MARINE BIOLOGICAL LABORATORY.

Received August, 1938
Accession No. 494^1
Given by Macmillan Co*
Place, New York City

***Jio book op pamphlet is to be removed from the Lab-
oratory uuithout the permission of the Trustees.

AN INTRODUCTION

TO THE

PHILOSOPHY OF SCIENCE

THE MACMILLAN COMPANY

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AN INTRODUCTION

TO THE

PHILOSOPHY OF SCIENCE

By A. CORNELIUS BENJAMIN

Assistant Professor of Philosophy
University of Chicago

THE MACMILLAN COMPANY

New York

1937

Copyright, 1937,
By THE MACMILLAN COMPANY

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Published August, 1937

SET UP AND ELECTROTYPED BY T. MOREY <k SON
• PRINTED IN THE UNITED STATES OF AMERICA •

To

My Wife

PREFACE

Recent years have witnessed the publication of a large
number of monographs, magazine articles, and books, whose
subject matter has seemed to defy classification. Though
they have been written, for the greater part, by scientists,
they are not properly scientific. They begin with science,
they talk about science, and they end with science, yet they
do not conform at all to the tradition of scientific writings.
Were it not for the fact that they differ in important ways
from the usual books on logic they might be placed in this
class. Yet they are not logical in the usual sense. Their
repeated reference to philosophical issues tempts one to
classify them with this group, yet the writings approach
these problems in a new spirit and with a new method,
which seem quite foreign to the traditional philosophy.

Confronted by such a state of affairs, one has two alterna-
tives. On the one hand, he may examine this extensive litera-
ture carefully, decide upon the existent discipline with which
it has the closest kinship, and force it into this compartment.
The essential disadvantage of such a procedure is that it
does violence to the traditional terminology. On the other
hand, he may simply collect all of the literature together and
define a new discipline ad hoc. This method has a corre-
sponding disadvantage, for it defines the field by the crude
extensional method rather than by classifying its problems;
one can say of the new discipline only that it involves prob-
lems like those discussed in such-and-such monographs,
articles, and books.

In spite of this important difficulty the latter method
seems to offer the greatest prospect of success. It prescribes
neither limits to the fieM nor structure within its domain.
It forces the problems into no predetermined form, yet it
does not leave the field amorphous for it allows the prob-
lems themselves to take form according to their own char-

vii

viii PREFACE

acters. Furthermore, it permits the field to achieve more
accurate formulation when the problems themselves have
become more or less standardized and organized.

It seems certain that no finally satisfactory definition of
the field in question is possible today. Not only are most of
the problems still unsolved — that is quite to be expected in
an embryonic science — but for the greater part the prob-
lems have not even been clearly stated or precisely differen-
tiated from one another. It may be that the field has not
yet reached that stage of development which permits even
a tentative formulation of its boundaries and structure.
Apparently the only way to decide is to attempt such a for-
mulation and examine the results. If the theoretical descrip-
tion of the type of problem corresponds closely with the
actual field of literature, the formulation may be looked
upon with favor. Furthermore, the choice as to the most
adequate term for describing the field is still an open matter.
General use seems to have favored the term "philosophy of
science," though the phrase is not without some disadvan-
tages. Here, again, all that one can do is to use the term
consistently in some well-defined sense, and see whether any
confusion arises. Such a definition of the field of the philos-
ophy of science will be attempted in the following pages.

The main practical considerations which have guided the
author in the arrangement and selection of material should
be stated at this point. The book has been written with a
definite view to textbook use. In recent years there has been
introduced into the colleges and universities of the country
an increasing number of courses in the philosophy of science.
Since the source material for such courses is to be found in
some hundreds of books, many of which contain only a few
pages of relevant subject matter, and in magazine articles
printed in periodicals not commonly found except in the
larger libraries, teachers have been somewhat at a loss for
supplementary readings. The present book has been written
in the attempt to include as much of this source material as
is possible, consistent with a unified presentation. Where

PREFACE ix

the material has not been actually quoted it has been
referred to in footnotes and in bibliographical lists at the
ends of the chapters. The aim has been to acquaint the
student with the literature of the field, as far as it is avail-
able in English, and to indicate where the more detailed
discussions of the various problems may be found. Reference
material is drawn both from philosophers and from scientists,
with, perhaps, undue emphasis on the latter, since sources
of this kind are not commonly known to the average student.
In view of the textbook character, certain principles have
been kept in mind in the selection and arrangement of
material. No attempt has been made to give a compre-
hensive survey of the field of the philosophy of science. In
fact there is some doubt as to whether the phrase "compre-
hensive survey' would have any meaning as applied to a
field whose limits have not yet been determined. Many
readers will be disturbed by what appear to be important
omissions. For example, in Part I there is a more or less
complete neglect of considerations pertaining to postulate
schemes and the formal structure of thinking, and less em-
phasis on such topics as classification, analogy, definition,
measurement, Mill's experimental methods, and the gen-
eral problem of induction, than would seem proper in a
book on the philosophy of science. The justification for
these omissions and weakened emphases lies in the fact
that a definite attempt has been made to avoid duplicating
problems usually discussed in courses in logic. The intention
has been to write a supplement .to a textbook on logic rather
than a substitute for it. Similarly, in Part II the concepts
chosen for analysis are meant to be illustrative rather than
exhaustive of problems in this field. It so happens that the
concepts of the mathematical and physical sciences have
undergone the greatest developments, and have been sub-
jected to repeated analysis in recent years. They are thus
especially valuable as illustrative of certain techniques of
abstraction and idealization. An exhaustive consideration of
problems at this level would require similar analyses of the

PREFACE

concept of life, with its associated problems of mechanism,
vitalism, and teleology; of the concept of society, and all
of the problems of value which it raises; of the concept of
consciousness, with its important problem of behaviorism
versus introspectionism ; and so on, perhaps even through
the special concepts of economics, political science, law,
religion, and art. It hardly seems the function of a general
textbook in the philosophy of science to deal with problems
of such scope.

Furthermore, the material has been chosen so as to make
it extremely unlikely that the book would overlap with any
of the texts in "introduction to philosophy by way of the
sciences." Courses centering about such books have a
definite function in the curriculum and there has been no
intention of replacing them by alternative approaches.
Survey courses of this kind pay much more attention to the
subject matter of science than does the present book. The
attempt has been made in the following pages to acquaint
the student not so much with the facts of science as with
the foundations of science. What is required for the philos-
ophy of science, as Russell points out, is knowledge not of
the complex features of science but of its abstract features —
a knowledge of its first chapters rather than of its last
chapters. This fact has permitted the elimination of many
of the highly complex illustrations, particularly those drawn
from relativity and quantum mechanics, which have ob-
scured much of the literature in the field for the non-tech-
nical reader. Except in connection with the analysis of the
basic concepts, where reference to the more complicated
problems is unavoidable, illustrative material has been
drawn from the more elemental theories, comprehensible to
the average reader. It seems likely that the important
philosophical features of science are located in the problems
which the scientist finds wherever he turns his head — in
classification, measurement, observation, hypothesis-forma-
tion, and so on — rather than in the comparatively rare
problems associated with advanced sciences.

PREFACE xi

Special acknowledgment is hereby made to the following
for reading the specified portions of the manuscript and sug-
gesting valuable improvements: To Dr. P. L. DeLargy for
examining Chapter V; to Professor Frank C. Hoyt for
reading Chapter XV; to Professor Carl Eckart for many
suggestions relevant to Chapters XIV and XVI; and to
Professor Raymond W. Rarnard for information pertaining
to the definition of "number' in Chapter XIII. None of
these men, however, is to be considered as in any way sub-
scribing to the ideas presented in the portion of the manu-
script which he examined. I wish also to express thanks to
Mr. Richard Schlegel who helped in the routine work con-
nected with the manuscript and prepared the index.

A. C. R.

Chicago, Illinois
July, 1937

° - «\#\

- ^W •/TABLE OF CONTENTS

INTRODUCTION
THE FIELD OF THE PHILOSOPHY OF SCIENCE

CHAPTER PAGE

I. PHILOSOPHY AND SCIENCE 3

Historical Approach 4

Description vs. Explanation 8

Factual Description vs. Symbolic Analysis .... 11

Facts vs. Values 13

Quantity vs. Quality 15

Analysis vs. Intuition 18

II. PHILOSOPHY OF SCIENCE 21

Emergence of the Philosophy of Science 21

The Philosophy of Science 28

Problems of the Philosophy of Science 33

General Character of the Study 35

PART ONE
PROBLEMS IN THE LOGIC OF SCIENCE

III. THE LOGICAL STRUCTURE OF SCIENCE ... 41

Importance of the Logic of Science 41

Possibility of the Logic of Science 43

The Known f 48

The Knowledge 50

The Knowing 56

IV. THE NATURE OF SYMBOLS 61

Sign Situations 62

Symbol Situations 63

Adequacy of Symbols 69

Kinds of Symbols 72

V. PERCEPTION 78

The Starting-Point of Science 78

Theories of Perception 81

Scientific Realism 88

• ••

Xlll

xiv TABLE OF CONTENTS

CHAPTER PAGE

VI. DESCRIPTIVE TECHNIQUES 103

Control of End-Object 104

Control of Physical Medium 109

Control of Sense Organs 115

Control of State of Mind 117

VII. DESCRIPTIVE SCIENCE 128

Extensional Features of Descriptive Science . . . . 130

Intensional Features of Descriptive Science . . 139

VIII. THEORIES OF SCIENTIFIC CONCEPTS .... 147

Strict Empiricism 151

Operationalism 154

Constructionalism 158

Conventionalism 160

Logical Positivism 164

Scientific Realism 167

IX. SCIENTIFIC DISCOVERY 173

Act of Discovery 175

Psychology of Discovery 178

Logic of Discovery 181

Techniques of Construction 189

Techniques of Hypothesis-Formation 192

X. EXPLANATORY SCIENCE 196

Nature of Explanation 197

Extensional Features of Explanatory Science . . . 205

Intensional Features of Explanatory Science .... 208

XI. VERIFICATORY TECHNIQUES 214

Development of a Theory 214

Prediction 218

Confirmation and Infirmation 223

PART TWO

PROBLEMS IN THE ANALYSIS OF THE
CONCEPTS OF SCIENCE

XII. PROBLEM OF THE ANALYSIS OF SCIENTIFIC

CONCEPTS 233

General Character of the Problem 234

Difficulties in Ascertainment of Empirical Foundation . 243

Difficulties in Ascertainment of Scientific Content . . 245

Difficulties in Ascertainment of Operational Derivation 250

TABLE OF CONTENTS xv

CHAPTER PAGE

XIII. ORDER, NUMBER, QUANTITY 253

Order: Empirical Foundation 254

Order: Operational Derivation 256

Order: Scientific Content 257

Number: Empirical Foundation 260

Number: Operational Derivation 266

Number: Scientific Content 267

Quantity: Empirical Foundation 271

Quantity: Operational Derivation 274

Quantity: Scientific Content 276

XIV. SPACE, TIME 279

Newtonian Time and Euclidean Space 281

Empirical Space and Time 289

Space and Time: Operational Derivation 296

Space-Time 303

XV. MOTION, FORCE, MATTER 312

Motion: Empirical Foundation 313

Motion: Scientific Content 317

Motion: Operational Derivation 321

Force: Empirical Foundation 323

Force: Scientific Content 327

Force: Operational Derivation 331

Matter: Empirical Foundation. ....... 337

Matter: Scientific Content 341

Matter: Operational Derivation 343

XVI. LAW, CAUSE 347

Law: Empirical Foundation 348

Law: Operational Derivation 355

Law: Scientific Content 366

Indeterminism 376

PART THREE
SPECULATIVE PROBLEMS

XVII. GENERAL CHARACTER OF SPECULATIVE PROB-
LEMS 387

The Main Speculative Problems 388

Characteristic Features of Speculative Problems . . . 394

XVIII. THE CLASSIFICATION OF THE SCIENCES ... 399

General Character of the Problem 399

Difficulties in the Classification of the Sciences . . . 403

xvi TABLE OF CONTENTS

CHAPTER PAGE

Historical Illustrations 408

Peirce 410

Bliss 412

General Comparisons 415

XIX. HUMAN FREEDOM 418

General Character of the Problem 422

Eddington 425

Compton 428

Planck 432

XX. THE NATURE OF REALITY 438

General Character of the Problem 439

Spiritual Idealism 442

Mathematical Idealism 448

Creative Evolution 451

Logical Realism 455

INDEX 461

INTRODUCTION

THE FIELD OF THE PHILOSOPHY

OF SCIENCE

CHAPTER I

PHILOSOPHY AND SCIENCE

The defining of a field of study is always a precarious
enterprise. The possible objects of knowledge are not
labeled, like the magic cakes in Alice in Wonderland, "Eat
me." One must learn what is edible and what is not by the
treacherous process of trial and error. This fact forbids one
to assert in advance of any investigation what is and what
is not to be included in the investigation. One cannot say
before science has begun what the possible objects of science
are, for one can know whether an object is scientific only
by trying to know it scientifically.

For this reason any preliminary delimitation of the field
of the philosophy of science, and, derivatively, of the fields
of philosophy and of science, must be viewed as tentative
only, and as subject to later revision. Definition has two
roles to play in the development of a discipline. It serves
first as an advance guard, preparing the way by a rough
demarcation of the path and by elimination of the most
formidable obstacles. In this function it cannot be examined
or criticized on logical grounds; it is essentially psycholog-
ical, and has merely an informative value. It is tentative
and conjectural, often expressed in vague language, and
serves rather to direct the attention of the listener to the
proper locus than to give a complete and accurate descrip-
tion of its object. But definition also plays the part of a
rear guard, organizing resources and fortifying the acquired
territory. In this function it can justly be criticized on
logical grounds, since it aims to indicate not merely the
boundaries of its object but also something of the internal
structure. The definition of the term " philosophy of science "
which will be undertaken here must be considered as psycho-
logical or preliminary rather than as logical or final.

3

4 INTRODUCTION TO PHILOSOPHY OF SCIENCE

The character of the term determines the nature of the
approach which must be made to its definition. It is obvi-
ously a composite term, taking its meaning from the more
elemental terms constituting it. No definition of the philos-
ophy of science is possible without a prior analysis of both
philosophy and science. But these terms, unfortunately,
have had a long history and a variety of meanings. Further-
more, if there is any uniformity at all noticeable in the
historical uses of these words, it is such as to establish the
essential opposition or antagonism of the two notions, and
hence would compel one to conclude that the philosophy of
science is a contradiction in terms. The fact seems to be,
however, that the difficulties experienced in the attempts to
define "philosophy" and "science," and the apparent in-
compatibility of the two terms, are themselves the main
factors which are responsible for the emergence of the
philosophy of science. Because of the heated controversy
over the precise demarcations of these two fields, there arises
a discipline whose precise task is the determination of such
boundaries.

This fact determines the approach to the definition of the
philosophy of science which will be made in the present
chapter and the one which follows. A brief consideration of
the historical problem will serve to introduce the thesis that
the terms are rival claimants to knowledge. The outstanding
attempts of recent and contemporary writers to eliminate
this antagonism by assigning to each of the disciplines a
certain type of subject matter or a certain type of method
will then be examined. Each of these attempts will be
briefly criticized with a view to determining what essential
truth it contains. The ground will then be prepared for the
positive attempt, in Chapter II, to construct a definition
of the philosophy of science.

HISTORICAL APPROACH

History seems to justify the conclusion that the term
'philosophy' in early Greek thought was relevant to no

PHILOSOPHY AND SCIENCE

particular subject matter. The philosopher was one who
loved wisdom without being greatly concerned as to the
specific kind of object to which he directed his devotion.
There is reason to believe that by the time of Plato and
Aristotle the term had narrowed somewhat in scope and
no longer included mathematics. At least it seems significant
that the two greatest philosophers of antiquity were not
mathematicians. Though Plato considered knowledge of
mathematics an important preliminary to the study of
philosophy, he apparently did not suppose it a part of
philosophy proper. Aristotle wrote authoritatively on a
wide range of subjects including logic, rhetoric, metaphysics,
physics, astronomy, meteorology, .cosmology, botany, zool-
ogy, psychology, ethics, and politics, and there is reason to
believe that all of these were in some sense a part of his
philosophy. It is probable that the shift of the center of
civilization from Greece to Rome is responsible for the
introduction of the word "science'' into the vocabulary of
culture, and it was quite natural that the term should be
adopted to characterize those intellectual disciplines which
were to be differentiated either by method or by subject
matter from philosophy as the mother study. Scholasticism
witnessed the separation of theology from philosophy. The
revival of learning and the turning of man's attention to the
natural world may have been responsible for the increased
use of the term "science" to characterize the disciplines
which had broken away from philosophy. Even as late as
the sixteenth century a candidate for the degree of doctor
of philosophy was regarded as equally competent to teach
mathematics, astronomy, physics, metaphysics, logic, rhet-
oric, ethics, and politics. Christian Wolff, almost two cen-
turies later, actually taught mathematics, physics, logic,
psychology, practical philosophy, and political science at
the University of Halle. The full title of Newton's great
work, The Mathematical Principles of Natural Philosophy,
determined the use of the term "natural philosophy' as a
characterization of physics — a use which persisted until

6 INTRODUCTION TO PHILOSOPHY OF SCIENCE

recent years. The term "mental philosophy" is still much
in vogue in English universities. Many disciplines are even
now in the act of breaking away from the mother stem.
Cosmological speculations are on the border line between
metaphysics and physics; psychology is still in many univer-
sities closely allied with philosophy; sociology is only with
difficulty distinguishable from social philosophy ; and the so-
called normative sciences, ethics, esthetics, science of re-
ligion— attempting as they are to apply measurement
techniques to the determination of value attitudes — are in
the unfortunate position of having been denied philosophical
status before they have been granted scientific recognition.

The generalization of this historical fact is clear. Philos-
ophy is progressively losing ground, and the ground which
is lost is promptly claimed by science. Philosophy, which
once meant the totality of knowledge, now means the residue
of knowledge after mathematics, theology, physics, biology,
psychology, ethics, esthetics, and still others which only the
future can disclose, have broken away and set themselves
up on independent bases. Philosophy, which once was the
glorification of knowledge, approaches indefinitely near to a
position of complete extinction. Science, on the other hand,
which was once non-existent, is taking over the field of
knowledge and promises soon to occupy the enviable posi-
tion which philosophy has been obliged to abandon.

It is reasonable to expect that no philosopher today would
be willing to accept such a conception of the difference be-
tween philosophy and science. But it is curious to note
that many have, on the basis of this historical accident,
attempted to formulate theoretical conceptions of the nature
and scope of each of these disciplines in terms of which the
opposition may be understood. The assumption is that the
gradual encroachment of science upon philosophy must be
due to some basic antagonism between them. More funda-
mentally, it must be due to some specific advantage which
science has over philosophy, either as to its subject matter
or as to its methods of approaching nature. Hence the

PHILOSOPHY AND SCIENCE

disciplines are defined around this opposition, and the studies
become sharply differentiated from one another.

The result of this attitude has been a conception of the
relation between science and philosophy which has placed
investigators in the respective fields into warring camps,
which has made any cooperative enterprises impossible, and
which has made the notion of a philosophy of science a con-
tradiction in terms. According to this view, science has
stood for exact knowledge, verified conclusions, and prog-
ress; philosophy, for obscure ideas, conjecture, and stagna-
tion. Science uses mathematical methods, which forbid
fuzzy thinking; philosophy uses meditation, imagination,
and speculation, all of which lack precision and permit the
intrusion of ambiguity, vagueness, and obscurity. Science
subjects all of its ideas to experimental test and corrobora-
tion, promptly rejecting all inadequate hypotheses; philos-
ophy proceeds by pure reasoning, often discounting the
evidences of the senses when they conflict with the results
of pure logic — a fact which eventuates in the merging of
philosophy with poetry and mythology, and in the retention
in philosophy of all sorts of imaginative and fanciful ideas
whose only justification is their emotional agreeability.
Science, in its history, has exhibited progress through co-
operative effort; philosophy, on the other hand, has engaged
in continuous war between opposing schools of ideas. Hence
philosophy and science differ from one another in the clarity,
certainty, and progressiveness of the resulting knowledge;
and in terms of this distinction the historical encroachment
of science upon philosophy is to be understood.

There is probably much in the history of these two disci-
plines to justify such a theory. Certainly most philosophical
concepts are incapable of the same precision in logical for-
mulation as are mathematical notions; probably too much
of philosophy has in the past proceeded by the "speculative"
method in which the philosopher retired into his study,
closed the doors, and endeavored to spin out a theory of the
universe; without doubt there has been less advancement

8 INTRODUCTION TO PHILOSOPHY OF SCIENCE

in philosophical ideas than in scientific knowledge. But the
recent point of view, while admitting the fact, has adopted
another explanation. It insists that the differences between
science and philosophy are fundamental but not irrecon-
cilable— that the disciplines, instead of being opposed and
antagonistic to one another, are really supplementary.
Nature is one, but there may be different kinds of objects
in nature, and there may be different ways of studying
natural objects. Science and philosophy are distinct, either
because there are scientific and philosophical objects and
the study of the one cannot be the study of the other, or
because there is only one general kind of object in nature
but alternative ways of viewing it. The result of this ap-
proach to the problem in recent years has been the formu-
lation of a number of points of view from which the apparent
opposition between the two fields may be understood. For
present purposes five of the contemporary theories may
be discussed: (1) Science describes, philosophy explains;
(2) science describes facts empirically, philosophy analyzes
symbols logically; (3) science describes facts, philosophy
describes values; (4) science describes quantities, philos-
ophy describes qualities; (5) science analyzes, philosophy
intuits.

DESCRIPTION VS. EXPLANATION

The view that science should limit its task to that of mere
description, leaving the more ultimate problems of explana-
tion and interpretation to philosophy, has been character-
istic of the so-called positivistic school, of which Mach,
Kirchhoff, and Karl Pearson are representatives. Even as
far back as Comte one finds an acknowledged positivism.
"Our business is — seeing how vain is any research into what
are called Causes, whether first or final — to pursue an accu-
rate discovery of . . . Laws, with a view to reducing them
to the smallest possible number. By speculating upon causes,
we could solve no difficulty about origin and purpose. Our
real business is to analyze accurately the circumstances of

PHILOSOPHY AND SCIENCE

phenomena, and to connect them by the natural relations of
succession and resemblance." 1 In the words of Pearson,
"the law of gravitation is a brief description of how every
particle of matter in the universe is altering its motion with
reference to every other particle. It does not tell us why
particles thus move; it does not tell us why the earth de-
scribes a certain curve around the sun. It simply resumes,
in a few brief words, the relationships observed between a
vast range of phenomena. It economises thought by stating
in conceptual shorthand that routine of our perceptions
which forms for us the universe of gravitating matter." 2
The scientist is not forbidden, however, to talk about the
super sensuous; he may, for example, talk about the atom.
But "either the atom is real, that is, capable of being a
direct sense-impression, or else it is ideal, that is, a purely
mental conception by the aid of which we are enabled to
formulate natural laws. It may pass . . . from the ideal
stage to the real; but till it does so, it remains merely a con-
ceptual basis for classifying sense-impressions, it is not an
actuality. On the other hand, the metaphysician asserts
an existence for the supersensuous which is unconditioned
by the perceptive or reflective faculties in man. His super-
sensuous is at once incapable of being a sense-impression,
and yet has a real existence apart from the imagination of
man. It is needless to say that such an existence involves an
unproven and undemonstrable dogma." 3

On the other hand, philosophy "is concerned not with
the accumulation of facts, but -with the interpretation of
previously ascertained facts, looked at broadly and as a
whole. When the facts of physical Nature and of Mind
and the special laws of their connection have been discovered
and systematised by the most adequate methods of experi-
ment, observation, and mathematical calculation at our
disposal, the question still remains, how we are to conceive
of the whole realm of such facts consistently with the gen-

1 A. Comte, Positive Philosophy, tr. by Martineau (New York, 1858), p. 28.

2 Grammar of Science (3d ed.; New York: Macmillan, 1911), p. 99.

3 Ibid., p. 96.

10 INTRODUCTION TO PHILOSOPHY OF SCIENCE

eral conditions of logical and coherent thought." * This
interpretation may involve reference to ultimates such as
first causes, things-in-themselves, essences, and the like,
on the grounds that the human mind cannot be completely
satisfied with mere description, and demands that we go
beyond to more basic interpretations.

It is clear that such an apportioning of the intellectual
task to science and philosophy need not result in a view
that the two disciplines are hostile to one another. For the
extreme positivists, who claim the exclusiveness of the
method of description, all philosophy becomes nonsense.
But for the more moderate proponents of the position,
science and philosophy constitute a cooperative enterprise
in which science assumes responsibility for the less ultimate
problems and philosophy for the more ultimate. The ground
for this attitude is the recognition that the distinction be-
tween description and explanation is not an ultimate one.
When one describes, he explains in terms of the more obvious
features of the given, and when he explains he describes in
terms of the less obvious features. With the advance in
instrumental techniques explanatory entities become de-
scriptive entities, e.g., molecules, as seen in the Brownian
movement. The answer to the question why is not funda-
mentally different from the answer to the question how;
when one explains he seems to be calling attention to the
more basic but somewhat more elusive features of nature —
he seems to be getting behind nature to enduring connec-
tions, more permanent substances, and the like. But it is
the fate of all explanatory entities whose existence becomes
well established that they become descriptive entities, which
must in turn be explained by still more basic entities. This
argues for the view that science and philosophy represent a
continuum with reference to one another — a continuum of
understanding, at one end of which the approach to nature
is through descriptive techniques, and at the other end of
which the approach is through explanatory methods. Hence

: A. E. Taylor, Elements of Metaphysics (New York: Macmillan, 1904), p. 47.

PHILOSOPHY AND SCIENCE 11

science and philosophy are not opposed but supplemen-
tary.

FACTUAL DESCRIPTION VS. SYMBOLIC ANALYSIS

A second theory of the relation between science and
philosophy has appeared in recent years among a group of
scholars who identify themselves as the Vienna Circle, and
are commonly called logical positivists, or logical empiricists.
The outstanding representatives of the school are Carnap,
Schlick, and Wittgenstein, and they consider themselves
the direct descendants of the earlier positivists. For them
the dichotomy between science and philosophy has become
absolute. To science is assigned the task of both description
and explanation; to philosophy is assigned the task of the
logical clarification of ideas. "The result of philosophy is
not a number of 'philosophical propositions,' but to make
propositions clear." * It is not the job of the philosopher,
therefore, to talk about the world of empirical facts, but
rather to talk about the propositions which one asserts
when he claims to be talking about such facts. Thus the
subject matter of philosophy is really propositions, and the
business of the philosopher is the logical analysis of proposi-
tions with a view to determining exactly what they mean.
If the propositions which he examines prove to be empirical
propositions, i.e., propositions of natural science, he must
clarify them by reducing them to other propositions which
are capable of direct verification. If the sentences prove to
be logical propositions, i.e., assertions about symbols and
their interrelations, he must clarify them through consid-
eration of the rules of syntax. Often he finds that the appli-
cation of these two types of technique reveals that a given
sentence is nonsense, i.e., a pseudo-proposition. Most of the
propositions of metaphysics as formulated in traditional
philosophy prove to be pseudo-propositions; the proposi-
tions of epistemology and of ethics reduce, respectively,

1 L. Wittgenstein, Traclatus Logico-Philosophicus (New York: Harcourt, Brace,
1922), prop. 4.112.

12 INTRODUCTION TO PHILOSOPHY OF SCIENCE

in so far as they have content, to propositions of psychology
and of sociology, and, in so far as they have no content, to
pseudo-propositions. The total range of sensible proposi-
tions, then, reduces to two classes: material propositions,
which assert about facts and therefore have empirical
sense; and formal propositions, which assert about symbols
and therefore have sense only in so far as symbols are them-
selves facts of a certain kind. For Wittgenstein even the
propositions of logic are without sense; for Carnap they
possess sense of their own peculiar kind.

What may be said in estimation of this important theory
of the interrelation of science and philosophy? Its neatness
gives it a strong appeal. Furthermore, any technique which
offers a method for simplifying the philosophical task by
eliminating a large number of pseudo-problems is certain
to be looked upon with favor. Again, even apart from the
general presuppositions of the position, the analysis of
logical techniques and the general contributions to logical
theory which have been made by this group have given it a
place of importance in the contemporary scene. But that
philosophy is adequately defined merely as the logical
analysis of symbols is, perhaps, questionable. Certainly
there are many highly general propositions about the world
which are not strictly a part of science and yet which are
not merely about symbols. Such propositions tend to be
considered as symbolic since their high generality suggests
the impossibility that they should be false, and they are
consequently taken to be legislative over the world merely
by virtue of an arbitrary use of symbols. In spite of the fact
that a proposition such as " an event is not both p and not-p ,!
obviously asserts something about events, it is presumed
by this group to be merely an assertion about symbols, i.e.,
"the symbols 'p' and 'not-p' are so defined as to make false
any proposition in which they are jointly predicated of an
event." A definition of philosophy which would retain its
obvious empirical reference seems to be preferable to one
which reduces it to symbolic analysis. Yet, in spite of this

PHILOSOPHY AND SCIENCE 13

feature, logical positivism has the same important advan-
tage that the preceding theory has — it does not create an
opposition between science and philosophy. In fact many
of the representatives of the group are themselves scientists,
and have been led to the problems of logical analysis by
some of the difficulties which were encountered in the scien-
tific pursuit. They recognize therefore the necessity for
cooperation between the investigators in the two fields.
Though the distinction between the two realms is sharp,
i.e., a scientific proposition is not a philosophical proposi-
tion, nevertheless the scientist should consider his proposi-
tions philosophically (logically) and the philosopher is bound
to apply his techniques to empirical propositions.

FACTS VS. VALUES

The third theory of the relation between science and
philosophy is based on the dichotomy of facts and values.
One finds in the intellectual enterprise that he may make
judgments of two kinds: he may assert that something is,
and he may assert that something is valuable. When he
makes judgments of the former kind he is asserting existen-
tial propositions, and when he makes judgments of the
latter kind he is asserting normative propositions. Factual
judgments are existential not merely in the sense that they
assert that something is or is not; they also characterize or
describe an object or relate it to another object, so long as
the characterization, description, or relation does not in-
volve preferential notions or activities. Valuational judg-
ments, on the other hand, assert about the goodness, or
beauty, or truth, or usefulness of objects, and thus involve
definite reference to standards or norms. To say that snow
is white is to utter a factual judgment, but to say that it is
beautiful is to make a normative judgment.

Such a distinction between kinds of judgments affords a
convenient basis for a differentiation of science and philos-
ophy. The realms of fact and value "are completely sep-
arate worlds, and the moral sciences must, in their own

14 INTRODUCTION TO PHILOSOPHY OF SCIENCE

highest interest, oppose the natural scientist when he oper-
ates with ideas as the 'art forms of nature' and the like.
That is not his business, he may pronounce judgments of
existence, but not of value. Conversely, the scientists them-
selves are accustomed to agree to this, since long historical
experience has taught them, that the introduction of judg-
ments of value into science has more than once dangerously
obscured the view of research as regards objective fact." l

Though Bavink believes that the scientist cannot avoid
considering questions of value, Patrick insists that problems
of this kind are really philosophical. "It is not the purpose
of science to study meanings, values and appreciations. . . .
But since our primary interests relate to meanings and
values, science must be supplemented by philosophy. My
new motor car, for instance, is a thing of beauty and it
gives me joy just to contemplate its curves and its gloss
and its correct proportions. It will have great value for me,
as I imagine, enabling me to keep distant appointments, to
economize time, to live more in the open air, to keep my
family entertained, to maintain or increase my social pres-
tige. . . . Hence it becomes necessary to go beyond science
to philosophy. Life must be interpreted, not merely de-
scribed. It must be seen as a whole, not broken into separate
parts. Its meaning and value must be sought, its purpose
inquired into. Perhaps it has no purpose, meaning or value;
but such a conclusion could be reached only after reflective
inquiry, and such reflective inquiry would be philosophy." 2

Recent science has done much to obliterate the distinction
between fact and value, and thus to destroy it as a basis for
the differentiation of science and philosophy. Value atti-
tudes are being drawn into the realm of scientific subject
matter and being described and measured by laboratory
techniques. Preferential states are, after all, psychological
facts, and to the extent to which one can classify and order
such facts he can talk about attitudes in scientific terms.

1 B. Bavink, The Natural Sciences (New York: Century, 1932), p. 594.
2G. T. W. Patrick, Introduction to Philosophy (New York: Houghton Mifflin,
1924), 1st ed., pp. 16-17.

PHILOSOPHY AND SCIENCE 15

Every value judgment is, in the last analysis, also a judg-
ment of fact, viz., the fact that someone has taken a value
attitude toward an object. Furthermore, from the other
side, every judgment of fact is probably, in some direct or
indirect way, the expression of a value attitude. Facts are
attended to through acts of selection which may express
unconscious interests and unrecognized desires. Even the
scientist must guard against the tendency to blind himself
to the existence of data which would constitute a refutation
of a pet theory. The very fact that the scientist prefers true
judgments to false is the result of a preferential state. Hence
the distinction between judgments of fact and judgments of
value, which has a certain practical working effectiveness,
becomes relatively unsatisfactory as a foundation for the
distinction between science and philosophy.

QUANTITY VS. QUALITY

A fourth view of the interrelation of the two fields is that
which apportions all discussions of the quantitative aspects
of experience to science and all considerations of the qualita-
tive aspects to philosophy. The following quotation from
Eddington is a classic as a description of the task of the
scientist. 'Let us examine the kind of knowledge which is
handled by exact science. If we search the examination
papers in physics and natural philosophy for the more intel-
ligible questions we may come across one beginning some-
thing like this: 'An elephant slides down a grassy hill-
side . . .' The experienced candidate knows that he need
not pay much attention to this; it is only put in to give an
impression of realism. He reads on: 'The mass of the ele-
phant is two tons.' Now we are getting down to business;
the elephant fades out of the picture and a mass of two tons
takes its place. What exactly is this two tons, the real
subject matter of the problem? It refers to some property
or condition which we vaguely describe as 'ponderosity'
occurring in a particular region of the external world. But
we shall not get much further that way; the nature of the

A

16 INTRODUCTION TO PHILOSOPHY OF SCIENCE

external world is inscrutable, and we shall only plunge into
a quagmire of indescribables. Never mind what two tons
refers to; what is it? How has it actually entered in so
definite a way into our experience? Two tons is the reading
of the pointer when the elephant was placed on a weighing-
machine. Let us pass on. 'The slope of the hill is 60°.' Now
the hillside fades out of the problem and an angle of 60°
takes its place. What is 60°? There is no need to struggle
with mystical conceptions of direction; 60° is the reading of
a plumb-line against the divisions of a protractor. Similarly
for the other data of the problem. The softly yielding turf
on which the elephant slid is replaced by a coefficient of
friction, which though perhaps not directly a pointer read-
ing is of kindred nature. . . . And so we see that the poetry
fades out of the problem, and by the time the serious appli-
cation of exact science begins we are left with only pointer
readings. . . . The whole subject-matter of exact science
consists of pointer readings and similar indications." l

What, then, is left for the philosopher? The philosopher
must tell us about elephants and hillsides and ponderosity,
or, more generally, about colors, sounds, odors, tastes, and
touch sensations, and the complexes called "objects' into
which they are united. But he must describe these in quali-
tative terms, not in measured values. Though red may be
measured by a wave length, red is not the wave length;
there is something in the qualitative given which eludes
analysis and quantification. Science abstracts from objects,
and by this act loses an important feature of them. The
artist, the religious man, the mystic all try to capture this
elusive element, each in his own way; but all of these ways
are essentially emotional and irrational. The philosopher
must pursue this qualitative element by rational techniques.
The philosopher must restore to the world its expansiveness
and durational character, which the scientist has replaced
by meter sticks and clocks; he must repopulate it with

1 From A. S. Eddington, Nature of the Physical World, pp. 251-252. By permis-
sion of The Macmillan Company, publishers.

PHILOSOPHY AND SCIENCE 17

heat and movement and pushes and pulls, which the scien-
tist has eliminated in favor of molecules and differential
velocities and pointer readings. Only through this sup-
plementation can one understand the world in its to-
tality.

It seems likely that a thorough-going analysis of the
notions of quality and quantity would do much to obliterate
the sharpness of this distinction. There certainly is a sense
in which quantities are themselves qualities. In fact a
quality becomes a quantity just to the extent to which it
may be shown to have a certain place in a series of a spec-
ifiable kind. Qualities which are orderable are also quanti-
ties. When one thinks, for example, of the natural numbers
he tends to picture them as arranged in the order of magni-
tude, 1, 2, 3, 4, ... , rather than as a mere aggregate,
2, 4, 3, 1, . . . . Hence he tends to think of the differences
between them as being quantitative rather than qualitative.
Actually one can discover the same qualitative difference
between 2 and 3 that he can between red and green, though
the ready ordering of the numbers compels him to neglect
this difference in favor of a quantitative one. Though the
insertion of intervening members in the series, for example,
the fractions, tends to turn attention away from the qualita-
tive difference and toward the quantitative difference, the
former distinction remains and is found at the new level be-
tween any two fractions. To order is not to eliminate quality.
Serial arrangement serves only to replace qualities which
are not readily orderable by qualities which are.

The distinction between science and philosophy can then
be expressed, though it takes a slightly different form. Sci-
ence is interested in the consideration of those qualitative
aspects of experience which are readily orderable, and es-
pecially in the supposed correlation between these qualities
and certain others of which they seem to be the measured
values. Physics, for example, is occupied with wave lengths
and with the functional relations between wave lengths and
colors. Philosophy, on the other hand, busies itself with those

18 INTRODUCTION TO PHILOSOPHY OF SCIENCE

qualities which are not so readily orderable, for example,
the colors themselves, and especially those other qualita-
tive manifestations of experience, such as life, intelligence,
pleasure, and pain where all ordering seems more or less
artificial. This, at any rate, proves to be a more satisfactory
working distinction between the two fields.

ANALYSIS VS. INTUITION

Closely related to this distinction, but not to be confused
with it, is the point of view maintained particularly by Berg-
son in recent years. Science proceeds by the method of
analysis while philosophy uses the method of intuition. Ac-
cording to Bergson, "it is easy to see that the ordinary
function of positive science is analysis. Positive science
works, then, above all, with symbols. Even the most con-
crete of the natural sciences, those concerned with life,
confine themselves to the visible form of living beings, their
organs and anatomical elements. They make comparisons
between these forms, they reduce the more complex to the
more simple; in short, they study the workings of life in
what is, so to speak, only its visual symbol. If there exists
any means of possessing a reality absolutely instead of
knowing it relatively, of placing oneself within it instead
of looking at it from outside points of view, of having the
intuition instead of making the analysis : in short, of seizing
it without any expression, translation, or symbolic repre-
sentation— metaphysics is that means. Metaphysics, then,
is the science which claims to dispense with symbols." l The
opposition between science and metaphysics is further clar-
ified by showing that the one is conceptual, fixed, descrip-
tive, mediate knowledge, while the other is intuitive, mobile,
acquaintive, immediate knowledge. Science sees objects
from the outside, metaphysics from the inside. Thus sci-
entific knowledge is artificial, illusory, and dangerous, while
metaphysical knowledge is real, true, and reliable. Through
science one grasps the world by means of an empty, static

1 Introduction to Metaphysics (New York: Putnam, 1912), pp. 8-9.

PHILOSOPHY AND SCIENCE 19

form ; through metaphysics one knows it without representa-
tion, as a full and changing reality.

