PART I

NATURAL PHILOSOPHY

BY

WILHELM OSTWALD

TRANSLATED

BY

THOMAS SELTZER

_With the author's special revision for the American edition_

NEW YORK

HENRY HOLT AND COMPANY

1910

COPYRIGHT, 1910,

BY

HENRY HOLT AND COMPANY

_Published November_, 1910

THE QUINN & BODEN CO. PRESS

RAHWAY N. J.

The original of this book was published

as volume I in Reclam's BÜCHER DER

NATURWISSENSCHAFT.

PREFACE

The beginning of the twentieth century is marked by a sudden rise of

interest in philosophy. This is especially manifest in the vast growth

of philosophic literature. The present movement, it is noteworthy, is by

no means a revival proceeding from the academic philosophy traditionally

represented at the universities, but has rather the original character

of _natural philosophy_. It owes its origin to the fact that after the

specialization of the last half century, the synthetic factors of

science are again vigorously asserting themselves. The need finally to

consider all the numerous separate sciences from a general point of view

and to find the connection between one's own activity and the work of

mankind in its totality, must be regarded as the most prolific source of

the present philosophic movement, just as it was the source of the

natural philosophic endeavors a hundred years ago.

But while that old natural philosophy soon ended in a boundless sea of

speculation, the present movement gives promise of permanent results,

because it is built upon an extremely broad basis of experience. The

laws of energy in the inorganic world and the laws of evolution in the

organic world furnish mental instruments for a conceptual elaboration

of the material provided by science, instruments capable not only of

unifying present knowledge, but also of evoking the knowledge of the

future. If it is not permissible to regard this unification as

exhaustive and sufficient for all time, yet there is still so much left

for us to do in working over the material we have on hand from the

general points of view just mentioned, that the need for systematizing

must be satisfied before we can turn our gaze upon things more remote.

The present work is meant to serve as the first aid and guide in the

acquisition of these comprehensive notions of the external world and the

inner life. It is not meant to develop or uphold a "system of

philosophy." Through long experience as a teacher the writer has learned

that those are the best pupils who soon go their own way. However, it

_is_ meant to uphold a certain method, that is, the scientific (or, if

you will, the _natural_ scientific), which takes its problems, and

endeavors to solve its problems, from experience and for experience. If,

as a result, several points of view arise that differ from those of the

present day, and consequently demand a different attitude toward

important matters in the immediate future, this very fact affords proof

that our present natural philosophy does not lead away from life, but

aims to form a part of our life, and has a right to.

CONTENTS

PAGE

INTRODUCTION 1

PART I

GENERAL THEORY OF KNOWLEDGE 11

1. The Formation of Concepts 11

2. Science 13

3. The Aim of Science 13

4. Concrete and Abstract 16

5. The Subjective Part 17

6. Empirical Concepts 18

7. Simple and Complex Concepts 19

8. The Conclusion 24

9. The Natural Laws 28

10. The Law of Causation 31

11. The Purification of the Causal Relation 34

12. Induction 38

13. Deduction 40

14. Ideal Cases 44

15. The Determinateness of Things 47

16. The Freedom of the Will 50

17. The Classification of the Sciences 53

18. The Applied Sciences 57

PART II

LOGIC, THE SCIENCE OF THE MANIFOLD, AND MATHEMATICS 61

19. The Most General Concept 61

20. Association 63

21. The Group 65

22. Negation 68

23. Artificial and Natural Groups 69

24. Arrangement of the Members 75

25. Numbers 78

26. Arithmetic, Algebra, and the Theory of Numbers 79

27. Co-ordination 80

28. Comparison 82

29. Numbers 85

30. Signs and Names 86

31. The Written Language 89

32. Pasigraphy and Sound Writing 92

33. Sound Writing 96

34. The Science of Language 97

35. Continuity 101

36. Measurement 107

37. The Function 109

38. The Application of the Functional Relation 112

39. The Law of Continuity 113

40. Time and Space 118

41. Recapitulation 124

PART III

THE PHYSICAL SCIENCES 127

42. General 127

43. Mechanics 128

44. Kinetic Energy 132

45. Mass and Matter 136

46. Energetic Mechanics 138

47. The Mechanistic Theories 140

48. Complementary Branches of Mechanics 144

49. The Theory of Heat 147

50. The Second Fundamental Principle 150

51. Electricity and Magnetism 154

52. Light 156

53. Chemical Energy 159

PART IV

THE BIOLOGIC SCIENCES 163

54. Life 163

55. The Storehouse of Free Energy 168

56. The Soul 171

57. Feeling, Thinking, Acting 174

58. Society 179

59. Language and Intercourse 182

60. Civilization 184

INDEX 187

INTRODUCTION

Natural science and natural philosophy are not two provinces mutually

exclusive of each other. They belong together. They are like two roads

leading to the same goal. This goal is the domination of nature by man,

which the various natural sciences reach by collecting all the

individual actual relations between the natural phenomena, placing them

in juxtaposition, and seeking to discover their interdependence, upon

the basis of which one phenomenon may be foretold from another with more

or less certainty. Natural philosophy accompanies these specialized

labors and generalizations with similar labors and generalizations, only

of a more universal nature. For instance, while the science of

electricity, as a branch of physics, deals with the relation of

electrical phenomena to one another and to phenomena in other branches

of physics, natural philosophy is not only concerned with the question

of the mutual connection of _all_ physical relations, but also endeavors

to include in the sphere of its study chemical, biological,

astronomical, in short, all the known phenomena. In other words,

_natural philosophy is the most general branch of natural science_.

Here two questions are usually asked. First, how can we define the

boundary line between natural philosophy and the special sciences,

since, obviously, sharp lines of demarcation are out of the question?

Secondly, how can we investigate and teach natural philosophy, when it

is impossible for any one person to master all the sciences completely,

and so obtain a bird's-eye view of the general relations between all the

branches of knowledge? To the beginner especially, who must first learn

the various sciences, it seems quite hopeless to devote himself to a

study that presupposes a command of them.

Since a discussion of the two questions will afford an excellent

preliminary survey of the work in hand, it will be well to consider them

in detail. In the first place, _the lack of complete and precise

boundary lines is a general characteristic of all natural things_, and

science is a natural thing. If, for instance, we try to differentiate

sharply between physics and chemistry, we are met with the same

difficulty. So also in biology if we try to settle beyond the shadow of

a doubt the line of separation between the animal and the vegetable

kingdoms.

If, despite this well-known impossibility, we consider the division of

natural things into classes and orders as by no means useless and do not

discard it, but regard it as an important scientific work, this is

practical proof that such classification preserves its essential

usefulness, even if it does not attain ideal definiteness. For, this

imperfection notwithstanding, classification reaches its end, which is

a comprehensive view, and thus a mastery, of the manifoldness of

phenomena. For example, with the overwhelming majority of organic beings

there is no doubt whether they are animals or plants. Similarly, most

phenomena of inorganic nature can readily be designated as physical or

chemical. For all such cases, therefore, the existing classification is

good and useful. The few cases presenting difficulty may very well be

considered by themselves wherever they occur, and we need merely take

cognizance of them here. It follows from this, to be sure, that

classification will be all the _better fitted to its purpose the less

frequently_ such doubtful cases arise, and that we have an interest in

repeatedly testing existing classifications with a view to finding out

if they cannot be supplanted by more suitable ones.

In these matters it is much the same as when we look upon the waves on

the surface of a large body of water. Our first glance tells us that a

number of waves are rolling there; and from a point giving us a

sufficiently wide outlook, we can count them and gauge their width. But

where is the line of division between one wave and the next? We

undoubtedly see one wave following another, yet it is impossible for us

to indicate precisely the end of one and the beginning of the next. Are

we then to deduce that it is superfluous or unfeasible to designate the

waves as different? By no means. On the contrary, in strictly

scientific work we will endeavor to find some suitable definition of the

boundary line between two consecutive waves. It may then be called an

arbitrary line, and in a degree arbitrary it will certainly be. But to

the investigator this does not matter. What concerns him is, if, with

the help of this definition, wave lengths can be unequivocally

determined, and if this is possible, he will use the definition as

suitable to the purposes of science, without dismissing from his mind

the idea that possibly some other definition may provide an even easier

or sharper determination. Such an one he would instantly prefer to the

old one.

Thus we see that these questions of classification are not questions of

the so-called "essence" of the thing, _but pertain merely to purely

practical arrangements for an easier and more successful mastery of

scientific problems_. This is an extremely important point of view, much

more far-reaching than is apparent here at its first application.

