I may say that the interest I know

you to take in speculations on such subjects makes me confident that

you will give a reasonable attention to what I may have to say on the

subject of that Article. With the Reviewal itself, I am so far from

having any quarrel, that when it appeared I received it as affording

all that I hoped from Public Criticism. The degree and the kind of

admiration bestowed upon my works by a writer so familiar with science,

so comprehensive in his views, and so equitable in his decisions, as

the Reviewer manifestly was, I accepted as giving my work a stamp of

acknowledged value which few other hands could have bestowed.

You may perhaps recollect, however, that the Reviewer dissented

altogether from some of the general views which I had maintained,

and especially from a general view which is also, in the main, that

presented in the accompanying Memoir, namely, that, besides Facts,

Ideas are an indispensable source of our knowledge; that Ideas are

the ground of necessary truth; that the Idea of Space, in particular,

is the ground of the necessary truths of geometry. This question,

and especially as limited to the last form, will be the subject of

my Remarks in the first place; and I wish to consider the Reviewer's

objections with the respect which their subtlety and depth of thought

well deserve.

The Reviewer makes objections to the account which I have given of

the source whence geometrical truth derives its characters of being

necessary and universal; but he is not one of those metaphysicians

who deny those characters to the truths of geometry. He allows in the

most ample manner that the truths of geometry _are_ necessary. The

question between us therefore is from what this character is derived.

The Reviewer prefers, indeed, to have it considered that the question

is not concerning the necessity, but, as he says, the universality of

these truths; or rather, the nature and grounds of our conviction of

their universality. He might have said, with equal justice, the nature

and grounds of our conviction of their necessity. For his objection to

the term _necessity_ in this case--"that all the propositions about

realities are necessarily true, since every reality must be consistent

with itself," (p. 206)--does not apply to our conviction of necessity,

since we may not be able to see what are the properties of real things;

and therefore may have no conviction of their necessity. It may be a

necessary property of salt to be soluble, but we see no such necessity;

and therefore the assertion of such a property is not one of the

necessary truths with which we are here concerned. But to turn back to

the necessary or universal truths of geometry, and the ground of those

attributes: The main difference between the Author and the Reviewer is

brought into view, when the Reviewer discusses the general argument

which I had used, in order to show that truths which we see to be

necessary and universal cannot be derived from experience. The argument

is this,--

"Experience must always consist of a limited number of observations;

and however numerous these may be, they can show nothing with regard

to the infinite number of cases in which the experiment has not been

made.... Truths can only be known to be general, not universal, if

they depend upon experience alone. Experience cannot bestow that

universality which she herself cannot have; nor that necessity of which

she has no comprehension." (_Phil._ _i._ pp. 60, 61.)

Here is that which must be considered as the cardinal argument on this

subject. It is therefore important to attend to the answer which the

Reviewer makes to it. He says,--

"We conceive that a full answer to this argument is afforded by the

nature of the inductive propensity,--by the irresistible impulse of

the mind to generalize _ad infinitum_, when nothing in the nature of

limitation or opposition offers itself to the imagination; and by our

involuntary application of the law of continuity to fill up, by the

same ideal substance of truth, every interval which uncontradicted

experience may have left blank in our inductive conclusion." (p. 207.)

Now here we have two rival explanations of the same thing,--the

conviction of the universality of geometrical truths. The one

explanation is, that this universality is imposed upon such truths by

their involving a certain element, derived from the universal mode of

activity of the mind when apprehending such truths, which element I

have termed an Idea. The other explanation is, that this universality

arises from the _inductive propensity_--from the _irresistible impulse

to generalize ad infinitum_--from the _involuntary application of the

law of continuity_--from the _filling up all intervals with the same

ideal substance of truth_.

With regard to these two explanations, I may observe, that so far as

they are thus stated they do not necessarily differ. They both agree

in expressing this; that the ground of the universality of geometrical

truths is a certain law of the mind's activity, which determines its

procedure when it is concerned in apprehending the external world.

One explanation says, that we impress upon the external world the

relations of our ideas, and thus believe more than we see,--the

other says, that we have an irresistible impulse to introduce into

our conviction a relation between what we do observe and what we do

not, namely, to generalize _ad infinitum_ from what we do see. One

explanation says, that we perceive all external objects as included

in absolute ideal space,--the other, that we fill up the intervals of

the objects which we perceive with the same ideal substance of truth.

Both sets of expressions may perhaps be admissible; and if admitted,

may be understood as expressing the same opinions, or opinions which

have much in common. The Author's expressions have the advantage, which

ought to belong to them, as the expressions employed in a systematic

work, of being fixed expressions, technical phrases, intentionally

selected, uniformly and steadily employed whenever the occasion recurs.

The Reviewer's expressions are more lively and figurative, and such

as well become an occasional composition; but hardly such as could

be systematically applied to the subject in a regular treatise. We

could not, as a standard and technical phrase, talk of filling up

the intervals of observation with the same ideal substance of truth;

and the inevitable impulse to generalize would hardly sufficiently

express that we generalize according to a certain idea, namely, the

idea of space. Perhaps that which is suggested to us as the common

import of the two sets of expressions may be conveyed by some other

phrase, in a manner free from the objections which lie against both the

Author's and the Critic's terms. Perhaps the mental idea governing

our experience, and the irresistible impulse to generalize our

observation, may both be superseded by our speaking of a law of the

mind's _activity_, which is really implied in both. There operates, in

observing the external world, a law of the mind's activity, by which it

connects its observations; and this law of the mind's activity may be

spoken of either as the idea of space, or as the irresistible impulse

to generalize the relations of space which it observes. And this

expression--_the laws of the mind's activity_--thus opposed to that

merely passive function by which the mind receives the impressions of

sense, may be applied to other ideas as well as to the idea of space,

and to the impulse to generalize in other truths as well as those of

geometry.