There is probably much in Bergson's theory of the ulti-
mate nature of reality that led him to this view of knowledge.
If the world is a changing, growing reality, and the expres-
sion of a vital urge to develop, there is reason to believe
that a conceptual scheme — which is by its very nature
static — cannot portray its essential nature. Hence a method
of knowing, peculiar to the subject matter, must be devised.
Furthermore there is probably a sound epistemological foun-
dation for the distinction between acquaintance and descrip-
tion, between synthetic and analytic methods of knowing,
between feeling a duration and conceptualizing time. But
it seems unlikely that any such feature can be employed
as a basis for distinguishing between philosophy and science.
It is much more probable that the differentiation of philos-
ophy from science must cut across this methodological dis-
tinction, since either one of the methods, if not supple-
mented by the other, can hardly result in anything that
can be called knowledge. Knowledge in its simplest form
is both acquaintance and description, synthesis and analysis,
feeling and conceptualization. Hence neither the philosopher
nor the scientist could be said to know in the strict sense
of the word unless he employed both methods. It is rather
significant that Bergson's thesis, in spite of its neatness
and emotional appeal, has been supported by comparatively
few scientists and philosophers in the contemporary scene.

Certain other minor attempts to differentiate the two
fields of knowledge may be mentioned in conclusion. It
is sometimes maintained that the distinguishing feature of
science is its use of laboratory and instrumental techniques,
as contrasted with philosophy which proceeds by observa-
tion, introspection, and other methods of passive reception.
Closely allied with this view is the theory that science is
empirical and inductive while philosophy is rational and
deductive. Or, again, it may be insisted that since science
arose out of the need for control over the world it should

20 INTRODUCTION TO PHILOSOPHY OF SCIENCE

be defined as practical knowledge, as opposed to the wisdom
and understanding which is the unique possession of the
philosopher. All of these distinctions seem to break down
when one attempts an actual classification of the existing
intellectual disciplines on the basis of one or more of them.
There are acknowledged sciences which do not employ lab-
oratory techniques; there are inductive philosophies and
deductive sciences; there is theoretical physics and practical
philosophy. Thus the adoption of any one of the distinc-
tions would be in essential violation of the terminology not
only of common sense but of critical thought as well, and
it would seem inadvisable to follow this procedure. The
alternative is to formulate the problem not in terms of
philosophy vs. science, but in terms of a philosophy of
science. The consideration of this problem will be found
in the following chapter.

REFERENCES

Bertrand Russell, The Scientific Outlook (London: Allen and Un-

win, 1931), Chap. XVII.
Problems of Philosophy (New York: Holt, 1912), Chap. XV.

F. Paulsen, Introduction to Philosophy (New York: Holt, 1895),

introd., sec. 2.

G. T. W. Patrick, Introduction to Philosophy (New York: Hough-

ton Mifflin, 2nd ed., 1935), Chap. II.
B. Bavink, The Natural Sciences (New York: Century, 1932),

Part IV, Chap. VIII.
Henri Bergson, Introduction to Metaphysics (New York: Putnam,

1912).
R. Carnap, Philosophy and Logical Syntax (London: Kegan Paul,

1935).
F. J. Sheen, Philosophy of Science (Milwaukee: Bruce, 1934),

Chap. I.

CHAPTER II

PHILOSOPHY OF SCIENCE

In the last chapter consideration was given to some of
the attempts which have been made in recent years to
"save" philosophy from the encroachment of science. In
each case, the resolution of the conflict was presumed to
lie in some apportioning of the intellectual task to the sep-
arate disciplines either on the grounds of method or on the
grounds of subject matter. It was maintained, for example,
that science talks only about certain types of natural entity
and leaves all others to philosophy. Or science talks about
natural entities through the medium of a certain type of
method and leaves alternative approaches to philosophy.
In all cases the presumed reconciliation lies in a precise
delimitation of the respective fields.

EMERGENCE OF THE PHILOSOPHY OF SCIENCE

The emergence in recent years of a new discipline called
"the philosophy of science'' was occasioned, I believe, by
three factors. One was the recognition of the obviously
temporary character of this presumed reconciliation between
science and philosophy. A second was the appearance,
within science itself, of certain inconsistencies, which com-
pelled it to become self-critical. A third was the claim on
the part of science that it had the right to legislate over
all features of the individual life. Each of these may be
examined briefly.

The unfortunate character of the type of reconciliation
suggested in the preceding chapter is that it can be, at best,
only temporary. Inevitably questions arise either as to the
importance of the respective disciplines, or as to the legit-
imacy of the type of problem which the one or the other

discipline is called upon to answer. The view that science

21

22 INTRODUCTION TO PHILOSOPHY OF SCIENCE

is description leads imperceptibly to the view that all knowl-
edge is description, and that problems of explanation and
interpretation are pseudo-problems. The claim that science
employs quantitative methods to understand qualities passes
gradually into the position which insists that when qualities
have been explained they have been explained away, hence
there is nothing left for philosophy. Or, on the other hand,
if philosophy knows things immediately and intuitively,
then science, which knows things only mediately and symbol-
ically, must be pseudo and illusory.

It was readily seen that no permanent harmony could be
established by means of such a reconciliation. But it was
also apparent that the very attempt to decide questions of
the importance of the scientific method as over against the
philosophical method, questions of the legitimacy of the
two types of problem, questions of the truth of the knowl-
edge obtained through the respective approaches, gave rise
to interesting speculations and, in many cases, to significant
answers. The suspicion immediately arose that the investiga-
tion of the methods of science and philosophy, of the limits
of the respective fields, and of the relative importance of
the two types of knowledge might itself become a discipline
with significant results to offer toward the solution of the
ultimate problem of knowledge. Since the method and sub-
ject matter of science seemed more definite than the method
and subject matter of philosophy, this new discipline was
called " the philosophy of science." The task of this new en-
terprise was the critical study of science from the point of
view of its presuppositions and unanalyzed notions, from
the point of view of its techniques and methods, and from
the point of view of the limits of its problems. By this means
a more or less permanent reconciliation was brought about,
for if philosophy is the study of science just as science is
the study of nature, there can no more be a conflict between
science and philosophy than there can between science and
nature. There can be no question of the relative importance
of the two disciplines for they are, so to speak, upon different

PHILOSOPHY OF SCIENCE 23

levels, and the question of importance depends upon the
level in which one is interested. Thus out of the attempt to
integrate the two fields there arose a study whose problem
was precisely the integration of the two fields, and this
gradually became the discipline which is now called "the
philosophy of science."

The second factor responsible for the emergence of the
philosophy of science was the appearance in science itself of
certain features which were responsible for its own instabil-
ity. The philosophy of science is inevitable whenever a
science becomes self-critical. But self-criticism arises only
when there is an obvious breakdown. So long as a machine
operates smoothly there is no occasion for the operator to
suspect that it is not in order. The smooth operation seems
a sufficient guarantee of efficiency and adequacy. But now
suppose the machine suddenly to stop, either because of
an internal breakdown or because of an external obstacle.
Immediately the question arises as to the cause of the inter-
ruption, and more specifically, as to the general character
of a machine which will suddenly stop in the face of a prom-
ise of continued functioning. A breakdown can never occur
unless it is potentially in the engine even when it appears
to be running smoothly. And an engine which has the
potentiality of breaking down is clearly an inferior engine,
as compared with one which has not this potentiality.
Thus the problem of preventing malfunctioning is as much
a problem in connection with machines as is the problem of
guaranteeing continued functioning. Now if the subject
matter of one's study is not an engine but science itself, the
problem is essentially the same. Science belongs to science
so long as it exhibits no inadequacies. But when science
proves inadequate it belongs to philosophy. This does not
mean that philosophy functions as the great intellectual
repair man. Mere repairing is essentially the same problem
as original construction, namely, a scientific problem. Phi-
losophy repairs only in the sense that it attempts to show
primary inadequacies, unwarranted original assumptions,

24 INTRODUCTION TO PHILOSOPHY OF SCIENCE

questionable predictions, doubtful methods. Thus when the
scientist looks at his product with a view to the presup-
positions which were employed in its construction, with a
view to the inherent weaknesses in its internal structure,
with a view to the possible inadequacies which may later
come to light — when a scientist does this he ceases to be a
scientist and becomes a philosopher.

Two examples of such crises in science, both drawn from
the last century, may be offered for consideration.

The first is taken from mathematics, and, more specifically,
from the field of geometry. Probably no one of the sciences
has had a more complacent history, a more continuous de-
velopment, and fewer regressive movements. Euclidean
geometry was a monument to scientific ingenuity, exhibiting
internally a high degree of consistency and affording ex-
ternally a highly accurate and extremely convenient method
for measuring land, constructing buildings, and meeting
innumerable problems of practical life. Then came two
individuals, about the middle of the last century, Riemann
and Lobachewski, who showed in a conclusive manner that
there could be alternative systems of geometry, i.e., that the
Euclidean system of geometry was not the geometry but
merely one among a large number of such systems. Each
such system was shown to be internally perfectly consistent;
from a group of axioms and postulates accepted as true the
total body of propositions could be deduced by strictly
logical processes. Rut between systems there was an essen-
tial contradiction. For example, in the Euclidean system,
the sum of the angles of a triangle is equal to 180° but in the
Lobachewskian system the sum of the angles of a triangle
is always less than 180°; and in the Riemannian system the
sum is always greater than 180°. Immediately the question
arises, which system is true? Clearly they cannot all be
true for they are incompatible; yet one of them must be true.

To answer this question would take one into the very
heart of recent physical science. What should be pointed
out here is the change in character which geometry experi-

PHILOSOPHY OF SCIENCE 25

enced as a result of this shock. It became self-critical.
Geometricians began to ask such questions as the following,
which, it should be noted, are not geometrical questions
but philosophical, i.e., logical and epistemological. What is
meant by the consistency of a system of propositions?
Can a system of propositions be consistent and not true?
What is truth? Does geometry describe the world? Is space
objective, i.e., independent of the knowing activities, and,
if so, which space — Euclidean space, Lobachewskian space,
or Riemannian space? Thus the geometrician was compelled
by the intrinsic inconsistencies of his system to turn his
attention to philosophical considerations. When he did so
he ceased to be a scientist and became a philosopher, and
he created that study which is called "the philosophy of
science," or, in this case, "the philosophy of geometry."

The second example is drawn from the field of physics.
At the end of the last century physics was also in a state of
great complacency. Though its youth and development had
not been so uneventful as that of mathematics, it had reached
a stage of relative quiescence. It was generally recognized
that the great discoveries in physics had all been made and
that progress would consist of the introduction of greater
accuracy. The point of view is well expressed by the state-
ment in the announcement of courses in the department of
physics in one of the great universities of this country near
the end of the last century, to the effect that research work
in physics in the future would consist essentially in the
transformation of physical laws so as to make them accurate
to the fourth rather than merely to the third decimal place.

Then came the shock of the relativity theory. A certain
experiment, devised to measure the variations in the velocity
of light due to the changes in the velocity of its source, was
performed. It was confidently predicted that the anticipated
outcome would be verified. But the results were unequivo-
cally negative. The crucial character of the experiment
made its negative outcome of great significance. Ordinarily
when an hypothesis fails of verification the scientist throws

26 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the theory aside and sets up a new one in its place. But here
the situation was different. For the theory which was negated
by the experiment was at the very foundation of the whole
physical structure; if it were to be thrown aside, most of
physical theory would have to be discarded. Physics was
thrown into turmoil. The problem of the future of physics
now seemed to lie in abandoning the entire structure and
starting again from the ground.

Again it is not important to solve the problem here raised.
What should be pointed out is that physics immediately
became self-critical. And in becoming self-critical it became
philosophical. For the problems which are raised by the
theory of relativity are unquestionably philosophical in char-
acter. They have to do with the nature of time, space, and
motion; with the assumptions implicit in the method of
measurement; with the applicability of geometrical concepts
to the world; with the very meaning of "truth," 'theory,"
"law," and other logical concepts. For example, if the re-
sults of this experiment are to be accepted, there seems to
be a peculiar interrelationship of space and time. This is
popularly, but very inaccurately, expressed by saying that
time turns out to be a fourth dimension of space. What is
meant is that space and time are shown to constitute a
four-dimensional system, of which three dimensions are
spatial and one dimension is temporal. In other words, in
order to locate a happening completely one must specify
not only where it occurs but also when it occurs. But, sur-
prisingly enough, one cannot tell when it occurs without
knowing at the same time where it occurs, nor can one tell
where it occurs without knowing when it occurs — hence the
puzzling interrelation of space and time which has been one
of the essential problems of the philosophy of science. Here
again what should be pointed out is merely that the physi-
cist, when he turns his attention to such problems as that
mentioned above, ceases to be a pure physicist and becomes
a philosopher of physics. This does not mean that he must
cease to be a physicist, but it does mean that he approaches

PHILOSOPHY OF SCIENCE 27

his subject matter with a different attitude, a different
method, and a different aim.

In the third place the emergence of the philosophy of
science occurred as a result of a fact which was essentially
social in character. The last century was, by all odds, a
period of outstanding scientific progress ; the present century
promises even to surpass it in the extent of knowledge, in
the application of this advance to the improvement of com-
fort and convenience, and in the effect which this increased
information is certain to exert upon individual and social
values. The fact is that we are better informed than we were
a hundred years ago, and the difference is essentially due to
science. Science has been so much popularized in recent
years that the average layman knows more today than the
specialist of a century ago. Furthermore, the advance in
knowledge has not been of a purely theoretical sort; instead
it has resulted in revolutionary transformations in the man-
ner of life of the ordinary individual. Man is today more
comfortable than he has ever been, and he has more oppor-
tunities for cultural advancement, education, and travel
than his ancestors ever dreamed of. Moreover, science is
claiming the right to legislate over his entire life; the cry
is to make religion scientific, to make behavior scientific,
to make politics scientific. Our age has been properly
characterized as the scientific age. Certainly it is scientific
in the sense that its ideals are essentially the ideals of sci-
ence, the spirit with which it approaches its problems is
preeminently the spirit of science, and the solution to its
problems seems to lie in further scientific knowledge.

All of this has turned man's attention to science. Science
is no longer being taken for granted; it is no longer a negli-
gible aspect of the social scheme, free to pursue its independ-
ent course. It has emerged as a dynamic factor, exerting
influences upon all phases of the contemporary scene —
religion, morality, art, education, and the cultural life in
general. Inevitably man, fundamentally a rational animal,
begins to ask the question: what is science? What is this

28 INTRODUCTION TO PHILOSOPHY OF SCIENCE

force which has taken the leading role in the modern scene ?
Is it entitled to the claim which it asserts — the claim that
every phase of life may justifiably be subjected to scientific
analysis, the claim that only the scientifically verifiable is
real, the claim that man's salvation is to be found in sub-
servience to the laws of nature as revealed through the tech-
niques of science ? The systematic attempt to answer this
question became the philosophy of science.

THE PHILOSOPHY OF SCIENCE

Through these three approaches there has gradually taken
form a new discipline which has been called, variously,
"the philosophy of science," "the science of science," "phil-
osophical science," "the logic of science," "the metaphysics
of science," and "metaphysical science." It is probably
impossible today to obtain any general agreement among
authorities as to what exactly constitutes a problem of the
philosophy of science. All that one can say is that a new type
of question is being asked, and that there is gradually grow-
ing up a body of literature which seems to be devoted to
the attempt to answer this kind of question. Some of the
literature tries definitely to answer the question; some of it
offers certain vague hints; some of it can hardly be said
to have contributed anything specific toward the solution.
Four new periodicals * have appeared in the last decade,
all of them devoted directly or indirectly to the attempt to
answer this question. The First International Congress
of the Philosophy of Science was held in Paris, September,
1935, and the plan calls for a continuance of the movement
in the form of annual meetings. Courses in the philosophy
of science are given in practically all of the leading colleges
and universities of the world. Contributors to the subject
include such eminent figures as Einstein, Eddington, Jeans,
Heisenberg, Poincare, Whitehead, Russell, Planck — to men-
tion only a few of those best known.

1 Philosophy of Science, Williams and Wilkins, Baltimore; Analysis, Basil Black-
well, Oxford; Erkennlnis, Felix Meiner, Leipzig; Theoria, Wettergren and Kerber,
Gothenberg.

PHILOSOPHY OF SCIENCE 29

At present one cannot set the limits of the field of the
philosophy of science; one can only list the problems which
are being discussed in contemporary literature — problems
which are neither scientific in the strict sense of the word
nor philosophical according to the traditional use of the
term. The following list occurred in the first number of
the Philosophy of Science. It is purely tentative and pre-
sented merely on the editor's responsibility.

I. Studies in the analysis of meaning, definition, symbolism.
II. Studies in presuppositions — axioms, postulates, maxims.

III. Studies in method.

IV. Studies of the nature and formulation of theoretical prin-
ciples.

V. Studies in the structure of the sciences, their hierarchies.
VI. Studies in the function and significance of science within
various contexts.1

The program of the First International Congress of the
Philosophy of Science was divided into sessions designated
by the following topics: unity of science, logic and mathe-
matics, pseudo-problems, definition and experience, protocol
propositions, language and logic, induction, probability, se-
mantics, psychology and sociology, history of logic, logic and
theory of groups.

If one cannot set the limits of the problems which belong
properly to the philosophy of science, so much the less can
one classify within themselves the problems which by a
more or less arbitrary act are assigned to the field. However,
a tentative classification may be^ made upon the grounds of
certain characteristics which are exhibited by the sciences.
The most obvious of these features are the following:

1. The most important characteristic of science is that
one finds not science but sciences. Every scientific investi-
gator is a physicist or a mathematician or a biologist, i.e.,
a specialist. In general he pursues his studies in his own
particular field without any concern for what is being dis-
covered in other fields except in so far as these have direct

1 Vol. I, No. 1, pp. 3-4.

30 INTRODUCTION TO PHILOSOPHY OF SCIENCE

bearing upon his own subject matter. The result is that the
individual scientist feels quite justified in neglecting con-
siderations of the following kind: the conclusions in any
field other than his own; the nature of the relationships
holding between his field and other fields, and between the
other fields themselves; the character of the total world
which has thus been departmentalized for purposes of study.

2. Another important feature is that the scientist, as
such, is not a logician, i.e., he is not clearly aware of the
method which he is employing and of the criteria in terms
of which its validity should be judged. The scientist proceeds
largely by hunches and guesses, by trial and error, by in-
tuition, by unconscious inferences and techniques based
primarily on habit. The point is not that these are bad
methods, but that they are accepted uncritically. It is not
unusual, for example, to find teachers of science advising
students against taking a course in logic on the grounds that
they become so much concerned with what is going on in
their minds that they are no longer able to observe what is
taking place before their eyes. Fortunately this extreme
attitude is not taken by the greater number of scientists.
But there is unanimity in the view that the techniques of
science should not be examined until there is an obvious
breakdown, indicating a fundamental weakness in the struc-
ture. On such an occasion either the scientist or the phi-
losopher may undertake the reconstruction, but if the scien-
tist does it he is not acting as a scientist but as a philosopher.

3. Still another feature is the scientist's acceptance of
many concepts without a careful analysis of their meaning,
and many beliefs without a careful justification of their
truth. These are often called the presuppositions or the
foundations of his system. It is not the task of the biologist,
for example, to examine the concept of matter, nor of the
psychologist to examine the concept of life, nor of the
physicist to examine the concepts of number and order,
nor of any of the scientists to examine the concepts of rela-
tion, quality, event. Nor is it the task of the individual

PHILOSOPHY OF SCIENCE 31

scientist to justify his belief in the uniformity of nature,
or in the independence of the world which he is studying,
or in the basic rationality of nature. These propositions are
accepted uncritically by the scientist, and presumed to be
true until evidence to the contrary is revealed.

These are facts about science, and can, I think, hardly
be called into question. But it is quite another matter to
ask whether the neglect of these problems by the scientist
produces any unfortunate consequences. Are these prob-
lems, after all, important? Granting that the scientist qua
scientist is justified in neglecting them, does it follow that
they may be disregarded by all investigators, or are they
of sufficient importance to warrant turning them over to
the philosopher or some other specialist for study ?

It is the presumption of the philosophy of science that
problems of this type are important and should be, if not
solved, at least clarified. Their importance resides in the
fact that their neglect leads to difficulties. More particu-
larly, the extreme specialization of any scientist almost
inevitably results in a warped outlook not only on the world
as a whole but even on his own field. The belief soon arises
that the aspect of nature which he is studying is the only
aspect, and that all other aspects are either reducible to it
or such as can be studied by methods applicable to it. This
results in all sorts of erroneous conceptions, on the one
hand, of contradictions and antagonisms between the special
fields, and, on the other, of unjustifiable continuities holding
between them. For example, it may be held that science
and religion are in irreconcilable opposition, and doomed
to wage war on one another until one or the other is ex-
terminated; or it may be maintained that religion is con-
tinuous with science and therefore reducible to it in the
sense that religion is merely the feeling of awe and wonder
in the presence of the marvelous organization of nature —
a feeling which the scientist experiences in its most acute
form, and which compels him, willy-nilly, to be religious.
Specialization, furthermore, often blinds the investigator

32 INTRODUCTION TO PHILOSOPHY OF SCIENCE

to the possibilities of cooperation in the scientific enterprise;
often newly discovered techniques in one field have proved
applicable to other fields, and frequently conclusions in one
department suggest analogies in other departments.

Moreover, whatever may be said as to the dangers run
by science when it becomes over-attentive to method, it
can hardly be said that science will profit by a complete
neglect of logical considerations. Though the scientist can-
not be expected to tell us what truth in the abstract is, he
can certainly improve his results by clarifying his notion
of the techniques to be employed in testing the truth of an
hypothesis, and the dangers to which such techniques are
exposed. It is not unlikely that knowledge of the most
common errors of observation will make the observer less
susceptible to them; it is reasonable to suppose that an
understanding of the principles of deduction will enable the
scientist more readily to discover faulty applications of
them in his own mental processes. Even the carpenter
must occasionally pay attention to his tools.

Finally, clarification of the implicit concepts and assump-
tions of science can only result in a corresponding clarifica-
tion of its explicit beliefs. Every intellectual enterprise
rests upon certain undefined notions and certain undemon-
strated propositions. These basic ideas, however, are the
foundations of the science in a logical sense rather than its
origin in a temporal sense. One makes no conscious assump-
tions to begin with but discovers in the course of his investi-
gation that his conclusions can be justified only if he makes
explicit certain beliefs which seem to have been implicitly
present from the beginning. But the fact that the science
rests upon these notions does not mean that they are clearly
understood; on the contrary they can be clarified only by a
slow and painful process which shows their derivation from
data which are more clearly given. "The truth is that
what is logically most primitive in nature is not what is
now most familiar to us, and therefore it is better for didactic
purposes to start with the logically derivative but practically

PHILOSOPHY OF SCIENCE 33

familiar, and work back to the logically primitive but prac-
tically unfamiliar." x The clarification of the basic concepts
and assumptions is the revelation of that part of science
which is logically primitive.

PROBLEMS OF THE PHILOSOPHY OF SCIENCE

On the basis of these three facts about science one may
formulate a tentative classification of the problems of the
philosophy of science. The philosophy of science has as
its task the consideration of three main types of problem:
(1) The ascertainment of the limits of the special sciences,
of their integrations one with another, and of their implica-
tions so far as these contribute to a theory either of the uni-
verse as a whole or of some pervasive aspect of it; (2) the
critical examination of the method of science, of the nature
of scientific symbols, and of the logical structure of symbolic
systems; (3) the clarification of the basic concepts and
postulates of the sciences, and the revelation of the empirical
grounds (or absence of grounds) upon which they are pre-
sumed to rest.

The first aspect of the philosophy of science may be called
speculative, synthetic, or synoptic philosophy. It differs from
traditional cosmology only in its insistence upon the fact
that philosophy in this sense is dependent upon the special
sciences, and therefore not free to pursue the uncontrolled
speculation which has been its characteristic method in the
past. According to Broad, "its object is to take over the
results of the various sciences, to add to them the results
of the religious and ethical experiences of mankind, and
then to reflect upon the whole." 2 He then goes on to point
out that it necessarily presupposes the more critical ex-
amination of the sciences; that it can, at best, consist only
of more or less happy guesses; and that it is almost certain
to be influenced by one's hopes and fears, likes and dislikes.
All of these condemnations are probably justified; but they

1 C. D. Broad, Scientific Thought (New York: Harcourt, Brace, 1923), p. 26.

2 Ibid., p. 20.

34 INTRODUCTION TO PHILOSOPHY OF SCIENCE

mean only that the study should be pursued with unusual
caution, and that its results should not claim to be more
than conjectures substantiated to a greater or lesser degree.

The second aspect of the philosophy of science may be
called the logic of science, or the philosophy of method. It
differs from traditional logic in its insistence that science
offers, by and large, the most effective method for acquiring
knowledge. Hence the task of philosophy toward science
is the analysis and criticism of its method, with a view to
estimating its scope and determining its limitations, with a
view to exposing its errors and revealing its criteria of valid-
ity, with a view to the clarification of the assumptions about
symbols, meaning, and language which are involved. This
is the fundamental part of what Broad calls critical philos-
ophy. 'It deals with such concepts as truth, implication,
probability, class, etc. In fact it may be defined as the sci-
ence which deals with propositional forms, their parts, their
qualities, and their relations." 1

The third aspect of the philosophy of science may be
called the metaphysics of science, or metaphysical science.
It is closely connected with the logic of science, and is in-
cluded by Broad under critical philosophy. "Common-
sense constantly makes use of a number of concepts, in
terms of which it interprets its experience. It talks of things
of various kinds; it says that they have places and dates,
that they change, and that changes in one cause changes
in others, and so on. . . . Science takes over these concepts
from common-sense with but slight modification, and uses
them in its work. . . . The most fundamental task of
Philosophy is to take the concepts that we daily use in
common life and science, to analyze them, and thus to de-
termine their precise meanings and their mutual relations."
Though the scientist may and does pursue this analysis,
whenever he 'begins to discuss the concepts of his science
in this thorough and disinterested way we begin to say that
he is studying, not so much Chemistry or Physics, as the

1 Ibid., p. 23.

PHILOSOPHY OF SCIENCE 35

Philosophy of Chemistry or Physics." x Unfortunately prob-
lems of this sphere merge imperceptibly into problems of the
logic of science, for often one can tell what the basic con-
cepts mean only by knowing how they are used as concepts
of explanation. Frequently the basic concepts are definable
through operations of generalization, serial extension, inter-
polation, idealization, etc., upon objects which are em-
pirically given; hence the analysis of their meanings is
essentially logical. But the empirically given must itself
be subjected to critical analysis, and this is essentially a
metaphysical activity.

GENERAL CHARACTER OF THE STUDY

Granting that there is a legitimate study which may be
called the philosophy of science whose task is the examina-
tion of the types of problems which have been enumerated,
the problem immediately arises as to who is to carry on
such study. More specifically, is it to be the scientist or
the philosopher, or, perhaps, an individual who is neither?
It is clearly within the rights of both scientist and phi-
losopher, at least according to the traditional senses of these
terms, to deny each in his own way responsibility for these
problems. The scientist may properly insist that there are
sufficient problems of a strictly scientific sort to occupy his
time — problems which are pressing and offer some prospect
of solution, as contrasted with considerations of assumptions,
methods, and interrelations which require philosophical
knowledge and can be postponed indefinitely on the grounds
of their unimportance and the unsatisfying character of
any solution which can be given to them. On the other
hand, the philosopher may justly insist that problems of
this sort require specialized scientific knowledge which he
does not and cannot possess without devoting his life to
scientific pursuits. Through some such arguments as these
there have arisen on the one hand scientists and on the other
philosophers, who insist that the two disciplines should

1 Ibid., pp. 15, 16, 17.

36 INTRODUCTION TO PHILOSOPHY OF SCIENCE

pursue their own independent ends, without hostility, to
be sure, but also without cooperation and without recogni-
tion of border-line problems.

Fortunately there has been in the last few years an ever
increasing group, consisting both of scientists with an in-
terest in philosophy and of philosophers with an interest in
science, who feel that the problems of the philosophy of
science are both genuine and important. It must be ad-
mitted that there is much literature in recent philosophy
of science which must be discounted either on the grounds
of its bad philosophy or on the grounds of its bad science.
It is well recognized that most scientists write bad phi-
losophy, and most philosophers write bad science. "The
recent advances in physical theory," writes Broad, "have
been so important and spectacular that they have only
too obviously 'gone to the heads' of some eminent physi-
cists, and have encouraged them and the public to believe
that their pronouncements on technical philosophical prob-
lems, for which they have no special training or aptitude,
are deserving of serious attention. This is of course a pro-
found mistake." * On the other hand many philosophers
who consider these border-line problems prove to be writing
not about science but about what philosophers think science
is. This is equally misleading. Yet it must also be recognized
that too great familiarity with one's own field may consti-
tute a disadvantage in seeing it in the large ; true perspective
is not gained from within. Many scientists think they are
writing about the philosophy of science when they are
merely considering problems of scientific theory, and many
philosophers when they are merely drawing sweeping con-
clusions on the basis of specific scientific hypotheses. The
peculiar combination of insights which entitles one to make
authoritative judgments in both fields is extremely rare.
Significant advances in the field of the philosophy of science
will be made neither by the scientist nor by the philosopher,

1 Examination of McTaggerV s Philosophy (Cambridge: Cambridge University,
1933), p. liii.

PHILOSOPHY OF SCIENCE 37

but by the philosophically minded scientist and the scien-
tifically minded philosopher.

Granting the legitimacy of such a discipline as the phi-
losophy of science, an important difficulty arises. What is
to be its method? Unfortunately it does not follow that a
philosophy of science will always be a scientific philosophy.
As Cohen insists, it often requires a specialist to know what
the results of the special sciences are, hence any synthesis
of these conclusions must be regarded as tentative and
subject to continual revision.1 The philosophy of science
is not for the lovers of fixed systems. Furthermore, as
Broad points out, the actual synthetic act is almost certain
not to be scientific since it passes immediately to broad
and sweeping generalizations and attempts to recognize the
claims of the emotions. Cohen asserts that it is dominated
more by "practical, dramatic, and aesthetic than by scien-
tific motives." 2 The philosophy of science runs these same
risks in its other aspects, though not to so great a degree.
Hence the problem arises as to how to pursue these precarious
studies with a hope of maximum success.

The answer, in lieu of anything better, must be that the
same cautious method which has characterized science itself
should be the method of the philosophy of science. For any
study a method must be presupposed, since a method cannot
be used and critically examined at the same time. If science
has attained a measure of success by means of its own
method, the presumption is that the method may itself be
examined in the same way. This does not mean that ex-
perimentation, measurement, and other laboratory tech-
niques must be employed in the philosophy of science. It will
be shown in the course of the following studies that these are
not the distinguishing features of the scientific method. Science
proceeds, rather, by formation of hypotheses which are based
upon clearly formulated data and verified in terms of conse-
quences. This must be the method of the philosophy of science.

1 M. R. Cohen, Reason and Nature (New York: Harcourt, Brace, 1931), p. 147.

2 hoc. cit.

38 INTRODUCTION TO PHILOSOPHY OF SCIENCE

It will be the task of the following pages to illustrate the
main types of problem which constitute the field of the
philosophy of science. For convenience the treatment will
be divided into three parts corresponding to the three prob-
lems. In connection with each problem the attempt will be
made to indicate its essential character, and to discuss some
of the most typical of the answers which have been sug-
gested in recent literature. Because of the importance of
method, problems of the logic of science will be examined
first. This will prepare the ground for the consideration
of those logico-metaphysical problems having to do with
the analysis of the basic concepts and presuppositions. Spec-
ulative problems, resting as they do upon both logical and
metaphysical problems, will be examined last.

REFERENCES

Robt. Flint, Philosophy as Scientia Scientiarum (London: Black-
wood, 1904), pp. 1-63.
F. R. Tennant, Philosophy of the Sciences (Cambridge: Cambridge

University, 1932).
C. D. Broad, Scientific Thought (New York: Harcourt, Brace,

1923), introd.
A. D. Ritchie, Scientific Method (London: Kegan Paul, 1923),

Chaps. I, VII.
Morris Cohen, Reason and Nature (New York: Harcourt, Rrace,

1931), Book I, Chap. IV.
E. W. Hobson, Domain of Natural Science (New York: Macmillan,

1923), Chap. III.
J. A.. Thomson, Introduction to Science (New York: Holt, 1911),

Chap. V.
A. C. Benjamin, The Logical Structure of Science (London: Kegan

Paul, 1936), Chap. I.

PART ONE

PROBLEMS IN THE LOGIC OF

SCIENCE

CHAPTER III

THE LOGICAL STRUCTURE OF SCIENCE

With preliminary considerations disposed of, attention
may be directed to the first of the three main problems of
the philosophy of science, viz., the nature of the logical
structure of science. What is this structure? The very
formulation of the question suggests that preliminary con-
siderations have not, perhaps, after all, been completely set
aside. There is clearly an assumption involved in asking
this question — an assumption which is twofold since one
may raise doubts both as to the necessity for asking such a
question and as to the possibility of answering it. Hence
two other questions are relevant: (1) Is it important to
know what the logical structure of science isP (2) Is it pos-
sible to know what the logical structure of science isP

IMPORTANCE OF THE LOGIC OF SCIENCE

The attempt to answer this question necessitates the
clarification of a significant distinction. Theories may be
logically, or they may be temporally, prior to investigation.
Every scientist employs a certain method. Such a method
is accepted uncritically and seldom called into question;
so long as it produces the desired results it is supposed to
be adequate. Now there is presumably for every technique
of investigation a theory which would justify it; this theory
consists of a set of postulates or hypotheses from which
the method could be deduced. The method could then be
established or shown to be adequate by actually deducing
it from the postulates. Now the important question at this
point is whether such a set, which is logically prior to the
use of the method, is also temporally prior to it. In other
words, must the scientist, before he can employ the scien-
tific technique, construct a theory in terms of which that

41

42 INTRODUCTION TO PHILOSOPHY OF SCIENCE

technique can be justified? Must his assumptions about
method be temporally prior to the use of that method? I
think the answer to this question is an unequivocal negative.
Certainly most scientists do not make such critiques prior
to engaging in their more specifically scientific pursuits. If
there are certain assumptions which antedate the procedure
of science, these are usually held implicitly rather than
explicitly and are correspondingly vague. Probably every
scientist believes with greater or less conviction that there
is a world which is in some sense external to him, and that
in his knowing activities he somehow gets into contact
with the world. But these are not held as conscious assump-
tions, and it would probably be difficult for the average
scientist to show in just what sense they justify his pro-
cedure. On the other hand it seems safe to say that there is
probably some set of postulates which would justify his
procedure, though the scientist may not know what that
set is. It may or may not correspond with the vague assump-
tions which he held prior to his use of the method, but cer-
tainly it need not be formulated anterior to the use of the
technique. However, it does seem true that in the long run
the scientist would be better off if he were aware of this
postulate scheme; hence it is important in this sense for
him to know what the logical structure of science is. He is
almost certain to find sooner or later that his knowledge is
the effect of his method in ways which he had not suspected,
and he will probably come upon situations in which his
method will prove inadequate. In both types of situation
he would be better able to overcome the difficulties if he
had an adequate theory of the structure of science.

This difference between temporal and logical priority
creates a difficulty in the treatment of problems of the logic
of science. In any question which refers to the logical foun-
dations of science one is confronted with the alternative of
considering these so-called foundations as they are held
implicitly by the scientist prior to his investigation, or as
they should be formulated from the point of view of a strictly

THE LOGICAL STRUCTURE OF SCIENCE 43

logical justification of science itself. The two questions can
be formulated as follows: (a) What does the scientist actu-
ally assume, explicitly or implicitly, with reference to an
external world, the uniformity of nature, the structure of
knowing ? (b) What theory of the external world, the uni-
formity of nature, and the structure of knowing will actually
justify logically the procedure of the scientist? The answers
to both questions are difficult, though for different reasons.
On the one hand it is not easy to ascertain what beliefs the
scientist holds implicitly, both because they are vague and
because they differ from scientist to scientist. But on the
other hand it is not easy to construct a system of postulates
which will justify all science, for science is an extremely
complicated thing and an adequate postulate scheme would
necessarily involve complete solutions to some of the most
profound problems of philosophy.

POSSIBILITY OF THE LOGIC OF SCIENCE

Granting the importance of understanding the logical
structure of science, is such an understanding itself pos-
sible ? It seems clear that the only way to answer this ques-
tion is to plunge into the study of science and see whether
results which are at all satisfactory can be attained. It was
suggested at the end of the preceding chapter that there
can be no critique of knowing which precedes all knowing.
Hence one cannot demand that an empirical study of science
be preceded by an examination of the empirical method
itself. Since science is empirical, however, the presumption
is that this method is by and large satisfactory. It seems
reasonable to believe, therefore, that the method is the best
one to employ in studying science itself. If one wishes the
assumption to be made explicit he may state it as follows:
an empirical study of science is possible. This means essen-
tially that one may study science just as the scientist studies
nature. Supposing that the scientist is attempting to photo-
graph nature, one may also presume the legitimacy of at-
tempting to photograph the scientist in this act. But one

44 INTRODUCTION TO PHILOSOPHY OF SCIENCE

must not make the mistake of supposing that it is only the
scientist who is significant in the resulting picture; properly
speaking, it is the act of the scientist which is the funda-
mental feature, and this act must be considered as tying
both the scientist and his own picture of nature with nature
herself. Thus it is really the knowledge of the scientist
which one is studying, but this is considered only as having
arisen through a certain act and as having been directed
upon a certain object. If one does not insist upon this at
the outset he runs the risk of committing the fallacy of
vicious abstraction.

Furthermore one should recognize that the act which is,
so to speak, the core of the scientific method is itself an
event in the life of the scientist, and as such to be inserted
into the background of his history. The pragmatist has
called attention to this fact in recent years. Thinking, he
has insisted, is a natural event happening in the fife of a
certain type of highly developed organism. It must there-
fore be understood genetically in terms of the situation out
of which it arose and for which it became an instrument of
adjustment. Thinking in general arises when the organism
finds itself in a situation for which it has no ready and suc-
cessful response; thought is explicable, therefore, as a some-
what complicated trial and error response, the ultimate aim
of which is the restoration to the organism of its previous
state of composure. This makes all reasoning, and deriva-
tively all science, instrumental in character, and hence in-
explicable apart from the situation for which it is the tool.
The scientist solves problems because they are irritating to
him, just as the fox seeks food in order to allay his feeling of
hunger, and one finds it impossible to explain either the
intelligence of the scientist or the slyness of the fox apart
from these facts.

While this is an important revelation, credit for which is
due to the pragmatist, its full implications make a considera-
tion of thought apart from problems impossible. But the
very essence of the empirical method involves a recognition

THE LOGICAL STRUCTURE OF SCIENCE 45

of the legitimacy of isolating systems for purposes of study.1
In every experimental situation certain forces, usually of
minor intensity, and having their loci in remote points, are
assumed to be negligible. For example, in describing the
rolling of a ball down an inclined plane, the attractions of
the fixed stars may be neglected. This does not involve a
denial of the existence of such forces, but simply a conven-
ient neglect of them for purposes of simplification. It is
similar with reference to the background of thought. Though
thinking arises out of problem situations and exists only as
an instrument of adjustment, one may conveniently neglect
this fact in his analysis of the scientific method. He may
consider thinking as a system which is temporarily isolated.
This simplifies the problem, and necessitates only that in
the final description the possible disturbing influences be
reintroduced through some method of successive approx-
imation.

One should also recognize that in speaking of the logic of
science as an empirical study he can hardly expect its data
to have the same clarity as those, say, of physics. The
physicist is confronted with readings of pointers on scales,
deflections of needles on galvanometers, clocks, and meter
sticks, and other sense-data. These constitute "hard" data,
about whose existence there can be little doubt, and as to
whose character there can be little disagreement. But the
data for the logician of science are elusive and vague. They
consist of the "ideas" and "mental processes" of the scien-
tist as these are described by the psychologist either in
introspective or in behavioristic terms. They consist of
symbols — pictures and diagrams drawn by the scientist,
words and mathematical formulas uttered and written by
him — but these symbols are considered not as mere physical
existents such as configurations of chalk, or ink, or series of
noises; they must be examined in their "meaning" aspect,
and this is their characteristically elusive feature. Further

1 This point has been well emphasized by H. Levy, The Universe of Science,
(New York: Century, 1933), especially Chapter II. More detailed examination of
the function of isolation in science will be made in Chapter VI.