As to the second objection, I will admit its validity. But here, too, we

have a phenomenon appearing in all branches and forms of science.

Therefore we must familiarize ourselves with it in advance. Science was

created by man for man's purposes, and, consequently, like all human

achievements, possesses the indestructible quality of imperfection. But

the mere fact that a successful working science exists, with the help of

which human life has been fundamentally modified, signifies that _the

quality of incompleteness in human learning is no hindrance to its

efficiency_. For what science has once worked out always contains a

portion of truth, hence a portion of efficiency. The old corpuscular

theory of light, which now seems so childishly incomplete to us, was

adequate, none the less, for satisfactorily explaining the phenomena of

reflection and refraction, and the finest telescopes have been built

with its help. This is due to the _true elements_ in it, which taught us

correctly to calculate the direction of rays of light in reflection and

refraction. The rest was merely an arbitrary accessory which had to fall

when new, contradictory facts were discovered. These facts could not

have been taken into consideration when the theory was propounded,

because they were not yet known. But when the corpuscular theory of

light was replaced by the theory of waves of an elastic ether, geometric

optics at first remained quite unchanged, because the theory of straight

lines of rays could be deduced from the new views also, though not so

easily and smoothly. And geometric optics was then concerned with

nothing but these straight lines, in no wise with the question of their

propagation. It did not become clear until recently that this conception

of straight lines of rays is incomplete, though, it is true, it made a

first approach toward the presentation of actual phenomena. It fails

when it comes to characterize the behavior of a pencil of rays of large

aperture. The old idea of a straight line of rays was to be replaced by

a more complex concept with more varied characteristics, namely, the

wave-surface. The greater variety of this concept renders possible the

presentation of the greater variety of the optical phenomena just

mentioned. And from it proceed the very considerable advances that have

been made, since the new theory was propounded, in optical instruments,

especially the microscope and the photographic objective, for the

purposes of which pencils of rays of large aperture are required. The

astronomic objective with its small angle of aperture has not undergone

particularly important improvements.

Experience in every province of science is the same as in this. Science

is not like a chain which snaps when only a single link proves to be

weak. It is like a tree, or, better still, like a forest, in which all

sorts of changes or ravages go on without causing the whole to pass out

of existence or cease to be active. The relations between the various

phenomena, once they become known, continue to exist as indestructible

components of all future science. It may come to pass, in fact, does

come to pass very frequently, that the form in which those relations

were first expressed prove to be imperfect, and that the relations

cannot be maintained quite generally. It turns out that they are

subjected to other influences which change them because they had been

unknown, and which could not have been taken into consideration at the

discovery and first formulation of these relations. But no matter what

changes science may undergo, a certain residue of that first knowledge

will remain and never be lost. In this sense, a truth that science has

once gained has life eternal, that is, it will exist as long as human

science exists.

Applying this general notion to our case, we have the following. How far

and how generally at any given time the relations of the various

phenomena are summed up in fixed forms, that is, in natural laws, will

depend upon the stage attained by each of the special sciences. But

since science has been in existence it has yielded a certain number of

such general laws, and these, though they have been filed down a good

deal in form and expression, and have undergone many corrections as to

the limits of their application, nevertheless have preserved their

essence, since they began their existence in the brains of human

investigators. The net of the relations of phenomena grows ever wider

and more diversified, but its chief features persist.

The same is true of an individual. No matter how limited the circle of

his knowledge, _it is a part of the great net, and therefore possesses

the quality by virtue of which the other parts readily join it as soon

as they reach the consciousness and knowledge of the individual_. The

man who thus enters the realm of science acquires advantages which may

be compared to those of a telephone in his residence. If he wishes to,

he may be connected with everybody else, though he will make extremely

limited use of his privilege, since he will try to reach only those with

whom he has personal relations. But once such relations have been

established, the possibility of telephone communication is

simultaneously and automatically established. Similarly, every bit of

knowledge that the individual appropriates will prove to be a regular

part of the central organization, the entire extent of which he can

never cover, though each individual part has been made accessible to

him, provided he wants to take cognizance of it.

The mere beginner in learning, therefore, when receiving the most

elementary instruction in school, or from his parents, or even from his

personal experiences in his surroundings, is grasping one or more

threads of the mighty net, and can grope his way farther along it in

order to draw an increasing area of it into his life and the field of

his activity. _And this net has the valuable, even precious quality of

being the same that joins the greatest and most comprehensive intellects

in mankind to one another._ The truths a man has once grasped he need

never learn afresh so far as their _actual content_ is concerned, though

not infrequently--especially in newer sciences--he may have to see the

_form_ of their presentation and generalization change. For this reason

it is of such especial importance for each individual from the first to

perceive these unalterable facts and realize that they are unalterable

and learn to distinguish them from the alterable forms of their

presentation. It is in this very regard that the incompleteness of human

knowledge is most clearly revealed. Time and again in the history of

science form has been taken for content, and necessary changes of

form--a merely practical question--have been confused with revolutionary

modifications of the content.

Thus, each presentation of a science has its natural philosophic

portion. In text-books, whether elementary or advanced, the chapter on

natural philosophy is found usually at the beginning of the book,

sometimes at the end, in the form of a "general introduction," or

"general summary." In the special works in which the latest advances of

science are made known by the investigators, the natural philosophic

portions are usually to be found in the form of theses, of principles,

which are not discussed, often not even explicitly stated, but upon the

acceptance of which depend all the special conclusions that are drawn,

in the case in hand, from the new facts or thoughts imparted. Whether at

the beginning or at the end of the book, these most general principles

do not quite occupy the place that befits them. If at the introduction

of the text-book, they are practically devoid of content, since the

facts they are meant to summarize are yet to be unfolded in the course

of the presentation. If at the end, they come too late, since they have

already been applied in numerous instances, though without reference to

their general nature. The best method is--and a good teacher always

employs this method, whether in the spoken or the written word--to let

the generalizations come whenever the individual facts imparted require

and justify them.

Thus, all instruction in natural sciences is necessarily interspersed

with natural philosophy, good or bad, according to the clearheadedness

of the teacher. If we wish to obtain a perfect survey of a complex

structure, as, for instance, the confusion of streets in a large city,

we had better not try to know each street, but study a general plan,

from which we learn the comparative situation of the streets. So it is

well for us in studying a special science to look at our general plan,

if for no other reason than to keep from losing our way when it may

chance to lead through a quarter hitherto unknown. This is the purpose

of the present work.

PART I

GENERAL THEORY OF KNOWLEDGE

=1. The Formation of Concepts.= To the human mind, as it slowly awakens

in every child, the world at first seems a chaos consisting of mere

individual experiences. The only connection between them is that they

follow each other consecutively. Of these experiences, all of which at

first are different from one another, certain parts come to be

distinguished by the fact that they are repeated more frequently, and

therefore receive a special character, that of _being familiar_. The

familiarity is due to our _recalling_ a former similar experience; in

other words, to our feeling that there is a relation between the present

experience and certain former experiences. The cause of this phenomenon,

which is at the basis of all mental life, is a quality common to all

living things, and manifesting itself in all their functions, while

appearing but rarely or accidentally in inorganic nature. It is the

quality by virtue of which _the oftener any process has taken place in a

living organism the more easily it is repeated_. Here is not yet the

place to show how almost all the characteristic qualities of living

beings, from the preservation of the species to the highest intellectual

accomplishments, are conditioned by this special peculiarity. Suffice it

to say that because of this quality all those processes which are

repeated frequently in any given living organism, assume spontaneously,

that is, from physiologic reasons, a character distinguishing them

essentially from those which appear only in isolated instances, or

sporadically.

If a living being is equipped with consciousness and thought, like man,

then the conscious recollections of such uniform experiences form the

enduring or permanent part in the sum-total of his experiences. Each

time a complex event, like the change of seasons, for example, which we

know from experience repeats itself--each time a part of such an event

reaches our consciousness, we are prepared also for the other parts that

experience teaches are connected with it. This makes it possible for us

to foresee future events. What significance the foreseeing of future

events has for the preservation and the development of the individual as

well as the species can only be indicated here. To give one instance, it

is our ability to foretell the coming of winter with the impossibility

of obtaining food directly during the winter that causes us to refrain

from at once using up all the food we have and to preserve it for the

day of need. The ability to foretell, therefore, becomes the foundation

of the whole structure of economic life.