So far, it would seem, that the Author and the Critic may be brought

into much nearer agreement than at first seemed likely, with regard

to the grounds of the necessity and universality in our knowledge.

But even if we adopt this conciliatory suggestion, and speak of the

necessity and universality of certain truths as arising from the laws

of the mind's activity, we cannot, without producing great confusion,

allow ourselves to say, as the Critic says, that these truths are thus

derived from _experience_, or from _observation_. It will, I say, be

found fatal to all philosophical precision of thought and language,

to say that the fundamental truths of geometry, the axioms, with the

conviction of their necessary truth, are derived from experience. Let

us take any axiomatic truth of geometry, and ask ourselves if this is

not so.

It is, for example, an axiom in geometry that if a straight line cut

one of two parallel straight lines, it must cut the other also. Is this

truth derived or derivable from observation of actual parallel lines,

and a line cutting them, exhibited to our senses? Let those who say

that we do acquire this truth by observation, imagine to themselves

the mode in which the observation must be made. We have before us two

parallel straight lines, and we see that a straight line which cuts

the one cuts the other also. We see this again in another case, it

may be the angles and the distances being different, and in a third,

and in a fourth; and so on; and generalizing, we are irresistibly

led to believe the assertion to be universally true. But can any one

really imagine this to be the mode in which we arrive at this truth?

"We see," says this explanation, "two parallel straight lines, cut by

a third." But how do we know that the observed lines are parallel?

If we apply any test of parallelism, we must assume some property of

parallels, and thus involve some axiom on the subject, which we have no

more right to assume than the one now under consideration. We should

thus destroy our explanation as an account of the mode of arriving

at independent geometrical axioms. But probably those who would give

such an explanation would not do this. They would not suppose that in

observing this property of parallels we try by measurement whether the

lines are parallel. They would say, I conceive, that we suppose lines

to be parallel, and that then we see that the straight line which cuts

the one must cut the other. That when we make this supposition, we are

persuaded of the truth of the conclusion, is certain. But what I have

to remark is, that this being so, the conclusion is the result, not of

observation, but of the hypothesis. The geometrical truth here spoken

of, after this admission, no longer flows from experience, but from

supposition. It is not that we _ascertain_ the lines to be parallel,

and then _find_ that they have this property: but we _suppose_ the

lines to be parallel, and _therefore_ they have this property. This is

not a truth of experience.

This, it may be said, is so evident that it cannot have been overlooked

by a very acute reasoner, such as you describe your Critic to be.

What, it may be asked, is the answer which he gives to so palpable an

objection as this? How does he understand his assertion that we learn

the truth of geometrical axioms from experience (p. 208), so as to make

it tenable on his own principles? What account does he give of the

origin of such axioms which makes them in any sense to be derived from

experience?

In justice to the Reviewer's fairness (which is unimpeachable

throughout his argumentation) it must be stated that he does give an

account in which he professes to show how this is done. And the main

step of his explanation consists in introducing the conception of

_direction_, and _unity of direction_. He says (p. 208), "The _unity of

direction_, or that we cannot march from a given point by more than one

path _direct to the same object_, is a matter of practical experience,

long before it can by possibility become matter of abstract thought."

We might ask here, as in the former case, how this can be a matter of

experience, except we have some independent test of directness? and we

might demand to know what this test is. Or do we not rather, here as

in the other case, _suppose_ the directness of the path; and is not

the singleness of the direct path a consequence, not of its observed

form, but of its hypothetical directness; and thus by no means a

result of experience? But we may put our remark upon this deduction

of the geometrical axiom in another form. We generalize, it is said,

the observations which we have made ever since we were born. But this

term "generalize" is far too vague to pass for an explanation, without

being itself explained. We are impelled to believe that to be true in

general which we see to be true in particular. But how do we see any

truth? How do we pick out any proposition with respect to a diagram

which we see before us? We see in particular, and state in general,

some truth respecting straight lines, or parallel lines, or concerning

direction. But where do we find the conception of straightness, or

parallelism, or direction? These conceptions are not upon the surface

of things. The child does not, from his birth, see straightness

and parallelism so as to know that he sees them. How then does his

experience bear upon a proposition in which these conceptions are

involved? It is said that it is a matter of experience long before it

is a matter of abstract thought. But how can there be any experience

by which we learn these properties of a straight line, till our

thoughts are at least so abstract as to conceive what straightness is?

If it be said that this conception grows with our experience, and is

gradually unfolded with our unfolding materials of knowledge, so as

to give import and significance to them: I need make no objection to

such a statement, except this--that this power of unfolding out of the

mind conceptions which give meaning to our experience, is something

in addition to the mere employment of our senses upon the external

world. It is what I have called the ideal part of our knowledge. It

implies, not only an impulse to generalize from experience, but also

an impulse to form conceptions by which generalization is possible. It

requires, not only that nothing should oppose the tendency, but that

the direction in which the tendency is to operate should be determined

by the laws of the mind's activity; by an internal, not by an external

agency.

One main ground on which the Reviewer is disposed to quarrel with and

reject several of the expressions used in the _Philosophy_;--such as

that space is an idea, a form of our perception, and the like,--is

this; that such expressions appear to deprive the external world of its

reality; to make it, or at least most of its properties, a creation of

the observing mind. He quotes the following argument which is urged in

the _Philosophy_, in order to prove that space is not a notion obtained

from experience: "Experience gives us information concerning things

without us, but our apprehending them as without us takes for granted

their existence in space. Experience acquaints us with the form,

position, magnitude, &c. of particular objects, but that they _have_

form, position, magnitude, pre-supposes that they are in space." From

this statement he altogether dissents. No, says he, "the reason why we

apprehend things as without us is that they _are_ without us. We take

for granted that they exist in space, because they _do_ so exist, and

because such their existence is a matter of direct perception, which

can neither be explained in words nor contravened in imagination:

because, in short, space is a _reality_, and not a mere matter of

convention or imagination."