46 INTRODUCTION TO PHILOSOPHY OF SCIENCE

data consist of the behavior of the scientist as he manipulates
telescopes and microscopes, as he applies burners to flasks
containing liquids, as he dissects organisms — but here again
the significant aspect is not so much what the scientist is
doing in a physical way as what he is "thinking about."
And this can be determined only by asking the scientist,
which involves all of the difficulties associated with the
formulation of the question in language, the possible mis-
understanding on the part of the scientist, his own doubtful
analysis of his mental processes, and the obstacles in the
way of communicating the results of this analysis to another.

However, the elusive character of the data for the study
does not compel one to abandon the empirical method. It
suggests, rather, that one should ascribe to his results no
more certainty than they are entitled to claim. It suggests
that he should recognize the dependence of his conclusions
on the results of psychology, biology, linguistics, and math-
ematics. It suggests, in other words, that the logic of science
is highly complex, and subject to revision as the more ele-
mental sciences of which it is composed progress and develop.
When psychology and biology are able to tell the logician of
science more about the symbolic process, when linguistics
is able to tell him more about the nature of symbols and
meaning, when mathematics and logic are able to tell him
more about the structure of deductive schemes, then he
will speak with greater authority in the field of the logic of
science. Until then he must recognize that his study is, so
to speak, twice removed from reality, and that its pursuit,
while empirical in character, must be subject to limitations
and inadequacies by virtue of the obscurity of its data.

When one turns to the actual analysis of scientific cogni-
tion, though he finds it to be complex, he can readily dis-
cern certain characteristic elements and certain dominant
features of structure. The elements are four in number. In
the first place, there is the scientist — a self or person who
instigates and controls the activities of investigation and
formulates their results in a system of symbols. In the

THE LOGICAL STRUCTURE OF SCIENCE 47

second place, there is the world of nature or fact, upon
which these knowing activities are directed; this may be
called the subject matter of science. In the third place,
there are the actual activities themselves — observing,
measuring, experimenting, reasoning, verifying; these taken
together and with others constitute the method of the
scientist. Finally, there is the result of the activities, the
knowledge itself, which may be looked upon as a system of
symbols or ideas either held privately by the scientist or
communicated freely to others who are cooperating in the
enterprise.

It is a great convenience to be able to speak of these four
elements of scientific cognition by means of a terminology
which does not create any prejudices as to their essential
natures. For this reason they will henceforth be spoken of
as the knower, the known, the knowing, and the knowledge.
By employing these derivative forms of the verb "to know"
one can avoid the risk of assuming that the subject matter
of science is a world of matter, or of space-time events, or of
sense-data, or of phenomena; or that the method of science
is observation, or intuition, or induction, or deduction; or
that knowledge is a complex of "psychical ideas," or images,
or words, or mathematical symbols. One can talk freely
about the elements and the way in which they function in
the total situation without attributing to them features
which are the result of certain theories of cognition.

Superficial analysis reveals the general way in which these
four elements are structurally united in the cognitive situa-
tion. It is primarily a causal complex in which knowledge
functions as the effect, and the knower, the known, and the
knowing together constitute a complex cause. Roughly
speaking, the knower operates upon the known in a manner
called knowing to produce knowledge. The complex cause is
sufficient to produce the effect, and each of the elements of
the cause is necessary. This conception does not assume any
specific theory of causal connection but merely that when a
knower is confronted with something to be known and sets

48 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the knowing activities into operation the outcome is usually
knowledge. It states further that in the absence of any one
of these elements knowledge will not normally occur.

Within this general matrix a great variety of interpreta-
tions of cognition is possible. One of these is the common
sense theory which will be examined in a later chapter.
Others, more critical in character, may be found in the his-
tory of philosophy, particularly since Locke. The theory
which will be proposed does not claim to be completely
adequate. Its justification lies mainly in the fact that it
was formulated with the scientific activity in view, and may
be said therefore to have been empirically derived from the
very situation which it was devised to explain. It is an
abstract theory, and endeavors to ascribe to cognition only
the very minimum of properties which it must have if it
is to meet the empirical demands of knowledge. Clearly,
some very general relations must hold between the four
basic elements of the cognitive situation if the theoretical
structure is to satisfy the demands of empirical thought.
What are these minimum requirements? J

THE KNOWN

One of the facts which has been brought to light in recent
years is the impossibility of ascertaining the subject matter
of science prior to science itself. This applies not only to
the individual sciences but to the totality of the sciences.
Physicists who begin by talking about matter end by con-
sidering electrons, fields of force, and probability waves;
mathematicians who limit their subject to number, order,
and quantity find themselves talking ultimately about the
structure of deductive systems; biologists who insist that
their discipline is a study merely of the reactions of living

1 Since the knower functions in the total situation in an impersonal way, he may be
neglected in what follows. This does not mean that the scientist is an unimportant
part of science. It means, rather, that the method of science is one, and that varia-
tions in the character of the outcome are due to individual differences in the skill
with which the method is employed. The neglect of the scientist in the analysis
of the logical structure of science does not imply a failure to recognize the place of
genius.

THE LOGICAL STRUCTURE OF SCIENCE 49

organisms to stimuli of various kinds find themselves obliged
to talk about the chemical structure of organic compounds.
From a more general point of view, all attempts to limit
science to the natural as opposed to the supernatural, or
the real as opposed to the unreal, or the measurable as
opposed to the unmeasurable, end with the recognition that
the drawing of such lines is precisely the scientific activity
itself. The task of science toward the supernatural, the
unreal, and the unmeasurable is the application of scientific
techniques in such a way as to transform them into the
natural, the real, and the measurable. The miracles of
yesterday are the normal phenomena of today; hallucina-
tory objects of a former age are now explicable in terms of
biological and psychological laws; value attitudes, once
thought to be purely intensive in character, are now being
portrayed as graphs on coordinate systems.

The result of all these considerations is that science be-
comes reluctant to characterize more specifically than is
necessary the type of entity about which it talks. Science
may justifiably study anything whatsoever, anything which
may be given in any sense. The realm of the known for
science is the realm of phenomena, whatever appears or
exhibits itself in a situation to which the general methods of
knowing are applicable. This will include the natural and
the supernatural, the real and the unreal, the measurable
and the unmeasurable, the material and the immaterial,
the public and the private, the past, present, and future,
the abstract and the concrete, the large and the small, the
extended and the brief. But science will not begin with
this unlimited complex; it will rather select those of its
aspects which are most clearly given and to which the
methods of science are most readily applicable. It will
direct its efforts, therefore, to the understanding of the
natural, the real, the measurable, the material, the public,
the present, the relatively concrete, the intermediary be-
tween the large and the small, and between the extended
and the brief. But since this represents simply a convenient

50 INTRODUCTION TO PHILOSOPHY OF SCIENCE

selection, the remaining elements will be placed on the shelf
to be subjected to later examination. They are not taken
out of the given but set aside in view of the abundance of
phenomena which are more clearly given and more directly
susceptible to the methods of science.

Recent literature in the philosophy of science seems to
have adopted the term event as the most adequate name for
the basic entity of science. The advantage of this term is
its high abstraction. Almost anything that one may men-
tion is an event — durations, spaces, relations, and numbers,
things as well as processes, happenings in the physical realm
as well as in "minds." The realm of the known may there-
fore be described as a complex of events. The events bear
to one another relationships of various kinds — spatial, tem-
poral, causal, similarity and difference, equality and in-
equality of magnitude. These relationships determine
associations and dissociations of events, containing and
contained events, dependent and independent events, ele-
mental events, collections, organic wholes, and Gestalts.
Thus in speaking of the realm of the known as a complex
of events one does not deny that it may also be an event,
i.e., events may unite together to form a system having
certain unitary properties.

THE KNOWLEDGE

In the most general sense, knowledge may be defined as
the awareness of the realm of events. That which is to be
known by science becomes known when it enters into the
proper relationship to the scientist. This relationship is the
activity of becoming aware. Thus knowledge may be de-
fined as that which terminates the activity of awareness
when this is directed by the scientist upon the realm of
events.

But to stop the analysis at this point would be to create
an impression of pseudo-simplicity. Knowledge is actually
a highly complex affair, exhibiting different aspects, mani-
festing itself under varying degrees of adequacy, and main-

THE LOGICAL STRUCTURE OF SCIENCE 51

taining conflicting claims with reference to its descriptive
values. One must, therefore, consider this element of cogni-
tion in greater detail.

The important feature of knowledge seems to be that
when one knows the realm of events he is aware of it in dif-
ferent ways, and knowledge itself is a composite of these
different kinds of awareness. A convenient approach to this
problem is through a distinction suggested by Russell be-
tween "knowledge by acquaintance' and "knowledge by
description." "We shall say that we have acquaintance with
anything of which we are directly aware, without the inter-
mediary of any process of inference or any knowledge of
truths. Thus in the presence of my table I am acquainted
with the sense-data that make up the appearance of my
table — its color, shape, hardness, smoothness, etc.; all these
are things of which I am immediately conscious when I
am seeing and touching my table. . . . My knowledge of
the table as a physical object, on the contrary, is not direct
knowledge. Such as it is, it is obtained through acquaintance
with the sense-data that make up the appearance of the
table. . . . My knowledge of the table is of the kind which
we shall call 'knowledge by description.' The table is 'the
physical object which causes such-and-such sense-data.' . . .
All our knowledge of the table is really knowledge of truths,
and the actual thing which is the table is not, strictly speak-
ing, known to us at all." * Elsewhere he speaks of descrip-
tive knowledge as knowledge expressible in the form "a so-
and-so' and "the so-and-so," and he suggests that when
we know descriptively through propositions, 'it is only
what we may call the concept that enters into the proposi-
tion." 2 "Common words, even proper names, are usually
really descriptions." 3

1 Bertrand Russell, Problems of Philosophy (New York: Henry Holt, 1912),
pp. 73-75.

2 Bertrand Russell, Introduction to Mathematical Philosophy (London: Allen and
Unwin, 1920), p. 168.

3 Bertrand Russell, Mysticism and Logic (London: Longmans, Green, 1921),
p. 216. For another formulation of the distinction see A. N. Whitehead, Symbolism,
Its Meaning and Effect (New York: Macmillan, 1927), pp. 7 el seq.

52 INTRODUCTION TO PHILOSOPHY OF SCIENCE

While Russell's distinction is of basic importance in the
understanding of cognition, it requires reinterpret at ion and
supplementation to be made adequate to the scientific
situation. In the first place something must be said with
reference to the directness which characterizes knowledge
by acquaintance. The presumption is that in acquaintance
one knows events directly, without the intermediary of
anything which is symbolic in its nature, and by this means
one avoids the difficulty of the common sense position which,
as we shall see later, considers mind to be limited to its own
contents. What is the nature of this directness, and what is
the nature of the event which is thus known ? Since the
detailed solution requires a consideration of the complicated
problem of the theory of knowledge, what is suggested here
may be taken for a mere outline, to be partially filled in by
the discussion of Chapter V. By the directness of knowing,
one means only the basic fact that in all cognition there
must be a situation which one can describe by the sentence :
"I am now aware of such-and-such." The presumption in a
situation of this kind is that the "I" is directly in contact
with the "such-and-such' in the sense that the latter is
known without any intermediary. The fact of direct acquaint-
ance does not prohibit the use of instrumental techniques
and measuring devices. It demands only that recording
machines be recognized for what they are, and not as sub-
stitutes for the observer. A registering instrument must be
read before it can affect knowledge, hence it is the instru-
ment itself which is directly known, though it may convey
inferential knowledge as to something else whose character
it is registering. One must be directly acquainted with
pointer readings if he is to be indirectly aware of that which
they measure. Even if one supposes that his sense organs
are recording devices, giving him information as to an ex-
ternal world, still he must suppose that he is immediately
aware of the sense-data though he may be only inferentially
aware of their causes.

In the second place, it seems important to recognize that

THE LOGICAL STRUCTURE OF SCIENCE 53

acquaintance must be not only direct but non-transforming
as well. It is an unavoidable assumption of science that
there is at least one kind of awareness which does not trans-
form events, i.e., there must be an awareness which does
not enter functionally into its object, hence may be neglected
without prejudice to the character of that which is known.
Awareness of this kind is a bare awareness which is 'ex-
ternal" to its object and therefore without effect upon it.
The reason for this assumption seems clear. A transforma-
tion is any act performed upon something given to produce
something else. Hence to say that awareness transforms
implies that it is performed upon something given. But a
thing can be given only in awareness, with the result that
there must be at least one kind of awareness which does not
transform.

What should be emphasized here is only the fact that in
awareness there is always something with which one is
acquainted. In the great majority of situations of actual
knowledge this direct awareness is associated with an infer-
ential act, often unconscious, by which another object is
called up before awareness. These two objects are frequently
confused, and it is often impossible to tell which one is
directly perceived. For example, it is difficult to say whether
one actually sees the softness of velvet or infers it through
the medium of past associations, and it is not easy to decide
whether a table- top is seen in its "true" rectangular shape,
or in its "apparent" shape as a parallelogram. In both of
these cases one object is given in direct awareness, and the
other is the result of inference. It is sometimes said that
the directly given object becomes the symbol of the inferred
object. Our limitation of the word "symbol " to its cognitive
use would make such a formulation confusing. But the fact
of inference seems undeniable, and all that need be insisted
upon is that an inferential act demands something which is
given as the starting-point for the act. This given may be
said to enter into knowledge through an act of direct and
non-transforming awareness.

54 INTRODUCTION TO PHILOSOPHY OF SCIENCE

In the third place, Russell's knowledge by description
should be recognized for what it is, viz., symbolic knowledge.
Symbolic knowledge is indirect. When one knows an event
descriptively he is not presented with the event; instead he
is directly aware of a symbol which has the peculiar power
of referring to the event by virtue of a meaning character.
Knowledge of this type is truly representative, since the
symbol acts as a substitute for the event. Hence one knows
an event symbolically when he knows it through words,
pictures, images, models, diagrams, indices, and gestures.
As will be shown in Chapter IV, symbols are of various kinds
depending on the way in which they refer to events. Conse-
quently there are different ways in which one may be aware
of events symbolically. Rut in all cases one is directly
aware of a symbol (which is, of course, an event) having the
capacity of meaning or referring to another event of which
the individual then becomes indirectly aware. Though Russell
calls this type of knowledge "descriptive," it will here be
called "symbolic" since a later chapter will show that there
are two ways in which one may symbolize events — by
description and by explanation.

In the fourth place, knowledge by acquaintance and
knowledge by description, or symbolic knowledge, cannot
constitute an exhaustive analysis of the aspects of cognition;
there must be a third type by means of which the two are
united. If the event is presented through acquaintance and
characterized through symbolic knowledge, there must be a
kind of awareness by which one may test the application of
the symbol to the event. This must be a composite aware-
ness which combines acquaintance and symbolic knowledge,
and adds the awareness of the relation which the symbol
bears to the event. One may be aware of a bit of metal, and
he may know what iron is, but neither of these types of
awareness will inform him whether the bit of metal is iron.
In the one case he is aware only of the event, in the other he
is aware only of the symbol; knowledge requires that he be
aware of the applicability of the symbol to the event. This

THE LOGICAL STRUCTURE OF SCIENCE 55

type of awareness is required in the movement of scientific
discovery where events are identified by means of symbols,
and in the movement of scientific verification where symbols
are verified by means of events. In fact awareness of this
kind may always occur in conjunction with acquaint-
ance; there probably is no such thing as a bare awareness
of an event without some awareness of a symbol which
is applicable to it. Intuitions without concepts are
blind, concepts without intuitions are empty. What is
also required is an activity of perception in which the
applicability of the concepts to the intuitions may be
ascertained.

With these three aspects of knowledge clearly indicated,
one can see what is meant by saying that knowledge is the
awareness of events. It is a composite awareness which
includes acquaintance with a realm of events, awareness
of a system of symbols referring to a realm of events, and
awareness that the realm of events referred to by the system
of symbols is precisely that given in direct awareness. This,
of course, represents knowledge in its ideal form. Actual
knowledge falls short of this to greater or lesser degrees. No
scientist is acquainted with the entire realm of events ; he is
obliged to make selections from it on the basis of the readi-
ness with which the events are given for examination, and,
as a consequence, his knowledge is only partial. No scientist
has devised a system of symbols which is adequate either
from the point of view of its internal organization or with
regard to its scope. No scientist is ever satisfied with the
directness in the reference of his symbolic scheme to the
realm of events; it is usually an idealization or schematiza-
tion which must be made more and more adequate by suc-
cessive approximations. Hence actual science fails in any
or all of these aspects of knowledge, and to this extent is
relatively inadequate. But the presumption is that by the
proper application of the techniques of knowing it may be
made progressively better. This fact necessitates a con-
sideration of the knowing activity.

56 INTRODUCTION TO PHILOSOPHY OF SCIENCE

THE KNOWING

By the knowing is meant the total complex of activities
which result in knowledge. More specifically, it is the aggre-
gate of activities devised to acquaint the scientist with
events, to enable him to derive (or discover) a system of
symbols representative of this realm, and to verify the
symbolic scheme by comparison with events. The tradi-
tional formulation of the scientific method in terms of
observation, induction, and deduction, represents an approx-
imate description of the knowing technique in terms of
these three features. Each of these aspects will be subjected
to analysis in the following chapters. For the present each
of them may be considered briefly.

Since the point of origin of all science is the world of events,
the initial technique in the knowing activity must be con-
cerned with the establishment of situations in which the direct
awareness of events is possible. It is a commonplace that
science begins with facts. But the discovery of these elemen-
tal facts is often a complicated matter. Facts are not all
displayed to view and open to direct inspection. Most
obviously, facts can be observed only in the proper spatial
and temporal situations. Many events in nature, such as
eclipses, occur only at temporal intervals, and one must
therefore wait for them to take place. Other events occur
only in certain localities, and one must go to these areas to
experience them. Still other events, though given in the
here and now, may be too minute or too brief to enter
readily into awareness ; in such cases one must employ instru-
mental aids such as microscopes and slow-motion pictures.
Often one can overcome these difficulties by reproducing
events in the laboratories under experimental conditions;
he can put his fingers into nature, so to speak, and thus pro-
duce observational situations which either would not nor-
mally occur at all in nature, or might occur only under un-
desirable conditions such as in a remote space or time, in
very intense or very weak manifestations, or in the prox-

THE LOGICAL STRUCTURE OF SCIENCE 57

imity of various interfering factors. Many events are known
primarily in terms of recording devices, such as deflections
of needles, photographic images, and pointer readings of
various kinds. The point with reference to all of these illus-
trations is that something is presented for direct awareness,
and that certain complicated techniques are necessary in
order to bring about situations in which such activity is
possible. Bacon suggested that the scientist proceeds by
collecting facts. His conception of the scientific method, as
Jevons points out, was a "kind of scientific bookkeeping.
Facts were to be indiscriminately gathered from every
source, and posted in a ledger, from which would emerge in
time a balance of truth." x The obvious truth in his method
is somewhat obscured by the fact that the behavior of the
scientist is one of activity rather than of passivity. Nature
is often reluctant to speak. Her utterances are frequently
produced only by prodding, and even then one is satisfied
with her statements only when he has introduced elaborate
recording and measuring devices. The fact that one's
recording instruments may lose the essence of that which
he is trying to observe need not be emphasized here, though
it becomes a problem of some significance in the deeper con-
sideration of science. For present purposes one need only
reemphasize the fact that at some point in the scientific set-
up the investigator is obliged to say "I am now experiencing
such-and-such." Without such an initial given science be-
comes meaningless.

But knowing is not merely the becoming aware of events;
it is also the symbolizing of them. The scientist knows nature
not only directly but mediately in terms of models, pictures,
and diagrams, in terms of mathematical equations, and in
terms of words and sentences. Hence the second significant
aspect of the scientific method is the large group of highly
intricate activities constituting the invention or discovery
of a symbolic system which is presumed to be the interpre-
tation of the realm of events. Unfortunately, very little is

1 W. S. Jevons, The Principles of Science (London: Macmillan, 1907), p. 576.

58 INTRODUCTION TO PHILOSOPHY OF SCIENCE

known as to the nature of the techniques which are em-
ployed at this stage of the knowing process. Many insist
that there is to be found here an ultimate irrationality — the
mystery of scientific discovery — which is explicable only in
terms of that still more basic mystery, scientific genius; the
fact seems to be that some scientists make significant dis-
coveries and others do not — and that is all that may be said
on the question. Others insist that there are techniques for
discovery. Still others maintain that the problem has not
been properly formulated; the scientist does not discover
a symbolic scheme and then suppose that the entities about
which he is talking have real existence; on the contrary he
invents it and then projects it upon the world as a pure con-
struction and merely a convenient mode of explanation.
One is forced to recognize, therefore, that one's view as to
the nature of the knowing activities depends upon his theory
of the nature of the scientific task in general. But it also de-
pends upon his conception of the nature of symbols, the
way in which they mean and take on meanings, the way
in which they unite to form symbolic schemes, whether they
claim to explain or merely to describe, and so on. All of these
considerations need simply to be mentioned at this early
stage. The point is that the scientist succeeds by means of
certain techniques, conscious or unconscious, in becoming
aware of a body of symbols through which he claims to
know the world of events. The important feature of this
symbolic system is its relative flexibility as compared with
the realm of events. Events have a given character which
is independent of the observer; but symbols may be
modified in such a way as to become progressively more
adequate in their representative task. A knowledge of the
knowing techniques is helpful in this task of constructing a
satisfactory symbolic scheme. But such knowledge is not
sufficient to bring about an immediate realization of the
ideal of a perfect system of symbols. For the proper tech-
niques are not yet known, and even those which are known
are not always correctly employed. Hence it is the fate of

THE LOGICAL STRUCTURE OF SCIENCE 59

every system of symbols to be tentative only, and to be
more or less completely abandoned as the realm of the given
becomes expanded and as the techniques of knowing become
more accurately formulated.

The fact that the construction or discovery of symbolic
schemes does not seem to be subject to control by any recog-
nizable techniques necessitates a third aspect of the scientific
method which is usually called verification. If symbols are
loosely tied to events so far as their origin is concerned, they
must be fastened to events more firmly through the tech-
nique of testing and checking. It is the function of the
elaboration of symbolic schemes to disclose new points at
which knowledge may be tied down to the real; thus more
or less freely expanded symbolic systems are instruments
through which discoveries become possible in the realm of
events. But this escape of thought from the realm of the
given is also a source of error; symbolic schemes may be
falsely elaborated, with the result that they become less
rather than more adequate. Hence a return to the realm of
events is obligatory. There is presumed in every verificatory
act some conception of the possibility of a correlation be-
tween the body of symbols and the realm of events. Whether
this is considered to be an actual correspondence, or mirror-
ing, or whether it is supposed to be merely a pragmatic
workability, depends, again, upon one's general theory of
the nature of the scientific task. Whatever the theory, the
testing is a fact. One must admit, then, a stage in knowing
in which the scientist is at once aware of events, of symbols,
and of the applicability of the symbols to the events.

It is, perhaps, unnecessary to point out that in concrete
reflection the stages of knowing are only vaguely distinguish-
able from one another and may vary greatly in the respective
parts which they play in constituting the total knowing act.
For the Baconian scientist the initial exploration of the
realm of events is the most important, if not the exclusive
method of knowing. Bacon, at least in one of his phases,
insisted upon the importance of making as complete a col-

60 INTRODUCTION TO PHILOSOPHY OF SCIENCE

lection of data as possible before passing to the act of inter-
pretation; the imagination should be held in leash until the
scope of the facts is broad enough to permit one actually to
read the explanation out of them. According to such an
analysis the stage of verification is superfluous. For the
speculative scientist, on the other hand, the act of discovery
is the most important phase. Data should be collected, to
be sure. But one should not waste valuable time poring over
the facts in the faint hope that the discovery of just one
more datum will set off the mind in the proper direction.
Data should be limited to a minimum, and the speculative
activities should be set into operation at the earliest possible
moment. The stage of verification then becomes of increas-
ing importance, for only in this movement can one check
the flight of the mind, which, in the absence of specific data,
may have been extensive.

The importance of symbols in the total structure of science
demands that a more detailed analysis of this notion be
made. This will be the topic of the following chapter.

REFERENCES

Bertrand Russell, Mysticism and Logic (London: Longmans,

Green, 1921), Chap. X.
R. M. Eaton, Symbolism and Truth (Cambridge: Harvard

University, 1925), Chap. III.
J. A. Thomson, Introduction to Science (New York: Holt, 1911),

Chaps. II, III.
A. D. Ritchie, Scientific Method (London: Kegan Paul, 1923),

Chap. II.
A. N. Whitehead, Concept of Nature (Cambridge: Cambridge

University, 1920), Chaps. I, II.
Symbolism, Its Meaning and Effect (New York: Macmillan,

1927), Chap. I.
John Dewey, How We Think (New York: Heath, 2nd ed., 1933),

Chaps. VI, VII.
A. C. Benjamin, The Logical Structure of Science (London: Kegan

Paul, 1936), Chap. II.

CHAPTER IV

THE NATURE OF SYMBOLS

It should be clear from the discussion in the preceding
chapter that the scientific activity is centered about the
attempt to devise a system of symbols which claims to be
representative in some sense of a realm of events with which
the scientist has direct acquaintance. The important point
to note is that mere awareness of events is not knowledge,
though it is the foundation upon which knowledge builds.
Events enter properly into knowledge only when they are
interpreted, described, or explained, and these supple-
mentary activities require the use of symbols. Whitehead
suggests that there is a great difference between direct
knowledge and symbolism. "Direct experience is infallible.
What you have experienced, you have experienced. But
symbolism is very fallible, in the sense that it may induce
actions, feelings, emotions, and beliefs about things which
are mere notions without that exemplification in the world
which the symbolism leads us to presuppose." : It seems
questionable, however, whether presentational immediacy
ought to be spoken of as infallible, since it is really not
knowledge, and hence not the kind of thing which can be
either fallible or infallible. The function of acquaintance is
simply the production of that givenness which is presup-
posed in all knowledge. There are operations by which this
may be brought about, but they are not properly cognitive
techniques; they are essentially exploratory and manipula-
tory. On the other hand, the techniques which result in
the formation of a symbolic scheme are significantly cogni-
tive in character; they do or do not terminate in knowledge
according as they are or are not correctly employed. Hence
the consideration of the nature of symbols, how and what

1 A. N. Whitehead, Symbolism, Its Meaning and Effect, p. 6.

61

62 INTRODUCTION TO PHILOSOPHY OF SCIENCE

they mean, how they are differentiated into kinds, plunges
one into the very heart of the cognitive situation. In the
present chapter the attempt will be made to examine symbols
and to describe their features so far as this is possible in the
limited space available.

SIGN SITUATIONS

The most convenient approach to the notion of symbol is
through a consideration of the more general idea of sign. " If
we stand in the neighborhood of a cross road and observe a
pedestrian confronted by a notice To Grantchester displayed
on a post, we commonly distinguish three important factors
in the situation. There is, we are sure, (1) a Sign which
(2) refers to a Place and (3) is being interpreted by a person.
All situations in which Signs are considered are similar to
this." 1 The accuracy of this as a statement of sign situations
in general is somewhat vitiated by the fact that animals
behave in a way which leads one to believe that they react
to signs. The dog who runs to the dining room at the sound
of the dinner bell is exhibiting a type of behavior which
can, in all fairness, be called interpretative response. Hence
the limitation which is introduced by Ogden and Richards
under (3) does not seem to be necessary for the description
of general sign situations. For the rest, however, the char-
acterization seems accurate. There must always be some-
thing which can be called a sign. This may be anything
whatsoever, subject only to the condition that it has the
capacity to refer or point when properly interpreted. Thus
a flag at half-mast may signify death, a cloud may signify
rain, and congested lungs may signify pneumonia. Further-
more, the sign must have the capacity to refer to something
outside itself. This, again, may be anything whatsoever,
subject only to the condition that it is the terminus of an
act of signification. Thus the word "Entrance" may signify
the actual doorway beneath the sign, an olive branch may

1 C. K. Ogden and I. A. Richards, Meaning of Meaning (New York: Harcourt,
Brace, 1930), p. 21.

THE NATURE OF SYMBOLS 63

signify the general notion of peace, and the arrow on a
weather-vane may signify north.

SYMBOL SITUATIONS

Within this general type of sign situation there are certain
specific types, of peculiar importance to man, which may be
called symbol situations. Ogden and Richards suggest that
these situations should be characterized as those in which
men use the signs as instruments of communication. Symbols
may then be specified as those signs which are words, images,
gestures, drawings, mimetic sounds. Such symbols are used by
men to produce certain responses in other men. The interpre-
tative act, as a result, becomes limited to the higher organisms,
and is commonly understood in terms of such psychological
notions as association, apperception, suggestion, and intension.

Rut symbol situations may be primarily emotive or pri-
marily cognitive. This distinction is based upon the two
important functions of symbols. Symbols are instruments
for the conveyance of feelings and attitudes, and they are
instruments for the conveyance of information. The former
may be called the emotive function of symbols, and the
latter may be described as the cognitive function. Probably
all symbols have both emotive and cognitive properties.
Rut some symbols are primarily emotive and others are
primarily cognitive. Many words call up pleasant or un-
pleasant sensations more directly than they call up ideas.
Political speeches and patriotic orations in oral discourse,
and poetry in the written form abound in emotive appeals.
Abstract science, on the other hand, especially mathematics,
is constituted primarily by cognitive symbols; the function
of such symbols is to say something and not to create feelings.

Since emotive symbols play a minor role in science they
may be neglected for the purposes of this study. Henceforth
by "symbol situation" will be meant "cognitive symbol
situation," and symbols will be presumed to be significant
in a purely cognitive way. One should be able to discover in
any symbol, then, (1) the event itself, which is the point to

64 INTRODUCTION TO PHILOSOPHY OF SCIENCE

which the referential property is attached ; (2) the referential
property, which somehow connects the event which is the
symbol with another event which is that referred to by the
symbol; and (3) the psychological interpretation of this
referential property when it enters into the awareness of an
individual. In order to make these three features clear they
may be discussed in greater detail in connection with some
particular symbol, say, the word "circle."

(1) Every symbol is an event or happening. It may con-
sist of a written word made up of particles of ink arranged
in a certain pattern; it may be a noise uttered by a person
in an act of communication; it may be a drawing, or pho-
tograph, or a material model; it may be a group of mathe-
matical symbols. Thus in the example one might replace
the written word "circle" by the spoken word, or by a pic-
ture of a circle, or by the equation x2 + y2 = r2; in all such
cases one would have what might be called physical sym-
bols of a circle. On the other hand, the symbol might con-
sist simply of the gesture of pointing to a circle, or of the
mental image which a given individual has of a specific
circle; in the former case the symbol would be called biologi-
cal, and in the latter case psychological. But in all cases
the symbol would be an event occurring roughly at a time
and place, and capable of analysis and description by the
ordinary techniques of science. Ideally there would be a
strict correlation between the properties of the symbol as a
mere event and its meaning. Actually this is not the case
since in language the same word may have different mean-
ings, and different words may have the same meaning.
There is, however, some correlation between the two; at
least one cannot determine what the symbol means until he
has ascertained its character as a physical, biological, or
psychological entity. Often this recognition is spontaneous,
but it is presumed in each individual case.

(2) Every symbol refers to something other than itself.1

1 This is not strictly true. For example, " word " refers to itself as well as to some-
thing other than itself.

THE NATURE OF SYMBOLS 65

This feature of a symbol is complex and involves (a) the
referential property or relationship, and (b) the entity which
is referred to. But these two features of the symbol do not
belong to it in the same sense. The referential property
must be given with the symbol; without it the symbol has no
meaning and is therefore not a symbol. But the referent
(as contrasted with the reference) need not be given in the
situation at the moment except under the form of another
symbol. To consider the example, the word "circle" must
have a referential character in order to be a symbol, i.e., it
must have the power to point to what would be identified as
a circle were it given; but no actual circle may be given,
though one may find himself aware of an image of a circle,
or of certain words such as "equality of radii," "conic sec-
tion," "two-dimensional plane figure," etc., and he may
believe that such a thing as these is the referent of the
symbol. It is the essential virtue of symbols that one can
use them in the absence of their referents, and, hence, as
substitutes for those events to which they refer. Just how
symbols refer to events is hard to say. It is convenient to
picture the referential property of a symbol by means of
an arrow ; this suggests in a vague sort of way certain of the
features of the reference. It suggests, for example, if the
arrow is properly drawn, that the reference somehow takes
its origin in the symbol itself as a mere event, and goes out
of and away from this source in the direction in which its
referent is to be found. It also calls attention to two of the
most important features of the reference, viz., its asymmetric
character, and its capacity to limit the range of possible
events referred to. For if the word "circle" refers to an
actual circle, the actual circle cannot refer to the word
in the same way. And through the word one is able to
know, in advance of seeing the actual circle in question, the
kind of event to which reference is made. Furthermore, the
arrow is a convenient mode of representing the referential
property because an arrow may point without pointing to
anything, i.e., it may have a general directional indication

66 INTRODUCTION TO PHILOSOPHY OF SCIENCE

but when one examines the locality thus called to his atten-
tion he may find nothing. Symbols enable one to talk about
absent objects, but, unfortunately, by virtue of this same
capacity, permit him to talk about objects which are not
even known to exist at all. Hence it is an important feature
of symbols that one may use them without any prejudice to
the existence or non-existence of their referents.

It may be well at this point to clarify a distinction in the
referential character of symbols, which will be of basic
importance in later chapters. As was pointed out in the
preceding paragraph, symbols have the power not only to
point to events but also to call to mind other symbols with
which they apparently have significant relations. This
suggests that every symbol has two very important types of
relationship: (1) reference to events which are not themselves
normally symbols; x and (2) reference to other symbols.
These two types of reference are approximately what are
called in the traditional logic, as applied to concepts, exten-
sion or denotation, and intension or connotation. The term
"intension" is here used in a slightly broader sense than it
has been historically, since it applies to all of the relations
of a concept to other concepts and not merely to its defining
relations. Furthermore, the notions of extension and inten-
sion are generalized so as to be applicable to all symbols
rather than merely to concepts. In this general sense, then,
one may say roughly that extension of symbols is that prop-
erty by virtue of which they assume relations with the
realm of events, and intension of symbols is that property
by virtue of which they assume relations with one another.
The intensional relations, as applied to symbols of a verbal
character, are usually called formal relations, and are illus-
trated by implication, equivalence, and incompatibility; they
are the relations through which symbolic schemes are
formed. The intensional relations of images, diagrams,
models, and other pictorial symbols cannot be of this kind

1 The events may, of course, be themselves symbols, but then the symbols which
refer to them are symbols of symbols.

THE NATURE OF SYMBOLS 67

but must be essentially pictorial in character. The exten-
sional relations, on the other hand, are the foundation for the
cognitive aspect of symbols since it is through this type of
relation that one may be said to know events in terms of
symbols. The character of the referential relation depends
on the kind of symbol involved; images and diagrams are
in some sense like their referents, hence refer by resemblance;
but words do not in general either sound or look like their
referents, hence refer by other routes.

(3) Symbols refer only through the intermediary of a
mind. "Words, as every one knows, 'mean' nothing by
themselves, although the belief that they did . . . was once
equally universal. It is only when a thinker makes use of
them that they stand for anything, or, in this sense, have
'meaning.' They are instruments." 1 Hence the only way to
understand the referential character of words is to ask one-
self what he experiences when confronted by them. Con-
sider again the word "circle." There is, first, the awareness
of the physical event, the word, which is the pattern of ink
on paper; this, however, does not usually enter into clear
consciousness and may not be distinguishable as an element
of the experience. But from this initial experience there
arises in a manner which appears to be causal a consciousness
of the meaning of the symbol. Yet the causal relation is
basically dependent on past experience; the awareness of the
physical symbol calls up the awareness of the meaning
through associative ties. Something is called to mind when
one is presented with a word of which one knows the mean-
ing. The fact that it is called to mind immediately, and
without conscious effort on the part of the individual, leads
him to believe that it is somehow a part of the physical word.
However, the attempt to read in a foreign language soon
convinces one of the contrary ; here the associations must be
made slowly and painfully before they arise with anything
like the readiness of meanings in one's own tongue. Just
what one is aware of when he is aware of a meaning, is hard

1 C. K. Ogden and I. A. Richards, Meaning of Meaning, p. 10.

68 INTRODUCTION TO PHILOSOPHY OF SCIENCE

to say. Eaton considers that the simplest solution to the
problem is to accept a unique meaning activity. "The mean-
ing activity is one of vague anticipation: the mind is poised
expectantly, awaiting something other than the thing, the
symbol, which is immediately before it; and this anticipation
is vague because it is not accompanied by a belief that the
object meant will appear or that it exists. When I mean an
object I do, in some sense, prepare my mind for a presenta-
tion of this object. Though I cannot be said to turn my
attention toward the thing I mean, since one cannot attend
to something not presented to him, there is no doubt that
I do more than attend to a symbol or an image. Indeed, I
turn my attention away from the symbol or the image, and
this constitutes the first step in preparation for the thing
meant." 1 The fact that the meaning activity itself is vague
creates all of the problems associated with the need for
definition in language. Since one cannot say clearly what the
meaning activity in general is, he cannot be sure in any given
case whether a symbol is understood. Symbols may be
graded in clarity, ranging from such words as "circle," where
the meaning is clearly grasped, to purely nonsense symbols,
where the verbal form suggests that there is a meaning yet
no meaning is forthcoming. In between would be found all
vague symbols, such as "love," "justice," and "self," where
the meaning is relatively vague. If one uses the arrow to
represent the referential character of the symbol in each
case, he is obliged to say that the word "circle" has a definite
arrow which points clearly to a limited area within which
the referent is to be found; nonsense symbols such as "boo-
jum" have no arrows at all, hence are not properly symbols;
symbols such as "love," "justice," and "self" have arrows
but they point to extensive areas within which their referents
may be found. Definition removes obscurity in two ways,
extensionally and intensionally. Extensionally, definition
clarifies meaning by pointing to situations in which the

1 R. M. Eaton, Symbolism and Truth (Cambridge: Harvard University, 1925),
p. 23.

THE NATURE OF SYMBOLS 69

referent is given for direct awareness; intensionally, it
clarifies by indicating relations to other symbols themselves
presumably better known.

ADEQUACY OF SYMBOLS

As was suggested in the preceding chapter, an adequate
system of symbols is presumed to have some sort of correla-
tion with the realm of events. Presumably the highest type
of adequacy would be one in which the system of events
and the system of symbols are isomorphic with reference to
each other. Two systems are isomorphic when there is a
one-to-one correlation of the elements and relations of the
respective systems. Ideally, therefore, a symbolic scheme
should be constructed so as to contain a distinct element for
every element of the realm of events, and a distinct relation
for every relation in the realm of events. Furthermore, every
event should be symbolized by one and only one elemental
symbol, and every relation between events by one and only
one relational symbol. This would enable one to say that in a
very general sense the system of symbols mirrors or repre-
sents the system of events, and that the relation of the
body of symbols or any element of it to its referent is the
relation of picturing. Such a system would be highly adequate.