=2. Science.= The prophecy of future events based upon the knowledge of

the details of recurring events is called _science_ in its most general

sense. Here, as in most cases in which language became fixed long before

men had a clear knowledge of the things designated, the name of the

thing is easily associated with false ideas arising either from errors

that had been overcome or from other, still more accidental, causes.

Thus, the mere knowledge of _past_ events is also called science without

any thought of its use for prophesying future events. Yet a moment's

reflection teaches that mere knowledge of the past which is not meant

to, or cannot, serve as a basis for shaping the future is utterly

aimless knowledge, and must take its place with other aimless activities

called _play_. There are all sorts of plays requiring great acumen and

patient application, as for example the game of chess; and no one has

the right to prevent any individual from pursuing such games. But the

player for his part must not demand special regard for his activity. By

using his energies for his personal pleasure and not for a social

purpose, that is, for a general human purpose, he loses every claim to

the social encouragement of his activity, and must be content if only

his individual rights are respected; and that, too, only so long as the

social interests do not suffer by it.

=3. The Aim of Science.=These views are deliberately opposed to a very

widespread idea that science should be cultivated "for its own sake,"

and not for the sake of the benefits it actually brings or may be made

to bring. We reply that there is nothing at all which is done merely

"for its own sake." Everything, without exception, is done for human

purposes. These purposes range from momentary personal satisfaction to

the most comprehensive social services involving disregard of one's own

person. But in all our actions we never get beyond the sphere of the

human. If, therefore, the phrase "for its own sake" means anything, it

means that science should be followed for the sake of the immediate

pleasure it affords, that is to say, as _play_ (as we have just

characterized it), and in the "for-its-own-sake" demand there is hidden

a misunderstood idealism, which, on closer inspection, resolves itself

into its very opposite, the degradation of science.

The element of truth hidden in that misunderstood phrase is, that in a

higher state of culture it is found better to disregard the _immediate_

technical application in the pursuit of science, and to aim only for the

greatest possible perfection and depth in the solution of its individual

problems. Whether this is the correct method of procedure and when it is

so, is solely a question of the general state of culture. In the early

stages of human civilization such a demand is utterly meaningless, and

all science is necessarily and naturally confined to immediate life. But

the wider and more complex human relations become, the wider and surer

must the ability to predict future events become. Then it is the

function of prophesying science to have answers ready for questions

which as yet have not become pressing, but which with further

development may sooner or later become so.

In the net-like interlacing of the sciences, that is, of the various

fields of knowledge, described in the introduction, we must always

reckon with the fact that our anticipation of what kind of knowledge we

shall next need must always remain very incomplete. It is possible to

foresee future needs in general outline with more or less certainty, but

it is impossible to be prepared for particular individual cases which

lie on the _border line_ of such anticipation, and which may sometimes

become of the utmost importance and urgency. Therefore it is one of the

most important functions of science to achieve as _perfect_ an

elaboration as possible of _all_ the relations conceivable, and in this

practical necessity lies the foundation of the general or _theoretical_

elaboration of science.

=The Science of Concepts.= Here the question immediately arises: how can

we secure such perfection? The answer to this general preliminary

question of all the sciences belongs to the sphere of the first or the

most general of all the sciences, a knowledge of which is presupposed

for the pursuit of the other sciences. Since its foundation by the Greek

philosopher Aristotle it has borne the name of _logic_, which name,

etymologically speaking, hints suspiciously at the _word_, and the word,

as is known, steps in where ideas are wanting. Here, however, we have to

deal with the very science of ideas, to which language bears the

relation only of a means--and often an inadequate means--to an end. We

have already seen how, through the physiologic fact of _memory_,

experiences are found in our consciousness which are similar, that is,

partially coinciding with one another. These coinciding parts are those

concerning which we can make predictions, for the very reason that they

coincide in every single instance, and they alone, therefore, constitute

that part of our experience which bears results and hence has

significance.

=4. Concrete and Abstract.= Such coinciding or repeated parts of similar

experiences we call, as already stated, _concepts_. But here, too,

attention must immediately be drawn to a linguistic imperfection, which

consists in the fact that in such a group of coinciding experiences we

designate by the same name both the isolated experience or the object of

a special experience and the totality of _all_ the coinciding

experiences; in other words, all the similar experiences. Thus, _horse_

means, on the one hand, quite a definite thing which for the moment

forms an object of our experience, and, on the other, the totality of

all possible similar objects which have been present in our former

experiences, and which we shall meet in our future experiences. It is

true that these two sorts of contents of consciousness bearing the same

name are distinguished also as _concrete_ and _abstract_, and there is

an inclination to attribute "reality" only to the first, while the

other, as "mere entities in thought," are relegated to a lesser degree

of reality. As a matter of fact, the difference, though important, is of

quite another kind. It is the difference between the _momentary

experience_, as opposed to the totality of the corresponding _memories_

and _expectations_. Hence not so much a difference in _reality_ as in

_presence_. However, our observations have already made it apparent that

presence alone never yields knowledge. A necessary part of knowledge is

the memory of former similar experiences. For without such memory and

the corresponding comparison, it is quite impossible for us to get at

those things which agree and which, therefore, may be predicted; and we

should stand before every one of our experiences with the helplessness

of a new-born babe.[A]

[A] Sometimes on suddenly awaking from a profound sleep a person finds

himself for the moment deprived of his personal stock of memories,

unable to recall where and in what circumstances he is. No one who has

experienced such a condition can ever forget the terrifying sense of

helplessness it brings.

=5. The Subjective Part.= We shall therefore have to recognize realities

in abstract ideas in so far as they must rest upon some experiences to

be at all intelligible to us. Since the formation of concepts depends

upon memories, and these may refer, according to the individual, to very

different parts of the same experience of different individuals,

concepts always possess an element dependent upon the individual, or a

_subjective_ element. This, however, does not consist in the _addition_

by the individual of new parts not found in the experience, but, on the

contrary, in the different _choice_ out of what is found in the

experience. If every individual absorbed all parts of the experience,

the individual, or subjective, differences would disappear. And since

scientific experience endeavors to make the absorption of experiences as

complete as possible, it aims nearer and nearer to this ideal by seeking

to equalize the subjective deficiency of the individual memory through

the collocation of as many and as various memories as possible, thus

filling in the subjective gaps in experience as far as possible and

rendering them harmless.

=6. Empirical Concepts.= First and unconditionally those concepts

possess reality which always and without exception are based on

_experienced_ facts. But we can easily make manifold arbitrary

combinations of concepts from different experiences, since our memory

freely places them at our disposal, and from such a combination we can

form a new concept. Of course it is not necessary that our arbitrary

combination should also be found in our past or future experiences. On

the contrary, we may rather expect that there could be many more

arbitrary combinations not to be found in experience than combinations

later "confirmed" by experience. The former are purposeless because

unreal, the latter, on the contrary, are of the utmost consequence

because upon them is based the real aim of knowledge, prediction. The

former are those which have brought the very "reality" of the concepts

into ill repute, while the latter show that the formation and the mutual

reaction of the concepts practically constitute the entire content of

all science. It is of the greatest importance, therefore, to distinguish

between the two kinds of concept combinations, and the study of this

differentiation forms the content of that most general of all the

sciences which we have characterized as logic, or, better, the science

of concepts.

=7. Simple and Complex Concepts.= The formation of concepts consists, as

we have seen, in the selection of those parts of different but similar

experiences which coincide with one another and in the elimination of

those that are different in kind. The results of such a procedure may

vary greatly according to the number and the difference of the

experiences placed in relation with one another. If, for example, we

compare only a few experiences, and if, moreover, these experiences are

very similar to one another, then the resulting concepts will contain

very many parts that agree. But at the same time they will have the

peculiarity of not being applicable to other experiences, since these

are without some of the coinciding parts of that narrower circle. Thus,

for example, the concept which a rustic chained to the soil all his life

has of human work does not apply to the work of the city man. A concept

will embrace a larger number of individual cases in proportion as it

contains fewer different parts. And by systematically following out this

thought we arrive at the conclusion that the concepts that are simple

and have no different parts at all find the widest application or are

the most general.

The elimination of the non-coinciding parts from the concept-forming

experience is called _abstraction_. Obviously abstraction must be

carried the farther the more numerous and the more varied the

experiences from which the concepts are abstracted, and the simplest

concepts are the most abstract.

By looking back over the ground just traversed, the less abstract ideas

may also be regarded as the _more complex_ in contradistinction to the

simpler ones. Only we must guard against the error of literal

interpretation and not suppose that the less simple concepts have really

been compounded of the simpler ones. In point of origin they actually

existed first, since the experience contains the ensemble of all the

parts, those which have been retained as well as those which have been

eliminated. It is only later, by a characteristic mental operation,

after we have analyzed the more complex concept, that is, after we have

disclosed the simpler concepts existing in it, that we can compound it

again; in other words, execute its synthesis.