Now, if by calling space an idea, we suggest any doubt of its reality

and of the reality of the external world, we certainly run the risk

of misleading our readers; for the external world is real if anything

be real: the bodies which exist in space are things, if things are

anywhere to be found. That bodies do exist in space, and that _that_ is

the reason why we apprehend them as existing in space, I readily grant.

But I conceive that the term Idea ought not to suggest any such doubt

of the reality of the knowledge in which it is involved. Ideas are

always, in our knowledge, conjoined with facts. Our real knowledge is

knowledge, because it involves ideas, real, because it involves facts.

We apprehend things as existing in space because they do so exist: and

our idea of space enables us so to observe them, and so to conceive

them.

But we want, further, a reason why, apprehending them as they are, we

also apprehend, that in certain relations they could not be otherwise

(that two straight linear objects could not inclose a space, for

instance). This circumstance is no way accounted for by saying that we

apprehend them as they are; and is, I presume to say, inexplicable,

except by supposing that it arises from some property of the observing

mind:--an Idea, as I have termed it,--an irresistible Impulse to

generalize, as the Reviewer expresses it. Or, as I have suggested, we

may adopt a third phrase, a Law of the mind's activity: and in order

that no question may remain, whether we ascribe reality to the objects

and relations which we observe, we may describe it as "a Law of the

mind's activity in apprehending what is." And thus the real existence

of the object, and the ideal element which our apprehension of it

introduces, would both be clearly asserted.

I am ready to use expressions which recognize the reality of space

and other external things more emphatically than those expressions

which I have employed in the _Philosophy_, if expressions can be

found which, while they do this, enable us to explain the possibility

of knowledge, and to analyze the structure of truth. It is, indeed,

extremely difficult to find, in speaking of this subject, expressions

which are satisfactory. The reality of the objects which we perceive

is a profound, apparently an insoluble problem[352]. We cannot but

suppose that existence is something different from our knowledge of

existence:--that which exists, does not exist merely in our knowing

that it does:--truth is truth whether we know it or not. Yet how can we

conceive truth, otherwise than as something known? How can we conceive

things as existing, without conceiving them as objects of perception?

Ideas and Things are constantly opposed, yet necessarily co-existent.

How they are thus opposite and yet identical, is the ultimate problem

of all philosophy. The successive phases of philosophy have consisted

in separating and again uniting these two opposite elements; in

dwelling sometimes upon the one and sometimes upon the other, as the

principal or original or only element; and then in discovering that

such an account of the state of the case was insufficient. Knowledge

requires ideas. Reality requires things. Ideas and things co-exist.

Truth _is_, and is known. But the complete explanation of these points

appears to be beyond our reach. At least it is not necessary for the

purposes of our philosophy. The separation of ideas and sensations

in order to discover the conditions of knowledge is our main task.

How ideas and sensations are united so as to form things, does not so

immediately concern us.

I have stated that we may, without giving up any material portion

of the Philosophy of Science to which I have been led, express the

conclusions in other phraseology; and that instead of saying that all

our knowledge involves certain Fundamental Ideas, the sources from

which all universal truth is derived, we may say that there are certain

Laws of Mental Activity according to which alone all the real relations

of things are apprehended. If this alteration in the phraseology will

make the doctrines more generally intelligible or acceptable, there is

no reason why it should not be adopted. But I may remark, that a main

purpose of the _Philosophy_ was not merely to prove that there _are_

such Fundamental Ideas or Laws of mental activity, but to enumerate

those of them which are involved in the existing sciences; and to state

the fundamental truths to which the fundamental ideas lead. This was

the task which was attempted; and if this have been executed with any

tolerable success, it may perhaps be received as a contribution to the

philosophy of science, of which the value is not small, in whatever

terms it be expressed. And this enumeration of fundamental ideas, and

of truths derived from them, must have something to correspond to it,

in any other mode of expressing that view of the nature of knowledge

which we are led to adopt. If instead of _Fundamental Ideas_, we speak

of Impulses of generalization, or of _Laws of mental activity_, we

must still distinguish such Impulses, or such Laws, according to the

distinctions of ideas to which the survey of science led us. We shall

thus have a series of groups of Laws, or of classes of generalizing

Impulses, corresponding to the series of Fundamental Ideas already

given. If we employ the language of the Reviewer, we shall have one

generalizing Impulse which suggests relations of Space; another which

directs us to properties of Numbers; another which deals with Time;

another with Cause: another which groups objects according to Likeness;

another which suggests a purpose as a necessary relation among

them; to which may be added, even while we confine ourselves to the

physical sciences, several others, as may be seen in the _Philosophy_.