There is reason to believe, however, that although such a
symbolic scheme would satisfy the demands of cognition
perfectly, no actual system, however limited in scope, even
approximates to that ideal. The reasons for this inadequacy
of existent knowledge schemes are to be found in the nature
of the knowing activities, and are at least two in number.
In the first place, the human mind seems to be fundamentally
incapable of grasping highly complex structures as a unit.
Certain Gestalts of a very simple sort enter into direct aware-
ness as k complexes, but configurations of anything like
moderate complexity must be grasped piece-meal. This fact
is responsible for one of the basic scientific procedures, viz.,
the method of isolation. Since the human mind is incapable
of grasping any event in all of its configurations, certain of

70 INTRODUCTION TO PHILOSOPHY OF SCIENCE

its relations are more or less arbitrarily neglected, and are
not included in the resulting symbol. As a consequence,
every symbol is abstract in its representation of nature; it
loses some of nature, and hence is not strictly adequate as a
representative. Thus the realm of symbols is less extensive
than the realm of events. But, in the second place, the
human mind seems to be unwillingly restrained to what is
given; it is prone to soar into flights of imagination and
theorizing, which go beyond the limits of the obvious data
and result in the formation of symbols having no known
existential correlates. These methods may be purely imagina-
tive, and guided by no recognized techniques, as in the case
of poetry and much common sense reflection; or they may be
subject to greater or less control, as in the case of science.
But even in the latter case a greater variation in methods is
possible. The operations by which the realm of the given is
extended may be essentially Active and creative, resulting in
such entities as perfect levers, ideal gases, disembodied
electrical charges, and mathematical points. Or they may
be more closely tied down to the realm of the given in the
sense that they are possible constructions out of it ; a physical
object, for example, may be defined as the class of its ap-
pearances,1 a mathematical point may be defined as the
series of "enclosing' events,2 space may be defined as the
totality of possibilities of relative position of bodies and
phenomena.3 Finally, the operations may be considered as
semi-exploratory in character, and hence as resulting in
entities which have at least a probable existence; such
techniques produce what are ordinarily called hypotheses.
What is important with reference to all of these entities
is that they are not, at least at the moment of creation,
considered as indubitably given. As a consequence one is
obliged, by virtue of a characteristic activity of the mind,

1 Bertrand Russell, Our Knowledge of the External World (Chicago: Open Court,
1915), p. 155.

2 A. N. Whitehead, Concept of Nature (Cambridge: Cambridge University Press,
1920), Chap. IV.

3 V. F. Lenzen, Physical Theory (New York: Wiley, 1931), p. 51.

THE NATURE OF SYMBOLS 71

to insert into any symbolic scheme elements which are not
known to have any direct representative value; the symbolic
system adds to nature, and hence ceases to be strictly ade-
quate. Thus the realm of symbols is more extensive than the
realm of events.

This control of symbolic schemes by human factors,
apparently working at odds to the theoretical ideal of
knowledge, has seemed to many to argue for the necessity of
recognizing an essentially pragmatic factor in knowledge.
Knowledge, it is claimed, must be adequate as a representa-
tive of events, but it must also be adequate to the knowing
demands of the human organism. Often, as in the cases
mentioned above, these two types of control are in conflict,
and one is obliged to make a choice between them. Conse-
quently it is one of the tasks of the philosophy of science to
make an analysis of all scientific schemes with a view to
showing which of their elements are traceable to that which
is to be known and which are traceable to the knowing
operations. The results of some of these analyses will be
discussed in Chapter VIII.

If one grants, then, that an adequate symbolic scheme is
isomorphic with reference to the realm of events, and that
every scientific system is more or less adequate depending
on the extent to which the knowing operations transform
and create, the problem immediately arises as to whether
there may be degrees of adequacy within the scope of
isomorphism. Are there some types of symbol which are
more adequate than others? Apparently, one-to-one correla-
tion implies only a highly abstract identity, hence there
need be no specific similarity between the elements and
relations of the one system and those of the other. What
seems to be required is merely that if there are different
elements and different relations in the one system, there must
be the same differences in the other. This seems to be about
all that one can say with regard to the general referential
character of symbols. But what may be said as to the
adequacy of specific kinds of symbols?

72 INTRODUCTION TO PHILOSOPHY OF SCIENCE

KINDS OF SYMBOLS

Some symbols are more directly pictorial than others.
Images, for example, are more directly representative than
verbal descriptions, and models convey information about
their referents more directly than do mathematical equa-
tions. Hence one may conveniently arrange symbols on a
scale according to their mirroring capacities. At the one ex-
treme will be that type which Peirce calls an icon. This is
defined by him as any symbol which "may represent its
object mainly by its similarity." Illustrations of icons are
to be found in images "which partake of simple qualities";
diagrams "which represent the relations, mainly dyadic, or
so regarded, of the parts of one thing by analogous relations
in their own parts";1 and metaphors which represent through
parallelism. "It is a familiar fact that there are such repre-
sentatives as icons. Every picture (however conventional its
method) is essentially a representation of that kind. So is
every diagram, even although there be no sensuous resem-
blance between it and its object, but only an analogy between
the relations of the parts of each." 2 At the other extreme
will be those which are not primarily pictorial. Here will be
found practically all words 3 and probably most mathe-
matical symbols other than the direct representation of
spatial figures.4 These symbols which have only a remote
pictorial value may be called, for want of a better term,
characterizing symbols, since they point to their referents by

1 C. S. Peirce, Collected Papers (Cambridge: Harvard University, 1932), Vol. II,
par. 2.276 and 2.277.

2 Ibid., par. 2.279.

3 One must say practically all words, for there are many which retain their pic-
torial character in their sounds, such as "pitter-patter," "bow-wow," and similar
onomatopoetic words, and others which retain their pictorial character in their
appearance, such as Egyptian hieroglyphics.

4 Peirce considers mathematical symbols to be icons. " A distinguishing property
of the icon is that by the direct observation of it other truths concerning its object
can be discovered than those which suffice to determine its construction. Thus, by
means of two photographs a map can be drawn, etc. Given a conventional or other
general sign of an object, to deduce any other truth than that which it explicitly
signifies, it is necessary, in all cases, to replace that sign by an icon. This capacity of
revealing unexpected truth is precisely that wherein the utility of algebraical for-
mulae consists, so that the iconic character is the prevailing one." Ibid., par. 2.279.

THE NATURE OF SYMBOLS 73

meaning them rather than by portraying them. It still re-
mains true, as Wittgenstein has insisted, that every proposi-
tion is a picture of a fact. But one cannot ascertain the fact
by a mere examination of the symbol as a physical event;
one must know what the symbol means. In fact one may say
that the difference between icons and characterizing symbols
is that in the former the determination of the referent must
be made primarily by examining the symbol itself and only
incidentally by examining the reference, and in the latter it
must be made primarily by examining the reference and only
incidentally by examining the symbol itself.

Supposing this general distinction between icons and
characterizing symbols to be valid, is there any reason why
the one type of symbol should be preferred to the other?
The problem has been formulated in terms of the rival
claims of pictorial representation, or models, and conceptual
representation, or abstractions. Whether the icon is a mental
image or a physical model consisting of pulleys, wires, and
rubber tubes is of no importance in the present considera-
tions; both are types of pictorial symbolism, one somewhat
ephemeral and intangible, the other permanent and material.
The insistence upon this type of concrete imagery has
characterized a group of English physicists, among whom are
Faraday, Lord Kelvin, Lodge, and Maxwell. Kelvin, for
example, says in effect that the question, Do we understand a
certain physical subject or not? means Can we construct a
corresponding model? ! "I advise you all who are engaged
in teaching, or in thinking of these things for yourselves, to
make little models." 2 Lodge puts this plan into practice
when he explains modern theories of electricity 3 by diagrams
of machines involving pulleys and cords, weights and drums.
As long as one limits himself, he insists, to the abstract
schemes of mathematicians who are "able to live wholly

1 W. T. Kelvin, Baltimore Lectures on Molecular Dynamics (Baltimore: Johns
Hopkins, 1884), p. 131.

2 Ibid., 2nd ed., 1904, p. 34.

3 Oliver Lodge, Modern Views of Electricity (2nd ed., New York: Macmillan,
1892), passim.

74 INTRODUCTION TO PHILOSOPHY OF SCIENCE

among symbols, dispensing with pictorial images and such
adventitious aids" * one does not truly understand the real
phenomena. On the other hand there is a large group of
scientists, among whom are Hobson, Mach, Ostwald, and
Poincare, who believe that images and models are apt to be
misleading and should be replaced by abstract conceptual
schemes and word-representations. Probably there would
also be found in the latter group all of those who argue that
physical events are simply measurable entities which can
be symbolized only by numbers and functional relations
between variables. The conflict may therefore be formulated
in terms of the relative adequacy of concrete as over against
abstract symbolism.

Unfortunately the problem is none too precise when
described in this way, for the dichotomy concrete-abstract is
itself ambiguous. It may refer to any one of a large number
of distinctions, all of which are considered as reducible to the
distinction between the perceivable and the unperceivable.
This is not a very helpful analysis for there are probably
many reasons why any event may or may not be readily
perceived. Events which are remote in space and time can-
not be readily perceived, nor can events which are very large
or very small, or very long or very brief. Events which are
highly complex, i.e., which exhibit many aspects, cannot
enter clearly into perception, nor can events which are
highly simple, i.e., the aspects of complex events considered
in isolation from one another. Thus one could construct such
a list of unobservable events as the following: Mars, the birth
of Caesar, the solar system, genes, life upon the earth, a
flash of lightning, a human organism, and length without
breadth or thickness — but in each case the elusive character
of the event would be due to a different factor. A thorough
examination of the problem at hand would require a detailed
consideration of these various dimensions of obscurity.

For present purposes, however, the problem of the relative
adequacy of icons and characterizing symbols may be left

1 Ibid., p. 13.

THE NATURE OF SYMBOLS 75

in the form of generalities. It seems possible to maintain
that the choice between these two types of symbol is deter-
mined primarily by one's ideational habits, and secondarily
by one's conception of the function of symbolism in the
development of science. Many investigators seem to think
habitually in terms of images and models, and do not feel
that any phenomenon is understood until it has been ac-
curately pictured. Others seem to grasp abstractions more
readily, and are apparently confused by the misleading
detail which is associated with concrete imagery. The ex-
treme types are represented by the artist and the mathe-
matician; the former has developed a sensitivity to qualita-
tive givens in perceptual configurations; the latter, to
quantitative constructions in abstract logical patterns. But
considerations of the ultimate task of science also enter in.
If one believes that the final goal of science is the adequate
representation of that portion of the realm of events which is
clearly, i.e., perceptually, given he will be inclined to favor
pictorial symbolism ; for if an event can be readily perceived
it can be readily imagined or modeled. But if he insists that
the task of science is not mere descriptive portrayal but
explanation, i.e., the revelation of less clearly given entities
in terms of which the perceivable realm is to be understood,
he will consider pictorial representation less useful; for if an
event cannot be readily perceived it cannot be readily
imagined or modeled. Hence one may say that the most
adequate representation of the perceptual realm is through
icons, and the most adequate representation of the non-
perceptual realm is through characterizing symbols. This
is not to deny the legitimacy either of characterizing the
perceptual or of mirroring the non-perceptual. It is merely
to recognize, for example, that a lecture about one's travels
does not have the same informative value as a portrayal
by means of a motion picture with sound effects. It is also
to recognize the dangers inherent in the concrete representa-
tion of events which cannot be readily perceived. Events
which are remote in space and time must be symbolized in

76 INTRODUCTION TO PHILOSOPHY OF SCIENCE

terms of the here and now ; events which are very large must
be reduced, and events which are very small must be en-
larged; events which endure must be shortened as to life,
and events which are very brief must be prolonged; events
which are highly complex must be schematized, and events
which are highly simple must be associated with possibly
irrelevant detail. Hence icons lose their essential pictorial
value when used in such realms, since they subtract from,
or add to, their referents in important ways. The result is
that unless one is very cautious in the use of these symbols he
is almost certain to read out of, or read into, the referents
certain properties whose absence or presence is suggested by
the character of the symbol. This becomes an important
source of error in science.

Before dismissing the subject of symbols, attention must
be called to a peculiar type of symbol which is apparently
required for every symbolic scheme. This is usually called a
"proper name" or an "index," and it is needed to relate an
event given in direct awareness with a symbol which is
presumed to be applicable to it. Both characterizing symbols
and icons refer to their referents through properties, and one
locates these referents by identifying the events possessing
the specified properties. But the referents which are thus
specified may not exist. An alternative means of identifica-
tion is through gestures, or through the employment of
certain words such as "this," "that," "here," 'now," and
certain other "pure" proper names. Events so located must
exist, since proper names in the absence of their referents are
meaningless and become mere noises. Hence a symbolic
scheme which has an actual application, as over against one
which has only an applicability, will always contain some-
thing which functions as a proper name. A map, for exam-
ple, must always contain not merely a label, such as "map
of Chicago," or "map of France," but it must contain a more
specific reference such as " I am now here " indicated by point-
ing to a spot on the map. Only through some such means can
the specific application of the symbolic scheme be determined.

THE NATURE OF SYMBOLS 77

REFERENCES

C. K. Ogden and I. A. Richards, Meaning of Meaning (New York:
Harcourt, Brace, 3rd ed., 1930).

R. M. Eaton, Symbolism and Truth (Cambridge: Harvard Uni-
versity, 1925), Chap. I.

C. S. Peirce, Collected Works (Cambridge: Harvard University,
Vol. II, 1932), Book II, Chaps. I, II, III.

A. Aliotta, Idealistic Reaction against Science (London: Macmillan,
1914), Part II, Chap. V.

Scott Buchanan, Symbolic Distance (London: Kegan Paul, 1932).

L. Wittgenstein, Tractatus Logico-Philosophicus (New York:
Harcourt, Brace, 1932).

A. C. Benjamin, The Logical Structure of Science (London: Kegan
Paul, 1936), Chaps. VII, VIII, IX, XI.

CHAPTER V

PERCEPTION

Now that the tools of science have been considered, the
way is prepared for an examination of the methods and
techniques by means of which science attains its end. The
task of science, as has been shown, consists in the examina-
tion of the realm of events and in the discovery or invention
of a system of symbols having as its main function the
portrayal of the essential features of that realm. How does
science set about this job?

THE STARTING-POINT OF SCIENCE

It may seem a commonplace to assert that science must
begin with the realm of events. Events are fixed and ob-
jective, and constitute both the origin of knowledge and
the point to which reference must be made in case verification
is desired. Knowledge, on the other hand, is flexible and must
be molded to suit the events which it is presumed to portray.
If the scientist describes nature he must start with nature.

On closer examination, however, the statement proves
to be not so obvious; in fact it may not even be true. Sci-
ence starts not with nature, but with a selection from na-
ture, and the particular selection is determined, presumably,
by the idea in the mind of the scientist at the moment.
The scientist does not respond to all events equally; on the
contrary, he attends to those which are relevant either
positively or negatively to a theory which he is debating
and seeking to verify. In fact, since attention is a selective
response, one may well ask whether there would be any data
at all were it not for specific interests. When one walks
down a busy street deeply immersed in thought, it is fair
to say that the busy scenes do not exist for him; and if he
does react he does so selectively, and, as a consequence,

78

PERCEPTION 79

one may say that only those events to which he makes a
conscious response really exist for him. Hence it seems that
science does not begin with uninterpreted data, but with
tentative ideas, conjectures, and hypotheses, verification of
which is sought in the medley of given events.

Still closer examination of this point of view, however,
reveals the fact that one has not yet arrived at funda-
mentals. Apparently data can be selected only through the
medium of hypotheses. But do either data or hypotheses
have any meaning apart from problems? Reflection has its
origin, as was shown in Chapter IV, in what might be called
problematic situations — situations in which the organism
experiences an interruption in its habitual and accustomed
behavior, and is obliged to try new responses in order to
reestablish the smooth functioning. In highly developed
organisms these situations involve the use of deliberation,
which is essentially the act of selecting from among a range
of possible responses whose projected consequences are pre-
figured in imagination, one which is judged to be the most
adequate in the situation at hand. So long as there are no
problematic situations there is no reflection, and so long
as there is no reflection there can be neither data nor hy-
potheses. Data and hypotheses are elements which are
selected from the given as tools for solving problems, and
until there are problems there is no need for tools.

The difficulty with this point of view, however, is that
even problems are such only within the range of sensitivity
of the organism. What is a problem for one organism may
not be for another, and what is a problem for an organism
at one time may not be at another. Hence what makes a
situation into a problem seems to be something in the organ-
ism itself — on the one hand an organized system of responses
which proves adequate to situations which for other organ-
isms might be occasions for the breakdown of reactions,
and on the other hand a sensitivity to certain types of sit-
uation which for other organisms might be occasions for
uninterrupted behavior.

80 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Fortunately these somewhat confusing features of the
scientific method may be neglected for the purposes of the
present study. Problems of this kind belong to the larger
field of the psychology and the physiology of thinking, and
no serious difficulties will arise if they are disregarded in
accordance with the general principle of isolation. Certainly
one can say that the issue as to whether a problematic sit-
uation or a general condition of sensitivity constitutes the
prior element in reflection is pre-scientific rather than sci-
entific. By the time the scientist reaches the stage in which
he responds to the delicate situations which one calls sci-
entific problems he has already developed a high sensitivity.
It seems rather futile, therefore, to ask whether he is sensi-
tive because he has recognized the problems, or whether he
recognizes the problems because he is sensitive. Further-
more, the issue between data and hypotheses as prior
elements cannot be settled without a knowledge of the stage
of development of the science under consideration. A sci-
ence which is still in its infancy emphasizes the collection
and arranging of data, though even here one cannot say
that these activities take place without regard for anterior
meanings and interpretations. On the other hand, a science
which has reached maturity adopts explanatory notions
very readily and employs them as guides for the selection
of data; however, here, again, one must insist that the hy-
potheses are not drawn from the blue but are suggested by the
data. The only point to be emphasized with reference to
this conflict is the fact that data and explanatory concep-
tions are not on precisely the same level in science. Theories
depend upon data in a way in which data do not depend
upon theories. Though one may say that the data are
principles on the basis of which he may select theories,
and theories are principles on the basis of which he may
select data, nevertheless he must acknowledge that data are
fixed while theories are flexible. Data may never be re-
futed, nor may they be modified to fit theories; theories,
on the other hand, are often refuted, and are frequently

PERCEPTION 81

modified to fit data. Theories, in other words, are the effect
of data in a way in which data are not the effect of theories.
In view of this conclusion it does seem safe to say that
science starts with facts, in the sense that it founds its
structure ultimately on facts. "Any scientific idea arising
in the mind of a scholar is based on a concrete experience,
a discovery, an observation, or a fact of any kind, whether
it is a physical or an astronomical measurement, a chemical
or a biological observation, a discovery among the archives
or the excavation of some valuable relic of an earlier civiliza-
tion." x Whether the events which thus constitute the basis
for science should be called "data" is, perhaps, questionable.
Properly speaking, an event becomes a datum only when
it is considered in the context of a problem, i e., only when
it is responded to by an organism. An event which is isolated
from the background of associated events by the selective
response of an organism becomes a datum. Hence a fact
cannot be a datum until it has been selected. But this may
be an attempt to introduce an over-precise terminology.
Certainly there can be no confusion in asserting that science
rests upon data. The problem which then arises has to do
with the methods for getting data.

THEORIES OF PERCEPTION

The act of getting data, at least in the natural sciences, is
ordinarily called observation, or perception. Clearly, if
knowledge is to be justified there must be some theory as
to the nature of the perceptual aGt. Prominent among such
theories is that of the ordinary man on the street. This
may be called the common sense theory, though it repre-
sents a somewhat sophisticated rather than a purely naive
theory. In other words, it is the position taken by any
observer who has recognized the fact of error, and who
therefore realizes that objects cannot be perceived directly
but must be known through the intermediary of something
which makes error possible. The theory is not at all clear

1 M. Planck, Philosophy of Physics (New York: Norton, 1936), p. 89.

82 INTRODUCTION TO PHILOSOPHY OF SCIENCE

in its formulation. In fact one may say that when the com-
mon sense theory becomes formulated it has already become
critical and has ceased to be the position of the ordinary
man. The purpose in examining it here is to draw con-
clusions as to the possibility of making it a foundation
for scientific procedure. Science is often described as
continuous with common sense and as differing from it
only in the degree of criticism which is introduced. This
suggests that some light may possibly be thrown on science
by examining common sense.

The theory is usually described as representative in char-
acter. It maintains that what is known through perception
is a realm of material objects existing in space and time,
and possessing certain properties such as shape, size, rest
or motion, color, sound, hardness, and on certain occasions,
taste, and odor. Sense perception is a process of receiving
from the material objects physical stimuli which enter the
sense organs and are transmitted through the nervous sys-
tem to the brain and thence into the mind. Knowledge is a
complex of immaterial entities called ideas, located some-
how in the mind, which is itself vaguely associated with
the brain and therefore presumed to be in the skull. The
ideas are consequently not in space or time in any precise
sense and they do not exhibit any of the properties of
physical objects such as hardness, rest, motion, shape, or
color. But they have the peculiar power of mirroring the
properties of physical objects, and are thus instruments of
knowledge. When they correspond to objects they are true
and constitute knowledge; when they fail to correspond
they are false and constitute error. The knower functions as
the recipient of the stimuli and as the residence of the ideas.

It requires no careful analysis to justify the conclusion
that such a theory of cognition can hardly be adequate as
an interpretation of science. Philosophy has long been
wrestling with this problem and has brought certain of the
difficulties inherent in it clearly to light. Two of its inade-
quacies may be suggested here. In the first place, no satis-

PERCEPTION 83

factory test of truth is possible upon its grounds. If one
knows the material world only through immaterial ideas
and if the truth of an idea consists in its correspondence
with an object, then truth can never be ascertained. One
can get ideas but one cannot get material objects, hence no
comparison can be made. One cannot compare his image
of a piece of gold with the piece of gold itself, for he can
know the latter only through the intermediary of an image;
hence he finds that he can only compare one image with
another. The result is that he is isolated within the realm
of ideas and can never know an external world. The second
inadequacy of the common sense theory is its failure to find
a place for thought creations, fictions, constructions, abstrac-
tions, and the like, in the cognitive situation. From the
point of view of science this is a serious limitation. Without
idealizations, isolated systems, serial extensions beyond and
interpolations between the elements of the given, science
would find it impossible to proceed. In other words, science
finds it useful to convey information about something which
does exist by talking about something which does not exist.
According to the common sense theory this would be impos-
sible; all ideas of things which do not exist would be false
and could not contribute to knowledge. Common sense
denies any creative activity to the knower, since any trans-
formation which is due to his activity could only result in
error. The perceiver is merely the passive recipient of stimuli,
and his efficiency is to be measured in terms of his receptivity.
As a result of these inadequacies various attempts have
been made in the history of thought to replace the common
sense theory of perception by one which allows for the
possibility of science. A detailed discussion of these the-
ories would be out of place in an introductory book of this
character. Two of them may be briefly considered here,
viz., positivism1 and subjectivism.

1 Positivism is both a theory of perception and a theory of description. It will be
considered only in the former sense here. Positivism as a theory of description will be
discussed in Chapter VIII.

84 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Positivism insists that the fundamental error in the com-
mon sense interpretation lies in the supposition that all
that any observer knows is ideas, private to his own mind.
One knows neither ideas nor objects, says positivism, but
neutral entities which are in themselves neither mental nor
physical. According to Ernst Mach, one of the most sig-
nificant representatives of the position, the stuff of knowledge
consists of such neutral entities — "colors, sounds, tem-
peratures, pressures, spaces, times, . . . feelings and voli-
tions." * These elements are not psychical in character, nor
private to the mind of the observer. Nor are they physical,
residing in a public world. Strictly speaking, they are in
themselves neither the one nor the other. However, they
have the capacity to occur in certain types of complexes
and in certain functional relationships to one another. "A
color is a physical object as soon as we consider its depend-
ence, for instance, upon its luminous source, upon other
colors, upon temperature, upon spaces, and so forth. When
we consider, however, its dependence upon the retina it is a
psychological object, a sensation. Not the subject-matter
but the direction of our investigation, is different in the
two domains." 2 "These elements — elements in the sense
that no further resolution has as yet been made of them —
are the simplest materials out of which the physical, and
also the psychological, world is built up." 3 Hence knowl-
edge cannot be an affair involving correspondence between
a psychical entity and a physical entity, for there is no such
difference of stuff. An element in one context is psychical,
and in another is physical; but it is the same element in
both cases.

Such a theory claims to avoid the unfortunate dualism
of common sense. When a color is known, there is not the
idea of the color which is known directly, and the physical
color itself which is outside of the mind and known only
indirectly. The color and the idea of the color are identical.

1 Analysis of Sensations (Chicago: Open Court, 1914), p. 2.

2 Ibid., p. 17. 3 Ibid., p. 42.

PERCEPTION 85

There is only one thing — a neutral color, which is known
directly. The fact that the color occurs in varied and com-
plex relations to other "elements' does not have any im-
mediate effect on the knowing, and does not change the
character of the color. Colors are acted upon by light sources
and various media, and the laws of such operations are
called physical laws. But colors are also acted upon by
the retina and optical nerve, and the laws of such operations
are called psychological laws. According to such a theory
one is no longer entitled to say that physical objects produce
ideas. One ought rather to say that certain elements which
are neither physical nor ideational occur in associations
which are sometimes physical and sometimes ideational.
The idea is different from the physical object only in the
sense that a man in the associations of his home life is
different from the man in the associations of his business.
There need be no problem of getting from one to the other,
for there is an identical element — the man himself. For
positivism, therefore, the dualism of common sense has
been avoided, and the problem of perception has been solved.
Positivism, however, represents an unstable position. The
neutral entities will not remain persistently neutral, but
tend to take on a private, subjective character. Unless
positivism is continually on its guard it passes imperceptibly
into a solipsistic idealism. This leads to the consideration
of a third theory of perception, viz., subjectivism. One of
the best expressions of this subjectivistic theory of percep-
tion is to be found in Eddington, at least in his later phase.1
His position claims to be founded on the actual procedure of
science, and is presumed to be the only interpretation of
observation which is in accord with the facts both of science
and of common sense experience. "Mind is the first and
most direct thing in our experience; all else is remote in-
ference." 2 The first task of science consists in the descrip-

1 Eddington's position becomes more solipsistic as he passes from The Nature of
the Physical World (1929) to New Pathways in Science (1935). His point of view as
developed in the earlier of these two works will be discussed in Chapter XX.

2 New Pathways in Science (New York: Macmillan, 1935), p. 5.

86 INTRODUCTION TO PHILOSOPHY OF SCIENCE

tion of 'regularities and recurrents" which are noticeable
in this immediately given content. "We call these regular-
ities of experience laws of Nature." 1 But science does not
remain in this limited realm. "Broadly speaking the task
of physical science is to infer knowledge of external objects
from a set of signals passing along our nerves." 2 This
proves to be necessary because "it is the inexorable law of
our acquaintance with the external world that that which is
presented for knowing becomes transformed in the process
of knowing." 3 From this, the character of the knowing sit-
uation is clearly ascertainable. So far as immediate and
certain knowledge is concerned, we are limited to our own
individual sense experiences ; we can classify them and formu-
late the laws of their interrelationships. But on the basis
of this knowledge we may make — indeed, we must make —
inferences to an "external' world, since we apparently
know that these sense experiences are the results of acts of
transformation and cannot therefore afford reliable informa-
tion as to their causes. Our knowledge of an external world
is wholly inferential in character.

If one examines the three theories of perception here
considered, viz., the common sense theory, positivism, and
subjectivism, he can recognize that each represents, in a
sense, an attempt to overcome the inadequacies of the
preceding. The common sense theory is unsuccessful be-
cause of two features: it makes all knowledge indirect and
thus denies the possibility of knowing an external world,
and it forbids the mind by its own creative acts to make
any contributions to knowledge. Positivism apparently
recognizes at least the first of these difficulties and attempts
to avoid it by supposing that knowledge is always direct.
There is reason to believe that this is an improvement on
the common sense position. But a new difficulty arises.
If knowledge is always direct, how is error possible? If
there is nothing which comes between the observer and the
object, and if observation is the passive response to the

1 Ibid., p. 8. 2 Ibid., p. 6. 3 Ibid., p. 7.

PERCEPTION 87

object, how can the observer ever be mistaken? The answer
is that he cannot be. As a consequence positivism must
give erroneous objects the same status as neutral entities;
the world then becomes populated with all kinds of fanciful
and imaginative objects. Subjectivism feels that it avoids
this difficulty, for it locates the things which are known
directly in the mind. This seems to place unreal objects
where they properly belong. But where does it place real ob-
jects? It gives them an inferred status beyond the contents
of the individual consciousness. The world of science is
precisely the result of such inference. By means of direct
knowledge and an inferential act one may obtain indirect
knowledge of something real and external. But a serious
difficulty immediately arises — a difficulty which seems to be
inherent in the subjectivistic position. If one can know
directly only the contents of his own consciousness, how can
he ever know the principles which will guide and justify
an inference leading outside that consciousness? According
to Eddington the justification for such an inference is to
be found in the laws of nature. But, as has already been
seen, the laws of nature are simply the regularities and re-
currencies which are noticeable among the data of the
individual consciousness. Hence the individual must be
presumed to be able, by means of a law which is private
and subjective, to infer the existence of something which is
public and objective. This is clearly an attempt on the
part of the individual to lift himself by his own bootstraps.
It proves to be, therefore, a very unsatisfactory technique
for locating real objects. A pure subjectivism is thus no
better off than a pure positivism. Whereas the latter has
difficulties in locating unreal objects, the former is unable
to locate real objects. Positivism seems to give unreal
objects a substantiality which does not belong to them,
and subjectivism seems to deny real objects a substantiality
which does belong to them.

From this examination of the problem of perception, one
seems obliged to draw certain conclusions. These, it will

88 INTRODUCTION TO PHILOSOPHY OF SCIENCE

be noted, are identical to those expressed in Chapter III
where cognition in general rather than perception was the
topic of discussion. It was found there, as it is now found
here, that knowledge is impossible unless there is (1) some-
thing which may be called direct awareness, and (2) some-
thing which may be called indirect awareness. The former
is required to make truth possible, and the latter to make
error possible. But one is now able to see more clearly
what this indirect or symbolic awareness is. The symbolic
function of mind is identical with its inferential function.
Symbols are the essential instruments by means of which
one extends the immediately given. Hence symbolic aware-
ness is an inferential awareness of something not immediately
given in direct awareness, but hinted at or suggested
with a greater or less degree of clarity. Many of my
"private" sense-data, which I know immediately, indi-
cate " public'' objects, and it is through the instrumen-
tality of symbols that I become aware of such objects.
The objects enter into my knowledge through symbols,
hence the symbols occupy an intermediary position between
the " private'' sense-data which are given immediately,
and the ''public' objects which these sense-data seem to
demand.

SCIENTIFIC REALISM

The correct understanding of the part which symbols
play in this general situation enables one to construct a
theory of perception which seems to be more adequate
than any of the three considered above. It may be called
scientific realism. Its fundamental claim is that the elements
of perception should be defined in terms of certain neutral
particulars, as in the case of positivism. But it argues that
the structure of perception is expressible only in terms of
complex relations between certain clusters of these neutral
elements. Hence its first problem is to show how these
elements become associated into groups which are called
objects of certain kinds.

PERCEPTION 89

Very early in the individual's experience he must have
noticed that elements such as colors, shapes, tastes, odors,
tensions, feelings, decisions, tendencies, and the like unite
into clusters having a certain permanency of existence and
of recurrence. Knowledge reveals not merely the fact of
such elements as these, but also the fact of their togetherness
in certain associative wholes. The unitary character of
such wholes is determined not merely by the fact of persist-
ence and recurrence but also by the fact that changes
tend to occur in clusters, i.e., changes in certain of the
elements tend always to be associated with changes in other
elements. By the observation of these persisting and recur-
ring associations, undergoing collective changes, the indi-
vidual selects certain wholes to which he attaches an indi-
viduality. These complexes he calls "objects," though it
must be recognized that such a term tends to suggest an
opposition to "subjects' and "subjective" — an implica-
tion which is misleading at this point. Certain complexes
exhibiting shape, color, size, spatial and temporal location,
hardness, rest or motion, and the like are called "physical
objects," changes in such objects being illustrated by break-
ing, dissolving, and burning. Certain complexes of this
kind are also called "physical media," since they have the
peculiar power of affecting other physical objects in certain
describable ways; for example, a glass of water is such a
medium since it causes a straight stick to appear bent when
immersed in it; also a microscope is such a medium since it
causes a small object to appear large when placed under it.
Certain other clusters are called "biological objects," one of
which is the individual's own organism; this also has the
power to induce changes in physical objects, as in the case
of an object which appears double when the individual is
under the influence of drugs or subjecting his eyeball to
pressure. Another cluster the individual calls "mind" or
"consciousness"; this again has the power to induce changes
in physical objects; for example, an object may be changed
by suggestion or by alteration in emotional attitude. Finally

90 INTRODUCTION TO PHILOSOPHY OF SCIENCE

there is a cluster, relatively simple in character, which is
perhaps part of the previous complex, and may be called
"awareness"; this is also capable of affecting objects, since
when it is absent objects disappear completely. This is the
direct acquaintance whose essentiality in knowledge was
demonstrated in Chapter III.

These types of object unite into perception in a way which
may be symbolized asA— M — B— P — 0. 0 represents
something which may be called the end-object; it is that
which is presumed in any perceptual act to be the ultimate
thing known at the moment, i.e., the content of the aware-
ness. Attention has already been called to the fact that all
knowledge demands a situation of the kind described by
saying, 'I am now aware of such-and-such." The. end-
object is the final "such-and-such" of perception, i.e., it is
that element of the perceptual act which cannot in the given
situation be considered as a tool or instrument of percep-
tion, and hence as a part of the awareness rather than of the
content. An end-object is that which one perceives, not
that by means of which something is perceived. P repre-
sents that complex of elements which constitute the physical
medium in which 0 is found. This includes its spatial and
temporal location, its illumination, the atmosphere or other
gas surrounding it, and so on; it also includes any instru-
ments placed in that medium for the purpose of recording,
measuring, magnifying, analyzing, intensifying, and other-
wise conveying information, through physical stimuli, of
the character of the end-object. Objects which function
as physical media may also function as end-objects, though
not usually in the same situation; for example, one may
make a physical study of a thermometer. But if a ther-
mometer is end-object of an act of perception, it is not
ordinarily at the same time a medium for conveying informa-
tion about some other event. An end-object indicates, at
the moment, nothing beyond itself; a medium is always a
vehicle. B represents that complex of elements which con-
stitute the body of the perceiver, i.e., the nervous medium

PERCEPTION 91

through which the stimulus from the end-object, or from
the medium, must pass before it is capable of entering into
awareness. It functions exactly as does the physical medium.
The human organism may itself function as an end-object,
though not when it is also functioning as a medium — unless
one is prepared for the difficulties to which this gives rise.
M signifies that complex of "mental" elements — conceptual
background, emotional set, purpose, and interest — which
constitute a third medium through which the stimulus must
pass. This, again, functions exactly as do the physical and
bodily media. A indicates the pure awareness by which an
object becomes a perceived object. It is non- transforming
in character, and therefore neither contributes to nor sub-
tracts from the object known; it is "external" to the object.
Even here one may say that awareness may become an
end-object, though the occasions in which it does so are
rare; the present situation is presumably such a case, since
we claim to have discovered awareness as an element of
perception. But if awareness is an end-object, there
must be another awareness which must be of it, for one
cannot get away from the fact that the awareness of a
content is the minimum situation in which knowledge
can exist.

The most important feature which emerges as a result of
this analysis is that the five factors, A, M, B, P, and 0
are not, so to speak, on the same level. Since every percept
tual act must contain an awareness and an end-object,
A and 0 function uniquely; A functions as the minimum
awareness, and 0 as the minimum object, i.e., A can never
be part of the end-object (without assuming another pure
awareness), and 0 can never be part of the pure awareness
(without assuming another end-object). The three factors,
M, B, and P, on the other hand, are parts neither of the
pure awareness nor of the end-object, but seem to lie between
the two. They are not that which is perceived, nor are they
the perceiving, in the strict sense of this word; they seem
to function as the conveyors of stimuli from the end-object

92 INTRODUCTION TO PHILOSOPHY OF SCIENCE

to the place where it may enter into awareness, and as
devices of inference by which one may gain information
as to the character of the end-objects. In this function
they may be called operators, to distinguish them from A
and 0. Then the perceptual situation may be symbolized
as follows:

Pure End-

awareness Operators object

A - M - B - P - 0

But to describe the operators as coming between A and 0
is somewhat confusing and may lead to all of the difficulties
of the common sense theory unless one specifies clearly just
what is meant by this. The operators, M, B, and P, are
more properly described by saying that they are those ele-
ments of perception which may be considered either as
parts of the gross object or as parts of the gross awareness.
In the former case they function in the determination of the
appearances of the end-object in the various contexts; in
the latter they function in the determination of the com-
plexity of awareness. Nothing can come between awareness
and its object, but there is no reason why both awareness
and object should not themselves be complex. By the object
of awareness one may mean only the end-object. But one
may mean on other occasions the end-object as operated
upon by the physical medium, or as operated upon by the
physical medium plus the sense organs and nervous system,
or as operated upon by the physical medium plus the sense
organs and nervous system plus the mind. In each case
the entity of which one is aware is the end-object as it
manifests itself through the influences of various operators.
It may be called the appearance of the object in the de-
scribed context, and awareness may be said to be of the
appearance of the object. This retains the directness of per-
ception, provided the appearances of an object are presumed
to be part of the object. But what is to be done with the
operators in case one wishes to speak merely of the end-

PERCEPTION 93

object? The operators are unavoidably present and in such
a case would appear to come between the awareness and
the object. But this can be avoided by supposing that when
the operators are not part of the object they are part of the
awareness. Any loss in the object must be equalized by a
gain in the awareness, and vice versa. If the object of aware-
ness is reduced to a bare minimum the awareness must be
increased to include all of the operators; one is then still
directly aware of an object, though the mode of his aware-
ness is highly complex. On the other hand, if the awareness
is reduced to a bare minimum the object must be increased
in such a way as to include all of the operators; one is then
still directly aware of an object, though the object of his
awareness is highly complex.

What should be emphasized here is the fact that the place
where the line is drawn between awareness and object is
arbitrary. Whether physical instruments, sense organs, and
conceptual background are considered to be part of the
gross object or part of the gross awareness makes no essen-
tial difference so long as one recognizes the inverse ratio
holding between the complexity of the object and the com-
plexity of the awareness. What is and what is not to be taken
as "part,: of an object is a relative matter; properties of
events are functions not only of the "events themselves'1
but also of the total situations in which they participate;
these situations may include not only extended spatial and
temporal volumes, but physical instruments, human organ-
isms, and minds contained therein. This recognition is im-
portant, for it means that events are, in a sense, everywhere.
But the possibility of an alternative interpretation somewhat
destroys the uniqueness of this fact. One must admit also
that what is and what is not to be taken as "part" of the
awareness is a relative matter; the perceiver functions not
only "where he is' but wherever an object perceived by
him exists. This means that the perceiver is, in a sense,
everywhere. As a result, there are alternative representa-
tions of the perceptual situation :

94 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Pure End-

awareness Operators object

- M - B - P - 0

Gross Gross

awareness object

Pure End-
awareness Operators object

- M - B - P - 0

Gross Gross

awareness object

Pure End-

awareness Operators object

- M - B - P - 0

Gross Gross

awareness object

Pure End-

awareness Operators object

- M - B - P - 0

Gross Gross

awareness object

But it remains true that in any specific situation the object
is only where its end-object is, though its causal influences
may be widespread ; and the perceiver is only where his body
is, though he may make inferences as to other localities. The
end-object can pass from its locus to that of the perceiver
only through causal transmission, and the perceiver can get
from his locus to that of the end-object only through inferen-
tial acts. This enables one to see the precise sense in which the
operators come "between" the end-object and the perceiver,
and the precise sense in which a perceiver can become aware
of an end-object. Clearly, the perceiver can be inferentially
aware of the end-object, i.e., he can be directly aware of
the M-appearance of 0, and from this and a knowledge of
the nature of the M-, JB-, and P-operators he can infer the

PERCEPTION 95

character of the end-object. But his knowledge of 0 can
not be solely inferential, for he could then never check the
validity of his inference. In order to do this he must, at
least in certain assumed situations, know 0 directly. Sim-
ilarly, in order to know the ways in which the M-, B-, and
P-operators function, he must have a knowledge of them
which is other than inferential. Hence, he must, at least in
certain assumed situations, know M, B, and P directly.
The character of these assumed situations has to do with the
notion of normal operators, and will be discussed presently.
Here all that need be insisted upon is the double function
of the operators. They may be considered, indifferently,
either as parts of the object, justifying inference to other
parts, or as parts of the awareness, conveying direct infor-
mation about end-objects.