These relations bear a striking resemblance to the relations known from

chemistry to exist between substances, namely, between elements and

compounds. From the chaos of all objects of experimentation (chemistry

purposely limits itself to ponderable bodies) the _pure_ substances are

sifted out--an operation corresponding to the formation of concepts. The

pure substances prove to be either _simple_ or _compound_, and the

compounds are so constituted that they can each be reduced to a limited

number of simple substances. The simple substances, or _elements_,

retain this quality of simplicity only until they are recalled; that is,

until it has been proved that they, too, can be resolved into still

simpler elements. The same is true of the simple concepts. They can

claim simplicity only until their complex nature is demonstrated.

With all these similarities we must be extremely careful never to forget

the differences existing alongside the agreements. So hereafter we shall

make no further use of the chemical simile. It was brought into

requisition merely in order to acquaint the beginner the more readily

with the entire method of investigation by means of a more familiar

field of thought and study. It is quite certain, however, that side by

side with the given similarities there are also radical differences.

Moreover, the notion of simple and complex concepts or "ideas" had been

elaborated by John Locke long before chemistry reached its present state

of clearness concerning the concept of the elements.

Nevertheless since then the relation has been completely reversed. While

the study of the chemical elements has in the meantime undergone great

development, so that not only have the elements of all the substances

coming under the observation of the chemist been discovered, but,

inversely, many compound substances have been constructed from their

elements, not even an approach to such a development is apparent in the

study of concepts. On the contrary, the whole matter has remained at

about the same point as that to which John Locke had brought it in the

second half of the seventeenth century. This is due above all to the

opinion of the most influential philosophers, that Aristotle's logic, or

science of concepts, is absolutely true as well as exhaustive and

complete, so that, at the utmost, what is left for later generations to

do is only to make a change in the form in which the matter is

presented. It is true that in more recent times the grave error of this

view is beginning to be recognized. We realize that Aristotle's logic

embraces but a very small part of the entire field, though in this part

he displays the greatest genius. But beyond this general recognition no

great step forward has been made. Not even a provisional table of the

elementary concepts has been propounded and applied since Locke.

Hence in the following investigation we shall have to speak of the

elements or the simpler parts of a complex concept only in the sense

that these concept elements are simpler as compared with the complex

concepts, but not in the sense that the simplest or truly elementary

concepts have already been worked out. It must be left to later

investigators to find these, and it may be expected that the reduction

of some concepts until then considered elementary into still simpler

ones will take place chiefly in times of great intellectual progress.

_Complex concepts_ can, in the first place, be formed from experience,

for in an empirical concept we meet with several conceptual component

parts which can be separated from one another by a process of

abstraction, but are always found together in the given experiences. For

example, the concept _horse_ has originated from a very frequent,

similarly repeated experience. On analysis it is found to contain a vast

number of other concepts, such as quadruped, vertebrate animal,

warm-blooded, hairiness, and so on. Horse, then, is obviously a _complex

empirical concept_.

On the other hand, we can combine as many simple concepts as we please,

even if we did not find them combined in experience, for in reality

there is nothing to hinder us from uniting all the concepts provided by

memory into any combinations we please. In this way we obtain _complex

arbitrary concepts_.

The task of science can now be even more sharply defined than before by

the fact that it _permits the construction of arbitrary concepts which

in circumstances to be foreseen become empirical concepts_. This is

another expression for _prediction_, which we recognized as the

characteristic of science. It goes deeper than the previous definition,

because here the means for its realization are given.

=8. The Conclusion.= First let us consider the scientific import of the

complex empirical concepts. It consists in the fact that they accustom

us to the coexistence of the corresponding elements of a concept. So

that when, in a new experience, we meet with some of these elements

together, we immediately suppose that we shall find in the same

experience the other elements also which have not yet been ascertained.

Such a supposition is called a _conclusion_. A conclusion always exceeds

the present experience by predicting an expected experience. Therefore,

the form of a conclusion is the universal form of scientific

predication.

A conclusion must contain at least two concepts, the one which is

experienced, and the one which, on the basis of this experience, is

expected. Every complex empirical concept makes such a conclusion

possible after it has been separated into simpler concepts. And the

simplest case is naturally the one in which there are only _two_ parts,

or in which only two parts are taken into consideration.

To what extent such a conclusion is valid, that is to say, to what

extent the experience produces the anticipated concept, obviously

depends upon the reply to a very definite fundamental question. If in

experience the union of the two parts of the concept occurs

_invariably_, so that one part of the concept is never experienced

unless the other part is also experienced, then there is the _greatest_

probability that the expected experience will also have the same

character, and that the conclusion will prove valid or true. To be sure,

there is no way of making certain that the coincident occurrence of the

two concepts, which experience has shown to be _without exception_

hitherto, will continue to be so also in the future. For our only means

of penetrating into the future consists in applying that conclusion from

previous experiences to future experiences, and it can therefore by no

means claim absolute validity. There are, however, different _degrees of

certainty_, or, rather, _probability_, attaching to such a conclusion.

In experiences that occur but rarely the probability is that so far we

have experienced only certain combinations of simple concepts, while

others, though occurring, have not yet entered within the limited circle

of our experience. In such a case a conclusion of the kind mentioned

above may be right, but there is also some probability of its being

false. On the other hand, in experiences which happen extremely

frequently and in the most diverse circumstances, and in which we always

find the constant and unexceptional combination, the probability is very

strong that we shall find the combination in future experiences also,

and the probability of the conclusion approaches practical certainty. Of

course, we can never quite exclude the possibility that new relations

never as yet experienced might enter, by which the conclusion which

hitherto has always been true would now become false, whether because

the expectation entertained prove invalid in single instances or in all

cases.

It follows from this that in general, our conclusions will have the

greater probability the more generally and the oftener the corresponding

experiences have occurred and are occurring. Such concepts as are found

consistently in many experiences otherwise different are called

_general_ concepts, and therefore the probability of the conclusions

described will be the greater the more _general_ the concepts to which

they refer. This obtains to such a degree that we feel that certain very

general conclusions must be true always and without exception, and it is

"unthinkable" to us that they can ever in any circumstances prove not

valid. Such a statement, however, is never anything else than a hidden

appeal to experience. For the mere putting of the question, whether the

conclusion can also be false, demonstrates that the opposite of what has

proved to be the experience so far can be conceived, and the assertion

of its "unthinkability" only signifies that such an experience cannot be

evoked in the mind by the _memory_ for the very reason that, as has been

premised, there are no such memories because the experiences did not

exist. But since, on the other hand, there is no hindrance to thinking

any combinations of concepts at will, we have not the least difficulty,

as everybody knows, in thinking any sort of "nonsense" whatsoever. Only

it is impossible to reproduce such combinations from memory.

The scientific conclusion, therefore, first takes the form: if A is,

then B is also. Here A and B represent the two simple concepts which are

known from experience to be found together in the more complex concept

C. The word "is" signifies here some empirical reality corresponding to

the concepts. The conclusion may therefore also be expressed, somewhat

more circumstantially and more precisely, in this form: if A is

experienced, the experience of B is also expected. The evoking of this

expectation, which implies its justification, is due to the recollection

of the coincidence of the two concepts in former experiences, and the

probability depends, in the manner described above, upon the number of

valid cases. Here it must be observed that even individual cases in

which our expectations have been deceived do not for the most part lead

us to regard the conclusion as generally untrue, that is, to abandon the

expectation of B from A. For we know that our experience is always

_incomplete_, that in certain circumstances we fail to notice existing

factors, and that, therefore, our failure to find that relation valid

which, on other occasions, has been found to be valid, may be attributed

to subjective causes. In case, however, of the repeated occurrence of

such disappointments, we will look elsewhere for relations between these

and other elements of experience, in order that thereafter we may

foresee such cases also and include them in our anticipations.

=9. The Natural Laws.= The facts just described have very frequently

found expression in the doctrine of the _laws of nature_, in connection

with which we have often, as in the man-made social or political laws,

conceived of a lawmaker, who, for some reasons, or perhaps arbitrarily,

has ordained that things should be as they are and not otherwise. But

the intellectual history of the origin of the laws of nature shows that

here the process is quite a different one. The laws of nature do not

decree what shall happen, but _inform us what has happened and what is

wont to happen_. The knowledge of these laws, therefore, makes it

possible for us, as I have emphasized again and again, to foresee the

future in a certain degree and, in some measure, also to determine it.