Now when the fundamental conditions and elements of truth are thus

arranged into groups, it is not a matter of so much consequence to

decide whether each group shall be said to be bound together by an

idea or by an impulse of generalization; as it is to see that, if

this happen in virtue of ideas, here are so many distinct ideas which

enter into the structure of science, and give universality to its

matter; and again, if this happen in virtue of an irresistible impulse

of generalization in each case, we have so many different kinds of

impulses of generalization. The main purpose in the _Philosophy_ was to

analyze scientific truth into its conditions and elements; and I did

not content myself with saying that those elements are Sensations and

Ideas; the Ideas being that element which makes universal knowledge

conceivable and possible. I went further: I enumerated the Ideas

which thus enter into science. I showed that in the sciences which

I passed in review, the most acute and profound inquirers had taken

for granted that certain truths in each science are of universal and

necessary validity, and I endeavoured to select the idea in which this

universality and necessity resided, and to separate it from all other

ideas involved in other sciences. If therefore it be thought better

to say that those principles in each science upon which, as upon the

axioms in geometry, the universality and necessity of scientific truth

depends, are arrived at, not by ideas, but by an irresistible impulse

of generalization, those who employ such phraseology, if they make a

classification of such impulses corresponding to my classification of

ideas, will still adopt the greater part of my philosophy, altering

only the phraseology. Or if, as I suggested, instead of "Fundamental

Ideas," we use the phrase "Laws of Mental Activity," then our primary

intellectual Code--the Constitution of our minds, as it may be

termed--will consist of a Body of Laws of which the Titles correspond

with the Fundamental Ideas of the _Philosophy_.

My object was, from the writings of the most sagacious and profound

philosophers who have laboured on each science, to extract such a

code, such a constitution. If I have in any degree succeeded in this,

the result must have a reality and a value independently of all forms

of expression. Still I do not think that any language can ever serve

for such legislation, in which the two elements of truth are not

distinguished. Even if we adopt the phraseology which I have just

employed, we shall have to recollect that Law and Fact must be kept

distinct, and that the Constitution has its Principles as well as its

History.

But I will not longer detain you by seeking other modes of expressing

the Fundamental Antithesis to which the accompanying Memoir refers.

The Remarks which I here send you were written three years ago, on the

appearance of the Review which I have quoted. If I succeed in obtaining

for them a few minutes' attention from you and a few other friends, I

shall be glad that they have been preserved.

I am, my dear Herschel,

always truly yours,

W. WHEWELL.

P.S. I have abstained from sending you a large portion of my Remarks

as originally written. I had gone on to show that, in my _Philosophy_,

I had not only enumerated and analyzed a great number of different

Fundamental Ideas which belong to the different existing sciences,

but that I had also shown in what manner these ideas enter into their

respective sciences; namely, by the statement or use of Axioms, which

involve the ideas, and which form the basis of each science when

systematically exhibited. A number of these Axioms belonging to most

of the physical sciences, are stated in the _Philosophy_. I might have

added also that I have attempted to classify the historical steps

by which such Axioms are brought into view and applied. But it is

not necessary to dwell upon these points, in order to illustrate the

difference and the agreement between the Reviewer and me.

_Sir John F. W. Herschel, Bart. &c._

APPENDIX G.

ON THE TRANSFORMATION OF HYPOTHESES IN THE HISTORY OF SCIENCE.

(_Cam. Phil. Soc._ MAY 19, 1851.)

1. The history of science suggests the reflection that it is very

difficult for the same person at the same time to do justice to two

conflicting theories. Take for example the Cartesian hypothesis of

vortices and the Newtonian doctrine of universal gravitation. The

adherents of the earlier opinion resisted the evidence of the Newtonian

theory with a degree of obstinacy and captiousness which now appears

to us quite marvellous: while on the other hand, since the complete

triumph of the Newtonians, _they_ have been unwilling to allow any

merit at all to the doctrine of vortices. It cannot but seem strange,

to a calm observer of such changes, that in a matter which depends

upon mathematical proofs, the whole body of the mathematical world

should pass over, as in this and similar cases they seem to have done,

from an opinion confidently held, to its opposite. No doubt this must

be, in part, ascribed to the lasting effects of education and early

prejudice. The old opinion passes away with the old generation: the new

theory grows to its full vigour when its congenital disciples grow to

be masters. John Bernoulli continues a Cartesian to the last; Daniel,

his son, is a Newtonian from the first. Newton's doctrines are adopted

at once in England, for they are the solution of a problem at which his

contemporaries have been labouring for years. They find no adherents

in France, where Descartes is supposed to have already explained

the constitution of the world; and Fontenelle, the secretary of the

Academy of Sciences at Paris, dies a Cartesian seventy years after

the publication of Newton's _Principia_. This is, no doubt, a part

of the explanation of the pertinacity with which opinions are held,

both before and after a scientific revolution: but this is not the

whole, nor perhaps the most instructive aspect of the subject. There

is another feature in the change, which explains, in some degree, how

it is possible that, in subjects, mainly at least mathematical, and

therefore claiming demonstrative evidence, mathematicians should hold

different and even opposite opinions. And the object of the present

paper is to point out this feature in the successions of theories, and

to illustrate it by some prominent examples drawn from the history of

science.

2. The feature to which I refer is this; that when a prevalent

theory is found to be untenable, and consequently, is succeeded by a

different, or even by an opposite one, the change is not made suddenly,

or completed at once, at least in the minds of the most tenacious

adherents of the earlier doctrine; but is effected by a transformation,

or series of transformations, of the earlier hypothesis, by means of

which it is gradually brought nearer and nearer to the second; and

thus, the defenders of the ancient doctrine are able to go on as if

still asserting their first opinions, and to continue to press their

points of advantage, if they have any, against the new theory. They

borrow, or imitate, and in some way accommodate to their original

hypothesis, the new explanations which the new theory gives, of the

observed facts; and thus they maintain a sort of verbal consistency;

till the original hypothesis becomes inextricably confused, or breaks

down under the weight of the auxiliary hypotheses thus fastened upon

it, in order to make it consistent with the facts.