The variability in the position of the "screen" separating
the awareness and the object can be made clear by an exam-
ple. Suppose one is attempting to determine the temperature
of a gas by immersing a thermometer in it. He inserts the
thermometer, waits a few moments, and reads off the num-
ber coincident with the height of the mercury column. He
then says that he is aware of the heat of the gas. But this is
not quite accurate. What he is directly aware of is only the
reading of the instrument; properly speaking, he should say
that from this reading he infers the heat of the gas. But he
soon realizes that there may be distortions in what he judges
to be the reading of the instrument, since he is obliged to
observe this through the intervening air and relative to his
own spatial position. Hence, he says that he is directly
aware only of the coincidence as it appears very close to his
eye and with all distorting influences removed. By these
two corrections the perceiver has moved the "screen"
separating the awareness and the object from the surface
of the end-object to the surface of the physical medium. He
is directly aware of the appearance of the recording instru-
ment, and from this he infers the character of the end-object.
However, he soon realizes that even this is not quite accu-

96 INTRODUCTION TO PHILOSOPHY OF SCIENCE

rate. He knows that his sense organs often transform the
stimuli which they receive; if his eyes are not good he may
misread the instrument. Hence, he says that he is directly
aware only of the coincidence as seen by his eyes, and under
the influence of his whole nervous mechanism as it exists
at the particular time of perception. He then corrects his
judgment by saying that on the basis of his own visual inter-
pretation of the reading of the instrument he infers the
actual reading and from this the heat of the gas. The
"screen" has again been moved and now is located between
the M- and 12-operators; the end-object is now " appearing' '
in a still more inclusive object. But even here a further cor-
rection is possible. He recognizes that what he observes in
any situation is often influenced by unconscious associa-
tions, emotional attitudes, and expectations; he often
"sees" what he wants to see or what he has been prepared
to see. Hence he says that he is directly aware only of the
coincidence as he interprets it at the moment; from which
he infers the way in which he must actually have seen it;
from which, again, he infers what the reading must actually
have been; from which, finally, he infers the heat of the gas.
At this stage he is obliged to correct his judgment by saying
that there is, at any rate, something of which he is directly
aware at the moment, and that if he allows for mental,
bodily, and physical transformations he can infer the
character of the end-object. The "screen" which separates
the object and the awareness has again been moved, for the
end-object is now considered in its mental context, and the
awareness has been reduced to a bare awareness of some-
thing given.

It should now be clear why attention was called at the
close of the last section to the need for admitting into knowl-
edge some type of awareness other than the direct sort.
Whether this additional aspect of knowledge which is infer-
ential rather than direct in character is properly a part of
perception, or something over and above perception, is
debatable. In a sense, reference to this aspect of knowledge

PERCEPTION 97

is somewhat premature at this point. Not until the end of
the next chapter will consideration be given to the symbol-
izing of data obtained through perception, and the making
of inferences represents a still more advanced stage of
knowledge. But since the proper understanding of percep-
tion itself demands reference to the possible inferences which
may be made from it, consideration of this feature will be
helpful at this point. If truth is to be possible there must be
direct awareness of objects. But if error is to be possible
there must be knowledge of an inferential sort. Inference
functions in knowledge as the technique by which from the
appearance of an end-object in a certain context its appear-
ance in another context, or the end-object itself, may be
ascertained. Error arises when one infers incorrectly from
the appearance of an end-object in one context to its appear-
ance in another, or to the end-object itself. Awareness is
always directly of objects, and cannot be erroneous; if
awareness and the object vary inversely awareness may be
complex and the object simple, or the object may be com-
plex and the awareness simple — yet awareness is always of
the object. But at any given moment what may be desired
is knowledge of the object in some context other than that
in which it is given for direct awareness. This additional
knowledge must be inferential. Perception permits one to
have direct awareness of an object in one context, on the
basis of which he constructs inferential knowledge of the
object in some other context, or of the end-object itself.
One of the important tasks of science is the justification of
precisely such inferences.

Clearly, this inferential act is of importance in the under-
standing of perception, and certain of its features must be
called to attention. In the first place it must be based, as
Eddington suggests, on the laws of nature. Inference be-
yond the object which is given in direct awareness becomes
possible only if one knows the laws according to which the
end-object manifests itself in the physical, bodily, and mental
media. One must know the laws of operators. One can infer

98 INTRODUCTION TO PHILOSOPHY OF SCIENCE

from the appearance of an object in a certain physical
medium to its character apart from such a medium only if
he knows the laws according to which radiations from
objects are transmitted by media. He can infer from a
pointer reading to the character of the object measured
only if he knows the principles according to which the meas-
uring instrument was constructed and calibrated. He can
infer from a sensation to the character of the object sensed
only if he knows something of the nature of nervous im-
pulses. Finally, he can infer from data as interpreted by
mental factors to the data as uninterpreted only if he knows
the principles according to which mental operators work.
The totality of such laws should make one acquainted
with facts like the following : the distinction between normal
and abnormal functioning of the operators; the range of
sensitivity, delicacy, extent, etc., of the physical media
(instruments), sense organs (considered as recording instru-
ments) , and states of mind ; the nature of the transformation
which any stimulus undergoes as a result of the functioning
of the operator, and hence what may be lost from or added
to the object; and so on. It is the task of physics, biology,
and psychology to reveal laws of this kind. On the basis of
them inference may be justified, for the principles by which
one infers the character of an object in a less extensive con-
text from its character in a more extensive context are the
reverse of the principles according to which the object in
its less extensive context causes its appearance in the more
extensive context.

But can one learn the laws of operators? Apparently not,
due to what has been commonly called the ego-centric
predicament. Since one cannot get away from his own sense
organs he can be aware of objects in the physical context
only as they appear in the bodily context. Furthermore,
since one cannot get away from his own mental state he
can be aware of objects in the bodily context only as they ap-
pear in the mental context. In order to know how 5-operators
act one would be obliged to get an object in the P-context,

PERCEPTION 99

first without the intermediary of /^-operators, and second
through 5-operators ; then by a comparison of the two he
could determine the laws according to which B-operators
work. But this is just what he cannot do, since he cannot
get outside of his own organism. And if he wished to deter-
mine the way in which M-operators act he would be obliged
to get an object in the 13-context, first without the inter-
mediary of M-operators, and second through M-operators;
then by a comparison of the two he could determine how
M-operators work. This, again, he cannot do, since he
cannot get outside of his own mind. Hence, since one cannot
learn the laws of the operators he cannot use such laws as a
foundation for inferring from objects in one context to
objects in another.

Though this difficulty cannot, perhaps, be avoided the-
oretically, it can be and is avoided practically. This is done
through the notion of normal operators. One decides, more
or less arbitrarily, that a certain type of situation may be
defined as a normal observational situation. Psychologically,
such a situation would be defined as one in which the ob-
server is attentive, deliberate, free from prejudices and pre-
conceptions, and without emotional biases. A situation of
this kind can be empirically distinguished from one in
which the designated attributes are lacking. Biologically, a
normal observational situation would be one in which the
observer is in possession of sense organs which have met
certain specified tests. These tests are, of course, compara-
tive in character and assure one only that the individual in
question, as indicated by the verbal responses which he
makes when he is presented with varying objects, can make
distinctions where the majority of individuals make dis-
tinctions, and fails to find differences where the majority
of individuals fail to find them. Physically, a normal ob-
servational situation would be one in which the object is at
the proper distance from the sense organ, in which there
are no intervening recording instruments, and in which
the unavoidable media such as fight, atmosphere, and electro-

100 INTRODUCTION TO PHILOSOPHY OF SCIENCE

magnetic and gravitational phenomena are present in as-
certainable amounts and kinds. Then a normal observa-
tional situation would be one which is psychologically,
biologically, and physically normal.

The possibility of determining laws of operators is then
based upon a practical assumption: in normal observation
the transforming effect of the operators may be neglected. This
is equivalent to saying that in this type of situation the
operators are considered as non-transforming. On this as-
sumption one is able to become "directly' aware of end-
objects, pointer readings, and sense-data. He may therefore
compare end-objects with pointer readings and by this
means determine the laws of P-operators; he may compare
pointer readings with sense-data and thus determine the
laws of B-operators; he may compare sense-data with " in-
terpretations'* and, as a result, formulate the laws of
M-operators. He then sees that his assumption with refer-
ence to the non-transforming power of operators represents
a first approximation, and he corrects it by means of the
laws already established. This then becomes a second
approximation, and he corrects the laws of the individual
operators accordingly. By this means he reaches a progres-
sively more accurate and reliable knowledge of the laws of
nature, and feels himself justified in using them as principles
of inference.

The second feature of inference which must be called to
attention has to do with its relation to symbols. Inference
functions in observation in affording a technique on the
basis of which from a knowledge of an object in a certain
context one may determine its character in another. How-
ever, although the appearance of which one is directly
aware is the basis for an inference to the character of the
object in a different context, the appearance should not
properly be called the symbol of the inferred object. The
greatest confusion is introduced into Eddington's position
by this terminology. For example, he fails to make a distinc-
tion between pointer readings — which are clearly events in

PERCEPTION 101

nature — and mathematical symbols — which, although they
are events in nature in the sense that they are physical
counters, are more properly described as symbols for under-
standing nature. There are superficial resemblances between
the two types of symbol. One might say, for example, that
red sky in the evening and the words "fair weather
tomorrow' are both symbols of tomorrow's weather; but
they are not so in the same sense. It is preferable to say
that the red sky is a sign of the ensuing weather, but the
words "fair weather tomorrow' are symbols of it. This
is in conformity with our earlier use of the word "symbol"
in its limited sense. Granting this distinction, one should
say not that the appearance of the object in one context
is a symbol of it in another context, but that the former calls
to mind a symbol — word, image, or other symbol — which is
then taken as having reference to the object in the other
context. This suggests the intimate association between
the symbolic and the inferential functions of thought. When
one infers an object he anticipates it by means of a symbol;
the symbol is the substitute for the object inferred, and acts
in its stead until the latter can be itself observed. But when
one anticipates an object through inference, he should not
confuse the object which is the origin of the inference with
the symbol through which the inferred object is grasped.
On the basis of such things as pointer readings, sense-data,
and interpretations, together with the laws of P-, B-, and
M-operators, one infers the character of objects in other
contexts; these objects, since they do not enter into direct
awareness at the moment, must exist for thought merely
as symbols. Pointer readings and the like are not themselves
symbols but foundations for inferring to symbols which
designate absent objects. From this point of view Edding-
ton's terminology is confusing.

The results of this chapter may be briefly summarized.
Science begins with data, at least in the sense that every
theory arises out of data and receives its verification in data.
The act of getting data is perception. Attempts to explain

102 INTRODUCTION TO PHILOSOPHY OF SCIENCE

perception by means of the common sense theory, by means
of Machian positivism, and by means of subjectivism prove
unsuccessful. An alternative theory, called scientific realism,
analyzes perception into three kinds of elements : pure aware-
ness, operators, and end-object. Operators do not come
between awareness and its object, but constitute a part
either of the gross awareness or of the gross object; hence
awareness is always in "contact" with its object. The task
of science is to ascertain from the appearance of the end-
object in direct awareness the character of the end-object or
of its appearance in another context. This is done by in-
ference, based upon the laws of operators. Perception may
be defined either as the direct awareness of an object, or
as this direct awareness plus the inferential act by which
something of the character of the object in another context
may be determined. This is approximately the structure of
perception. The problem, now, is to determine how it func-
tions in science in the actual collection and interpretation of
data. This will be the topic of the next chapter.

REFERENCES

Ernst Mach, Analysis of Sensations (Chicago: Open Court, 1914).
A. S. Eddington, New Pathways in Science (New York: Macmillan,

1935), Chap. I.
H. H. Price, Perception (London: Methuen, 1932).
W. P. Montague, Ways of Knowing (London: Allen and Unwin,

1928), Chaps. VIII, IX, X.
Bertrand Russell, Philosophy (New York: Norton, 1927),

Chap. XII.
Analysis of Matter (New York: Harcourt, Brace, 1927),

Chaps. XX, XXI, XXV.
E. B. Holt et al.9 New Realism (New York: Macmillan, 1922),

introd.

CHAPTER VI

DESCRIPTIVE TECHNIQUES

The present chapter is essentially a continuation of the
preceding one. The problem under consideration is that of
getting the data. At this point, however, the emphasis
changes slightly. Interest is no longer directed so much
to the understanding of the passive receptivity of the observer,
i.e., his capacity to receive messages from external objects,
as to his activity, i.e., what the scientist does to himself
and to nature in order to make it yield its secrets.

Attention should be called immediately to the fact that
there is no contradiction between these two aspects of the
scientific method. It seems obvious, on the one hand, as
has already been indicated, that man must proceed by
listening to nature. Nature is a given, stubborn, and brute
fact, and one must take it as it is. Fortunately, it chooses
on somewhat rare occasions to speak about itself — often
haltingly, and usually enigmatically. But one must be
continually on the watch, lest through his inattentiveness
he lose one of those golden opportunities when it discloses
its secrets. At best, therefore, one can only wait.

But it seems equally obvious, on the other hand, that
nature often responds to prodding. Through properly ad-
ministered techniques it may be. forced to speak. Nature
is not only what takes place, but what may be made to
take place. By putting one's finger into nature one often
succeeds in bringing about situations which would occur
rarely or not at all without his intervention. Thus by com-
bining, separating, moving, increasing, diminishing, heating,
cooling, and a thousand other operations he incites nature
to manifest itself in unaccustomed forms. He suspects
nature to be more than it obviously is, and he finds the

variety of its responses to be capable of almost indefinite

103

104 INTRODUCTION TO PHILOSOPHY OF SCIENCE

increase. He soon recognizes that the task of science is
not merely getting the data, but increasing the variety and
scope of data by definable techniques. It is what man does
to nature that counts, for what nature tells him is a function
of his own exploratory operations.

The descriptive techniques of modern science are many
and various. A detailed discussion of them would belong
properly in a laboratory manual rather than in a book on
scientific methodology. The details of the laboratory pro-
cedure will not, of course, be discussed here. The problem
is rather to consider these techniques only in their most
general features, and in so far as they have bearing on a
logic of science.

For the purposes of rough classification one may divide
descriptive techniques on the basis of the contexts within
which they have major application. If the function of the
descriptive methods is to increase the range and variety
of data without introducing 'abnormal' appearances, a
discussion of such methods may conveniently follow the
analysis of the perceptual situation into its elements. Ac-
cordingly, descriptive techniques may be considered under
the following heads: (1) control of the end-object; (2) control
of the physical medium; (3) control of the sense organs; and
(4) control of the state of mind.

CONTROL OF END-OBJECT

A strictly descriptive science would be passive toward
nature. It would neither manipulate nor control, neither
move about nor transform objects. For on the presupposi-
tions of a purely positivistic approach to nature, the world
must be only what it obviously is; nothing conjectural or
doubtful can be included in science. But there is no science
which is purely and simply descriptive. The implication of
the study of nature is that objects are not only what they
are apart from man's intervention, but what they may be
made to become through his intervention. Objects are the
totality of their manifestations. Hence anything which one

DESCRIPTIVE TECHNIQUES 105

can do to an object to make it otherwise conveys important
information about that object, for the object becomes the
potentiality of precisely that transformation. Sodium is not
only metallic in appearance, but readily combustible; com-
mon salt is not only white in color, but soluble in water;
gold is not only yellow, but highly malleable, etc. In each
of these cases important information about the substance
is conveyed by describing the transformations through which
it passes when subjected to certain operations.

In the present section mention will be made only of those
operations which may be said to bring about changes in the
end-object. It is obvious that the distinction between oper-
ations which transform, and operations which do not, is
relative and practical. Modifications in the physical medium
are not ordinarily presumed to affect the end-object, though
they do, of course, affect the appearance of the end-object
in the physical medium. The insertion of a microscope, for
example, between one's eye and a bit of cell tissue does not
change the tissue in any appreciable way, though it does
change the appearance of the tissue to the observer. So,
in general, it is possible to multiply the manifestations of an
end-object through the introduction of measuring and re-
cording devices without "doing anything" to the end-object
itself. The relative character of the distinction here main-
tained can be seen in the fact that the observation of an
object may involve such a transformation without one's
being aware of it. "In the street white flakes are falling
steadily. I stretch out my warm hand to examine them, and
discover that they are merely drops of water. Allowed to
fall on a sheet of cold metal, they are small flakes of snow. A
sheet of ice is stretched out and the particles that fall are
frozen. A red-hot plate shows them up as hot spheres of
liquid, while a fire as puffs of steam. What, we ask, is this
mysterious and fickle entity, that may show itself as ice,
snow, water, or steam according to how it is examined?
The answer to the riddle is, of course, obvious in this case.
These instruments for examining the white flakes have not

106 INTRODUCTION TO PHILOSOPHY OF SCIENCE

been neutral." * Similar difficulties of a more significant
character are revealed by the Heisenberg principle of in-
determinacy. In the case of the observation of small
particles the method of observation, e.g., the use of a light
wave, may influence their states in such a way that one
cannot assign to them with a high degree of precision both
location and velocity. It seems likely that as science ad-
vances there may be disclosed an increasing dependence of
the end-object upon all kinds of environmental changes,
including the introduction of instruments and other recording
devices.

A complete listing of the operations which may be per-
formed upon objects would be impossible. Characteristic
among them are analyzing and synthesizing, speeding and
slowing, intensifying and diminishing, melting, burning, so-
lidifying, dissolving, boiling, condensing, pulverizing, re-
shaping, magnetizing, stretching, compressing, dyeing, de-
composing, and ionizing. All of these may be said, in some
sense, to introduce changes in the object — changes which
are in some cases reversible and in some cases not. In each
case the aim is to bring about a new manifestation or ap-
pearance of the object, but by doing something to the object
itself rather than merely to the physical medium.

An interesting feature of this type of technique is that it
tells the observer not what objects are but what they were.
It defines objects not in terms of their actual characters
but in terms of their potentialities. It identifies objects
only by destroying them in the very act of identification.
Though such a method does give the observer information
about objects, this knowledge is of the kind which Edding-
ton 2 calls "retrospective inference." The presumption in
each case is that the objects in question are defined not
merely in terms of retrospective inference but exhibit some
properties which can be directly observed, and hence permit
knowledge of the present rather than merely of the past.
Clearly if one's knowledge of objects were obtained only

1 H. Levy, Universe of Science, p. 66. 2 New Pathways in Science, p. 93.

DESCRIPTIVE TECHNIQUES 107

by retrospective inference he could never identify objects
without destroying them, and they would reduce to mere
bundles of potentialities. The very fact that the observer
speaks of these operations as changes indicates that he is
able to become independently aware of the objects prior to
the changes. Practically, one avoids difficulties of this kind
by employing as materials upon which operations are per-
formed not all of the objects of a given kind, but merely
samples from them. In destroying the samples, therefore,
he still has left objects of the kind which have been destroyed,
and which can be characterized in terms of their capacities
to behave in this particular way when subjected to this
particular kind of operation.

The manipulation of objects in this way constitutes what
is ordinarily called experimentation. But a rather sharp
distinction may be made between experiments for discovery
and experiments for verification. The type which is here
being considered belongs in the former category, but the
more usual sort belongs in the latter. Experimentation for
discovery belongs among the descriptive techniques, and is
analogous to the more or less random toying, pinching,
turning, and tasting activities which the child uses to explore
a new object. The operations are performed without specific
direction or control, and without any well-defined idea as
to what they may reveal. They are thus activities in which
one discovers something which he had not previously known
about the object. Verificatory experiments, on the other
hand, as will be seen in Chapter XI, although they involve
discovery, are definitely planned in advance, and involve a
more or less precise prediction that a certain outcome will
ensue. The latter presuppose that one has already learned
enough about nature to anticipate certain other of its fea-
tures ; the former presuppose nothing but the general capacity
of nature to reveal itself under different guises.

There is some doubt as to whether changes in the location
of an object should be included among the controls of the
end-object or among the controls of the physical medium.

108 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Is an object changed by being moved about? On the one
hand, the presumption is that a simple change of location —
either of space or of time — does not modify an object in an
appreciable manner; where or when an object exists is not
an important fact about it. Though such a change would
bring about an alteration in the location of the appear-
ances it would presumably involve no modification in the
object itself. But, on the other hand, it must be recognized
that change in location is inseparable practically from change
in events; space and time are relations not merely between
empty points but between objects which may act causally
on one another. Change in location amounts practically to
change in environment, and this is often of great significance.
A piece of metal in a magnetic field is not the same as a
piece of metal outside of such a field, and if Julius Caesar
were alive today he would be a different man. The issue
cannot be settled by asking whether the operation is per-
formed on the object or on its physical medium, for often
the same result may be brought about either by moving
the object into a new medium or by setting up a new en-
vironment about the object. The dispute is not important
so long as one recognizes the intimate association between
position and causal influences. One of the important ad-
vantages of the laboratory is that it permits one to place
objects in situations in which he has a more or less complete
control over possible disturbing factors.

In a great many situations, however, change of location
cannot be brought about in nature. Change of temporal
location is, except in a very limited sense, impossible. One
cannot reenact history, nor can one transport himself back
into the past. The possibilities of change in spatial location
are somewhat more extensive, though even here there are
definite limitations. Man cannot bring the stars down to
earth, nor can he travel far either above or beneath the
surface of the globe. Hence his information about certain
kinds of events is largely indirect in character, and occurs
through the instrumentality of other events. The inter-

DESCRIPTIVE TECHNIQUES 109

mediary events are called records in the case of historical
objects, and messages in the case of spatially remote objects.
Both records and messages may be defined as appearances
of their respective end-objects at certain points in a physi-
cal medium — in the one case the medium being essentially
temporal in character, and in the other essentially spatial.
If the transmission of messages always requires time, as
the theory of the maximum velocity of light requires, and
if historical records are simply more or less permanent
impressions of messages from past objects, it follows that
there is no essential difference between messages and records.
They are both appearances of their end-objects. Hence
there will be no significant difference between historical
documents, verbal reports, and scratches on rocks, on the
one hand, and telescopes, spectroscopes, and photometric
devices, on the other. In both cases one has something
which is given directly, viz., written and spoken words,
marks, light images and light bands, on the basis of which,
knowing the character of the recording device, he infers the
corresponding end-objects, e.g., the Golden Age of Greece,
the North American glacier, the moons of Jupiter, and
helium in the sun. The fact that a human being is simply a
somewhat complex recording instrument has been greatly
emphasized in recent behavioristic psychology. It has im-
plications to be referred to later in the chapter.

CONTROL OF PHYSICAL MEDIUM

Modifications in the physical medium, i.e., in the P-
operators, serve to multiply the appearances of the end-
object. Since the object is, in its broadest sense, the totality
of actual and potential appearances, modifications in the
physical medium are techniques for disclosing more and
more of the object. The end-object itself, in fact, is simply
those of the total appearances which are observed under
so-called "normal" conditions of perception. Those appear-
ances which constitute the end-object itself are selected, as
was suggested in the preceding chapter, by designating,

110 INTRODUCTION TO PHILOSOPHY OF SCIENCE

more or less arbitrarily, a situation in which the physical
medium is presumed to produce a minimum of transforma-
tions. Then changes are introduced into the medium with a
view to determining how the appearances of the end-object
are affected by these modifications. Every new appearance
affords further insight into the character of the object.
Most important of these modifications are those which
involve the insertion into the medium of recording and
measuring devices, such as thermometers, ammeters, bal-
ances, micrometer screws, microscopes, telescopes, spectro-
scopes, phonographs, hydrometers, counting and sorting ma-
chines, clocks, and compasses. Other modifications include
manipulative techniques, such as applying meter bars to
objects, isolating objects from "disturbing' environmental
factors, changing illumination, and varying the position of
the observer. The function of these instrumental and
manipulative methods is to multiply and vary as greatly
as possible the appearances of the end-object to the observer.
If the object is the totality of its appearances, one learns
more about the object every time he discovers it under a
new manifestation. Hence it is to his advantage, in his
desire to explore the realm of nature, to increase the range
of possible appearances. If one limits the modifications to
such as are introduced through measuring instruments, then
he is justified in defining physical objects, in the words of
Eddington, as "schedules of pointer readings." x But if
one includes modifications which are not of this specific
kind, he cannot define physical objects so narrowly. It
seems better to employ the more general definition and to
say that a physical object is a schedule of its various ap-
pearances at different places and times and under the influ-
ence of controlled modifications in the intervening medium.
One of the most important of the transformations intro-
duced by the P-operators is the act of isolation. An iso-
lational act is the foundation not only of science but of
common sense as well. All observation is analytic and

1 Nature of the Physical World, p. 259.

DESCRIPTIVE TECHNIQUES 111

neglective. Perception is incapable of grasping events of
more than a moderate degree of complexity, whether the
complexity is spatial, temporal, or qualitative. Hence at-
tention proceeds by focusing itself upon that core of the
perceptual field which is considered to be especially relevant,
and by either neglecting the remainder entirely or else
merging it into the background of consciousness and at-
tending to it only vaguely. In this way simple events, and
events of only a moderate complexity, become isolated from
their environmental associates and considered as individu-
als. It is recognized that the neglect is not necessarily a
denial of the existence of the associates but merely a dis-
regard of them for the purpose of the problem at hand.
One notes, simply, that the complex seems to exist and vary
in relative independence of its environmental factors, and
one concludes, on this basis, that the complex is neutral
to the system in which it is found. "We talk of objects,
tables and chairs, as if they were systems neutral to their
environments. We shift our furniture from one house to
another, and the shape of the table and the comfort of the
easy-chair are unaffected by the change of location. We
take it for granted because we have found it so. If the
softness of an easy-chair varied with the room in which
it was placed it is possible that we should not regard it as
the completely separate and isolated object we do. We
might possibly widen the conception of chair to chair-
room. . . . The first function of experimental inquiry is,
if possible, to find precisely how little of an environment need
be included to render a system neutral." 1 The more refined
and controlled activities of science are continuous with the
common sense procedures. The concept of an isolated
system, which plays so large a part in scientific enquiry, is
simply the notion of perceptual object made precise.

Is isolation a transforming operation? This question
cannot, perhaps, be answered in general. There is reason
to believe that every event is related to every other event

1 H. Levy, Universe of Science, pp. 50, 51, 52.

112 INTRODUCTION TO PHILOSOPHY OF SCIENCE

in a way which may be significant for each of the events;
if so, only the entire universe could be an isolated system.
For science, however, the notion of isolated system is rela-
tive. Scientific procedure does not demand that one start
with isolated situations. Isolation is "a first step in the
process of finding out the truth about the universe by ex-
amining it in chips. The first step is succeeded by a second
more detailed, more refined. It embraces yet a little more
of the changing environment as soon as it finds that its
initial law is not precisely fulfilled, for by that failure it
recognizes that the isolation was not neutral." 1 Hence
by a method of successive approximation one makes his
systems more and more inclusive.

The isolational act which is here indicated is physical in
character, and refers to the actual elimination of disturbing
factors from the physical situation. This may involve either
moving the end-object into a new environment, such as a
laboratory, where the medium can be more or less com-
pletely controlled, or merely removing from the given en-
vironment as many as possible of the disturbing factors.
Often the environmental forces cannot be eliminated but
must be neutralized or balanced by counteracting forces.
But what is important here is that the isolational acts
here indicated are physical in character. There are also
selective acts which are of a biological and others which are
of a psychological character.

Very important for physical science are measuring tech-
niques. The problem of the nature of operations of meas-
urement is too extensive to permit consideration here.2
Measurement may be defined, in its most general sense, as
any technique by which numbers are correlated with events.
(This definition makes numbering, or counting, a special

1 Ibid., p. 54.

2 The problem will be considered again in Chapter XIII. Some important
subsidiary references are the following: W. S. Jevons, Principles of Science,
Book III; Norman Campbell, Physics, the Elements (Cambridge University, 1920),
Part II; J. Venn, Empirical Logic (London: Macmillan, 1907), Chaps. XVIII,
XIX; A. D. Ritchie, Scientific Method (London: Kegan Paul, 1923), Chap. V;
M. R. Cohen and E. Nagel, Introduction to Logic and Scientific Method (New York:
Harcourt, Brace, 1934), Chap. XV.

DESCRIPTIVE TECHNIQUES 113

case of measuring.) The actual operations by which num-
bers are applied to events vary according to the kinds of
events to be measured, and according to the range within a
given kind of events. For example, one measures the length
of an object at rest in one way and of an object in motion
in another way; one measures ordinary lengths by yard
and meter sticks, but he measures great lengths by triangula-
tion; one measures the distance of the stars from the earth
by parallaxes, but he measures the size of the small particles
of matter by micrometer screws. Events which are not
readily measurable by direct methods are measured by
means of other events with which they vary concomitantly,
as in the measurement of heat by the height of a column of
mercury. Often the attaching of numbers to events indicates
nothing more significant in the event itself than the pos-
sibility of placing it at a certain point in a series of events
similar to it but differing in the degree of some quantitative
manifestation; this is well illustrated in the measurement of
hardness. All operations of measurement, whether tech-
niques of applying standards to events themselves, or opera-
tions of inserting automatic recording instruments at the
proper points in the physical media, are methods for in-
creasing the manifestations of events. In the broadest
sense of the word, the numbers which are obtained through
measuring techniques are simply appearances of the end-
object when the corresponding modifications are introduced
into the environment.

Three features of measurement may be singled out for
brief attention. In the first place, the measuring instrument
must be relatively unaffected by the event measured. In
general one does not employ a red-hot meter stick to ascer-
tain the length of a block of ice. As was pointed out earlier
in the chapter, the strict neutrality of the measuring instru-
ment cannot always be guaranteed. In quantum phenomena
the mere introduction of a light impulse interferes with the
particle to be measured; a micrometer screw, however del-
icate, exerts a slight pressure upon the object and therefore

114 INTRODUCTION TO PHILOSOPHY OF SCIENCE

flattens it slightly; a thermometer, unless of exactly the
same temperature as the object whose heat is to be recorded,
modifies its temperature and consequently does not indi-
cate accurately the character of the phenomenon which it
presumes to measure. Hence one is obliged to remain satis-
fied with a relative neutrality. In the second place, the
system which is made up of the event and the instrument
must itself be a relatively isolated complex. "Every good
experimenter has to compensate for all sorts of extraneous
effects that enter into his experiments — slight changes in
temperature in the room during the progress of the test,
draughts, vibration of the building, heat radiation from the
body of the experimenter himself, and so on." * Finally,
no value obtained through an operation of measurement
can be divorced from the technique used in obtaining it.
Numbers are always applied values and one should never
lose sight of the character of the application in each specific
case. This implies that in measurement acts one should recall
what he has done, and in the employment of measuring
devices one should be aware of the principles according to
which the instrument is constructed and operates.

An important problem, which may be merely mentioned
at this point, arises in the attempt to give measurement a
sound theoretical foundation. Is the meaning of any physical
concept exhausted when one has stated the techniques by
which its measured value may be ascertained? Does time
mean simply clock readings? Does space mean simply
numbers on scales? Does force mean simply readings on the
indicators of balances? More detailed examination of the
theory which is implied in an affirmative answer to these
questions will be made in connection with the analysis of
the basic concepts of the sciences in Part II. Probably the
issue can be decided only by examining completely the
techniques which are involved in the measurement of any
given event, and determining whether the methods of con-
structing and calibrating instruments, as well as the methods

1 H. Levy, Universe of Science, pp. 49-50.

DESCRIPTIVE TECHNIQUES 115

of setting them up and reading them in any given case,
properly belong in the group of measurement techniques
and hence in the definition of the concept under considera-
tion. Bavink criticizes the view that the meaning of a
physical concept can be completely described in terms of
its measured values. All such concepts, he insists, have
meaning before the ascription of numbers to their corre-
sponding objects. "The difference between two lengths of
time, or two degrees of loudness of sound, or a high and low
musical note, already forces itself upon the child and the
savage, before they have any notion of counting and meas-
uring, and pairs of concepts such as loud and soft, long and
short, bright and dark, are therefore found at every stage
of human thought. Are we then to say of a savage or a
child, that they have no concept of loudness of sound or
intensity of light, because they are not able, as is the trained
physicist, to ascribe numbers to the scale of their sensation?
This is surely going too far." 1 The fact to which Bavink
refers is frequently forgotten by those who insist that science
is aware only of pointer readings. An instrument exhibiting
pointers must be both constructed and calibrated. Unless
one knew independently of the instrument what the instru-
ment was designed to measure, it could never have been
created. Thermometers are meaningless unless one knows
what heat is; spring balances have no significance unless
one knows what force is; lie detectors are valueless unless
one knows independently of them what is meant by a lie.
A measured value is always a^ value of something, and
obtained from that something by a describable technique.

CONTROL OF SENSE ORGANS

It is important to notice that the sense organs function
in knowledge in the same general way that the physical
medium does. In fact the sense organs and nervous system
of the observer constitute a new context within which events
may be observed. Hence the eye, for example, may properly

1 Berahard Bavink, The Natural Sciences (New York: Century, 1932), p. 226.

116 INTRODUCTION TO PHILOSOPHY OF SCIENCE

be considered as a recording instrument which discloses the
appearance of the end-object in the biological medium in
much the same way that a camera reveals its manifestation
in the physical medium. In other words, the visual image
of an end-object is simply that object as it appears in the
bodily context. The same is true of all sense-data. Hence
the aim of the scientist should be, at this point, as in the
case of the physical media, to increase as much as possible
the range and variety of appearances.

That this is in accord with actual procedure, both of
common sense and of science, seems clear. One observes
the end-object in the widest possible range of contexts.
He supplements the information received through vision by
that obtained through audition, touch, smell, and taste, and
he supplements his private information by calling upon
other observers to report their findings. In this way he
multiplies the appearances of the end-object by inserting
different sense organs and different observers in the medium.

But in this control of the organism, a new motive has
emerged. This motive centers about the desire to establish,
so far as is possible, normal conditions of observation. It
is commonly recognized that the sense organs are important
sources of error. Unfortunately, however, one is not always
able to detect the presence of error. This is due mainly to
ignorance of the nature of the J5-operators. Nerve physi-
ology has not yet reached a stage of development which
permits the accurate description of the physical impulse in
its course through the organism. Thus one is in the position
of being able to read the recording instrument, but unable
to interpret its information since he knows neither the
nature of that which it was designed to record nor the prin-
ciples according to which the instrument operates. All
that he can do is to multiply the reports of the instrument,
and determine their consistency with one another. For this
reason the multiplication of appearances serves not so much
to increase information about the object as to test the
accuracy of some one bit of information about which the

DESCRIPTIVE TECHNIQUES 117

observer may be in doubt. If I am not sure as to what I
hear, I look; if I am then not sure, I touch; if I am still in
doubt, I call upon others to corroborate my judgment.
If the results are consistent, I conclude that my sense organs
are functioning normally; if they are not, I decide that
they are operating abnormally. Thus control of the physical
situation differs from control of the observer in that the
former serves to provide him with more information about
the end-object whereas the latter serves to check the accuracy
of observation.

It should be pointed out, further, that the variation in
possible appearances is much more limited when one is
concerned only with E-operators. At best man is limited
to five senses. But although practically all objects of science
manifest themselves visually, a more limited group exhibits
touch and sound properties, and very few have taste and
smell properties. Hence there is really only one type of
appearance which is important. The scientific observer,
says Eddington, "has one eye (his only sense organ) which
is color-blind. He can distinguish only two shades of light
and darkness so that the world to him is like a picture in
black and white. The sensitive part of his retina is so limited
that he can see in only one direction at a time ... we have
left the observer power to recognize that a pointer coincides
with a gradation on a scale." 1 It is somewhat doubtful
whether an observer of this kind would be able to progress
very far, even in astronomy. Certainly he would make a
poor biologist. But the important point is that significant
information about objects comes through a very limited
number of routes.

CONTROL OF STATE OF MIND

The essential problem in the control of the M-operators
is, again, that of assuring oneself that he has normal con-
ditions of awareness. Though present knowledge of the
psychological medium is even less adequate than that of

1 New Pathways in Science, p. 13.

118 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the physiological medium, nevertheless one can easily con-
vince himself of the existence of certain factors which may
be lumped under the term "state of mind" having a poten-
tially disturbing influence. His problem is either to elim-
inate these elements or to ascertain the character of the
modification which is due to them. What must be assured
is that there is no error in the location of the appearances
of the object in their proper contexts.

The first of these factors is the selective activity of atten-
tion. This can hardly be called a disturbing factor, since
only by means of it can one become clearly aware of any-
thing. Furthermore, it is not an abnormality in the sense
that it would be absent from normal observation. What
should be emphasized with reference to it is simply that it
determines isolated systems in much the same sort of way
that physical operations do. The isolation, however, is
not one which eliminates or counteracts environmental in-
fluences, as is the case with physical operations, but rather
one which neglects. The observer pays no attention to the
associated factors, and thus considers them as non-existent.
When there is a conscious recognition of this act of neglect,
the selective act of attention cannot be called disturbing.
But attention is often unconsciously selective. Frequently
one neglects environmental factors without being aware
that he is doing so. For example, one easily overlooks mis-
spelled words even when he is reading proof. It is a common
experience that one observes in any situation what he expects
to observe and fails completely to note other elements,
even when they are of great intensity. Hence the selectivity
of attention must be admitted as a potential source of error.

Second, and most important among the factors in the
control of the state of mind, are those associated with
symbolizing the data. As was indicated in Chapter III,
knowing is not merely acquaintance but description as well.
Science must not only get its data; it must endeavor to
portray them by various symbolic devices. Events are
private and transitory as they enter into awareness, and if

DESCRIPTIVE TECHNIQUES 119

they are to be used in science they must be made communi-
cable and fixed. This is accomplished by the important
device of the symbol.

The initial difficulty in discussing this problem is the
fact that direct awareness may, perhaps, never occur apart
from symbolic awareness. There is reason to believe that
merely attending to an event requires some conception as
to what the event is. A pure sense-datum probably never
occurs apart from some interpretation. It may be that one
cannot be aware of a blue object unless he knows what
blueness is, or of a round object unless he knows what cir-
cularity is, and — since one could be aware of blueness and
circularity only as symbols — the presumption would be that
a non-symbolic awareness of events could not exist. It
has already been shown that direct awareness without in-
ference is of comparatively rare occurrence. Certainly in-
ference always involves symbols, and there is probably
some truth in the statement that all symbolism involves
inference. For example, to symbolize an object as "blue'!
is to attribute to the object all of the meaning of the symbol —
its relation to wave lengths, to other shades in the color
chart, and so on. Since all of these associations are called
to mind immediately in the presence of a blue object, there
is reason to doubt whether one ever gets such a pure aware-
ness of an uninterpreted object.

However, although the two types of awareness may never
occur in isolation from one another, they do obviously
occur in distinction from one another. This is all that is
required for purposes of analysis. It is possible in some sense
to compare the symbol with the event, and thus to test its
adequacy. This act of comparison is accomplished, as has
already been seen, through a third distinct type of knowing.
What is important is merely that if the symbolic interpreta-
tion is more or less automatically applied to the event, error
can be detected only by separating the two. Practically,
this means that one's interpretations must be deliberate
and critical rather than hasty and unreflective.

120 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Granting that data may be symbolized by a more or less
deliberate act, there arise the problems as to what this
operation is and as to what form the symbols take. These
two problems may be discussed briefly in the order given.

The nature of the operation is determined by one's con-
ception of the general task of science. Does science merely
describe or does science also explain? The more detailed
analysis of these two basic notions will be given later. For
the present it may suffice to point out that in description
one endeavors to symbolize the obvious features of events,
whereas in explanation he tries to represent their less obvious
features — their causes and effects, their constituents, their
appearances under different conditions, and so on. Now
since a knowledge of the less obvious features is presumably
based on a knowledge of the more obvious, description must
precede explanation. If one adopts the positivistic point
of view that the task of science is merely to describe and
not to explain, he will insist that science has completed
its work when it has pointed out the obvious features of
events. But since, presumably, no one would maintain
that the task of science is merely to explain and not to
describe, one may conclude that the very minimum which
science can do is to symbolize the obvious features of events.
Hence science is at least description.