We determine the future by constructing those relations in which the

desired results appear. If we cannot do so either because of ignorance

or because of inaccessibility to the required relations, then we have no

prospect of fashioning the future according to our desires. The wider

our knowledge of the natural laws, that is, of the actual behavior of

things, the more likely and more numerous the possibilities for

fashioning the future according to our desires. In this way science can

be conceived of as the study of how to become happy. For he is happy

whose desires are fulfilled.

In this conception the natural laws indicate what simpler concepts are

found in complex concepts. The complex concept _water_ contains the

simpler ones _liquid_, a certain _density_, _transparency_,

_colorlessness_,[B] and many others. The sentences, water is a liquid,

water has a density of one, water is transparent, water is colorless,

or, pale blue, etc., are so many natural laws.

[B] More precisely, a very pale blue.

Now what predictions do those natural laws enable us to make?

They enable us to predict that when we have recognized a given body as

water by virtue of the above properties, we are justified in expecting

to find in the same body all the other known properties of water. And so

far experience has invariably confirmed such expectations.

Furthermore, we may expect that if in a given specimen of water we

discover a relation which up to that time was unknown, we shall find

this relation also in all the other specimens of water even though they

were not tested for that particular relation. It is obvious how

enormously this facilitates the progress of science. For it is only

necessary to determine this new relation in some one case accessible to

the investigator to enable us to predict the same relation in all the

other cases without subjecting them to a new test. As a matter of fact,

this is the general method that science pursues. It is this that makes

it possible for science to make regular and generally valid progress

through the labors of the most various investigators who work

independently of one another, and often know nothing of one another.

Of course, it must not be forgotten that such conclusions are always

obtained in accordance with the following formula: _things have been so

until now, therefore we expect that they will be so in the future_. In

every such case, therefore, there is the possibility of error. Thus far,

whenever an expectation was not realized, it was almost always possible

to find an "explanation" for the error. Either the inclusion of the

special case in the general concept proved to be inadmissible because

some of its other characteristics were absent, or the accepted

characterization of the concept required an improvement (limitation or

extension). In other words, one way or another, there was a discrepancy

between the concept and the experience, and, as a rule, sooner or later

it becomes possible for us to arrive at a better adjustment between

them.

This general truth has often been interpreted to mean that in the end

such an adjustment must of necessity always be possible to reach,

without exception; in other words, that absolutely every part of an

experience can be demonstrated as conditioned by natural law. Evidently

such an assertion far exceeds the demonstrable. And even the usual

conclusion cannot be applied here, that because it has happened so in

the past it will happen so in the future also. For the part of our

experiences that we can grasp by natural laws is infinitesimally small

in comparison with that in which our knowledge still fails us entirely.

I will mention only the uncertainty in predicting the weather for only

one day ahead. Moreover, when we consider that until now only the

_easiest_ problems had been solved, and naturally so, because they were

most accessible to the means at hand, then we can readily see that

experience offers no basis whatever for such a conclusion. We must not

say, therefore, that because we have been able so far to explain all

experiences by natural laws it will be so in the future likewise. For we

are far from being able to explain all experiences. In fact, it is only

a very small part that we have begun to investigate. We are as little

justified in saying that we have explained all the problems of our

experience that have been subjected to scientific investigation. We have

by no means explained all of them. Every science, even mathematics,

teems with unsolved problems. So we must resign ourselves to the present

status of human knowledge and ability, and may at best express the

_hope_ founded upon previous experience, that we shall be able to solve

more and more of the incalculable number of problems of our experience

without indulging in any illusions as to the perfection of this work.

=10. The Law of Causation.= By reason of its frequency and importance

the mental process above described has been subjected to the most

diverse investigations, and that most general form of the scientific

conclusion (which we apply in ordinary life even much more frequently

than in science) has been raised, under the name of the law of

causation, to a principle anteceding all experience and to the very

condition making experience possible. Of this so much is true, that

through the peculiar physiological organization of man, _memory in the

most general sense_--the easier execution of such processes as have

already repeatedly taken place in the organism, as against entirely new

kinds of processes--the formation of concepts (of the recurring parts in

the constantly changing variety of processes), is especially stimulated

and facilitated. By it the recurring parts of experience step into the

foreground, and on account of their paramount practical importance for

the security of life, it may well be said in the sense of the theory of

evolution and adaptation, that the entire structure and mode of life of

the organism, especially of the human organism, nay, perhaps life

itself, is indissolubly bound up with that foresight and, therefore,

with the law of causation also. Of course, there is nothing in the way

of calling such a relation an _a priori_ relation, if it is so desired.

As far as the individual is concerned it no doubt antedates all his

experience, since the entire organization which he inherits from his

parents had already been formed under such an influence. But that there

can be forms or existence _without_ such an attribute is shown by the

whole world of the _inorganic_, in which, as far as our knowledge goes,

there is no evidence of either memory or foresight, but only of an

immediate passive participation in the processes of the world around

them.[C]

[C] It cannot be objected that inorganic nature also is known to be

subject to the law of causation. The causal mode of regarding inorganic

phenomena is a distinctly human one, and nothing justifies the assertion

that the same phenomena cannot be viewed in an entirely different

manner.

Further, the circumstance that the causal relation is brought about by

the peculiar manner in which we react upon our experiences, has

sometimes been expressed in this way--the relation of cause and effect

does not exist in nature at all, but has been introduced by men. The

element of truth in this is, that a quite differently organized being,

it is to be supposed, would be able to, or would have to, arrange its

experiences according to quite different mutual relations. But since we

have no experience of such a being, we have no possibility of forming a

valid opinion of its behavior. On the other hand, we must recognize that

it is possible, at least formally, to conceive also of kinds of

experiences with no coinciding parts, or a world in which there are no

experiences at all with coinciding parts. In such, therefore, prediction

is impossible. Such a world will not call forth, even in a being endowed

with memory, a conception and generalization of the various experiences

in the shape of natural laws. Consequently we must recognize that in

addition to the _subjective_ factor in the formation of our knowledge of

the world, or that factor which is dependent upon our physico-psychical

structure, there is also the _objective_ character of the world with

which we must decidedly reckon, or that character which is independent

of us; and that in so far the natural laws contain also objective parts.

To represent the relation clearly to our minds by a figure, we may

compare the world to a heap of gravel and man to a pair of sieves, one

coarser than the other. As gravel passes through the double sieve

pebbles of apparently equal size accumulate between the sieves, the

larger ones being excluded by the first sieve and the smaller ones

allowed to pass by the second. It would be an error to assert that all

the gravel consisted of such pebbles of equal size. But it would be

equally false to assert that it was the sieves that _made_ the pebbles

equal.

=11. The Purification of the Causal Relation.= If by experience we have

found a proposition of the content, If A is, then B is also, the two

concepts A and B generally consist of several elements which we will

designate as a, a´, a´´, a´´´, etc., and as b, b´, b´´, b´´´. Now the

question arises, whether or not all these elements are essential for the

relation in question. It is quite possible, in fact, even highly

probable, that at first only a special instance of the existing

phenomena was found, that is, that the concept A, which has been found

to be connected with the concept B, contains other determining parts

which are not at all requisite to the appearance of B.

The general method of convincing oneself of this is by eliminating one

by one the component parts of the concept A, namely, a, a´, a´´, etc.,

and then seeing whether B still appears. It is not always easy to carry

out this process of elimination. Our greater or less ability to conduct

such investigations depends upon whether we deal with things that are

merely the objects of our _observation_, and which we ourselves have not

the power to change (as, for example, astronomical phenomena), or with

things which are the objects of our _experimentation_, and which we can

influence. In the latter case one or another factor is usually found

which can be eliminated without the disappearance of B, and then we must

proceed in such a way as to form a corresponding new concept A´ from the

factors recognized as necessary (which new concept will be more general

than the former A), and to express the given proposition in the improved

form: If A´ is, then B is also.

Quite similar is the case with the other member of this relation. It

often happens that when a, or a´´, a´´´ is found, somewhat different

things appear, which do not fit the concept as first constructed. Then

we must multiply the experiences as much as possible in order to

determine what constant elements are found in the concept B, and to form

from these constant elements the corresponding concept B´. The improved

proposition will then read: if A´ is, then B´ is also.