This often-occurring course of events might be illustrated from the

history of the astronomical theory of epicycles and eccentrics, as

is well known. But my present purpose is to give one or two brief

illustrations of a somewhat similar tendency from other parts of

scientific history; and in the first place, from that part which has

already been referred to, the battle of the Cartesian and Newtonian

systems.

3. The part of the Cartesian system of vortices which is most

familiarly known to general readers is the explanation of the motions

of the planets by supposing them carried round the sun by a kind

of whirlpool of fluid matter in which they are immersed: and the

explanation of the motions of the satellites round their primaries by

similar subordinate whirlpools, turning round the primary, and carried,

along with it, by the primary vortex. But it should be borne in mind

that a part of the Cartesian hypothesis which was considered quite as

important as the cosmical explanation, was the explanation which it

was held to afford of terrestrial gravity. Terrestrial gravity was

asserted to arise from the motion of the vortex of subtle matter which

revolved round the earth's axis and filled the surrounding space. It

was maintained that by the rotation of such a vortex, the particles

of the subtle matter would exert a centrifugal force, and by virtue of

that force, tend to recede from the center: and it was held that all

bodies which were near the earth, and therefore immersed in the vortex,

would be pressed towards the center by the effort of the subtle matter

to recede from the center[353].

These two assumed effects of the Cartesian vortices--to carry bodies

in their stream, as straws are carried round by a whirlpool, and to

press bodies to the center by the centrifugal effort of the whirling

matter--must be considered separately, because they were modified

separately, as the progress of discussion drove the Cartesians from

point to point. The former effect indeed, the _dragging_ force

of the vortex, as we may call it, would not bear working out on

mechanical principles at all; for as soon as the law of motion was

acknowledged (which Descartes himself was one of the loudest in

proclaiming), that a body in motion keeps all the motion which it has,

and receives in addition all that is impressed upon it; as soon, in

short, as philosophers rejected the notion of an inertness in matter

which constantly retards its movements,--it was plain that a planet

perpetually dragged onwards in its orbit by a fluid moving quicker than

itself, must be perpetually accelerated; and therefore could not follow

those constantly-recurring cycles of quicker and slower motion which

the planets exhibit to us.

The Cartesian mathematicians, then, left untouched the calculation of

the progressive motion of the planets; and, clinging to the assumption

that a vortex would produce a tendency of bodies to the center, made

various successive efforts to construct their vortices in such a manner

that the centripetal forces produced by them should coincide with those

which the phenomena required, and therefore of course, in the end, with

those which the Newtonian theory asserted.

In truth, the Cartesian vortex was a bad piece of machinery for

producing a central force: from the first, objections were made to the

sufficiency of its mechanism, and most of these objections were very

unsatisfactorily answered, even granting the additional machinery which

its defenders demanded. One formidable objection was soon started,

and continued to the last to be the torment of the Cartesians. If

terrestrial gravity, it was urged, arise from the centrifugal force of

a vortex which revolves about the earth's axis, terrestrial gravity

ought to act in planes perpendicular to the earth's axis, instead

of tending to the earth's center. This objection was taken by James

Bernoulli[354], and by Huyghens[355] not long after the publication of

Descartes's _Principia_. Huyghens (who adopted the theory of vortices

with modifications of his own) supposes that there are particles of the

fluid matter which move about the earth in every possible direction,

within the spherical space which includes terrestrial objects; and

that the greater part of these motions being in spherical surfaces

concentric with the earth, produces a tendency towards the earth's

center.

This was a procedure tolerably arbitrary, but it was the best which

could be done. Saurin, a little later[356], gave nearly the same

solution of this difficulty. The solution, identifying a vortex of some

kind with a central force, made the hypothesis of vortices applicable

wherever central forces existed; but then, in return, it deprived the

image of a vortex of all that clearness and simplicity which had been

its first great recommendation.

But still there remained difficulties not less formidable. According

to this explanation of gravity, since the tendency of bodies to the

earth's center arose from the superior centrifugal force of the

whirling matter which pushed them inward as water pushes a light body

upward, bodies ought to tend more strongly to the center in proportion

as they are less dense. The rarest bodies should be the heaviest;

contrary to what we find.

Descartes's original solution of this difficulty has a certain degree

of ingenuity. According to him (_Princip._ IV. 23) a terrestrial body

consists of particles of the _third element_, and the more it has

of such particles, the more it excludes the parts of the _celestial

matter_, from the revolution of which matter gravity arises; and

therefore the denser is the terrestrial body, and the heavier it will

be.

But though this might satisfy him, it could not satisfy the

mathematicians who followed him, and tried to reduce his system to

calculation on mechanical principles. For how could they do this,

if the celestial matter, by the operation of which the phenomena

of force and motion were produced, was so entirely different from

ordinary matter, which alone had supplied men with experimental

illustrations of mechanical principles? In order that the celestial

matter, by its whirling, might produce the gravity of heavy bodies,

it was mechanically necessary that it must be very dense; and _dense_

in the ordinary sense of the term; for it was by regarding density in

the ordinary sense of the term that the mechanical necessity had been

established.

The Cartesians tried to escape this result (Huyghens, _Pesanteur_, p.

161, and John Bernoulli, _Nouvelles Pensées_, Art. 31) by saying that

there were two meanings of _density_ and _rarity_; that some fluids

might be rare by having their particles far asunder, others, by having

their particles very small though in contact. But it is difficult to

think that they could, as persons well acquainted with mechanical

principles, satisfy themselves with this distinction; for they could

hardly fail to see that the mechanical effect of any portion of fluid

depends upon the total mass moved, not on the size of its particles.

Attempts made to exemplify the vortices experimentally only showed more

clearly the force of this difficulty. Huyghens had found that certain

bodies immersed in a whirling fluid tended to the center of the vortex.