Description may be defined as the operation by which the
more obvious features of an event are symbolized. Gold
would be described as a hard, yellow, lustrous substance;
a robin as a bird about ten inches in length, slate-gray above
and chestnut-brown beneath; an orange as a spherical fruit,
orange in color, having a spicy smell and a sweet taste.
If the complex term in each of these cases means simply the
properties enumerated, the application of the term itself
to the event would also be description. Since description
passes imperceptibly into explanation, an enumeration of
some of the less obvious properties might be called descrip-
tion by contrast with a characterization of the highly ob-
scure features. Thus one might also describe gold as a sub-

DESCRIPTIVE TECHNIQUES 121

stance which is highly malleable, melting at 1075°, having
a specific gravity of 19.3, and so on, which would contrast
with its explanation in terms of atomic structure. Descrip-
tion may be inventive in character in case one wishes to
devise a symbol for a property not yet adequately symbol-
ized in the language system. This occurs commonly in the
naming of heavenly bodies, chemical elements and com-
pounds, scientific instruments, and animal and plant forms.
Or description may involve simply the application to the
event of a symbol which is already a part of the language
system and used to represent an event of the same kind as
that under consideration. Concepts fluctuate in meaning
by virtue of this general applicability. In the cases both of
invented and of borrowed symbols the presumption is that
the event as a whole, or certain of its apparent qualities,
has been directly observed, and that the symbolic activities
of the mind are then called into operation with a view to
constructing a representative of the event which will preserve
it in a more permanent and communicable form.

The particular form which the symbol takes will be deter-
mined by the problem. It has already been seen that there
are different types of symbol, each having its own function.
If one is interested in the vividness and accuracy of his
symbol, he will employ an icon, i.e., he will form a clear
image, or draw a picture or diagram, or construct a model.
But if one is interested rather in talking or writing about
the event he will employ the symbolism of ordinary language,
i.e., he will employ concepts or propositions.

Supposing that one has adopted linguistic symbols, he
then finds that there are at least three important descriptive
techniques. These are classifying, ordering, and correlating.
These may be called operations, since they are of essentially
the same kind as the manipulative operations in the physical
sphere. They are various things which one does to events.
But they should properly be called mental operations, since
they clearly are not operations on events in the ordinary
sense of the word, i.e., they do not transform the events

122 INTRODUCTION TO PHILOSOPHY OF SCIENCE

physically. They are ways of thinking about events, though
they are presumably based upon the characters of the
events themselves, and there are right and wrong ways of
performing them.

Classifying may be briefly described as the operation of
representing an event or its properties by a concept. The
concept may be chosen because of the general character
of the event as a whole, as when one describes a substance
as gold, or it may be chosen because of some obvious feature
of the event, as when one describes gold as yellow, lustrous,
and hard. Concepts are class-notions, having generality of
reference. A concept refers extensionally or denotatively
to the totality of events exemplifying or illustrating it.
This totality is called a class. Classes are determined
extensionally if one enumerates the members and then
searches for the concept which will describe all of them;
classes are determined intensionally if one starts with a
concept and then looks about for events exemplifying it.
When a given event is classified it is placed (mentally)
with other events exemplifying the same concept. When a
concept is available for use, classification is identification or
recognition; but when no concept in the language has pre-
cisely the required meaning, classification is the devising of
a new symbol which will prepare for future identification or
recognition. An event may lie in many classes if it has
many properties; gold, for example, lies in the class of
yellow things, of lustrous things, and of hard things.

Ordering may be described as the operation of representing
a certain specific relational property of events by a concept.
Events may be ordered if (1) they may be classified, and
(2) there exists between every two members a relation
which is (a) asymmetrical and (6) transitive. This is the
technical definition of the notion. Property (1) states that
events which are capable of order must be like one another
in some respect, usually the respect according to which
they are to be ordered. For example, all hard objects
may be put into a class, or all lengths. Property (2) states

DESCRIPTIVE TECHNIQUES 123

that events which are capable of order must bear a certain
type of relation to one another. This relation must be
(a) asymmetrical. A relation is asymmetrical when the
order of terms is significant, i.e., when an interchange of
the terms would produce a relation-complex incompatible
with the original. For example, if a substance A scratches B,
then B cannot scratch A; or if X is longer than Y, then
Y cannot be longer than X. The relation must also be
(6) transitive. A relation is transitive when, if it holds
between P and Q, and between Q and R, it then holds be-
tween P and R. A transitive relation is one which has a
carrying-over power. For example, if a substance A scratches
B, and B scratches C, then A scratches C, or if X is longer
than y, and Y is longer than Z, then X is longer than Z.
The presence of this common property and such an order-
ing relationship permits the members of the class to be
arranged into a series. Events have not only membership
in the class, but position. For example, hard objects may be
arranged in a series, beginning with A which scratches all
other members, and ending with, say K, which is capable
of being scratched by all members — all other members being
properly placed between. Also all lines may be arranged
on the basis of length. In the same way events may be
arranged according to weight, size, temperature, specific
gravity, melting point, etc. Each event capable of such
arrangement possesses a relational property by virtue of
which the ordering is possible. When this property has
been conceptualized, the event may be placed in its proper
position in the series. The placing in a series is, of course, a
mental operation, though it may take on pictorial representa-
tion as well, as in the case of museum displays.

Correlating may be described as the operation of repre-
senting the association or the connection of events. Events
have the property of occurring together, and thus uniting
into complex events. Usually the "togetherness'' implies
proximity in time and space, though remote events may be
connected by intermediate events. The presumption of any

124 INTRODUCTION TO PHILOSOPHY OF SCIENCE

association is that there is some dependence of one event
on the other. When the association is of a very close spatial
or temporal kind, there is almost always conceived a new
event which is the associative union of the two; in this
respect the correlation of events is the opposite of their
isolation, discussed earlier in the chapter. When the as-
sociation of the two events is infrequent, the dependence
of the one upon the other is slight; when it occurs often
the dependence is more pronounced; when it occurs univer-
sally the dependence is absolute. Correlation is the mental
operation by which one symbolizes the fact of connections
in nature, and symbols for such correlations, when they occur
repeatedly, are called scientific laws. If one should note
that two or three of his acquaintances who have red hair
are quick tempered, he might be led to believe that the
properties are related, though he would attach slight prob-
ability to it; if he found it to be illustrated in a much more
extended group he would begin to suspect a connection; if
he found it to be true universally he would be obliged to
express it in a universal law. (The problem has, of course,
been enormously simplified for purposes of illustration.)
There is reason to believe that the correlations which occur
in descriptive science, i.e., where one is concerned only with
the most obvious features of nature, are not universal.
That events are universally connected in nature is not one
of its apparent features, but discernible only through elab-
orate exploratory devices. Hence correlations at this stage
of study are primarily statements of frequencies.

The third factor in the control of the state of mind is
unconscious inference. Here, again, there is some doubt
as to whether this should be called a disturbing factor since
it may be present in all observation. But that it is a very
common source of error cannot be doubted. One reads into
situations and supposes to be actually present elements
which are the results of unconscious inference. A snow
scene looks cold, and velvet looks soft; a table-top which
is observed as a parallelogram is assumed to be rectangular;

DESCRIPTIVE TECHNIQUES 125

a reading on a thermometer tells one that the day is hot.
It is a common experience that one may observe as present
in a situation elements which have been suggested in advance
as likely to be present, or elements which the observer
would prefer to have present, or even elements which he
would prefer not to have present. In all of these cases the
ascertainment of the strictly given is quite impossible, for
the inferred objects are fused with it or substituted for it,
and no act of attention is able to single it out.

This inferential act is precisely that to which reference
was made in the preceding chapter in connection with the
discussion of perception. It was suggested at that point
that one's concern is not always with the immediately
given but with the appearances of the end-object in other
contexts. Such information can be gained only through an
inferential act. Now there is no danger in this inferential
act provided it is recognized as present and, consequently,
as a possible source of error. One of the essential tasks of
science, in fact, is the making and justifying of precisely
such inferences. But when the inferences are unconscious
they are important sources of error, for one supposes to
be immediately given something which is only inferentially
present. This results in a confusion of contextual realms,
and hence in an erroneous conception of the part which
P-, B-, and Af -operators play in the determination of ap-
pearances. So long as the inference is conscious, justifica-
tion is sought for it in the knowledge of the laws of operators ;
so long as it is unconscious, it enters as a 'disturbing"
factor and becomes an important source of error.

The outcome of these physical, physiological, and psy-
chological considerations is the recognition that the task
of getting and increasing data is one of great difficulty.
In addition to the problem of controlling the object itself
and the environment, the aim of which is the production
of the maximum of manifestations, there is the difficulty in
assuring oneself that what he gets through these activities
are indeed genuine data rather than aberrations of his sense

126 INTRODUCTION TO PHILOSOPHY OF SCIENCE

organs and states of mind. Such considerations serve to
show that the collection of data is hardly a preliminary
scientific technique, in the strict sense of the word. More
accurately, the accumulation and testing of data constitute
a task which is part and parcel of the scientific method it-
self. One does not start with data, for one never knows
whether his data are data until he has made a critical
analysis of them. And this very analysis involves an as-
sumption of many of the laws of science, which are them-
selves demonstrable only in terms of such data. In order
to assure oneself that he has normal conditions of observa-
tion he must use the laws of physiology and of psychology.
But these laws are themselves simply generalizations from
other data which are questionable upon similar grounds.
Hence, in order to ascertain the correctness of data one
must assume other data — which may themselves be in-
correct. This difficulty is unavoidable.

When one has obtained his data through perception;
when he has increased them by operations performed upon
the end-objects and the physical media; when he has con-
trolled observation by attention to the possible disturbing
factors in the physiological media; finally, when he has dis-
cerned the various psychological factors, such as isolational,
symbolic, and inferential acts, he has completed the so-
called preliminary operations of science. What he gets
through this series of operations is a system of symbols
presumed to have the power of representing the data which
first called them into being. This system of symbols con-
stitutes a science. The next chapter will be devoted to an
examination of such an embryonic science.

REFERENCES

Morris Cohen, Reason and Nature (New York: Harcourt, Brace,

1931), Chap. Ill, sects. I, II.
E. A. Burtt, Principles and Problems of Right Thinking (New

York: Harper, 1928), Chap. V.
J. A. Creighton, Introductory Logic (New York: Macmillan, 1922),

Chap. XIV.

DESCRIPTIVE TECHNIQUES 127

Francis Bacon, Novum Organum, Works (London: Routledge,

1905).
M. T. McClure, Logic of Reflection (New York: Holt, 1925),

Chap. V.
J. S. Mill, System of Logic (London: Longmans, Green, 7th ed.,

1868), Book III, Chap. VII; Book IV, Chaps. I, VII, VIII.
W. S. Jevons, Principles of Science (London: Macmillan, 1907),

Chaps. XVIII, XIX.
H. Levy, Universe of Science (New York: Century, 1933), Chap. II.
A. Wolf, Essentials of Scientific Method (New York: Macmillan,

1925), Chap. III.

CHAPTER VII

DESCRIPTIVE SCIENCE

Science, in the broadest sense of the word, is any body of
symbols presumed to be applicable to the realm of events.
In this definition the term " applicable ': is conveniently
obscure. The widest disagreements exist among the logicians
of science as to the precise nature of the relation which the
symbolic scheme bears to the world. The symbols may
describe'' or they may "explain"; they may be merely

conventions'* or they may be "instruments of practical
adjustment"; they may be mere " constructions ': or they
may "reveal the true nature of things." It will be the task
of the next chapter to make a critical examination of some
of these notions.

For the present, attention will be directed to a more
empirical question. There are, clearly, certain sciences
which claim to be empirical or descriptive in character;
biology, geography, sociology, economics, and psychology
are presumably such sciences. If there is any meaning in
this characterization, it seems reasonable to suppose that
such sciences as these exhibit certain features by virtue of
which they may be thus grouped together. Are there any
aspects of subject matter, or method, or symbolic reference,
or integration, by which an empirical science may be
recognized ?

An alternative approach to the same problem is indicated
by the considerations brought forward in the preceding
chapter. The initial stage of every science, as was shown,
lies in the accumulation and symbolism of data. Supposing
that these preliminary processes have been completed, is
one justified in saying that the result is science? If the term
is defined sufficiently broadly, there seems little doubt as
to the answer. Such a body of symbols is at least an em-

128

DESCRIPTIVE SCIENCE 129

bryonic science, and should reveal many of the features of
more highly developed knowledge. It may thus be worth
while to make an analysis of such a system with a view to
determining its significant features.

Furthermore, even the sciences which are characterized
as non-empirical, or rational, contain aspects which sug-
gest that they are not to be sharply divorced from the
descriptive sciences. Jevons argues that every science con-
tains facts of four different kinds. "(1) We may be ac-
quainted with facts which have not yet been brought into
accordance with any hypothesis. Such facts constitute
what is called Empirical Knowledge. (2) Another extensive
portion of our knowledge consists of facts which having
been first observed empirically, have afterwards been brought
into accordance with other facts by an hypothesis concerning
the general laws applying to them. This portion of our
knowledge may be said to be explained, reasoned or general-
ized. (3) In the third place comes the collection of facts,
minor in number, but most important as regards their sci-
entific interest, which have been anticipated by theory and
afterwards verified by experiment. (4) Lastly, there exists
knowledge which is accepted solely on the ground of theory,
and is incapable of experimental confirmation, at least with
the instrumental means in our possession." 1 If one admits,
with Jevons, that every science contains facts of the type (1),
he is obliged to conclude that it is, to that extent, empirical
or descriptive. Furthermore, if one admits that the lines
separating these four kinds of facts cannot be sharply drawn,
he is obliged to conclude that the difference between a
descriptive and a rational science is itself a relative matter.
This argues, at least, for the importance of clarifying the
distinction as much as possible.

Granting, then, that there are descriptive sciences, one
may attempt to determine their features. Such a science,
according to Jevons, is any body of symbols which is
"derived directly from the examination of detached facts,

1 Principles of Science, p. 525.

130 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and rests entirely on those facts, without corroboration
from other branches of knowledge. It is contrasted with
generalized and theoretical knowledge, which embraces many
series of facts under a few comprehensive principles, so that
each series serves to throw light upon each other series of
facts. Just as, in the map of a half-explored country, we see
detached bits of rivers, isolated mountains, and undefined
plains, not connected into any complete plan, so a new
branch of knowledge consists of groups of facts, each group
standing apart, so as not to allow us to reason from one to
another." x

Allowing this to serve as a preliminary, one may attempt
to discuss somewhat more systematically the features of
descriptive science. Since it is a body of symbols, and every
symbol has, as was shown in Chapter IV, extensional and
intensional relations, one may suggest the examination of
descriptive science from the point of view of (a) extension,
i.e., the character of its reference to events, and (b) inten-
sion, i.e., the character of the interrelations of the symbols
among themselves.

EXTENSIONAL FEATURES OF DESCRIPTIVE SCIENCE

Extensionally every descriptive science aims (1) to repre-
sent the most clearly given events, by symbolizing the more
obvious of (2) their classificatory, (3) their serial, and
(4) their correlational features. The precise meaning to be
attributed to each of these aspects is important, and warrants
a more detailed consideration.

(1) Since every descriptive science is presumably a linguis-
tic system, the representation involved in any such science
is that kind which is peculiar to word symbols. (Numbers
and other mathematical symbols may here be considered
as condensed word symbols.) No word symbol, as has al-
ready been seen, portrays its referent in any direct or pic-
torial sense. Words do not look or sound like the events to
which they refer. But they have the capacity, by virtue of

1 Ibid., p. 526.

DESCRIPTIVE SCIENCE 131

peculiar meaning properties which are attached to them, to
refer to events in a less direct way. If one knows the mean-
ing property of any word symbol, he knows in advance the
kind of event which is being referred to, though he need
not be aware of the event at the moment. The symbol
enables one to ascertain whether any event which may be
given is or is not the referent of the symbol. This selective
feature of the symbol permits it to be correlated with its
referent. Ideally there is a one-to-one correlation between
the elements of a system of symbols and the elements of a
system of events. For every event there should be one and
only one symbol, and for every symbol there should be one
and only one event. Actual language is far from ideal in
this respect. There are words which are ambiguous in
meaning, and there are diverse linguistic forms which are
practically synonymous in meaning. Descriptive science
aims to be representative only in the sense that it tries to
set up a one-to-one correlation between events and sym-
bols. Hence such a science is inadequate either if there
are clearly given events for which there are no symbols,
or if there are symbols which refer to no events or to events
ambiguously. The former inadequacy would be illustrated
by a botanical science which has not yet identified and
classified all known plant forms, and the latter by a physics
which talks about perfect levers and gases or by a chemistry
which has only one symbol to designate the various isotopes
of a substance.

The essential difficulty in determining precisely what is
meant by a descriptive science is the fact that data are
given with varying degrees of clarity and obviousness. One
of the most significant conclusions to be drawn from the
history of thought is that investigators disagree among
themselves as to what is and what is not clearly given.
The problem, what are the ultimate data for knowledge,
has never itself been satisfactorily solved. What is clearly
given for one individual may not be so for another; and
what is clearly given for an individual at one time may not

132 INTRODUCTION TO PHILOSOPHY OF SCIENCE

be so at another. One cannot draw the limits of the given,
and relegate all beyond the limits to invention and fancy.
One of the facts which seems to be given clearly is the fact
that some things are given more clearly than others, and
one of the facts which seems to be given quite obscurely
is the precise location of the line separating these two
realms. As a result it becomes impossible to say with pre-
cision what the limits of a descriptive science are. If descrip-
tive science is defined in terms of a criterion which is itself
variable, the result must be a recognition that sciences are
not properly descriptive or non-descriptive, but more or
less descriptive according as they endeavor to symbolize
the more or less obvious data.

This fact of the variability in the given may be clearly
indicated by illustrations drawn from recent and contem-
porary writers on the philosophy of science. The problem
under consideration is to determine precisely what kinds
of things the data of science are. About what, in other
words, does the scientist really talk? The question is so
simple that one would be led to expect a simple answer,
and a general agreement among investigators. But the
contrary proves to be the case. Hear the report, for example,
of an eminent scientist. "Science is in reality a classification
and analysis of the contents of the mind; and the scientific
method consists in drawing just comparisons and inferences
from the stored impresses of past sense-impressions, and
from the conceptions based upon them." x "An external
object is in general a construct — that is, a combination of
immediate with past or stored sense-impressions." 2 The
only events which are clearly given, therefore, are sense-
impressions, which are both subjective and private. All
else is inference and construction. But Planck is not satisfied
with this. It is one of the basic theorems of science, he
insists, that "there is a real outer world which exists inde-
pendently of our act of knowing." 3 This is no longer

1 Karl Pearson, Grammar of Science, p. 52. 2 Ibid., p. 41.

3 Where Is Science Going? (New York: Norton, 1932), p. 82.

DESCRIPTIVE SCIENCE 133

solipsism. According to Norman Campbell what the sci-
entist investigates is not a private world but a public one,
for "science is the study of those judgments concerning
which universal agreement can be obtained." 1 Again,
Emile Meyerson, one of the most energetic of the critics of
subjectivism in science, writes, "There can be no doubt
from the start as to the mental attitude of the physicist
who studies nature; he does not believe at all that he is
investigating merely the relations between sensations, but,
on the contrary, that he is penetrating into a mystery
which is independent of his sensation." 2 The given, there-
fore, includes not merely sense-impressions, but public and
external objects, beyond which all else is inference and
construction. But still other writers, recognizing the vari-
ability in the clarity with which objects may be given,
insist that the data of science are even more extensive.
Hypothetical entities, such as molecules and electrons, are,
according to Whitehead, natural objects. "Scientific laws,
if they are true, are statements about entities which we
obtain knowledge of as being in nature ... if the entities
to which the statements refer are not to be found in nature,
the statements about them have no relevance to any purely
natural occurrence. Thus the molecules and electrons of
scientific theory are, so far as science has correctly formu-
lated its laws, each of them factors to be found in nature." 3
Since nature consists of all those events which are given
in a definable sense, and there is a definable sense in which
molecules and electrons are given, it follows that they are
natural objects. The given, therefore, includes not merely
sense-impressions and external objects but a large number
of entities not even theoretically observable. But if the
given is sufficiently flexible to include both an extreme
solipsism and a radical realism, there seems only one con-
clusion to be drawn. The given must be a variable.

But even if one grants that science is bound to admit the

1 What Is Science? (London: Methuen, 1926), p. 27.

2 De V explication dans les sciences (Paris: Payot, 1927), p. 33.

3 Concept of Nature, pp. 45-46.

134 INTRODUCTION TO PHILOSOPHY OF SCIENCE

existence of molecules and electrons, he is not obliged at the
same time to acknowledge that it must give to these entities
the same status as observed data. Though they may be
given, they are less obviously given than sense qualities.
Hence a science which talks about hypothetical and the-
oretical entities, constructs, fictions, idealizations, and other
suppositional entities must be less rather than more descrip-
tive. This is all that need be admitted in order to establish
the existence of sciences which are predominantly descrip-
tive. A descriptive science can therefore be defined as one
which minimizes rather than maximizes the importance of
such entities. Descriptive science frankly admits that it
has no concern for considerations of this kind, since they
arise only when questions of the rationality or intelligibility
of nature are raised — questions which are foreign to the
program of empirical science. The task of descriptive sci-
ence is the complete description, classification, and organ-
ization of objects as they appear to the observer. A perfect
science is the most inclusive and the most orderly formula-
tion of the laws connecting appearances. The desire to
explain the interconnections of nature has not yet arisen,
hence there is no urge to get beneath or behind phenomena.
Descriptive physics would contain no symbols for molecules,
atoms, or electrons; instead it would describe as exactly
as possible the way in which the macroscopic, i.e., the ordi-
nary, objects of everyday experience influence and are in-
fluenced by one another. Descriptive biology would make
no mention of genes and vital forces; instead it would en-
deavor to express as accurately as possible the variations
in the behavior of organisms under different stimuli. Descrip-
tive sociology would not refer to vague social forces, minds,
and wills, but would rest content with the statistical descrip-
tion of the behavior of individuals in society. Descriptive
psychology would reduce to descriptive biology, except that
the behavior reactions would be more complex.

(2) The essential method of descriptive science is classifi-
cation. This is involved in the very notion of the Unguis tic

DESCRIPTIVE SCIENCE 135

symbol, which is the essential tool for handling data on any
level. Every linguistic symbol (except proper names and
certain applicational symbols such as "the," "a," "some,"
etc.) is either itself universal or contains elemental symbols
which are universal. Hence such symbols determine classes
of referents. In the very act of representing an event by a
symbol there has been performed an operation of classifica-
tion. If this is true, classification cannot be considered as
the peculiar feature of descriptive science; on the contrary
any science must, in so far as it employs linguistic symbols,
use classificatory techniques. What distinguishes descriptive
science from other science, therefore, must be the way in
which classification is employed. The essential feature seems
to be that emphasis is laid on specific and narrow rather than
highly abstract and inclusive classes. If one is to remain as
close as possible to the clearly given, he must avoid wide
and sweeping generalizations. High abstractions are vague
and indefinite, and classes defined by them involve an ex-
tensive anticipation of experience. For this reason descrip-
tive science, in its attitude of caution, classifies events only
in terms of those obvious features which are called to one's
attention by the fact that he observes other objects which
do not possess them. Color, sound, smell, taste, shape,
size, weight, hardness, and so on constitute the apparent
properties of events. "The usual mode in which an in-
vestigator proceeds to form a classification of a new group
of objects seems to consist in tentatively arranging them
according to their most obvious similarities. Any two ob-
jects which present a close resemblance to each other will
be joined and formed into the rudiment of a class, the defi-
nition of which will at first include all the apparent points
of resemblance. Other objects as they come to our notice
will be gradually assigned to those groups with which they
present the greatest number of points of resemblance, and
the definition of a class will often have to be altered in order
to admit them. The early chemists could hardly avoid
classing together the common metals, gold, silver, copper,

136 INTRODUCTION TO PHILOSOPHY OF SCIENCE

lead and iron, which present such conspicuous points of
similarity as regards density, metallic lustre, malleability,
etc." x

It seems to be essential to the notion of classification as
employed in empirical science that its results are considered
merely as tentative. A property which appeared to be ob-
vious may prove to be somewhat obscure on more careful
examination; superficial resemblances may hide deeper dif-
ferences, and superficial differences may hide deeper re-
semblances. Jevons goes on to point out that the early
classification of metals is soon seen to exhibit difficulties.
"Antimony, bismuth, and arsenic are distinctly metallic as
regards lustre, density, and some chemical properties, but
are wanting in malleability. ... In this way it comes to
pass that almost every classification which is proposed in
the early stages of a science will be found to break down as
the deeper similarities of the objects come to be detected." 2

The classificatory schemes found in such a science may be
called "diagnostic'' or 'indexical." They are essentially
practical in character and serve merely as techniques for
locating events conveniently. Their purpose is not to reveal
remote similarities or abstruse connections, but merely to
afford simple devices by which objects may be referred to
their proper classes, and other properties inferred. Often the
classificatory scheme is nothing more than an index or cat-
alogue by means of which one establishes a correlation
between a place where an object may be found and a certain
tag which is attached to the object, as in the case of a tele-
phone directory. Negatively, one may say that classificatory
schemes at this level of science do not exhibit hidden re-
semblances. For example, one would not expect to find
circles classified with rectilinear figures, though abstractly
they may be considered as rectilinear figures of an infinite
number of sides; nor would one expect chlorine which is a
gas, bromine which is a liquid, and iodine which is a solid
to be classified together in spite of their similarity in

1 W. S. Jevons, Principles of Science, p. 690. 2 Ibid., p. 691.

DESCRIPTIVE SCIENCE 137

chemical properties; nor would one expect to find light and
electrical phenomena to be grouped together, though modern
physics has shown that they are identical. Resemblances
such as these are revealed only in the more advanced stages
of the science, and through the application of highly com-
plicated techniques. For a purely descriptive science they
are non-existent.

(3) Similar remarks apply to the serial properties of
events. It seems safe to say that recognition of order re-
quires greater abstraction than recognition of mere simi-
larities. Hence it is likely that a purely descriptive science
will contain only a minimum of ordered groups. Such as
are found will be based on obvious properties, like size,
shape, weight, motion, color, and sound. Most of these
sense qualities exhibit apparent variations in degree and
thus may be arranged in series. Where there are no obvious
differences in degree there are relations such as that of
"betweenness" which permit the establishment of ordered
groups. For example, green is quite obviously between
blue and yellow, yellow between green and orange, orange
between yellow and red, and so on; in this way the usual
spectrum arrangement of the colors becomes possible. Sim-
ilarly, a square is clearly between a triangle and a pen-
tagon, and a pentagon between a square and a hexagon;
in this way regular rectilinear figures may be arranged in
order.

When the order of events is of a certain kind, measuring
techniques become applicable. Descriptive science does not
employ measuring operations unless it wishes to introduce
greater precision than is possible through the crude judg-
ments of sense perception. Man's unaided awareness enables
him to make relatively satisfactory judgments as to which
of two objects is larger, or heavier, or softer, or moving
faster. The techniques for such decisions are simple. Ob-
ject A is larger than object B if when the two coincide in
certain points certain other points of A extend beyond the
corresponding points of B; object L is heavier than object M

138 INTRODUCTION TO PHILOSOPHY OF SCIENCE

if the former 'pulls' more than the latter when they are
unsupported; object P is softer than object Q if a given
force makes a deeper impression on P than on Q; object X
is moving faster than object Y if they are placed in a race
and object X reaches a certain point before object Y.
Measuring techniques are essentially the continuation of
this process in the direction of greater refinement. Elaborate
measurement techniques will presumably not be found in
purely descriptive sciences, for these are often founded upon
hidden correlations, as in the case of the measurement of
heat by the expansion of a column of mercury, and in the
case of the measurement of weight by the distortion of a
coiled spring.

(4) The correlational features of descriptive science con-
stitute its most distinctive properties. "Things are correlated
(con, relata) when they are so related or bound to each other
that where the one is the other is, and where one is not the
other is not. ... In geometry the occurrence of three
equal angles in a triangle is correlated with the existence
of three equal sides; in physics gravity is correlated with
inertia; in botany exogenous growth is correlated with the
possession of two cotyledons, or the production of flowers
with that of spiral vessels." 1 But the correlations here used
for illustrative purposes are not such as are found in em-
pirical science. Descriptive science asserts not universal
laws but merely enumerative generalizations. Often these
correlations are merely statistical in character. The cau-
tious attitude which is characteristic of science at this stage
does not permit rash generalization. Laws are asserted
only over the range of examined cases. Descriptive anthro-
pology avoids extending to society as a whole customs of
monogamous marriage found only in a limited group ; biology
refuses to apply the principles of sexual generation to the
organic world as a whole on the basis of its apparent omni-
presence in the higher living forms. Correlations in descrip-
tive science are properly stated in the form of frequencies.

1 W. S. Jevons, Principles of Science, p. 681.

DESCRIPTIVE SCIENCE 139

The result is that descriptive science cannot be said to
exhibit the necessary features of the realm of events. It
affirms merely that events are occasionally or frequently
associated. That events are sometimes associated may be
ascertained with a high degree of certainty, but that they
are universally and inevitably associated cannot be estab-
lished without elaborate assumptions and complicated oper-
ational techniques. A universal law extends beyond the
actual cases examined, and therefore involves an anticipa-
tion as to the behavior of the still-unexplored. But the
notion of anticipation is essentially opposed by descriptive
science, which maintains that symbols should follow events,
not precede them. This is in line with the spirit of extreme
caution which is characteristic of descriptive science. If
events cannot be known to be necessarily related, they
should not be presumed to be so related.

INTENSIONAL FEATURES OF DESCRIPTIVE SCIENCE

Intensionally every descriptive science is (1) loosely inte-
grated, and (2) non-explanatory. Considerations of the
intensional character of science involve turning attention
away from events and toward the interrelations of the
symbols. Intension was defined in Chapter IV as the rela-
tion of a symbol to other symbols in the system. At this
point examination will be made of the internal features of
empirical science.

(1) By the loosely integrated character of descriptive
science is meant the aggregational rather than the systematic
character of the body of symbols. Loosely integrated com-
plexes are commonly characterized as collections, conglomer-
ates, or heaps, whereas highly integrated complexes are
usually called systems, or organic and organized wholes.
A pile of stones exemplifies an aggregate, while a machine
or a human organism illustrates a system. Descriptive
science resembles the former in that no concept has important
relations to other concepts, and no law is intimately con-
nected with any other law. Classificatory schemes, involving

140 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the sub- and super-ordination of classes have not been
established, and special laws have not been shown to be
cases of more highly abstract laws. Any element of the
scheme might be modified or taken from it without seriously
influencing the remaining elements; a novel feature might be
added without necessitating any changes within the body of
symbols.

The best way to describe this feature is to suggest that
the order of elements in an empirical science is that of
acquisition rather than of demonstration. The propositions
take on the order in which they have been discovered,
rather than the order in which they could be deduced.
The order of discovery, however, is more or less accidental,
and might have been otherwise; but the order of logical
deducibility is a fixed one: premise is always more basic
than conclusion. Descriptive science is quite without deduc-
tive organization; the distinction between derived and un-
derived propositions has not yet arisen. All propositions
are on the same level logically; no proposition is the ground
of another. Propositions in descriptive science merely follow
one another; they do not follow from one another. No
element of the totality, therefore, determines any other
element; the elements are independent of one another, and
the complex is an aggregate rather than a system.

An illustration of the difference between the order of the
acquisition of propositions, which is descriptive of the struc-
ture of empirical science, and the order of the deduction of
propositions, which is descriptive of the structure of rational
science, is to be found in the distinction between a scientific
biography and a scientific textbook. If a scientist were to
write his autobiography he would describe his discoveries
in the order in which they occurred to him. Chapter I
would disclose the conclusions of his early period; Chapter II
would indicate how his reflections were turned in a certain
direction by these results, and how he was led to perform
experiments of a certain kind; Chapter III might show
how these conclusions led him to modify the formulations

DESCRIPTIVE SCIENCE 141

of his early life; Chapter IV might indicate how a chance
observation led him to formulate still another theory; and
so on. The total body of propositions representing his
conclusions in the field would be contained in his biography.
But their order would not be significant of their logical
relations to one another; the propositions in Chapter II
would not be logically derivable from those in Chapter I,
though there might be a relation of psychological suggestion
between them. Contrast this with the order of propositions
in a textbook on science. Chapter I usually contains the
most general principles, both of method and of subject
matter. Chapter II, perhaps, indicates either their most
immediate deductive consequences or their most apparent
applications to phenomena of a certain kind. Succeeding
chapters show progressively how more complicated theorems
and corollaries can be deduced by the use of more compli-
cated logical techniques. As in the case of a biography, the
total body of propositions contained in the book indicates
the conclusions of the scientist in the field. But their order
is significant of their logical relations to one another. By
learning where a proposition occurs in the book one would
be able to conclude as to its position in the logical scheme.
The structure of descriptive science, if it has any structure
at all, is that of a biography, not that of a textbook. On
the other hand, the structure of rational science, as will be
shown later, is that of a textbook, not that of a biography.
An alternative formulation of the same feature of descrip-
tive science is to say that there are no highly integrating
propositions. If a system of symbols is organic, its relational
aspects must be important. But the relational aspects of a
symbolic system must themselves be expressed by symbols.
A law, for example, expresses a relation between concepts,
and a highly general law states a relation between more
specific laws. A highly integrated symbolic scheme, there-
fore, would be one which contains many necessary and
universal laws. But this is precisely the kind of symbol
which is lacking in descriptive science. The correlations

142 INTRODUCTION TO PHILOSOPHY OF SCIENCE

are merely occasional or frequent associations, and the only
laws possible are statistical. Hence the concepts interrelated
by such laws are not as determinately related to one an-
other as they would be in the case of universal laws. To
know that an event is occasionally or frequently associated
with another does not tell one as much about the event
as to know with what it is universally or inevitably associ-
ated. As a consequence, in descriptive science one can gain
no important information about a symbol by exploring its
intensional features, i.e., its relations to other symbols.
One determines what a symbol means not by definition
(intension) but by illustration (extension). In other words,
one determines the properties of an event by pointing to
the event, rather than through the indirect route of finding
some other event of known properties with which the event
in question is universally associated.

This is equivalent to asserting that in descriptive science
extension is taken as regulative over intension. Every
symbol has its meaning determined by that to which it
refers empirically, not by other symbols to which it has
relations. In the language of the traditional logic, all prop-
ositions of descriptive science are synthetic propositions, not
analytic. A synthetic proposition is one whose predicate
contains something not contained in the subject; an analytic
proposition is one whose predicate can be obtained from
the subject by mere analysis of its meaning. The proposi-
tion, "All bodies have weight," would presumably be syn-
thetic, since its truth cannot be determined by analysis
of the subject term, i.e., by "body' one does not mean
"something possessing weight." On the other hand the
proposition, "All triangles are three-sided figures," would be
analytic, since its truth can be determined by a mere anal-
ysis of its subject term, i.e., by "triangle" one does mean
"a figure which has three sides." For a descriptive science
this distinction does not exist; all propositions are synthetic.
The truth of every proposition must be determined by an
examination of the cases to which it refers. No predicate

DESCRIPTIVE SCIENCE 143

is "contained' in a subject because there are no logical
relations of the kind which would be described in this way.
The only way to determine whether a predicate is contained
in a subject is to examine the referent of the subject and
the referent of the predicate and decide whether they have
the required relation. Since no proposition of descriptive
science is analytic, any proposition may prove to be false,
since it may assert a state of affairs which is found not to
be the case. Analytic propositions cannot be shown to be
false, since they prescribe the way in which symbols are
to be united, and no state of affairs can contradict such a
prescription. But in descriptive science no such legislative
action can be taken, for it presumes more empirical knowl-
edge than can be justified. To legislate over events supposes
that one is able to predict the behavior of events, and this
is just what descriptive science is not entitled to do. The
structure of events determines the interrelation of symbols,
the interrelation of symbols does not prescribe the structure
of events.

Still another formulation of the same feature is the as-
sertion that a descriptive science is relatively insensitive to
shocks from the outside. Any science must permit the pos-
sibility of its own falsity; new discoveries may at any time
require the revision of an established science. Descriptive
science is especially favored in this respect. Being loosely
integrated, its symbolic scheme permits a change at any
one point without necessitating a change at another. Hence
the discovery that any proposition is false requires only
the substitution of a true proposition for the false one, but
no modification in other propositions. On the other hand,
the discovery of a false proposition in a highly integrated
science constitutes a crisis, for the proposition is both de-
termined by and determinative of other propositions, and
the substitution of an alternative proposition requires a
revision of all related propositions. It is not to be expected
today that any discovery, say, in biological or sociological
science would constitute a crisis for these sciences; the

144 INTRODUCTION TO PHILOSOPHY OF SCIENCE

sciences themselves are not sufficiently integrated to neces-
sitate an important and extensive revision should such occur.
In other words, these sciences are continually adapting
themselves to important discoveries, but the changes re-
quired are of a minor character and hence are not critical
events.

(2) Descriptive science is non-explanatory. Unless this
statement is interpreted it may amount to a mere identity,
i.e., a statement that a descriptive science is descriptive.
Ordinarily the distinction between description and explana-
tion is formulated in terms of the respective questions which
they are designed to answer. Description answers the ques-
tion "How?" and explanation answers the question "Why?"
Descriptive science, then, symbolizes the way in which
events exhibit themselves and behave; explanatory science
symbolizes other events (or hidden features of the events
themselves) in terms of which this behavior is to be under-
stood. A simple formulation of the problem is to say that
explanatory science is concerned with the premises from
which the propositions of descriptive science may be deduced
as theorems. Hence when one explains he searches for
reasons, grounds, or causes, and the relation between any
such entities and the events which they explain is that of
logical implication. It follows that a descriptive science
cannot explain, for its structure is not logical. As was
pointed out, its propositions are independent of one another,
and therefore in no sense derivable from one another. Hence
descriptive science cannot answer the question "Why?"
but must confine its activity to the statement of the mere
"How?' The laws of gravitation will not state why bodies
fall, but how they fall; the principles of natural selection
will not state why organic forms develop, but how they
develop.

It follows that facts for descriptive science are simply
brute facts. One knows that they exist, but he does not
know why. Nature might have chosen to be otherwise.
Every fact in descriptive science suggests its own alternative.

DESCRIPTIVE SCIENCE 145

Water boils at 100° Centigrade, but it might just as well
have boiled at 200° or 50°; bodies attract each other ac-
cording to the inverse square law, but the inverse cube law
or some other law might have been found to hold; objects
expand when heated, but there is no reason why they
should not have contracted. Every fact is an isolated fact,
and receives nothing from other facts. Since everything
which occurs has an alternative, anything is possible in
nature. What one knows about nature does not enable
him to predict as to the character of the unexplored parts.
Science in this form has no anticipatory function. This
does not mean that nature may offer surprises; surprises
are impossible unless one has expectations, and descriptive
science justifies no expectations. It means rather that one
must take nature as he finds it, and that he must never
force laws or concepts on events. Symbols are determined
by events, not events by symbols.

Such are the features of descriptive or empirical science.
Many would deny that such disciplines are properly sciences
at all. A science, they insist, must contain hypotheses,
theories, and conjectures; it must make predictions; it must
experiment; it must attempt to get behind or beneath phe-
nomena to discover their deeper features and their essential
connections. Certainly, if one means by descriptive science
a pure descriptive science, i.e., one which makes no reference
to hypotheses, predictions, experiments, and hidden aspects
of events, there are probably no such sciences in existence.
But this fact does not destroy the value of the characteriza-
tion presented in the preceding pages. For there are sciences
which approximate to this ideal character, and which de-
velop under the impetus of techniques which are directed
to the realization of precisely such an ideal character.
Though there may be no scientists who deny the inevitabil-
ity of hypotheses, predictions, and the like in science, there
are many who feel that hypotheses should be avoided where-
ever it is possible to do so and limited to a very minimum
where it is necessary to introduce them, who feel that

146 INTRODUCTION TO PHILOSOPHY OF SCIENCE

anticipations of nature are justified only on very rare occa-
sions and only in very limited fields, who feel that experi-
ments involve artificial situations and hence mislead, and
who feel that the search for the hidden features and con-
nections of things is bound to be more or less futile and not
to be undertaken until the possibilities of their more obvious
features and connections have been completely exhausted.
If there are scientists who profess some such beliefs as
these, there are sciences which represent their approximate
embodiment. It is only in this sense that descriptive science
may be claimed to exist. The next chapter will show that
there are investigators who at least claim that this narrow
conception of science is the true one.