This entire process may be called the purification of the causal

relation. By this term we express the general fact that in first forming

such a regular connection, the proper concepts are very seldom brought

into relation with one another at once. The cause of it is that at first

we make use of _existing_ concepts which had been formed for quite a

different purpose. It must therefore be regarded as a special piece of

good fortune if these old concepts should at once prove suited to the

new purpose. Furthermore, the existing concepts are as a rule so vaguely

characterized by their names, which we must employ to express the new

relation, that for this reason also it is often necessary to determine

empirically in what way the concept is to be definitely established.

The various sciences are constantly occupied with this work of the

mutual adaptation of the concepts that enter into a causal relation. By

way of example, we may take the "self-understood" proposition which we

use when we call out to a careless child when it sticks its finger into

the flame of a candle, "Fire burns!" We discover that there are

self-luminous bodies which produce no increase of temperature, and

therefore no sensation of pain. We discover that there are processes of

combustion that develop no light, but heat enough to burn one's

fingers. And, finally, the scientific investigation of this proposition

arrives at the general expression that, as a rule, chemical processes

are accompanied by the development of heat, but that, conversely, such

processes may also be accompanied by the absorption of heat. In this way

that casual sentence which we call out to the child develops into the

extensive science of thermo-chemistry when it is subjected to the

continuous purification of the causal relation, which is the general

task of science.

It remains to be added that in this process of adapting concepts it is

necessary also sometimes to follow the opposite course. This is the case

when _exceptions_ are noticed in a relation as expressed for the time

being; when, therefore, the proposition if A is present, then B is

present also, is in a great many instances valid, but occasionally

fails. This is an indication that in the concept A an element is still

lacking. This element, however, is present in the instances that tally,

but absent in the negative cases, and its absence is not noticed because

it is not contained in A. Then it is necessary to seek this part, and

after it has been found, to embody it in the concept A, which thus

passes into the new concept A´.

This case is the obverse of the former one. Here the more suitable

concept proves to be less general than the concept accepted temporarily,

while in the first case the improved concept is more general. Hence we

formulate the rule: exceptions to the temporary rule require a

limitation, while an unforeseen freedom requires an extension, of the

accepted concept.

=12. Induction.= The form of conclusion previously discussed, _because

it has been so, I expect it will continue to be so in the future_, is

the form through which each science has arisen and has won its real

content, that is, its value for the judgment of the future. It is called

_inference by induction_, and the sciences in which it is

preponderatingly applied are called _inductive sciences_. They are also

called experiential or empirical sciences. At the basis of this

nomenclature is the notion that there are other sciences, the deductive

or rational sciences, in which a reverse logical procedure is applied,

whereby from general principles admitted to be valid in advance,

according to an absolutely sure logical process, conclusions of like

absolute validity are drawn. At the present time people are beginning to

recognize the fact that the deductive sciences must give up these claims

one by one, and that they already have given them up to a certain

extent; partly because on closer study they prove to be inductive

sciences, and partly because they must forego the title and rank of a

science altogether. The latter alternative applies especially to those

provinces of knowledge which have not been used in prophesying the

future or cannot be so used.

To return to the inductive method--it is to be noted that _Aristotle_,

who was the first to describe it, proposed two kinds of induction, the

_complete_ and the _incomplete_. The first has this form: since _all_

things of a certain kind are so, each _individual thing_ is so. While

the incomplete induction merely says: since _many_ things of a certain

kind are so, _presumably_ all things of this kind are so. One instantly

perceives that the two conclusions are essentially different. The first

lays claim to afford an absolutely certain result. But it rests upon the

assumption that _all_ the things of the kind in question are known and

have been tested as to their behavior. This hypothesis is generally

impossible of fulfilment, since we can never prove that there are not

more things of the same kind other than those known to us or tested by

us. Moreover, the conclusion is _superfluous_, as it merely repeats

knowledge that we have already directly acquired, since we have tested

_all_ the things of the one kind, hence the special thing to which the

predication refers.

On the other hand, the _incomplete_ induction affirms something that has

not yet been tested, and therefore involves as a condition an

_extension_ of our knowledge, sometimes an extremely important

extension. To be sure, it must give up the claim to unqualified or

absolute validity, but, to compensate, it acquires the irreplaceable

advantage of lending itself to practical application. Indeed, in

accordance with the scientific practice justified by experience,

described on p. 29, the scientific inductive conclusion assumes the

form: because it has _once_ been found to be so, it will _always_ be so.

From this appears the significance of this method for the enlargement of

science, which, without it, would have had to proceed at an incomparably

slower pace.

=13. Deduction.= In addition to the inductive method, science has (p.

38) another method, which, in a sense, should be the reverse of the

inductive and is claimed to provide absolutely correct results. It is

called the _deductive_ method, and it is described as the method that

leads from premises of general validity by means of logical methods of

general validity to results of general validity.

As a matter of fact, there is no science that does or could work in such

a way. In the first place, we ask in vain, how can we arrive at such

general, or absolutely valid, premises, since all knowledge is of

empiric origin and is therefore equipped with the possibility of error

as ineradicable evidence of this origin. In the next place, we cannot

see how from principles at hand conclusions can be drawn the content of

which exceeds that of these principles (and of the other means

employed). In the third place, the absolute correctness of such results

is doubtful from the fact that blunders in the process of reasoning

cannot be excluded even where the premises and methods are absolutely

correct. In practice it has actually come to pass that in the so-called

deductive sciences doubts and contradictions on the part of the various

investigators of the same question are by no means excluded. To wit,

the discussion that has been carried on for centuries, and is not yet

ended, over Euclid's parallel theorem in geometry.

If we ask whether, in the sense of the observations we have just made of

the formation of scientific principles, there is anything at all like

deduction, we can find a procedure which bears a certain resemblance

with that impossible procedure and which, as a matter of fact, is

frequently and to very good purpose applied in science. It consists in

the fact that general principles which have been acquired through the

ordinary incomplete induction are _applied to special instances which,

at the proposition of the principle, had not been taken into

consideration_, and whose connection with the general concept had not

become directly evident. Through such application of general principles

to cases that have not been regarded before, specific natural laws are

obtained which had not been foreseen either, but which, according to the

probability of the thesis and the correctness of the application are

also probably correct. However, the investigator, bearing in mind the

factor of uncertainty in these ratiocinations feels in each such

instance the need for testing the results by experience, and he does not

consider the _deduction_ complete until he had found _confirmation_ in

experience.

Deduction, therefore, actually consists in the searching out of

particular instances of a principle established by induction and in its

confirmation by experience. This conduces to the growth of science, not

in breadth, but in profundity. I again resort to the comparison I have

frequently made of science with a very complex network. At first glance

we cannot obtain a complete picture of all the meshes. So, at the first

proposition of a natural law an immediate survey of the entire range of

the possible experiences to which it may apply is inachievable. It is a

regular, important, and necessary part of all scientific work to learn

the extent of this range and investigate the specific forms which the

law assumes in the remoter instances. Now, if an especially gifted and

far-seeing investigator has succeeded in stating in advance an

especially general formulation of an inductive law, it is everywhere

confirmed in the course of the trial applications, and the impression

easily arises that confirmation is superfluous, since it results simply

in what had already been "deduced." In point of fact, however, the

reverse is not infrequently the case, that the principle is _not_

confirmed, and conditions quite different from those anticipated are

found. Such discoveries, then, as a rule, constitute the starting-point

of important and far-reaching modifications of the original formulation

of the law in question.

As we see, deduction is a necessary complement of, in fact, a part of,

the inductive process. The history of the origin of a natural law is in

general as follows. The investigator notices certain agreements in

individual instances under his observation. He assumes that these

agreements are general, and propounds a temporary natural law

corresponding to them. Then he proceeds by further experimentation to

test the law in order to see whether he can find full confirmation of it

by a number of other instances. If not, he tries other formulations of

the law applicable to the contradictory instances, or exclusive of them,

as not allied. Through such a process of adjustment he finally arrives

at a principle that possesses a certain range of validity. He informs

other scientists of the principle. These in their turn are impelled to

test other instances known to them to which the principle can be

applied. Any doubts or contradictions arising from this again impel the

author of the principle to carry out whatever readjustments may have

become necessary. Upon the scientific imagination of the discoverer

depends the range of instances sufficing for the formulation of the

general inductive principle. It also frequently depends upon conscious

operations of the mind dubbed "scientific instinct." But as soon as the

principle has been propounded, even if only in the consciousness of the

discoverer, the deductive part of the work begins, and the consequent

test of the proposition has the most essential influence on the value of

the result.