But when Saulmon[357] a little later made similar experiments, he had

the mortification of finding that the heaviest bodies had the greatest

tendency to recede from the axis of the vortex. "The result is," as

the Secretary of the Academy (Fontenelle) says, "exactly the opposite

of what we could have wished, for the [Cartesian] system of gravity:

but we are not to despair; sometimes in such researches disappointment

leads to ultimate success."

But, passing by this difficulty, and assuming that in some way or

other a centripetal force arises from the centrifugal force of the

vortex, the Cartesian mathematicians were naturally led to calculate

the circumstances of the vortex on mechanical principles; especially

Huyghens, who had successfully studied the subject of centrifugal

force. Accordingly, in his little treatise on the _Cause of

Gravitation_ (p. 143), he calculates the velocity of the fluid matter

of the vortex, and finds that, at a point in the equator, it is 17

times the velocity of the earth's rotation.

It may naturally be asked, how it comes to pass that a stream of fluid,

dense enough to produce the gravity of bodies by its centrifugal force,

moving with a velocity 17 times that of the earth (and therefore

moving round the earth in 85 minutes), does not sweep all terrestrial

objects before it. But to this Huyghens had already replied (p. 137),

that there are particles of the fluid moving _in all directions_, and

therefore that they neutralize each other's action, so far as lateral

motion is concerned.

And thus, as early as this treatise of Huyghens, that is, in three

years from the publication of Newton's _Principia_, a vortex is made

to mean nothing more than some machinery or other for producing a

central force. And this is so much the case, that Huyghens commends

(p. 165), as confirming his own calculation of the velocity of his

vortex, Newton's proof that at the Moon's orbit the centripetal force

is equal to the centrifugal; and that thus, this force is less than the

centripetal force at the earth's surface in the inverse proportion of

the squares of the distances.

John Bernoulli, in the same manner, but with far less clearness

and less candour, has treated the hypothesis of vortices as being

principally a hypothetical cause of central force. He had repeated

occasions given him of propounding his inventions for propping up the

Cartesian doctrine, by the subjects proposed for prizes by the Paris

Academy of Sciences; in which competition Cartesian speculations were

favourably received. Thus the subject of the Prize Essays for 1730

was, the explanation of the Elliptical Form of the planetary orbits

and of the Motion of their Aphelia, and the prize was assigned to

John Bernoulli, who gave the explanation on Cartesian principles. He

explains the elliptical figure, not as Descartes himself had done,

by supposing the vortex which carries the planet round the sun to be

itself squeezed into an elliptical form by the pressure of contiguous

vortices; but he supposes the planet, while it is carried round by the

vortex, to have a limited oscillatory motion to and from the center,

produced by its being originally, not at the distance at which it would

float in equilibrium in the vortex, but above or below that point. On

this supposition, the planet would oscillate to and from the center,

Bernoulli says, like the mercury when deranged in a barometer: and

it is evident that such an oscillation, combined with a motion round

the center, might produce an oval curve, either with a fixed or with

a moveable aphelion. All this however merely amounts to a possibility

that the oval _may_ be an ellipse, not to a proof that it will be so;

nor does Bernoulli advance further.

It was necessary that the vortices should be adjusted in such a manner

as to account for Kepler's laws; and this was to be done by making

the velocity of each stratum of the vortex depend in a suitable

manner on its radius. The Abbé de Molières attempted this on the

supposition of elliptical vortices, but could not reconcile Kepler's

first two laws, of equal elliptical areas in equal times, with his

third law, that the squares of the periodic times are as the cubes

of the mean distances[358]. Bernoulli, with his circular vortices,

could accommodate the velocities at different distances so that they

should explain Kepler's laws. He pretended to prove that Newton's

investigations respecting vortices (in the ninth Section of the Second

Book of the _Principia_) were mechanically erroneous; and in truth,

it must be allowed that, besides several arbitrary assumptions, there

are some errors of reasoning in them. But for the most part, the more

enlightened Cartesians were content to accept Newton's account of the

motions and forces of the solar system as part of their scheme; and to

say only that the hypothesis of vortices explained the origin of the

Newtonian forces; and that thus theirs was a philosophy of a higher

kind. Thus it is asserted (_Mém. Acad._ 1734), that M. de Molières

retains the beautiful theory of Newton entire, only he renders it

in a sort less Newtonian, by disentangling it from attraction, and

transferring it from a vacuum into a plenum. This plenum, though

not its native region, frees it from the need of attraction, which

is all the better for it. These points were the main charms of the

Cartesian doctrine in the eyes of its followers;--the getting rid of

attractions, which were represented as a revival of the Aristotelian

"occult qualities," "substantial forms," or whatever else was the

most disparaging way of describing the bad philosophy of the dark

ages[359];--and the providing some material intermedium, by means of

which a body may affect another at a distance; and thus avoid the

reproach urged against the Newtonians, that they made a body act where

it was not. And we are the less called upon to deny that this last

feature in the Newtonian theory was a difficulty, inasmuch as Newton

himself was never unwilling to allow that gravity might be merely an

effect produced by some ulterior cause.

With such admissions on the two sides, it is plain that the Newtonian

and Cartesian systems would coincide, if the hypothesis of vortices

could be modified in such a way as to produce the force of gravitation.

All attempts to do this, however, failed: and even John Bernoulli,

the most obstinate of the mathematical champions of the vortices,

was obliged to give them up. In his Prize Essay for 1734, (on the

Inclinations of the Planetary Orbits[360],) he says (Art. VIII.), "The

gravitation of the Planets towards the center of the Sun and the weight

of bodies towards the center of the earth has not, for its cause,

either the attraction of M. Newton, or the centrifugal force of the

matter of the vortex according to M. Descartes;" and he then goes on to

assert that these forces are produced by a perpetual torrent of matter

tending to the center on all sides, and carrying all bodies with it.