REFERENCES

W. S. Jevons, Principles of Science (London: Macmillan, 1927),

Chap. XXIV.
F. M. Chapman and Paul Henle, Fundamentals of Logic (New

York: Scribners, 1933), Chap. XIV.
John Dewey, How We Think (New York: Heath, 2nd ed., 1933),

Chap. XIII.
R. H. Dotterer, Philosophy by Way of the Sciences (New York:

Macmillan, 1929), Chap. X.
C. J. Keyser, Thinking about Thinking (New York: Dutton, 1926).
A. C. Renjamin, The Logical Structure of Science (London: Kegan

Paul, 1936), Chap. XII.

CHAPTER VIII

THEORIES OF SCIENTIFIC CONCEPTS

There has been lurking in the background of the discus-
sion thus far an important problem, whose consideration
can no longer be postponed. It lies at the very foundation
of the logic of science, and determines not merely one's
general theory of science, but also, at times, one's concep-
tion of the actual techniques of procedure within science
itself. This basic problem must be examined without further
delay.

All who choose to express their ideas on the question of
the logical structure of science recognize that the task of
science, at least in a very general sense, is the construction
of a system of symbols which is presumed to be representa-
tive of such portion of the realm of events as lies within
the subject matter of the particular science concerned. It
is not the purpose here to discuss the possible ambiguities
in the notion of "representation." The term may be used
at this point to include such extreme views as, on the one
hand, that of Bergson, who insists that what one gets through
science is always a system of static and discrete forms which
is quite inadequate to reveal a world which is enduring and
continuous, and, on the other, that of the pragmatists,
who argue that scientific symbols are merely instruments
of practical adjustment whose value is to be measured rather
in terms of their effectiveness than in terms of any sort of
correspondence with events.

But within this general agreement there are the widest
sorts of differences of opinion as to the way in which sci-
entific symbols are to be defined, and the roles which they
play in the systems of symbols of which they are parts.
Do scientific symbols describe or do they explain? Are
they defined by physical operations, by logical construc-

147

148 INTRODUCTION TO PHILOSOPHY OF SCIENCE

tions, or by conventions? Are such things as atoms merely
conceptual shorthand, or are they existent events? What
is the difference between such things as molecules which
presumably could exist, and perfect levers which presumably
could not exist? Such questions as these demand answer if
an adequate logic of science is to be constructed.

A satisfactory classification of the various answers to
these questions is very difficult to make, for it itself pre-
supposes a general theory of the logic of science. The
classification which is here proposed is offered merely as a
convenient method for presenting the theories which are
to be discussed in this chapter. It makes no claim to general
adequacy. The names listed in connection with each of the
positions are those of the outstanding recent and contempo-
rary representatives. The names in italics designate those
individuals whose views will be considered as illustrative of
the general positions.

A. Positivisms

1. Strict Empiricism: Mill, Mach, Pearson

2. Operationalism : Bridgman

B. Modified Positivisms (Fictionalisms)

1. Constructionalism : Russell, Hobson

2. Conventionalism: Vaihinger, Poincare

3. Logical Positivism: Schlick, Wittgenstein, Carnap

C. Realisms

Scientific Realism: Planck, Meyerson, Whitehead, Bavink

The principles underlying this table are as follows : Grant-
ing that the task of science is the construction of a system
of symbols having a certain representative value toward the
realm of events, the important problem is to determine in
just what way the system has been built up. Presumably
the simplest formulation of this task is to say that the sci-
entist confronts himself with the data, sets into operation
certain activities usually called "knowing" or "thinking,"
and ends with the required system of symbols. This formu-
lation, at any rate, indicates clearly that the symbols are

THEORIES OF SCIENTIFIC CONCEPTS 149

the end-result, and that their meanings are a function of
two factors — the data and the knowing activities. Using
S to designate any scientific symbol such as a concept or
law, D to designate the data, and 0 to designate the know-
ing operations, the dependence of the symbol upon these
two factors may be represented,

S=f(D,0).

Now the first problem is to determine the character of
this functional relation. To what extent is the meaning of the
symbol a function of the data, and to what extent is it a func-
tion of the knowing operations? Positivism insists that it is
primarily a function of the data, and only incidentally a
function of the operations; hence the operations may be
neglected or relegated to a position of unimportance. All
modified positivisms and all realisms insist that the meaning
of a symbol is at least as significantly a function of the
operations as it is of the data; hence the operations may
not be neglected. All rationalisms insist that the meaning
of a symbol is primarily a function of the operations, and
only incidentally a function of the data ; hence the data may
be neglected. It is interesting to note that theories of science
rarely take rationalistic form; they are, almost without
exception, either positivistic in the extreme or modified
form, or else realistic. Hence there will be no further occasion
to refer to rationalistic positions.

But there is another problem. Though the ascertainment
of the importance of the operation serves to differentiate
pure positivisms, on the one hand, from modified positivisms
and realisms, on the other, an additional consideration is
required to distinguish modified positivisms from realisms.
Both of these positions insist on the importance of the
operations. But whereas modified positivisms insist that the
operations are essentially inventive, and hence result in sym-
bols for entities which are not presumed to exist, realisms insist
that the operations are essentially exploratory, and hence result
in symbols for entities which are presumed to exist.

150 INTRODUCTION TO PHILOSOPHY OF SCIENCE

As a guide to the more detailed expositions which are to
follow immediately, it will be well here to indicate the gen-
eral positions of the representatives of these various views.
Pearson and Bridgman are both positivists in their insistence
upon the importance of data and the unimportance of
knowing. For Pearson science is the mere classification and
shorthand description of the data; when the more highly
imaginative activities resulting in symbols for atoms and
molecules intervene the importance of these operations is
minimized, for the resulting symbols are themselves simply
devices for classification and simplified description. Bridg-
man' s insistence on the importance of operations does not
remove him from the positivist group, for the operations
with which he is concerned are mainly physical, i.e., they
are concerned with getting the data, not with knowing them;
hence Bridgman is essentially a positivist.

Hobson, Poincare, and Carnap are all modified positivists
in their insistence that there are at least some symbols in
science whose meanings are determined in an important
sense by knowing operations, and in their conviction that
the operations are in some sense arbitrary, i.e., inventive.
Hence they all call attention to the fact that there are some
symbols in science which do not "apply' in any direct
sense to nature. For Hobson these are abstractions, obtained
through selective acts and therefore idealizations of the
data. For Poincare they are conventions, having their origin
in data but transformed so as to be in accord with certain
more or less arbitrarily set up definitions. For Carnap they
are formal propositions, having both meaning and truth
determined by the structure of the language which one
employs to symbolize them — a language which is, in fact,
simply the result of certain agreed-upon rules for the use of
symbols.

Bavink is a realist. He insists both upon the importance
of the knowing operations, and upon the necessity for sup-
posing that atoms and molecules are existent entities, not
different in kind from stones and trees. "Our knowledge

THEORIES OF SCIENTIFIC CONCEPTS 151

of reality is not a conceptual structure, forever suspended
over things, and based solely on conventions and definitions
created for the purpose of thought economy; it offers us a
picture of reality, that is of an objective body of facts
already existing before all knowledge; a picture which is
continually becoming more and more adequate." *

In the discussion which follows, no attempt will be made
to criticize the various theories presented. The positions
are examined merely for the purpose of illustrating some
of the main views as to the status of scientific concepts.
For the more detailed understanding of the theories the
reader is advised to turn to the authors themselves, whose
main works are listed at the end of the chapter.

STRICT EMPIRICISM

In the light of the discussion in the preceding chapter,
positivism may be easily explained. It maintains that the
complete task of science is description; hence, descriptive
science represents science in its maturity. Description rep-
resents not the beginning stage of science, but the final
stage; science never goes beyond description. The position
indicated in the table as "strict empiricism" represents the
most rigid adherence to the positivistic thesis, and it will be
examined first.

The task of science, argues Pearson, "consists in the
careful and often laborious classification of facts, in the
comparison of their relationships and sequences, and finally
in the discovery by the aid of, the disciplined imagination
of a brief statement or formula, which in a few words resumes
a wide range of facts. Such a formula ... is termed a
scientific law. The object served by the discovery of such
laws is the economy of thought." 2 "The man who classifies
facts of any kind whatever, who sees their mutual relation
and describes their sequences, is applying the scientific
method and is a man of science. . . . When every fact,
every present or past phenomenon of the universe, every

1 The Natural Sciences, p. 246. 2 Grammar of Science, pp. 77-78.

152 INTRODUCTION TO PHILOSOPHY OF SCIENCE

phase of present or past life therein, has been examined,
classified, and coordinated with the rest, then the mission
of science will be completed." l The essential instrument
in this task is the concept, by which thought classifies im-
pressions, "analyses or simplifies their characteristics, and
forms general notions of properties and modes." 2 For
example, the concept of an object is simply a convenient
shorthand device for associating present sense-impressions
with stored or memory impressions. All of science, in fact,
is inspired by this spirit of economy. It is searching a brief
description, a mental resume of the universe. Pearson
quotes with approval Kirchhoff's definition of mechanics:
"Mechanics is the science of motion; we define as its object
the complete description in the simplest possible manner of
such motions as occur in nature." 3

But what can be said about such things as atoms, mole-
cules, geometrical surfaces, particles, and absolute rigidity?
Science contains symbols for such entities, and every logic
of science must account for them. Pearson's answer is clear.
In the process of constructing concepts to express in sim-
plified form the relationships and sequences of phenomena
"we often analyse the material of sense-impressions into
elements which are not themselves capable of forming dis-
tinct sense-impressions; we reach conceptions which are not
capable of direct verification by the senses; that is to say,
we can never, or at least we cannot at present, assert that
the elements have objective reality. Thus physicists reduce
the groups of sense-impressions which we term material
substances to the elements molecule and atom, and discuss
the motion of these elements, which have never been, and
perhaps never can become, direct sense-impressions. No
physicist ever saw or felt an individual atom." 4 Hence
there is no doubt that there are at least symbols of this kind
in science.

But what is their function? Here, again, Pearson is quite
clear. They do not explain, for in science there is no ex-

1 Ibid., pp. 12-13. 2 Ibid., p. 46. 3 Ibid., p. 115. * Ibid., p. 95.

THEORIES OF SCIENTIFIC CONCEPTS 153

planation. "The law of gravitation is a brief description of
how every particle of matter in the universe is altering its
motion with reference to every other particle. It does not
tell us why particles thus move; it does not tell us why the
earth describes a certain curve around the sun. . . . Such
laws simply describe, they never explain the routine of our
perceptions." 1 Even in causal and mechanistic explanations
the necessity "is no categorical must, it is the descriptive
how of the formula, the mere summary of what has been
observed, the inexplicable routine." 2 "For science, cause,
as originating or enforcing a particular sequence of percep-
tions is meaningless — we have no experience of anything
which originates or enforces something else. Cause, how-
ever, used to mark a stage in a routine, is a clear and valu-
able conception, which throws the idea of cause entirely
into the field of sense-impressions, into the sphere where
we can reason and can reach knowledge." 3

The function of such concepts in science is therefore not
to explain but to describe. "Atom and molecule are intel-
lectual conceptions by the aid of which physicists classify
phenomena and formulate the relationships of their se-
quences." 4 "The fundamental conceptions of geometry
are only ideal symbols which enable us to form an approx-
imate, but in no sense absolute, analysis of our sense-
impressions. They are the scientific shorthand by which
we describe, classify, and formulate the characteristics of
that mode of perception which we term perceptual space." 5
It seems safe to say that by such concepts as these we mean
simply the sense-impressions which they serve to classify.
Hence the imaginative operations which call such symbols
into being prove to be nothing more than techniques of
classification.

It follows that we must not ascribe to symbols which are
merely simplifying devices any phenomenal existence other
than that of the sense-impressions which they classify. ' To

1 Ibid., p. 99. 3 Ibid., pp. 128-129. 5 Ibid., pp. 198-199.

2 Ibid., pp. 126-127. 4 Ibid., p. 95.

154 INTRODUCTION TO PHILOSOPHY OF SCIENCE

no concept, however invaluable it may be as a means of describ-
ing the routine of perceptions, ought phenomenal existence to
be ascribed until its perceptual equivalent has been actually
disclosed" 1 'Science takes the universe of perceptions as
it finds it, and endeavors briefly to describe it. It asserts
no perceptual reality for its own shorthand." 2

Such a position is definitely positivistic. It defines clearly
the realm about which the scientist is permitted to talk —
the realm of sense-impressions. These alone can be said to
be given clearly. The task of science with reference to these
entities is that of mere classification, ordering, and cor-
relating. Any symbols which presume to refer to entities
not directly observable must be recognized for what they
are, viz., merely devices for classification, ordering, and
correlating. Science does not explain, but describes.

OPERATIONALISM

A somewhat more recent form of positivism is that of
P. W. Bridgman. This physicist's starting-point is the
recognition of two facts: the presence of discontinuities in
the realm of experience, and the necessity for a pure empiri-
cism. "The first lesson of our recent experience with rela-
tivity is merely an intensification and emphasis of the les-
son which all past experience has also taught, namely,
that when experiment is pushed into new domains, we must
be prepared for new facts, of an entirely different character
from those of our former experience." 3 We must not be
surprised, therefore, if we find that the concepts defined in
terms of the " middle-sized' objects of ordinary experience
fail of application, or become meaningless when extended
to the range of cosmic phenomena on the one hand, or to
microscopic phenomena on the other. "As we approach
the experimentally attainable limit, concepts lose their indi-
viduality, fuse together, and become fewer in number." 4
Heat, for example, does not apply to molecules, nor do space

1 Ibid., p. 277 (italics are the author's). 2 Ibid., p. 208.

3 Logic of Modern Physics (New York: Macmillan, 1927), p. 2. * Ibid., p. 24.

THEORIES OF SCIENTIFIC CONCEPTS 155

and time and the laws of gravitation apply to small bodies;
electrical laws and the principles for the ascertainment of
length through the application of meter sticks do not fit
when the phenomena are cosmical. But since progress in
physics consists in the gradual expansion of the known into
the realm of border-line events, we must expect that our
conceptual schemes will be subjected to shocks of varying
degrees of intensity, to the extent to which we have not
modified them in favor of the probable novelties which they
will be called upon to explain.

The second fact to be recognized is the necessity for an
empirical attitude in physics. The physicist "recognizes
no a priori principles which determine or limit the possibil-
ities of new experience. Experience is determined only by
experience. This practically means that we must give up
the demand that all nature be embraced in any formula,
either simple or complicated." 1 And it also means that
concepts, which are the sole instrument for exploring ex-
perience, should themselves be empirically defined. "Con-
cepts can be defined only in the range of actual experiment,
and are undefined and meaningless in regions as yet un-
touched by experiment. It follows that strictly speaking
we cannot make statements at all about regions as yet un-
touched, and that when we do make such statements, as
we inevitably shall, we are making a conventionalized extra-
polation, of the looseness of which we must be fully con-
scious, and the justification of which is in the experiment
of the future." 2

The safest procedure, in the face of such a situation, is
to adopt an operational theory for the definition of concepts.
Concepts must be defined in terms of the processes by
which the objects in question are found. "We may illus-
trate by considering the concept of length: what do we
mean by the length of an object? We evidently know what
we mean by length if we can tell what the length of any
and every object is, and for the physicist nothing more is

1 Ibid., p. 3. 2 Ibid., p. 7.

156 INTRODUCTION TO PHILOSOPHY OF SCIENCE

required. To find the length of an object, we have to per-
form certain physical operations. The concept of length is
therefore fixed when the operations by which length is
measured are fixed: that is, the concept of length involves
as much as and nothing more than the set of operations by
which length is determined. In general, we mean by any
concept nothing more than a set of operations; the concept
is synonymous with the corresponding set of operations." l
Bridgman illustrates further by pointing out that the word
"length' means something different according as it meas-
ures a concrete object such as a house, a moving street car,
a very large object (for which a theodolite is required), the
distance from the earth to the moon, and the distance
between the planes of atoms in a certain crystal. Nothing
but confusion can result if we suppose that "length' in
each of these cases means the same thing, for the operations
employed in each case are different, and the operations
employed in one realm are in general meaningless if applied
in another.

The result is that "if we deal with phenomena outside
the domain in which we originally defined our concepts, we
may find physical hindrances to performing the operations
of the original definition, so that the original operations
have to be replaced by others; . . . but we must recognize
in principle that in changing the operations we have really
changed the concept, and that to use the same name for
these different concepts over the entire range is dictated
only by considerations of convenience, which may sometimes
prove to have been purchased at too high a price in terms
of unambiguity." 2 Our procedure, when we find ourselves
confronted with a new range of phenomena, should be
somewhat as follows: We should "start by applying the
older concept until it got us into trouble; after it had got us
into trouble often enough we would begin to find some sort
of regularity in the way in which the trouble occurred, just
exactly like the rat trying to get out of a maze and running

1 Ibid., p. 5 (italics are the author's). 2 Ibid., p. 23.

THEORIES OF SCIENTIFIC CONCEPTS 157

his nose into the end of a blank passage, and we would then
formulate a set of verbal rules, instructing us at a certain
stage of operations to switch our procedure and begin oper-
ating in a new way which we had found appropriate by the
method of trial and error." 1

The position here defined is clearly positivistic. It insists
that concepts be defined in terms of data which are them-
selves operationally determined, and that the mind proceed
very cautiously when it attempts to explore the realm of
less clearly given objects. "Since our concepts are con-
structed of operations, all our knowledge must inescapably
be relative to the operations selected." 2 Hence we cannot
impose a concept defined in one realm upon another; this
expresses the attitude of caution which is characteristic of
positivism. Furthermore, a large number of our so-called
concepts prove to be pseudo-concepts because they are,
strictly speaking, meaningless. 'If a specific question has
meaning, it must be possible to find operations by which
an answer may be given to it. It will be found in many
cases that the operations cannot exist, and the question there-
fore had no meaning. For instance, it means nothing to ask
whether a star is at rest or not." 3

Both Pearson and Bridgman, therefore, insist upon the
basic importance of data. For Pearson the data are merely
given; for Bridgman they must often be produced opera-
tionally, and, having been so obtained, take on their opera-
tional origin as part of their content. For both writers,
symbols are simply classificatory and descriptive. Pearson
insists upon this fact even in connection with such apparently
remote notions as atoms; Bridgman argues that concepts
must be kept empirical by defining them in terms of their
proper range of application, and by re-defining them in
case they are to be applied to novel spheres. It seems safe
to characterize both positions as positivisms, though one
must admit that Bridgman' s variety is somewhat less nar-

1 Nature of Physical Theory (Princeton: Princeton University, 1936), p. 28.

2 Logic of Modern Physics, p. 25. 3 Ibid., p. 28.

158 INTRODUCTION TO PHILOSOPHY OF SCIENCE

rowly conceived than Pearson's. For this reason Bridgman's
position offers a convenient transition to the consideration
of the modified positivisms or fictionalisms.

CONSTRUCTIONALISM

The term " constructionalism ' has been employed in the
table to characterize, perhaps not very aptly, a large num-
ber of theories which are not sharply differentiated from
positivism of the type exhibited by Pearson. The common
feature of such positions is the more or less conscious recog-
nition that "knowing makes a difference." They are dis-
tinguished from the more "pure'' positivisms in their
insistence that the knower has something more to do in sci-
ence than to record in shorthand the succession of sense-
impressions. They recognize that the knower is unavoidably
active, and in his very attempt to record introduces in
spite of himself changes of a significant character. They
maintain, therefore, that representation usually involves
construction — a term which may be here used to describe a
variety of mental acts such as abstraction, idealization,
serial extension, and association. The presumption is that
these operations are all of a more significant character
than mere classification and description, hence the task of
science cannot be formulated merely in terms of these
latter processes.

Though E. W. Hobson considers himself to have adopted
a position similar to that of Pearson, there are outstanding
differences. Most important of these is Hobson's insistence
that the mental operations employed in building up a con-
ceptual scheme involve more than classification. These
operations are variously described as "constructive," "ab-
stractive," "synthetic," "selective," and "idealizing." Laws
are not discovered, but constructed. "The discovery, or
rather construction, of a scientific law involves that syn-
thetic activity of thought which manifests itself in a con-
structive process in which actual percepts are employed
only as the raw material and starting point of the mental

THEORIES OF SCIENTIFIC CONCEPTS 159

process." * Certain concepts of science have no direct
perceptual counterparts; "they are formed by an effort of
constructive imagination, for the purposes of the representa-
tive scheme . . . they must be regarded, at least provision-
ally, as purely ideal elements of the scheme, in fact as
auxiliaries necessary for the purpose of the formation of a
self-contained conceptual scheme which shall serve its pur-
pose of providing a sufficient mode of representation in
thought of the particular domain of physical events and
objects." 2

Hobson also differs from Pearson in his conception of the
"representative" function of a conceptual scheme. He does
not believe that science merely describes, in Pearson's lim-
ited use of that word. The possibility of setting up a con-
ceptual scheme "has actual physical experience as its essen-
tial condition, but the constructive and generalizing work
of thought is no less essential. The original function of
such a scientific theory, or conceptual scheme, is to provide
an ideal representation of some more or less restricted range
of physical phenomena as actually observed, that is of
certain sequences and regularities in percepts. But the
functions of a conceptual scheme are much wider than those
of merely describing symbolically what has actually been
observed. The scheme is applied hypothetically to predict
what will be observed in circumstances which differ in some
degree, or in some characteristics, from those in which the
experiments or observations which led up to the theory
were made. The value and the range of validity of the partic-
ular conceptual scheme have to be estimated by its actual
success in the fulfillment of this function of prediction." 3

Yet Hobson is not to be considered a realist. He disagrees
sharply with Whitehead in the latter's insistence that mole-
cules and electrons are natural objects.4 'Whatever else
they are, molecules and electrons are concepts . . . they
are concepts in scientific theories, and the only question

1 Domain of Natural Science (New York: Macmillan, 1923), p. 28.

2 Ibid., p. 32. 3 Ibid., p. 31. 4 See above, Chapter VII, p. 133.

160 INTRODUCTION TO PHILOSOPHY OF SCIENCE

about a scientific theory is . . . whether it is logically co-
herent and how far it is adequate for the purpose of repre-
sentation. . . . Natural Science postulates, as a working
hypothesis, only that the perceptual complex is such that
tracts of it are capable of conceptual description by scientific
schemes. It does not require any postulate as to detailed
systems of relations or of entities within that perceptual
complex, or within any supposed reality behind that complex,
which shall account for the fact that the working hypothesis
has proved successful." 1 It is unnecessary for the purposes
of Natural Science "to make the assumption that a single
law has a precise correspondence with a single definite set
of relations which actually subsist in nature." 2

Hobson's position can be characterized, therefore, as a
modified positivism, which insists that data are only the
raw material of knowledge. These data must be worked
over by an active mind and transformed into idealized
symbols, which are then combined into symbolic schemes.
Many elements of such schemes have lost all direct cor-
respondence with the data from which they were derived,
hence the system as a whole has no immediate representa-
tive value. It is therefore no longer descriptive, but is
considered as "applicable" in a somewhat less direct sense.
In addition to applicability it must have internal consistency,
relative simplicity, and predictive value. It is the task of
science to construct a system of symbols of this kind.

CONVENTIONALISM

Conventionalism may be described as a more extreme
constructionalism. It is distinguished from the latter in its
recognition of the increased importance of the knowing
operations. If scientific concepts are merely constructed
out of the raw material given in perception, they are still
related to it in the sense that they have been derived by
describable techniques ; abstraction and idealization are oper-
ations of transformation, but one can, by retracing the

i Ibid., p. 59. 2 Ibid., p. 26.

THEORIES OF SCIENTIFIC CONCEPTS 161

routes, recover the events which were thus operated upon;
hence there is some justification for saying that scientific
concepts still have applicability to events. But in conven-
tionalism this applicability has been more or less completely
lost. One does not, strictly speaking, derive his concepts at
all. He is tempted to say that he creates them. Yet this is
not quite true; conventionalism does not reduce to nominal-
ism. It insists that scientific symbols of this particular kind are
suggested by the data, but that they are given meaning through
elaborate mental operations. The extent and importance of
these operations are demonstrated by the fact that the symbols
thus devised can no longer be spoken of as true or false, but
must be characterized as convenient or inconvenient.

Quotations from Henri Poincare will illustrate the partic-
ular way in which he develops this position. While he admits
that there are to be found in science not only empirical
laws, i.e., descriptive generalizations, but also hypotheses in
the ordinary sense, i.e., imaginative notions which can be
verified and falsified, he nevertheless insists that the most
important kinds of symbol are those which — mistakenly
called "hypotheses" — are more properly characterized as
"disguised definitions," or "conventions." The best ex-
amples of them are to be found in the principles of geometry
and of mechanics. They are like laws in that they have
their foundation in experience, but they are different from
laws in that they are not dictated by data. "We see that
experience plays an indispensable role in the genesis of
geometry; but it would be an error thence to conclude that
geometry is, even in part, an experimental science. . . .
If it were experimental . . . geometry would be only the
study of the movements of solids; but in reality it is not
occupied with natural solids, but has for object certain ideal
solids, absolutely rigid, which are only a simplified and very
remote image of natural solids. . . . Experience guides us
in this choice without forcing it upon us." 1 In the same

1 Foundations of Science (New York: Science Press, 1921), p. 79. This is his
Science and Hypothesis, Value of Science, and Science and Method bound in a single
volume.

162 INTRODUCTION TO PHILOSOPHY OF SCIENCE

way the principles of mechanics, though suggested by ex-
perimental data, describe not these data but idealized enti-
ties, such as perfectly isolated bodies.

But if the meaning and truth of these principles are not
determined completely by data, how are they determined?
Poincare's answer is definite. They are determined by
convenience, i.e., the principles are defined in such a way as
to make them most convenient. " The axioms of geometry . . .
are conventions; our choice among all possible conventions
is guided by experimental facts; but it remains free and is
limited only by the necessity of avoiding all contradiction.
Thus it is that the postulates can remain rigorously true
even though the experimental laws which have determined
their adoption are only approximative. In other words,
the axioms of geometry . . . are merely disguised definitions ." *
The same description applies to the principles of mechanics.
They have been drawn from experimental laws but "have,
so to speak, been exalted into principles to which our mind
attributes an absolute value." 2

Unfortunately Poincare has not told us precisely what is
meant by a convention. Presumably a convenient symbol
would be one which is useful, and he tells us that a useful
science is one which enables us to foresee,3 hence it would
seem legitimate to conclude that the principles of geometry
and mechanics are convenient because they enable us to
make predictions which are later verified. If this is the proper
interpretation of Poincare, his position reduces in this respect
to Hobson's. But he would disagree with Hobson in the
claim that principles of this kind should be called true.
"It is just as unreasonable to inquire whether they are true
or false as to ask whether the metric system is true or
false." 4 Definitions are not properly true or false, they are
only convenient.

The exact nature of this transition from a law into a
principle must be exhibited if one is to understand fully

1 Ibid., p. 65 (italics are the author's). 3 Ibid., p. 324.

2 Ibid., p. 125. 4 Ibid., p. 124.

THEORIES OF SCIENTIFIC CONCEPTS 163

Poincare's position. If we have two bodies A and B, we
may formulate their relations in a law. But these relations
will be extremely complicated, hence we are led to suppose
two ideal bodies A' and B' whose ideal relations will be
described by the principles of geometry. 'The relation
between A and B was a rough law, and was broken up;
we now have two laws which express the relations of A
and A', of B and B\ and a principle which expresses that
of A' and B'" l But the principle is absolutely true in the
intensional sense, because it has been made so by definition,
i.e., we define A' and B' in such a way as to make the prin-
ciple necessarily true. But the principle cannot be true in
the empirical or extensional sense, for it is not applicable
to anything empirical. Hence we describe it as con-
venient.

The net result of Poincare's view is somewhat as follows:
There are to be found in science symbols of a peculiar sort
called "conventions." These are not merely classificatory
in Pearson's sense, nor are they simply abstractions in
Hobson's sense. On the contrary, they are derived by elab-
orately creative processes which free them almost completely
from the data. Thus, in contrast with strict positivism,
the symbols have their meanings determined primarily by
the knowing operations and only incidentally by the data.
The creative operations, however, are performed with a
definite end in view; the symbols thus produced must be
convenient for science as a whole, i.e., they must be such
as to permit valid predictions. Hence the symbols — which
are at this stage essentially "empty" of meaning — are oper-
ationally defined in such a way as to make the predictions
possible. The creative knowing processes are precisely these
operational definitions. The symbols, once defined in this
way, cease to be true or false in the empirical sense, and
become only convenient. " The scientific fact [the convention]
is only the crude fact [the data] translated into a convenient
language ." 2

1 Ibid., p. 336. 2 Ibid., p. 330.

164 INTRODUCTION TO PHILOSOPHY OF SCIENCE

LOGICAL POSITIVISM

The placing of logical positivism 1 in the context of con-
ventionalism and construct ionalism may strike one as some-
what unusual. Yet there is an important sense, it seems,
in which this position has close affiliations with these mod-
ified positivisms. It certainly is positivistic in its high esteem
for Mach, in its insistence that every statement of science
"should be based on and reducible to statements of empirical
observations," 2 and in its definite rejection of the a priori.
But it cannot be a strict positivism for it recognizes the
existence of certain types of statement which play a part in
science and yet are not empirically verifiable. One thinks
immediately of Hobson's idealizations in this connection,
until he is told that these statements are incapable of truth
or falsity in the ordinary sense of the term, and hence cannot
be mere idealizations of the data. One then suspects that
they are simply Poincare's conventions; but this proves
also to be an erroneous interpretation, for they are strictly
without content or meaning — purely formal statements
which say nothing and therefore could not be even con-
venient or inconvenient. Hence they are symbols which
have so completely lost their reference to data that the lat-
ter do not function at all in the determination of the char-
acter of the symbols. Are the symbols, then, purely arbi-
trary? No, they are subject to the rules of language —
rules according to which one constructs complex symbols
out of simple symbols, and translates symbols into other
symbols. But if language itself is merely a device which
one employs when he knows — an operator, so to speak —
then the purely formal symbols of the logical positivists are
descriptive of this device. They are symbols which de-
scribe the operations of knowing rather than the data
known. They are the values which & takes in the formula
aS =f(D,0), when D becomes zero and 0 becomes the

1 See Chapter I, pp. 11-13.

2 R. Carnap, The Unity of Science (London: Kegan Paul, 1934), p. 27.

THEORIES OF SCIENTIFIC CONCEPTS 165

complex body of operations associated with the invention
and use of language.

The justification for this interpretation of logical pos-
itivism may be found in the writings of Carnap. Attention
must be called, first, to the more positivistic aspects of his
system. 'Science is a system of statements based on direct
experience, and controlled by experimental verification. . . .
Verification is based upon 'protocol statements,' a term . . .
understood to include statements belonging to the basic
protocol or direct record of a scientist's (say a physicist's or
a psychologist's) experience. Implied in this notion is a
simplification of actual scientific procedure as if all experi-
ences, perceptions, and feelings, thoughts, etc., in everyday
life as well as in the laboratory, were first recorded in writ-
ing as ' protocol ' to provide the raw material for a subsequent
organization." x A protocol statement would therefore de-
scribe what Pearson called sense-impressions, and what we
have called in the course of this discussion the most clearly
given data. Statements in the scientific language which
are not protocol statements, can, in general, be verified by
the technique of deducing from them statements which are
protocol. This is the indirect method of verification which,
for Hobson, constitutes the test of the applicability of
idealizations and abstractions.

But science, in the broadest sense of the word, contains
more than this. "Scientific research may be concerned with
the empirical content of theorems, by experiment, observa-
tion, by the classification and. organization of empirical
material; or again it may be concerned with establishing
the form of scientific statements, either without regard for
content (formal logic) or else with a view to establishing
logical connections between certain specific concepts." 2 Ev-
ery scientific statement, in other words, may be considered
either in its 'material' mode, i.e., as asserting about
"objects," and "states of affairs," or in its "formal" mode,
i.e., as referring only to linguistic forms. To logic and

1 Ibid., pp. 42-43. 2 Ibid., p. 33.

166 INTRODUCTION TO PHILOSOPHY OF SCIENCE

mathematics are assigned the analysis of the "formal"
mode of statements. Such statements "are tautologies,
analytic propositions, certified on account of their form
alone. They have no content, that is to say, assert nothing
as to the occurrence or non-occurrence of some state of
affairs. If to the statement: ' The (thing) A is black' we add
'or A is blue1 the supplemented statement still conveys
some information though less than at first. If, however, we
replace the supplementary phrase previously chosen by ' or A
is not black' the compound statement no longer conveys
any information at all. It is a tautology, i.e., is verified
by all circumstances." 1

But to consider a proposition formally is to consider it
linguistically . ' We will call ' formal ' such considerations or
assertions concerning a linguistic expression as are without
any reference to sense or meaning." 2 By a language is
meant the "system of the rules of speaking. Such a language-
system consists of two kinds of rules, which we will call
formation rules and transformation rules. The formation
rules of a certain language-system S determine how sentences
of the system S can be constructed out of the different kinds
of symbols." 3 "The transformation rules . . . determine
how given sentences may be transformed into others; in other
words: how from given sentences we may infer others." 4
"Given any language-system, or set of formation rules and
transformation rules, among the sentences of this language
there will be true and false sentences. But we cannot define
the terms 'true' and 'false' in syntax, because whether a
given sentence is true or false will generally depend not
only upon the syntactical form of the sentence, but also
upon experience; that is to say, upon something extra-
linguistic." 5 Formal propositions, however, are true or
false simply by virtue of the rules of language.

These statements seem to justify an interpretation of
Carnap's position which affiliates him rather closely with

1 Ibid., pp. 33-34.

2 R. Carnap, Philosophy and Logical Syntax (London: Kegan Paul, 1935), p. 39.

3 Ibid., p. 41. * Ibid., p. 43. 6 Ibid., p. 48.

THEORIES OF SCIENTIFIC CONCEPTS 167

the more traditional positivists such as Hobson and Pearson.
Carnap's formal sentences are those types of symbols which
are determined simply linguistically. But language itself is
simply a technique of knowing, a set of rules formulated
and agreed upon by which symbolic devices may be con-
structed and transformed. Hence one may say that formal
symbols are such that their meaning and truth — in the only
sense in which they can be said to have meaning and truth —
are determined rather by the methods of knowing, i.e., the
operations, than by that which is known, i.e., the data. They
have no content — except linguistic content. They do not
therefore make assertions — except about the linguistic tech-
niques which are employed in all knowing. It seems safe
to say, therefore, that Carnap's position represents an ex-
treme in the class of what were characterized at the begin-
ning of the chapter as "modified positivisms." In his case,
however, the symbols which are not directly descriptive
cease to be even indirectly descriptive; they are exhaustively
determined by the knowing operations concerned with the
formation of symbols, and not determined at all by data.

SCIENTIFIC REALISM *

Common to all positivisms, both of the strict type and of
the modified type, is the attitude which Bavink calls 'hy-
potheseophobia." For the purer forms of positivism this
attitude expresses itself in a definite rejection of hypothetical
and theoretical entities of all kinds except in so far as they
serve merely as classificatory concepts. Mach expresses
the hope that atoms will finally disappear from the theory
of heat. Modified positivism admits such entities, but
somewhat reluctantly; it insists that they have only a con-
ceptual status and are therefore to be called constructs,
conventions, and fictions. Characteristic among such beliefs
is that of Vaihinger, who insists that the proper attitude
of the scientist is one of "as if"; atoms do not exist, but
nature behaves just "as if" they did.

1 This is not, of course, to be confused with "scientific realism" as a theory of
perception, developed in Chapter V.

168 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Scientific realism insists that this view is not plausible.
The words of Bavink indicate clearly the attitude of the
realist. "The truth which we state in opposition to this
excessive criticism of hypotheses is this, that precisely those
elements of the 'explanatory hypothesis' found by hypo-
thetical and speculative means form the truest and most
valuable contributions to knowledge made by science. Far
from being mere aids to work, pictures, models or the like,
they are in truth the most important matter, and contain
exactly that around which the whole of investigation turns." 1
"Atoms are just as real things as cannon balls or grains of
sand, as waves on water or mountains" 2 Reasons can be
given "which have forced present day physics and chemistry
to recognize the real existence of atoms and molecules as an
undoubted fact." 3 "The whole question of the physics of
today turns about the question: What is the atom? No
one asks any longer: in what respects do things behave
'as if they consisted of atoms?" 4

Bavink develops his position by pointing out two im-
portant kinds of theories. First there are those which may
be called "elaborative." 'Their characteristic is that they
contain practically no hypothetical elements; the funda-
mental assumptions in them . . . are themselves data of
experience. ... If the word theory is understood as the
logical arrangement of a large number of single laws to
form a closed system of reasons and consequences, these
examples from physics are without doubt patterns for such
theories. Even philosophers who are not positivists will
have no objection to make to this statement." 5 But there
is another class of theories called "explanatory," and il-
lustrated by the atomic theory. 'The characteristic of this
kind of theory is that the desired logical connection and
unification of the facts is only reached on the basis of a
speculative assumption, which is described as the hypothesis
upon which the theory is based." 6 "A physical hypothesis

1 The Natural Sciences, p. 38.

2 Ibid., p. 29.

3 Ibid., p. 19.

* Ibid., pp. 37-38.

5 Ibid., p. 34.

6 Ibid., p. 34.

THEORIES OF SCIENTIFIC CONCEPTS 169

is the presumption of the existence of a general state of affairs,
lying at the back of certain phenomena which are matters of
experience, and allowing the phenomena in the field of facts
in question to be deduced qualitatively and quantitatively (math-
ematically) from the presence of the said state of affairs and
its assumed laws." l This is "a supposition which was
arrived at by purely speculative methods,"2 but it requires
the physicist to admit that "molecules and light waves,
fields and their tensors, have just the same kind of reality
as stones and trees, plant cells or fixed stars." 3

Some of Bavink's statements lead one to believe that he
would insist on this realistic attitude not only toward
hypotheses but also toward all idealizations and even to-
ward concepts themselves. In his criticism of convention-
alism, for example, he argues that idealizations cannot be
the result of arbitrary acts of mind, for "both the matter
and the manner of neglect is completely dictated to us by
the object; . . . the world is so constructed, that it can be
known, by means of rational concepts, in rational judgments
(laws) of increasing approximation, and it prescribes the path
of these approximations to our understanding" 4 "Even
concepts such as plant and animal, or oak or beech, have
not been put into nature by us or invented in order to make
it more easy for us to grasp; they are forced upon us by an
objective something that was there long before men with
power of conceptual thought existed." 5

Such quotations as these indicate the legitimacy of as-
serting— as was suggested early in the chapter — that for
realists the knowing operations are operations of discovery
or of exploration rather than of construction or invention.
When we look at cells through a microscope "we do not
see the cells directly in the literal sense. However, no one
seriously doubts that the picture seen in the microscope is
in general similar to reality, and even geometrically similar,
if we leave distortion out of account, which itself can be
exactly calculated. ... In principle, Rutherford is doing

1 Ibid., p. 42. 2 Ibid., p. 35. 3 Ibid., p. 243. 4 Ibid., p. 233. 6 Ibid., p. 234.

170 INTRODUCTION TO PHILOSOPHY OF SCIENCE

no more than this when he interposes between the flying
atom and the eye a somewhat more complicated apparatus,
consisting of an ionisation chamber together with a galva-
nometer; only in this case the way is somewhat longer. All
investigation of nature depends upon an enlargement of our
senses of this description." 1 Theories, therefore, are, like
microscopes, instruments for exploring nature; consequently,
both the mental operation required in devising and using a
theory, and the end-result of such an operation must be
properly interpreted; the operation is not one of invention
but simply one of exploration, and the result of the operation
is not a creation but simply a datum.