It is immediately evident that this _deductive_ part is of all the more

weight, the more _general_ the concepts in question are. If, in

addition, the inductive laws posited soon prove to be of a comparatively

high degree of perfection, we obtain the impression described above,

that an unlimited number of independent results can be deduced from a

premise. _Kant_ was keenly alive to the peculiarity of such a view,

which had been widely spread pre-eminently by _Euclid's_ presentation of

geometry, and he gave expression to his opinion of it in the famous

question: _How are a priori judgments possible?_ We have seen that it is

not always a question of _a priori_ judgments, but also of inductive

conclusions applied and tested according to deductive methods.

=14. Ideal Cases.= Each experience may generally be considered under an

indefinite number of various concepts, all of which may be abstracted

from that experience by corresponding observations. Accordingly an

indefinite number of natural laws would be required for prophesying that

experience in all its parts. Likewise the indefinite number of premises

must be known through the application of which those natural laws

acquire a certain content. Thus it seems as if it were altogether

impossible to apply natural laws for the determination of a single

experience to come, and in a certain sense this is true (p. 30). For

example, when a child is born, we are quite incapable of foretelling the

peculiar events that will occur in its life. Beyond the statement that

it will live a while and then die, we can make only the broadest

assertions qualified by numerous "ifs" and "buts."

If, in spite of this, we arrange a very great part of our life and

activity according to the prophecies we make in regard to numerous

details in life, basing them upon natural laws, the question arises, how

we get over the difficulty, or, rather, the impossibility just referred

to.

The answer is, that we repeatedly so find or can form our experiences

that certain natural relations _preponderatingly_ determine the

experience, while the other parts that remain undetermined fall into the

background. _The prophecy will cover so considerable a part of the

experience that we can forego previous knowledge of the rest._ We can

foretell enough to render a practical construction of life possible, and

increasing experience, whether the personal experience of the individual

or the general experience of science, constantly enlarges this

controllable part of future experiences.

The procedure of science is similar to that of practical life, though

freer. Whenever an investigator seeks to test a natural law of the form:

if A is so, then B is so, he endeavors to choose or formulate the

experiences in such a way that the fewest possible extraneous elements

are present, and that those that are unavoidable should exert the least

possible influence upon the relation in question. He never succeeds

completely. In order, nevertheless, to reach a conclusion as to the form

the relation will take without extraneous influences, the following

general method is applied.

A series of instances are investigated which are so adjusted that the

influence of the extraneous elements grows less and less. Then the

relation investigated approaches a limit which is never quite reached,

but to which it draws nearer and nearer, the less the influence of the

extraneous elements. And the conclusion is drawn that if it were

possible to exclude the extraneous elements entirely, the limit of the

relation would be reached.

A case in which none of the extraneous elements of experience operate is

called an _ideal case_, and the inference from a series of values

leading to the limit-value is an _extrapolation_. _Such extrapolations

to the ideal case_ are a quite natural procedure in science, and a very

large part of natural laws, especially all quantitative laws, that is,

such as express a relation between measurable values, have precise

validity only in ideal cases.

We here confront the fact that many natural laws, and among them the

most important, are expressed as, and taken to be, conditions _which

never occur in reality_. This seemingly absurd procedure is, as a matter

of fact, the best fitted for scientific purposes, since ideal cases are

to be distinguished by this, _that with them the natural laws take on

the simplest forms_. This is the result of the fact that in ideal cases

we intentionally and arbitrarily overlook every complication of the

determining factors, and in describing ideal cases we describe the

simplest conceivable form of the class of experiences in question. The

real cases are then constructed from the ideal cases by representing

them as the sum of all the elements that have an influence on the

experience or the result. Just as we can represent the unlimited

multitude of finite numbers by the figures up to ten, so we can

represent an unlimited quantity of complicated events by a finite number

of natural laws, and so reach a highly serviceable approximation to

reality.

Thus geometry deals with absolutely straight lines, absolutely flat

surfaces, and perfect spheres, though such have never been observed, and

the results of geometry come the closer to truth, the more nearly the

real lines, surfaces, and spheres correspond to the ideal demands.

Similarly, in physics, there are no ideal gases or mirrors, or in

chemistry ideally pure substances, though the expressed simple laws in

these sciences are valid for only such bodies. The non-ideal bodies of

these sciences, which reality presents in various degrees of

approximation, correspond the more closely to these laws, the slighter

the deviation of the real from the ideal. And the same method is applied

in the so-called mental sciences, psychology and sociology, in which the

"normal eye" and a "state with an entirely closed door" are examples of

such idealized limit-concepts.

=15. The Determinateness of Things.= A very widespread view and a very

grave one, because of its erroneous results, is _that by the natural

laws things are unequivocally and unalterably determined down to the

very minutest detail_. This is called _determinism_, and is regarded as

an inevitable consequence of every natural scientific generalization.

But an accurate investigation of actual relations produces something

rather different.

The most general formulation of the natural law: _if A is experienced,

then we expect B_, necessarily refers in the first place only to certain

_parts_ of the thing experienced. For perfect similarity in two

experiences is excluded by the mere fact that we ourselves change

unceasingly and one-sidedly. Consequently, no matter how accurate the

repetition of a former experience may be, our very participation in it,

an element bound to enter, causes it to be different. Therefore we deal

with only a _partial_ repetition of any experience, and the common part

is all the smaller a fraction of the entire experience, the more

_general_ the concept corresponding to this part. But the most general

and most important natural laws apply to such very general ideas, and

accordingly they determine only a small part of the whole result. Other

parts are determined by other laws, but we can never point out an

experience that has been determined completely and unequivocally by

natural laws known to us. For example, we know that when we throw a

stone, it will describe an approximate parabolic curve in falling to the

ground. But if we should attempt to determine its course accurately, we

should have to take into consideration the resistance of the air, the

rotatory motion of the stone upon being thrown, the movement of the

earth, and numerous other circumstances, the exact determination of

which is a matter beyond the power of all sciences. Nothing but an

_approximate_ determination of the stone's course is possible, and every

step forward toward accuracy and absoluteness would require scientific

advances which it would probably take centuries to accomplish.

Science, therefore, can by no means determine the exact linear course

that the stone will take in its fall. It can merely establish a certain

broader path within which the stone's movement will remain. And the path

is the wider the smaller the progress science has made in the branch in

question. The same conditions prevail in the case of every other

prediction based upon natural laws. Natural laws merely provide a

certain frame within which the thing will remain. But which of the

infinitely numerous possibilities within this frame will become reality

can never be absolutely determined by human powers.

The belief that it is possible has been evoked merely by a far-reaching

method of abstraction on the part of science. By assuming in place of

the stone "a non-extended point of mass" and by disregarding all the

other factors which in some way (whether known or unknown) exercise an

influence on the stone's movement, we can effect an apparently perfect

solution of the problem. But the solution is not valid for real

experience, merely for an ideal case, which bears only a more or less

profound similarity to the real. It is only such an ideal world, that

is, a world arbitrarily removed from its actual complexity, that has the

quality of absolute determinateness which we are wont to ascribe to the

real world.

We might point to the method of abstraction generally adopted in science

and to the extrapolation to ideal cases which has just been explained,

and regard the assertion of the absolute determinateness of events in

the world as a justified extrapolation to the ideal case. In other

words, we might say that we know all the natural laws and how to apply

them perfectly to the individual instances. In controversion of this it

must be said that the ulterior justification of such ideal extrapolation

is not yet feasible. The justification lies in the demonstration that

the real cases approximate the ideal the more closely the more we

actualize our presumptions. But in this case this is not feasible,

since, for the greater part of our experiences, we do not even know the

approximate or ideal natural laws by the help of which we can construct

such ideal cases. For instance, the whole province of organic life is at

present essentially like an unknown land, in which there are only a few

widely separated paths ending in _culs-de-sac_.

=16. The Freedom of the Will.= This relation explains why, on the one

hand, we assume a far-reaching determinateness for many things, that is,

for all those accessible to scientific treatment and regulation, and

why, on the other hand, we have the consciousness of acting _freely_,

that is, of being able to control future events according to the

relations they bear to our wishes. Essentially there is no objection to

be found to a fundamental determinism which explains that this feeling

of freedom is only a different way of saying _that a part of the causal

chain lies within our consciousness_, and that we feel these processes

(in themselves determined) as if we ourselves determined their course.