Such a hypothesis is very difficult to refute. It has been taken up in

more modern times by Le Sage[361], with some modifications; and may be

made to account for the principal facts of the universal gravitation

of matter. The great difficulty in the way of such a hypothesis is,

the overwhelming thought of the whole universe filled with torrents

of an invisible but material and tangible substance, rushing in every

direction in infinitely prolonged straight lines and with immense

velocity. Whence can such matter come, and whither can it go? Where

can be its perpetual and infinitely distant fountain, and where the

ocean into which it pours itself when its infinite course is ended?

A revolving whirlpool is easily conceived and easily supplied; but

the central torrent of Bernoulli, the infinite streams of particles

of Le Sage, are an explanation far more inconceivable than the thing

explained.

But however the hypothesis of vortices, or some hypothesis substituted

for it, was adjusted to explain the facts of attraction to a

center, this was really nearly all that was meant by a vortex or a

"tourbillon," when the system was applied. Thus in the case of the last

act of homage to the Cartesian theory which the French Academy rendered

in the distribution of its prizes, the designation of a Cartesian

Essay in 1741 (along with three Newtonian ones) as worthy of a prize

for an explanation of the Tides; the difference of high and low water

was not explained, as Descartes has explained it, by the pressure, on

the ocean, of the terrestrial vortex, forced into a strait where it

passes under the Moon; but the waters were supposed to rise towards the

Moon, the terrestrial vortex being disturbed and broken by the Moon,

and therefore less effective in forcing them down. And in giving an

account of a Tourmaline from Ceylon (Acad. Sc. 1717), when it has been

ascertained that it attracts and repels substances, the writer adds, as

a matter of course, "It would seem that it has a vortex." As another

example, the elasticity of a body was ascribed to vortices between its

particles: and in general, as I have said, a vortex implied what we now

imply by speaking of a central force.

4. In the same manner vortices were ascribed to the Magnet, in order

to account for its attractions and repulsions. But we may note a

circumstance which gave a special turn to the hypothesis of vortices as

applied to this subject, and which may serve as a further illustration

of the manner in which a transition may be made from one to the other

of two rival hypotheses.

If iron filings be brought near a magnet, in such a manner as to be

at liberty to assume the position which its polar action assigns to

them; (for instance, by strewing them upon a sheet of paper while

the two poles of the magnet are close below the paper;) they will

arrange themselves in certain curves, each proceeding from the N. to

the S. pole of the magnet, like the meridians in a map of the globe.

It is easily shown, on the supposition of magnetic attraction and

repulsion, that these _magnetic curves_, as they are termed, are each

a curve whose tangent at every point is the direction of a small line

or particle, as determined by the attraction and repulsion of the two

poles. But if we suppose a _magnetic vortex_ constantly to flow out

of one pole and into the other, in streams which follow such curves,

it is evident that such a vortex, being supposed to exercise material

pressure and impulse, would arrange the iron filings in corresponding

streams, and would thus produce the phenomenon which I have described.

And the hypothesis of _central torrents_ of Bernoulli or Le Sage which

I have referred to, would, in its application to magnets, really become

this hypothesis of a magnetic vortex, if we further suppose that the

matter of the torrents which proceed to one pole and from the other,

mingles its streams, so as at each point to produce a stream in the

resulting direction. Of course we shall have to suppose two sets of

magnetic torrents;--a boreal torrent, proceeding to the north pole,

and from the south pole of a magnet; and an austral torrent proceeding

to the south and from the north pole:--and with these suppositions,

we make a transition from the hypothesis of attraction and repulsion,

to the Cartesian hypothesis of vortices, or at least, torrents, which

determine bodies to their magnetic positions by impulse.

Of course it is to be expected that, in this as in the other case,

when we follow the hypothesis of impulse into detail, it will need to

be loaded with so many subsidiary hypotheses, in order to accommodate

it to the phenomena, that it will no longer seem tenable. But the

plausibility of the hypothesis in its first application cannot be

denied:--for, it may be observed, the two _opposite_ streams would

counteract each other so as to produce no local _motion_, only

_direction_. And this case may put us on our guard against other

suggestions of forces acting in curve lines, which may at first sight

appear to be discerned in magnetic and electric phenomena. Probably

such curve lines will all be found to be only resulting lines, arising

from the direct action and combination of elementary attraction and

repulsion.

5. There is another case in which it would not be difficult to devise

a mode of transition from one to the other of two rival theories;

namely, in the case of the emission theory and the undulation theory

of Light. Indeed several steps of such a transition have already

appeared in the history of optical speculation; and the conclusive

objection to the emission theory of light, as to the Cartesian theory

of vortices, is, that no amount of additional hypotheses will reconcile

it to the phenomena. Its defenders had to go on adding one piece of

machinery after another, as new classes of facts came into view, till

it became more complex and unmechanical than the theory of epicycles

and eccentrics at its worst period. Otherwise, as I have said, there

was nothing to prevent the emission theory from migrating into the

undulatory theory, and as the theory of vortices did into the theory

of attraction. For the emissionists allow that rays may _interfere_;

and that these interferences may be modified by alternate _fits_ in the

rays; now these fits are already a kind of _undulation_. Then again the

phenomena of polarized light show that the fits or undulations must

have a _transverse_ character: and there is no reason why emitted rays

should not be subject to _fits_ of _transverse_ modification as well

as to any other fits. In short, we may add to the emitted rays of the

one theory, all the properties which belong to the undulations of the

other, and thus account for all the phenomena on the emission theory;

with this limitation only, that the emission will have no share in the

explanation, and the undulations will have the whole. If, instead of

conceiving the universe full of a _stationary_ ether, we suppose it

to be full of etherial particles moving in every direction; and if we

suppose, in the one case and in the other, this ether to be susceptible

of undulations proceeding from every luminous point; the results of the

two hypotheses will be the same; and all we shall have to say is, that

the supposition of the emissive motion of the particles is superfluous

and useless.