Nor can we prove this idea to be false, that, since the number of

factors which influence each experience is indefinitely great and their

nature indefinitely complex, each event would appear to be determined in

the eyes of an all-comprehensive intellect. But to our finite minds an

undetermined residue necessarily remains in each experience, and to that

extent the world must always remain in part practically undetermined to

human beings. Thus, both views, that the world is not completely

determined, and that it really is, though we can never recognize that it

is, lead practically to the same result: _that we can and must assume in

our practical attitude to the world that it is only partially

determined_.

But if two different lines of thought in the whole world of experience

everywhere lead to the same result, they cannot be materially, but

merely formally or superficially, different. For those things are alike

which cannot be distinguished. There is no other definition of

alikeness. Thus, if we see that the age-long dispute between these two

views always breaks out afresh without seeming to be able to reach an

end, this is readily understood, from what has been said, since the very

same essential arguments which can be adduced of _one_ view can be used

as a prop for the _other_ view, because in their essential results the

two are the same. I have discussed this matter because it presents a

very telling example of a method to be applied in all the sciences when

dealing with the solution of old and ever recurrent moot questions. Each

time we encounter such problems, we must ask ourselves: what would be

the difference empirically if the one or the other view were correct? In

other words, we first assume the one to be correct, and develop the

consequences accordingly. Then we assume the second to be correct and

develop the consequences accordingly. If in the two cases the

consequences differ in a certain definite point, we at least have the

possibility of ascertaining the false view by investigating in favor of

which case experience decides on this point. However, we may not

conclude that by this the other view has been proved to be entirely

correct. It likewise may be false, only with the peculiar quality that

in the case in question it leads to the correct conclusions. That such

a thing is possible, every one knows who has attentively observed his

own experiences. How often we act correctly in actual practice, though

we have started out on false premises! The explanation of this

possibility resides in the highly composite nature of each experience

and each assumption. It is quite possible--and, in fact, it is the

general rule--that a certain view contains true elements, but _along

with them false elements also_. In applications of the view where the

true elements are the decisive factors, true results are obtained,

despite the errors present. Likewise, false results will be achieved

where the false elements are decisive, despite the true results that can

be had, or have been had, elsewhere, by means of the true elements.

Hence, in case of the "confirmation," we can only conclude that that

portion of the view essential for the instance in question is correct.

One readily perceives that these observations find application in all

provinces of science and life. There are no absolutely correct

assertions, and even the falsest may in some respect be true. There are

only greater and lesser probabilities, and every advance made by the

human intellect tends to increase the degree of probability of

experiential relations, or natural laws.

=17. The Classification of the Sciences.= From the preceding

observations the means may be drawn for outlining a complete table of

the sciences. However, we must not regard it complete in the sense that

it gives every possible ramification and turn of each science, but that

it sets up a frame inside of which at given points each science finds

its place, so that, in the course of progressive enlargement, the frame

need not be exceeded.

The basic thought upon which this classification rests is that of graded

abstraction. We have seen (p. 19) that a concept is all the more

general, that is, is applicable to all the more experiences, the fewer

parts or elementary concepts it contains. So we shall begin the system

of the sciences with the most general concepts, that is, the elementary

concepts (or with what for the time being we shall have to consider

elementary concepts), and, in grading the concept complexes according to

their increasing diversity, set up a corresponding graded series of

sciences. One thing more is to be noted here, that this graded series,

on account of the very large number of new concepts entering, must

produce a correspondingly great number of diverse sciences. For

practical reasons groups of such grades have been combined temporarily.

Thereby a rougher classification, though one easier to obtain a survey

of, has been made. The most suitable and lasting scheme of this sort was

originated by the French philosopher, _Auguste Comte_, since whom it has

undergone a few changes.

Below is the table of the sciences, which I shall then proceed to

explain:

I. _Formal Sciences._ Main concept: order

Logic, or the science of the Manifold

Mathematics, or the science of Quantity

Geometry, or the science of Space

Phoronomy, or the science of Motion

II. _Physical Sciences._ Main concept: energy

Mechanics

Physics

Chemistry

III. _Biological Sciences._ Main concept: life

Physiology

Psychology

Sociology

As is evident, we first have to deal with the three great groups of the

formal, the physical, and the biological sciences. The formal sciences

treat of characteristics belonging to all experiences, characteristics,

consequently, that enter into every known phase of life, and so affect

science in the broadest sense. In order immediately to overcome a

widespread error, I emphasize the fact that these sciences are to be

considered just as experiential or empirical as the sciences of the

other two groups, as to which there is no doubt that they are empirical.

But because the concepts dealt with by the first group are so extremely

wide, and the experiences corresponding to them, therefore, are the most

general of all experiences, we easily forget that we are dealing with

experiences at all; and our very firmly rooted consciousness of the

unqualified similarity of these experiences causes them to seem native

qualities of the mind, or _a priori_ judgments. Nevertheless,

mathematics has been proved to be an empirical science by the fact that

in certain of its branches (the theory of numbers) laws are known which

have been found empirically and the "deductive" proof of which we have

as yet not succeeded in obtaining. The most general concept expressed

and operative in these sciences is the concept of order, of _conjugacy_

or _function_, the content and significance of which will become clear

later in a more thorough study of the special sciences.

In the second group, the physical sciences, the arbitrariness of the

classification becomes very apparent, since these sciences are among the

best known. We are perfectly justified in regarding mechanics as a part

of physics; and in our day physical chemistry, which in the last twenty

years suddenly developed into an extended and important special science,

thrust itself between physics and chemistry.

The most general concept of the physical sciences is that of _energy_,

which does not appear in the formal sciences. To be sure it is not a

fundamental concept. On the contrary, its characteristic is undoubtedly

that of compositeness, or, rather, complexity.

The third group comprehends all the relations of living beings. Their

most general concept, accordingly, is that of _life_. By physiology is

understood the entire science dealing with non-psychic life phenomena.

It therefore embraces what is called, in the present often chance

arrangement of scientific activities, botany, zoology, and physiology of

the plants, animals, and man. Psychology is the science of mental

phenomena. As such, it is not limited to man, even though for many

reasons he claims by far the preponderating part of it for himself.

Sociology is the science which deals with the peculiarities of the human

race. It may therefore be called anthropology, but in a far wider sense

than the word is now applied.

=18. The Applied Sciences.= It will be remarked that the grouping of the

table gives no place at all in its scheme to certain branches of

learning taught in the universities and equally good technical

institutions. We look in vain not only for theology and jurisprudence,

but also for astronomy, medicine, etc.

The explanation and justification of this is, that for purposes of

systematization we must distinguish between _pure_ and _applied_

sciences. By virtue of their strictly conceptual exclusiveness the pure

sciences constitute a regular hierarchy or graded series, so that all

the concepts that have been used and dealt with in the preceding

sciences are repeated in the following sciences, while certain

characteristic new concepts enter in addition. Thus logic, the science

of the manifold, exercises its dominion over all the other sciences,

while the specific concepts of physics and chemistry have nothing to do

with it, though they are of importance to all the biologic sciences.

Through this graded addition of new (naturally empiric) concepts, the

construction of the pure sciences proceeds in strict regularity, and

their problems arise exclusively from the application of new concepts to

all the earlier ones. In other words, their problems do not reach them

accidentally from without, but result from the action and reaction of

their concepts upon one another.

At the same time there are problems that each day sets before us without

regard to system. These come from our endeavor to improve life and avert

evil. In the problems of life we are confronted by the whole variety of

possible concepts, and under the day's immediate compulsion we cannot

wait, if we are sowing crops or helping a sick man, until physiology and

all the other appropriate sciences have solved all the problems of plant

growth and the changes of the human body and human energy. When other

signs fail, we use the position of the stars for finding our way on the

high seas. In this manner we turn the teaching of the stars, or

astronomy, into an applied science, in which at first mechanics alone

seemed to have a part. Later physics took a share in it, then optics

took a particularly prominent share, and in recent times not only did

chemistry find its way into astronomy, but the specifically biologic

concept of evolution was applied in astronomy with success.

Thus, side by side with the pure sciences are the applied, which are to

be distinguished from the pure sciences by the fact that they do not

unfold their problems systematically, but are assigned them by the

external circumstances of man's life. The pure sciences, therefore,

almost always have a larger or smaller share in the tasks of the applied

sciences. For instance, in building a bridge or railroad, physical

problems have to be taken into consideration as well as sociologic

problems (problems of trade), and a good physician should be a

psychologist as well as a chemist.

But since all the individual questions arising in the applied sciences

may be considered essentially as problems of one or other pure science,

they need not be explicitly enumerated along with the pure sciences,

especially since their development is greatly dependent upon temporary

conditions and is therefore incapable of simple systematization.