6. This view of the manner in which rival theories pass into one

another appears to be so unfamiliar to those who have only slightly

attended to the history of science, that I have thought it might be

worth while to illustrate it by a few examples.

It might be said, for instance, by such persons[362], "Either the

planets are not moved by vortices, or they do not move by the law by

which heavy bodies fall. It is impossible that both opinions can be

true." But it appears, by what has been said above, that the Cartesians

did hold both opinions to be true; and one with just as much reason as

the other, on their assumptions. It might be said in the same manner,

"Either it is false that the planets are made to describe their orbits

by the above quasi-Cartesian theory of Bernoulli, or it is false that

they obey the Newtonian theory of gravitation." But this would be

said quite erroneously; for if the hypothesis of Bernoulli be true,

it is so because it agrees in its result with the theory of Newton.

It is not only possible that both opinions may be true, but it is

certain that if the first be so, the second is. It might be said again,

"Either the planets describe their orbits by an inherent virtue, or

according to the Newton theory." But this again would be erroneous,

for the Newtonian doctrine decided nothing as to whether the force of

gravitation was inherent or not. Cotes held that it was, though Newton

strongly protested against being supposed to hold such an opinion.

The word _inherent_ is no part of the physical theory, and will be

asserted or denied according to our metaphysical views of the essential

attributes of matter and force.

Of course, the possibility of two rival hypotheses being true, one

of which takes the explanation a step higher than the other, is

not affected by the impossibility of two contradictory assertions

of the _same order_ of generality being both true. If there be a

new-discovered comet, and if one astronomer asserts that it will return

once in _every_ twenty years, and another, that it will return once in

every thirty years, both cannot be right. But if an astronomer says

that though its interval was in the last instance 30 years, it will

only be 20 years to the next return, in consequence of perturbation and

resistance, he may be perfectly right.

And thus, when different and rival explanations of the same phenomena

are held, till one of them, though long defended by ingenious men, is

at last driven out of the field by the pressure of facts, the defeated

hypothesis is transformed before it is extinguished. Before it has

disappeared, it has been modified so as to have all palpable falsities

squeezed out of it, and subsidiary provisions added, in order to

reconcile it with the phenomena. It has, in short, been penetrated,

infiltrated, and metamorphosed by the surrounding medium of truth,

before the merely arbitrary and erroneous residuum has been finally

ejected out of the body of permanent and certain knowledge.

FOOTNOTES:

[Footnote 352: These remarks were written in 1841. The accompanying

Memoir contains a further discussion of this problem.]

APPENDIX H.

ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA.

(_Cam. Phil. Soc._ MAY 21, 1849.)

The Newtonian doctrine of universal gravitation, as the cause of

the motions which take place in the solar system, is so entirely

established in our minds, and the fallacy of all the ordinary arguments

against it is so clearly understood among us, that it would undoubtedly

be deemed a waste of time to argue such questions in this place, so far

as physical truth is concerned. But since in other parts of Europe,

there are teachers of philosophy whose reputation and influence are

very great, and who are sometimes referred to among our own countrymen

as the authors of new and valuable views of truth, and who yet reject

the Newtonian opinions, and deny the validity of the proofs commonly

given of them, it may be worth while to attend for a few minutes to the

declarations of such teachers, as a feature in the present condition

of European philosophy. I the more readily assume that the Cambridge

Philosophical Society will not think a communication on such a subject

devoid of interest, in consequence of the favourable reception which it

has given to philosophical speculations still more abstract, which I

have on previous occasions offered to it. I will therefore proceed to

make some remarks on the opinions concerning the Newtonian doctrine of

gravitation, delivered by the celebrated Hegel, of Berlin, than whom no

philosopher in modern, and perhaps hardly any even in ancient times,

has had his teaching received with more reverential submission by his

disciples, or been followed by a more numerous and zealous band of

scholars bent upon diffusing and applying his principles.

The passages to which I shall principally refer are taken from one of

his works which is called the _Encyclopædia_ (Encyklopädie), of which

the First Part is _the Science of Logic_, the Second, the _Philosophy

of Nature_, the Third, the _Philosophy of Spirit_. The Second Part,

with which I am here concerned, has for an _aliter_ title, _Lectures

on Natural Philosophy_ (Vorlesungen über Natur-philosophie), and would

through its whole extent offer abundant material for criticism, by

referring it to principles with which we are here familiar: but I

shall for the present confine myself to that part which refers to the

subject which I have mentioned, the Newtonian Doctrine of Gravitation,

§ 269, 270, of the work. Nor shall I, with regard to this part, think

it necessary to give a continuous and complete criticism of all the

passages bearing upon the subject; but only such specimens, and such

remarks thereon, as may suffice to show in a general manner the value

and the character of Hegel's declarations on such questions. I do not

pretend to offer here any opinion upon the value and character of

Hegel's philosophy in general: but I think it not unlikely that some

impression on that head may be suggested by the examination, here

offered, of some points in which we can have no doubt where the truth

lies; and I am not at all persuaded that a like examination of many

other parts of the Hegelian _Encyclopædia_, would not confirm the

impression which we shall receive from the parts now to be considered.