The contemporary scene in the philosophy of science is
characterized by more or less heated controversies between
the exponents of the various theories discussed in this chap-
ter. Of these conflicts the most sharply defined is that
between the positivists and the realists. The antagonism
between the extreme and the moderate positivists cannot
become intense, for the differences between the two positions
are essentially relative. The absence of rationalistic theories
of scientific concepts, to which reference was made earlier
in the chapter, is, perhaps, not surprising; science is so
obviously empirical in spirit and method that a rationalistic
explanation seems hardly plausible. Yet it is not altogether
untrue to say that constructionalism, conventionalism, and
logical positivism are the rationalisms of modern scientific
theory. All of these positions deny the necessity for any
conception of the a priori; yet it is significant that in these
theories the knowing operations function essentially in the
place of the a priori. The knowing operations — abstraction,
idealization, definition, linguistic invention and manipula-
tion— are not, according to the upholders of these points of
view, themselves determined by the character of the data;
they are imposed by the mind and become techniques by
which the knowing activities are fostered and developed.
They function, therefore, as something which must be given,

1 Ibid., pp. 28-29.

THEORIES OF SCIENTIFIC CONCEPTS 171

not as part of the data, but along with the data, if knowledge
as a whole is to be understood. It is not asserted that man
is born with any concepts or ideas, hence the theories are
not a priori in this sense of the phrase; but man is born with
certain capacities for abstracting, idealizing, defining, and
inventing and manipulating symbols. These capacities are
not part of the data, but part of the knower, and they
contribute to the final form of knowledge in much the way
that the traditional a priori did. This is not, of course, a
condemnation of the positions; it is merely an attempt to
throw them in their proper light.

It was the task of this chapter to show, not only that a
strict positivism is possible, but that there are alternative
theories of science. All of these theories insist upon the
necessity for going beyond obviously given data. Whether
the movement is considered to be a matter of invention or
a matter of discovery is of no importance here. What
must be emphasized is that if science does go beyond
data, it must do so by means of some sort of technique.
The next chapter will attempt to determine what this
technique is.

REFERENCES

Positivism:

E. Mach, Analysis of Sensations (Chicago: Open Court, 1914).
K. Pearson, Grammar of Science (New York: Macmillan, 1911).
J. S. Mill, System of Logic (London: Longmans, Green, 7th ed.,

1868).
P. W. Bridgman, Logic of Modern Physics (New York: Macmillan,

1927).
Nature of Physical Theory (Princeton: Princeton University,

1936).

Modified Positivism:

Bertrand Russell, Our Knowledge of the External World (Chicago:

Open Court, 1915).
E. W. Hobson, Domain of Natural Science (New York: Macmillan,

1923).
Henri Poincare, Foundations of Science (New York: Science Press,

1921).

172 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Hans Vaihinger, Philosophy of 'As If' (New York: Harcourt,

Brace, 1925).
L. Wittgenstein, Tradatus Logico-Philosophicus (New York:

Harcourt, Brace, 1932).
R. Carnap, Unity of Science (London: Kegan Paul, 1934).
Philosophy and Logical Syntax (London: Kegan Paul, 1935).

Realism:

B. Bavink, The Natural Sciences (New York: Century, 1932).

A. N. Whitehead, Concept of Nature (Cambridge: Cambridge Uni-
versity, 1920).

Emile Meyerson, Identity and Reality (New York: Macmillan,
1930).

CHAPTER IX

SCIENTIFIC DISCOVERY

At the very core of the logic of science lies the problem of
scientific discovery. The status of the problem today is well
indicated by its formulation as "the mystery of scientific
discovery." That the scientist makes important discoveries
and that these discoveries, in fact, constitute the essential
motivating factor in the scientific method are truths which
are well recognized. But the conditions of the occurrence of
the act, the "rules" according to which it takes place, the
factors in the scientific personality which are responsible
for it — all of these are either recognized to be insoluble
problems or else explained by reduction to something equally
mysterious, viz., scientific genius.

Certain refinements in the formulation of the problem
may help to place it in the proper perspective. In the first
place, the discovery which is usually referred to in this con-
nection is of hypotheses rather than of data. This is not to
say that the scientist does not discover facts. But the dis-
covery of facts occurs in science in two important ways —
prior to the formulation of hypotheses, and after such
formulation. In the former type, the discovery is primarily
due to the data rather than to the scientist; the data impress
themselves upon his attention because of their obviousness,
or because of their intensity, or because of their unusual
character, or because of some other more or less accidental
factor. But in the latter type, the data are discovered
through the instrumentality of the theory; because the
scientist has, through freely creative activities of the imagi-
nation, devised a theory having certain definitely predictable
consequences, he is able to anticipate what nature will
reveal in certain definitely specified localities. He then
turns his observation to these areas and discovers what

173

174 INTRODUCTION TO PHILOSOPHY OF SCIENCE

occurs. But the data thus discovered might have remained
unknown had it not been for the directed attention; hence
their discovery is a result of the theoretical activity of the
scientist. For this reason the real problem in this connection
centers about the discovery of the hypothetical and theoret-
ical notions which are to serve as the guiding factors in
observation. The mystery in science is not how one dis-
covers facts which are obvious, but how one discovers
theories which in turn enable him to discover facts which
are not obvious.

In the second place, for the descriptive view of science
there is no problem of scientific discovery. Hence the in-
troduction of this chapter into the discussion implies that
science is not merely positivistic. The reason for this can be
seen in the considerations of the preceding chapter. For
strict positivism science does not anticipate nature through
imaginative devices; instead it merely records and classifies
what is directly given. For modified positivism science does
anticipate nature through such techniques, though it looks
upon them merely as working instruments. For realism
science definitely posits entities "behind' the data in terms
of which the latter are to be explained and through which
they are to be supplemented. Now it is, perhaps, a more or
less arbitrary question as to just where in this continuum
explanation enters; the positivists deny that they explain,
the realists insist that they explain, the modified positivists
maintain that they explain only in a carefully specifiable
sense. But it is clear that the admission of significant acts of
mind — be they concerned with the formation of constructs,
conventions, or language — involves more than mere classifi-
cation and correlation of data. Hence a recognition of the
presence of acts of mind, i.e., movements of scientific dis-
covery, is equivalent to the admission that science is more
than descriptive.

In the third place, the formulation of the problem in terms
of discovery rather than invention should not be taken as
prejudicial to the positivism-realism controversy. As was

SCIENTIFIC DISCOVERY 175

suggested in the preceding chapter, modified positivism in-
sists that hypotheses are invented, while realism maintains
that they are discovered. The essential difference seems
to be that invented entities do not exist prior to the act of
invention, and hence seem to exist only because of the act;
but discovered entities do exist prior to the act of discovery,
and hence do not seem to exist merely because of the act.
However, though this may be a genuine distinction, it is not
relevant here; so long as one confines his attention to the
mental operations by which the symbols for such entities are
called into consciousness, the question as to whether or not
anything corresponds to the symbols is unimportant. That
the invented or discovered entities exist first merely as con-
cepts would be granted by both modified positivists and
realists; differences arise only when the further question of
the existence of the referents of the concepts is raised.
Hence one may formulate the problem here, indifferently,
as the problem of scientific discovery or as the problem of
scientific invention.

ACT OF DISCOVERY

The generally creative character of the act, and its in-
timate association with the fact of imagination, have been
well recognized. " The physicist is bound, by the very nature
of the task in hand, to use his imaginative faculties at the
very first step he takes. For the first stage of his work must
be to take the results furnished by a series of experimental
measurements and try to organize these under one law.
That is to say, he must select according to a plan which
will in the first instance be hypothetical and therefore a
construction of the imagination. And when he finds that the
given results will not fit into one plan he discards it and tries
another. This means that his imaginative powers must
always be speculating on the significance of the data which
have been furnished through experimental measurements." 1
Faraday, whose researches are responsible for much of the

1 M. Planck, Where Is Science Going?, pp. 86-87.

176 INTRODUCTION TO PHILOSOPHY OF SCIENCE

modern theory of electricity, acknowledges that he "was a
very lively, imaginative person, and could believe in the
' Arabian Nights' as easily as in the 'Encyclopedia.' ' l
Tyndall's "Essay on the Scientific Use of the Imagination" 2
has become the classic exposition of this aspect of scientific
discovery.

Another feature of the act which has been called to atten-
tion is the unusual circumstances in which it seems to occur.
The history of science abounds in examples, many of them
doubtlessly spurious, illustrating the spontaneity of the
flash of insight: Archimedes discovering the principle of
specific gravity while bathing; Newton discovering the
principle of gravitation on seeing an apple fall from a tree;
Watt discovering the principle of the steam engine while
watching the tea kettle on the stove; Poincare discovering
the fuchsian functions while boarding an omnibus; Gauss
discovering the law of induction at 7 o'clock one morning
before arising; and so on. Hamilton's formulation of his dis-
covery of the Quaternions may well be quoted as descriptive
of a typical act of this kind. He says of these important
mathematical concepts, "They started into life, or light,
full-grown, on the 16th of October, 1843, as I was walking
with Lady Hamilton to Dublin, and came up to Brougham
Bridge. That is to say, I then and there felt the galvanic
circuit of thought closed, and the sparks which fell from it
were the fundamental equations between I, J, K; exactly such
as I have used them ever since. I pulled out, on the spot, a
pocket-book, which still exists, and made an entry, on which,
at the very moment, I felt that it might be worth my while to
expend the labours of at least ten (or it might be fifteen)
years to come. But then it is fair to say that this was because
I felt a problem to have been at that moment solved, an in-
tellectual want relieved, which had haunted me for at least
fifteen years before." 3

1 J. H. Gladstone, Michael Faraday (London: Macmillan, 1873), p. 89.

2 J. Tyndall, Fragments of Science (London: Longmans, Green, 1871), Vol. II.

3 North British Review, Vol. XIV, p. 57; quoted by G. Gore, Art of Scientific Dis-
covery (London: Longmans, Green, 1871), p. 366.

SCIENTIFIC DISCOVERY 177

Helmholtz has given us an enlightening description of his
own methods of discovery. "Often enough it [the inspira-
tion] steals quietly into one's thoughts and at first one does
not appreciate its significance; it is only sometimes that
another fortuitous circumstance helps one to recognize
when, and under what conditions, it occurred to one; other-
wise it is there, one knows not whence. In other cases it
comes quite suddenly, without effort, like a flash of thought.
So far as my experience goes it never comes to a wearied
brain or at a writing-table. I must first have turned my
problem over and over in all directions, till I can see its
twists and windings in my mind's eye, and run through it
freely, without writing it down; and it is never possible to
get to this point without a long period of preliminary work.
And then, when the consequent fatigue has been recovered
from, there must be an hour of perfect bodily recuperation
and peaceful comfort, before the kindly inspiration rewards
one. Often it comes in the morning on waking up. . . .
It came most readily, as I experienced at Heidelberg, when
I went out to climb the wooded hills in sunny weather. The
least trace of alcohol, however, sufficed to banish it. Such
moments of fertile thought were truly gratifying." 1

It is unfortunately true, however, that in spite of the
recognized importance of such acts as this very little has
been done toward explaining their nature or accounting for
their occurrence. Whether this is due to the complexity of
the acts and the elusiveness of the factors involved, or to an
ultimate irrationality in what Carmichael calls the "highest
movements of the mind" 2 need not be considered at this
point. The fact is that originality, or genius, does not seem
to yield to analysis. Certain conclusions of a rather general
sort, however, have been drawn in recent years, and they do
throw some light on the problem. For the purposes of this
discussion these may be divided into the psychological and

1 L. Koenigsberger, Herman von Helmholtz (Oxford: Clarendon Press, 1906).
pp. 209-210.

2 R. D. Carmichael, Logic of Discovery (Chicago: Open Court, 1930), p. 2.

178 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the logical analyses. The former exhibit the general setting
of the act, the emotional factors presumably responsible for
its occurrence, and the stages into which it seems to break
up; the latter attempt to show the technique of discovery
and the principles of thought upon which it is based.

PSYCHOLOGY OF DISCOVERY

Graham Wallas x analyzes the act of discovery into four
stages which he calls Preparation, Incubation, Illumination,
and Verification. The first stage is one of "hard, conscious,
systematic, and fruitless analysis of the problem." 2 It in-
cludes the entire process of intellectual education — acquiring
facts, collecting and arranging them, memorizing them,
developing critical attitudes of mind, and so on. It is the
stage of tiring labor without the rewarding consciousness of
progress. The second stage is essentially negative in that it
involves "voluntary abstention from conscious thought on
any particular problem"; it may be spent "either in con-
scious mental work on other problems, or in a relaxation
from all conscious mental work." 3 Many scientists, for
example, obtain the proper diversion by immersion in detec-
tive stories; others by vigorous exercise, such as a brisk
walk or a game of tennis. The third stage is less directly
under control. Usually the idea occurs as a sudden flash,
totally without antecedents in consciousness. There is some
justification, however, for believing that it is the culmination
of a successful train of association, which has itself been
preceded by innumerable unsuccessful trains. The immediate
antecedents of the flash of insight may often be discovered
by careful introspective analysis. James 4 says that "every
definite image in the mind is steeped and dyed in the free
water that flows around it. With it goes the sense of its
relations, near and remote, the dying echo of whence it came
to us, the dawning sense of whither it is to lead." It is often
preceded by an intimation of its forthcoming appearance.

1 Art of Thought (New York: Harcourt, Brace, 1926), Chap. IV.

2 Ibid., p. 81. 3 Ibid., p. 86.
* Principles of Psychology (New York: Holt, 1904), Vol. I, p. 255.

SCIENTIFIC DISCOVERY 179

The final stage — which is not properly a part of the act of
discovery in its most limited form — is one in which the idea
is tested and made precise. Though there is almost always
associated with the act of discovery an overwhelming con-
viction that the problem in question has been instantane-
ously solved, the actual justification for this feeling in the work-
ing out of a logical demonstration often requires great labor.

R. S. Woodworth 1 emphasizes the part which is played in
the act by the factor of originality. The ordinary man, even
the animal, in his knowing response, is not purely passive.
"Ideas are not delivered to us ready-made by our teachers,
but are modes of response which we have to develop for
ourselves." 2 They are of the same general kind as the
acquisition of learned reactions in the more ordinary affairs
of life, such as in the conditioning of reflexes, and in the
compounding of responses. To be sure, the novel reactions
which eventuate in great acts of scientific discovery occur
only under conditions in which the necessity for a new ad-
justment furnishes the proper drive. But there is nothing
distinctive about the acts themselves; they are analogous to
the simple techniques of problem-solving in the more com-
monplace situations of life. Hence experiments conducted
with a view to ascertaining some of the factors involved in
these humble cases can be expected to throw light on the
more complicated problems. One cannot formulate rules
which eventuate inevitably in acts of discovery, but he can
offer guiding principles which contribute to effectiveness in
solving problems. For example, one should keep his mind
open to possibilities which have not yet suggested them-
selves, but one should also retain a certain rigidity in follow-
ing out a suggestion; generalization from past experience,
and keenness of observation, are also important; but in the
final analysis "to have the 'detective instinct' that fixes on
the right clue is the mark, in any given field, of the man who
has a real gift for original thinking in that field." 3

1 Dynamic Psychology (New York: Columbia University, 1918), Chap. VI.

2 Ibid., p. 136. 3 Ibid., p. 147.

180 INTRODUCTION TO PHILOSOPHY OF SCIENCE

J. M. Montmasson * suggests that the act of discovery may
be considered from the point of view of three types of factor
which enter into it. The first is the phenomenon of feeling.
All discovery is motivated by desire. This may be a desire
for knowledge, for fame or money, or for esthetic values
such as order and symmetry. And all discovery culminates
in intense joy. 'This took the form of a mystical exaltation
in the case of Keplar, Gutenberg, and Descartes; of an
ecstasy produced by the unveiling of a new order in the case
of Newton, Pasteur, and Ampere. In all these cases it was
an enthusiasm evoked by an original vision of rational
beauty." 2 The second factor is the conscious intellectual
phenomena. Here Montmasson discloses three stages —
conscious preparation, sudden intuition, and conscious
verification — corresponding roughly to the last three stages
of Wallas. The first of these stages exhibits a discontinuity
between the work of research and the appearance of the new
idea. In the second state there is often no element of sur-
prise or suddenness; physics, biology, and technology are
characterized by the slow progressive revelation of ideas
through analogies, while mathematics and the moral sci-
ences exhibit more often the sudden revelation. In the third
stage the mind enters into a new period of conscious activity.
' 'The mind, delighted to have glimpsed the end, cannot be
satisfied until it has illuminated the road which it appears to
have passed over like a bird in flight. This is the phase of
experimental verification, of the justification which is
necessary for the hypothesis." 3 The final factor is the
unconscious element — the idea in its potential or hidden
state prior to its entrance into consciousness. One can-
not say that such an idea is a mere nothing. "It is a
being which already exists, although incomplete; it
awaits its perfection, its complements, its act." 4 The
birth of an idea requires certain psychical antecedents;
these are the potentiality of the resulting idea in the same

1 Invention and the Unconscious (New York: Harcourt, Brace, 1932).

2 Ibid., p. 189. 3 Ibid., p. 117. * Ibid., p. 194.

SCIENTIFIC DISCOVERY 181

way that a block of marble is the potentiality of the result-
ing statue.

LOGIC OF DISCOVERY

The precise sense in which there can be said to be a logic
of discovery should be made clear at the outset. It seems
safe to say that there is no deductive logic of discovery ; data
do not contain their own explanatory hypotheses in the
same way that premises contain their conclusions. Even in
deductive logic there exists the important problem of how
the conclusion of a deductive argument can be both novel and
true. To the extent to which it seems to be new, it cannot be
contained in the premises; hence it cannot be implied by
them. But to the extent to which it seems to be true, it must
be contained in the premises; hence it cannot exhibit novelty.
The usual way of avoiding this difficulty is to deny that
deductive conclusions have any genuine novelty. But
hypotheses obtained by inductive discovery are obviously
new, and one's only recourse, therefore, is to deny that they
have necessary relations with the data. It is therefore
impossible to look upon inductive discovery as a process
analogous to the operation of a computing machine; one
should hardly expect to pour data into one spout, turn a
crank, and grind out an explanatory hypothesis from another.

Yet there is clearly some sense in which data may be said
to "contain" their own explanatory hypothesis. Hypotheses
are not drawn from the blue by purely creative acts of mind.
On the contrary they are determined by data in at least
three ways. They are determined in the sense that if there
were no data there would be no hypothesis and if the data
were different the hypothesis would be different. They are
determined by a more inclusive range of facts in the sense
that every hypothesis is probably based to some extent on
an analogy. They are determined, finally, by the general
nature of the explanatory relation, i.e., by the fact that the
symbols which describe the hypothesis must be such as to
imply the symbols which describe the data.

182 INTRODUCTION TO PHILOSOPHY OF SCIENCE

None of these relations, however, is sufficiently deter-
minate to permit the ascertainment of one hypothesis to the
exclusion of all alternates. One is obliged to say, therefore,
not that any hypothesis is proved by being derived from the
data, but that it is given a certain probability by virtue of the
more or less definite hints offered by the data. Data do not
imply an hypothesis, they merely suggest it. The function of
hypotheses in the total scientific situation makes it ex-
tremely unplausible that an explanatory conception could
be read out of the data in a necessary way. Hypotheses, as
will be seen later, serve as instruments of anticipation; they
are devices by which the accumulated knowledge of nature
is combined with the imaginative envisagement of possibil-
ities, in such a way as to predict the character of the still
unexplored portions of nature. It is unlikely that the un-
explored is exactly like the explored; hence nature as known
cannot imply nature as unknown. Yet it is equally unlikely
that the unexplored is totally different from the explored;
hence nature as known must offer the only available hints
as to the character of nature as unknown. These two facts
suggest that prediction is possible only by what Tyndall
calls a prepared imagination, i.e., an imagination which en-
deavors to include all relevant data as guiding factors in
determining the creative insight.

A logic of discovery is possible, therefore, only in a limited
sense. It offers no technique of prediction. But it does offer a
technique by which the imagination may be prepared for
the creative leap. Much that is ordinarily included in the
act of discovery is of this preparatory character. Hence in
recognizing the principles of a logic of discovery one is in a
better position to see that the act is really of a twofold
character — one part capable of a certain formalization, the
other essentially mysterious and unpredictable. Though
this approach does not solve the problem of scientific dis-
covery as traditionally conceived, it does reduce it to two
more sharply defined problems, each of which is capable or
incapable of solution upon its own grounds.

SCIENTIFIC DISCOVERY 183

The best approach to this analysis of the act of discovery
is to be found in a distinction which has been made fre-
quently in the philosophy of science. It is usually formulated
as the distinction between the abstractive and the hypothetical
methods. In a passage already quoted * Bavink expresses an
equivalent opposition in terms of the " elaborative " and the
"hypothetical'' methods. Two other formulations of the
distinction may be given. According to Cassirer we can
proceed in two ways in science. "We can, by a pure * abstrac-
tive' method, separate from a group of given things or
phenomena that group of determinations which is common
to all members of the class, and which belongs to them di-
rectly in their sensuous appearance; or we can go behind the
phenomena to certain hypotheses for the explanation of the
field of physical facts in question. Only the first procedure
strictly corresponds to the demands of scientific and phil-
osophic criticism. For only here are we sure that we do not
falsify the observations by arbitrary interpretation; only
here do we remain purely in the field of the facts themselves,
for while we divide the facts into definite classes, we add no
foreign feature to them." 2 Dingle's terminology is essen-
tially the same. ''Abstraction is the detection of a common
quality in the characteristics of a number of diverse observa-
tions: it is the method supremely exemplified in the work of
Newton and Einstein. Newton, for example, gave us 'laws of
motion.' Now motion is not an experience; what we observe
are moving bodies. Motion is an abstraction, a quality con-
ceived to be possessed by all moving bodies, however much
they may differ in size, shape, color, beauty, virtue, or any-
thing else. The laws of motion express the characteristics of
this common quality, and they are therefore a rational
means of correlating a vast body of common experience. . . .
A hypothesis serves the same purpose, but in a different way.
It relates apparently diverse experiences, not by directly
detecting a common quality in the experiences themselves,

1 Chapter VIII, pp. 168-169.

2 E. Cassirer, Substance and Function (Chicago: Open Court, 1923), pp. 193-194.

184 INTRODUCTION TO PHILOSOPHY OF SCIENCE

but by inventing a fictitious substance or process or idea, in
terms of which the experiences can be expressed. A hy-
pothesis, in brief, correlates observations by adding some-
thing to them, while abstraction achieves the same end by
subtracting something." 1

There is no doubt but that the distinction here expressed is
fundamental to the logic of science. But it requires two
important refinements before it can be inserted in a general
theory of scientific explanation. The first refinement appears
to be merely a matter of terminology, though it is more than
this. The method of abstraction should not be so called,
since abstraction is only one of several processes which play
essentially the same role in science. Abstraction is associated
with classification. But, as has already been seen, ordering
and correlating are two other important processes by which
data are put into manageable form. If classification is the
operation by which abstractions are obtained, one may say
equally well that ordering is the process by which series are
obtained, and correlating, or associating, is the operation
by which complexes are obtained. What is required, there-
fore, is a term broad enough in its significance to include
operations of classifying, ordering, and correlating. Pre-
sumably, "describing' would be precisely the word de-
manded, since these are all descriptive techniques. Certainly
the positivist would be well satisfied with this choice. For
him science consists of two methods — the descriptive, which
is the essential method of science, and the hypothetical,
which is dangerous and to be avoided at all costs. But for
the modified positivist and for the realist this term would
not be adequate; the essential feature of these methods is
that they involve the creation of entities by definite acts of
thought. Pure description never does this. In this connec-
tion Bavink's choice of the word "elaborative" to character-
ize these methods is particularly apt. Russell describes such
techniques as methods of "logical construction " ; they result in

1 H. Dingle, Science and Human Experience (London: Williams and Norgate,
1931), pp. 22-23.

SCIENTIFIC DISCOVERY 185

"fictions " since they create entities such as classes, series, and
complexes, not certainly known to exist. The question as to
whether or not operations of construction eventuate in fictions
is unimportant here. What is to be emphasized is merely the
kinship of classifying, ordering, and correlating, and the fact
that they are all, in a sense, more than mere descriptions.
For this reason it will be well to speak of the method of con-
struction in preference to the method of abstraction.

But in the second place, the two methods should not be
looked upon as alternative, for neither can be employed
without the other, and taken together they constitute only
one method which is the method of science. This can be
made clear by examining the distinction between them. It is
the acknowledged aim of the method of construction to avoid
any unjustified addition to the data; the method merely
elaborates or clarifies by emphasizing features of the given.
The method of hypothesis, on the other hand, consciously
adds to the given "by inventing a fictitious substance or
process or idea," as Dingle says. Hence it seems fair to say
that the aim of the method of construction is to produce
nothing new, while the aim of the method of hypothesis is to
produce something new. Expressing the same idea in other
words, one may say that the aim of the method of construc-
tion is to make as precise as possible the data which are
relevant to the problem, while the aim of the method of
hypothesis is to devise a symbol by which these data may be
explained. This suggests that the method of construction
is not alternative to the method of hypothesis but prepara-
tory to it; it also suggests that the method of hypothesis is
not alternative to the method of construction but its neces-
sary outcome. Together, the methods make up the act of
discovery; singly they constitute the stage in which the
imagination is prepared, and the stage in which it makes its
leap into the unknown.

This analysis permits a reinterpretation of the methods.
If one speaks of both methods as operations for the creation
of symbols he may then distinguish them in the following

186 INTRODUCTION TO PHILOSOPHY OF SCIENCE

terms: The method of construction permits one to attribute to
the symbols such content as they must have by virtue of the data
from which they have been derived, and the method of hypothesis
permits one to attribute to the symbols such additional content
as they may be presumed to have if they are to be successful
instruments of prediction. This indicates clearly that the
former is essentially a method of description and the latter is
essentially a method of explanation; in the former one "re-
mains close to the data," in the latter he "leaps into the
unknown"; in the former one merely elaborates, in the latter
he creates; in the former one is simply making more clear
what he has already observed, in the latter he is anticipating
what he has not yet observed.

A very important consequence of this distinction of meth-
ods is that a pure construction can never explain. This may
appear at first sight to be quite contradicted by the facts.
It seems obvious that science is continually explaining in
terms of abstractions, series, and complexes. But a moment's
reflection will convince one that in so far as these entities do
explain they cannot be pure constructions. For a pure con-
struction must have only such content as one is entitled to
give it from the data; but an explanatory entity — if it is to
explain — must contain more content than the data which
it is to explain. Explanation consists, as will be seen in the
next chapter, in the transfer of properties and relations
from the explanatory entity to that which is to be explained ;
in explanation one increases the content of the data by add-
ing to them the features of the hypothesis. But if a construct
has been obtained by direct derivation from the data, there
is clearly no possibility of turning about and explaining the
data in terms of the construct. The construct does not con-
tain that increment of novelty without which explanation is
impossible. A pure construct used as an explanatory entity
produces an ad hoc or verbal explanation. One cannot use the
soporific quality of opium to explain the fact that it produces
sleep unless he knows more about the soporific quality than
the fact of its producing sleep. In the same way, one cannot

SCIENTIFIC DISCOVERY 187

explain actual levers in terms of perfect levers, matter in
terms of space-time, heat in terms of molecules, or life in
terms of a vital force, if in each case the explanatory notion
is a mere construction from that which it presumes to ex-
plain. It is likely that many explanations in science are of
this pseudo-hypothetical character. Mention may be made
of potentials, capacities, unconscious purposes, tendencies,
instincts, affinities, powers, urges, and causal efficacies.
There is reason to believe that most of these notions — unless
they are definitely increased through the hypothetical
method — are constructs rather than hypotheses, and hence
have no explanatory function.

It follows that the problem of the logic of discovery reduces
to two more specific problems: (a) What are the techniques
of construction or of elaboration? (b) What are the techniques
of hypothesis-formation? Unfortunately no very sharp line
can be drawn between these problems. The task of the logic
of discovery, presumably, is to formulate the techniques by
which nature may be anticipated. But this problem is not
likelv to admit of solution. The best that one can do is to
list the various techniques which may be employed as prac-
tical aids to the performance of the act of discovery. But an
examination of these methods reveals the fact that they vary
among themselves in determinateness. By determinateness
is meant the degree to which the operation permits one to
infer the content of the explanatory entity from the data. It
has already been pointed out that the data never imply the
hypothesis, yet they do seem to determine its content in
certain limited ways. The purpose of a classification of the
techniques of discovery is to exhibit the most common of
these methods in such a way as to disclose their degrees of
determinateness. Abstraction, for example, is relatively
highly determinate; synthesis and analysis, on the other
hand, are not so highly determinate since logic has not yet
provided the principles according to which the properties
of wholes may be inferred from the properties of parts, or
vice versa.

188 INTRODUCTION TO PHILOSOPHY OF SCIENCE

The principle to be kept in mind in such a classification is
that the techniques which are highly determinate are to be
grouped under the techniques of construction, while those
which are less highly determinate belong under the tech-
niques of hypothesis-formation. The reason for this is the
fact that the highly determinate operations permit one to
extract the explanatory entity, so to speak, from the data;
the inferential movement is simply an elaboration of what is
already given; the suppositional entity is, in a sense, de-
manded by the data and hence may be read out of them. Its
content may, therefore, be determined more or less com-
pletely by the data, and there is little room for the free play
of the imagination. It is important to note, however, that
constructs obtained in this way are often enlarged through
the method of hypothesis. Abstractions, for example, are
readily definable in terms of the data from which they have
been derived; but entities thus defined are frequently aug-
mented by acts of imagination in such a way as to permit
their use as strict hypotheses. Hence to say that the method
of abstraction is a method of construction is not to deny that
it may also be a method of hypothesis-formation. In the
same way, wholes and parts are not readily definable in
terms of their respective parts and wholes and therefore
afford a wide range for the free play of imagination; hence
synthesis and analysis are properly to be classed as opera-
tions of hypothesis-formation. But there are clearly some
ways in which parts and wholes are interrelated, hence
there is a minimal logic of synthesis and analysis. It follows
that the classification of these methods as operations of
hypothesis-formation is not a denial of their possible con-
sideration also as operations of construction. The best that
one can do, therefore, is to construct a scale of discovery
techniques, indicating that those at one end of the scale are
essentially methods of construction and those at the other
end are essentially methods of hypothesis-formation.

It is likely that all such techniques are based ultimately
upon analogy. One can anticipate the unknown only if he

SCIENTIFIC DISCOVERY 189

has had previous samples of it. By a sample of the unknown
is meant an idea, once conjectural and hypothetical in
character, but now verified to such an extent as to have been
incorporated into the known. Hence one's previous success-
ful anticipations become the foundations for new anticipa-
tions. But the samples, by themselves, cannot afford such a
basis, for one cannot presume that nature is everywhere
alike. The principle of the uniformity of nature, so often
considered to be the sole justification for inferences as to the
future, asserts not that nature is everywhere the same but
that there are pervasive and repeating structures. The realm
of events is much more constant in its structural features
than in its contentual features. Hence the principle of
analogy entitles one only to infer that there will be the same
type of connection between the present known and the
present unknown that there was between the past known
and the past unknown. It justifies only the assumption
that one will continue to meet with success if he attempts to
explain in terms of abstractions, serial operations, associa-
tions, causes and effects, microscopic elements, and so on —
but it does not tell him specifically what content these
explanatory notions will have. It is therefore very limited as
a principle of anticipation. It enables one to predict the
character of the unknown only upon the basis of these highly
general structural features of the known, and does not enable
him to anticipate anything as to its specific contentual fea-
tures. These hmitations justify the claim that there really
is no logic of discovery in the strict sense of the term.

TECHNIQUES OF CONSTRUCTION

The techniques of construction are not distinguished in any
significant way from the techniques of description, discussed
in Chapter VI. That the former are "elaborative" rather
than "descriptive" means only that they refer to the less
obvious features of events. Hence they are such operations
as are involved in classifying, ordering, and correlating
events when the properties determining these operations are

190 INTRODUCTION TO PHILOSOPHY OF SCIENCE

not so apparent as they are in the case of description. To
speak of a piece of gold as a deformation in space- time is to
say something more abstruse about it than to say that it is
yellow and hard, though both are cases of classification; to
characterize time as an instance of the mathematical con-
tinuum is to speak in more abstract terms than to say that
it is a succession of events, though both are cases of ordering;
to say that the space covered by a falling body is a function
of the time of fall is to correlate events in nature, though in a
less obvious way than to say that every falling body occupies
space and endures through time.

Classification and ordering, when employed as techniques
of elaboration, are usually characterized as abstractive. The
foundation for this use lies in the fact that the properties
specified, whether non-serial or serial, are highly general,
and such as apply to a wide range of events. Hence any
characterization of events by means of mathematical or
logical properties constitutes an abstract representation of
them. One of the best examples of abstractive techniques is
to be found in measurement.1 This is an operation which
involves recognition of the quantitative features of events
and the possibility of ordering them on the basis of certain
types of relationships. The operation is called measurement,
and the number so obtained is called the measured value;
through the operation it becomes applied to the event as an
abstract feature of it. The use of mathematics as a tool in
science is based upon its abstract character. Similar applica-
tions of abstractive techniques may be seen in the "reduc-
tion'1 of consciousness to physiological processes, and of
physiological processes to physico-chemical processes.

Correlation and associational techniques may be called,
by contrast, concretive. They are concerned not with sim-
plification through neglect of specific differences, but with
complication through the association of events into more
inclusive wholes. As was seen in Chapter VI, any association
of events determines a more complex event of which the

1 See Chapter VI, pp. 112-115.

SCIENTIFIC DISCOVERY 191

associated events become parts or aspects. The concretive
method is employed whenever diverse events are considered
to be explicable by the same complex entity, e.g., when ex-
pansion, surface tension, and solubility are presumed to be
explicable in terms of the molecular constitution of matter.
The definition of a substance as the totality of its properties
or manifestations is also a case of the concretive method,
i.e., it is an attempt to devise a construct in terms of which
it will be possible to understand the association of these
properties. Often the concretive method involves uniting
apparent incompatibles, as in the case of the supposition
that the ether is both a fluid and a solid, and in the hypoth-
esis that light is both wavelike and corpuscular. Frequently
the concretive method is concerned not with the supposition
of a complex entity, but merely with the postulation of a
more intimate correlation than that which is obviously
given. Inferences from some to all may be considered as
instances of the concretive method.

Both of these methods, however, have been considered in
this connection merely as methods of construction, not as
methods of hypothesis. The method of abstraction attempts
to determine the properties of abstract features of events
on the basis of the events themselves, and the method of
concretion attempts to determine the properties of complex
events on the basis of what is known of the individual
events. But both abstractions and concretions, having
been defined by the method of construction, may be in-
creased by the method of hypothesis. Through this method
the meanings of the abstractions and concretions are in-
creased in such a way as to permit the deduction of further
descriptive propositions. For example, measured values
take on all of the features of the mathematical systems of
which they are parts, and, as a result, the quantities which
are measured by means of them take on additional properties.
In the same way, the notion of molecules is enlarged through
imaginative activities, and, as a result, new properties de-
scriptive of the behavior of bodies are predictable. Such

192 INTRODUCTION TO PHILOSOPHY OF SCIENCE

anticipations as these are possible only through the use of
the hypothetical method.

TECHNIQUES OF HYPOTHESIS-FORMATION

Since the remaining techniques of discovery are less highly
determinate in character, they may be conveniently dis-
cussed under the present heading. As was pointed out, the
techniques of hypothesis-formation are simply those methods
which permit only a very limited ascertainment of the con-
tent of the explanatory entity, hence leave room for the
activity of the imagination. It should be remembered,
therefore, that the following techniques are also methods
of construction. Three types will be discussed: (a) serial
operations, (b) cause and effect inferences, and (c) opera-
tions of analysis and synthesis.

(a) Serial operations. These are of two kinds, depending
upon whether the operation is from a given segment of a
series to an element beyond the segment, or between two
supposedly adjacent members. The former may be called
the method of serial extension, or of extrapolation, and has
been aptly characterized by Eddington as the method of
"just like this only more so." * It permits extension beyond
any given range of data when they are capable of serial
arrangement; the property of gradual increase or decrease
exhibited by the known segment of the series is taken as a
defining principle by which the character of the elements
beyond the limits of observation may be ascertained. The
latter is the method of interpolation, and involves the in-
sertion of an element between two apparently contiguous
members. Serial operations are employed in all of the sciences
for the purpose of defining "ideal" entities, such as perfect
levers, frictionless motion, ideal gases, Utopias, and per-
fectly isolated individuals; they are the characteristic meth-
ods of mathematics and are used in the definition of infinity,
irrationals, fractions, zero, and the negatives. More specific
illustrations of their employment will be given in Part Two.

1 Nature of the Physical World, p. 247.

SCIENTIFIC DISCOVERY 193

(b) Cause and effect inferences. Operations involving the
discovery of causes and effects are commonly considered to
be the sole concern of science. The more detailed analysis
of this notion, which is to be the topic of Chapter XVI,
will reveal the truth which there is in this statement. Here
the problem is only to point out that the techniques for
determining causes and effects are not highly determinate.
They do not enable one to infer the characters of causes
from effects, or vice versa. Instead, they are principles for
telling one when and where to look for causes, given effects,
and when and where to look for effects, given causes. They
thus enable one to identify causes and effects by their
temporal and spatial locations. Certain hoary principles,
e.g., that cause resembles effect, supposed by many phi-
losophers to be descriptive of the cause-effect connection in
nature, do not seem to have any important application in
science, and there is reason to doubt whether they have
any clearly defined meaning. A precise logic of causal
connections has not yet been formulated. As a consequence
no operational construction of causes from effects, or of
effects from causes, is possible; specific causes and effects
cannot be anticipated with any high degree of certainty.
Causes and effects are therefore hypothetical rather than
constructual in character; they are given content through
activities which are essentially imaginative, though the oper-
ations are often guided by analogies.

(c) Operations of analysis and synthesis. The demand for
operations of this kind is based upon the fact that a whole is
better understood when the properties of its parts are known,
and the parts are better understood when the properties of
the whole are known. The behavior of social groups is more
intelligible when the modes of behavior of the individual
members are known, and the modes of behavior of the in-
dividual members are more intelligible when the nature of
social behavior is understood. In the one case the data
constitute the complex, and the inferential route is analytic;
in the other case the data are the elements, and the inferen-

194 INTRODUCTION TO PHILOSOPHY OF SCIENCE

tial route is synthetic. The justification for such an opera-
tional route is a logic of analysis and synthesis, which aims
to show to what extent the properties of the whole deter-
mine the properties of the parts, and vice versa. As in the
case of cause and effect connections, such a logic has not
yet been written; philosophers have debated endlessly over
the question of the "validity" of analysis. Consequently
there is no definable technique for this mode of operation,
and the discovery of parts from wholes and of wholes from
parts is essentially imaginative in character, guided, as in the
case of causal inferences, by loose analogies.

In transition to the next chapter reference should be
made to the analogy between techniques of discovery and
of verification, and descriptive techniques. The former
determine an explanatory science in much the same way
that the latter determine a descriptive science. In other
words, when one sets about to control the objects of percep-
tion and the perceptual act, and when he endeavors to
classify, order, and correlate the results, he is constructing
the body of symbols which constitutes a descriptive science;
similarly when one sets into operation the techniques of
construction and of hypothesis-formation, and when he
endeavors to predict and verify, he is constructing the body
of symbols which constitutes an explanatory science. The
latter type of science is one which attempts to integrate both
the data which are obtained by observation, and the hypotheses
and theories which are obtained through acts of discovery and
verification. Its structure will be described in the next chapter.

REFERENCES

G. Gore, Art of Scientific Discovery (London: Longmans, Green,

1871), Part III.
R. D. Carmichael, Logic of Discovery (Chicago: Open Court, 1930),

Chap. I.
G. Wallas, Art of Thought (New York: Harcourt, Rrace, 1926),

Chap. IV.
R. S. Woodworth, Dynamic Psychology (New York: Columbia

University, 1918), Chap. VI.

SCIENTIFIC DISCOVERY 195

J. M. Montmasson, Invention and the Unconscious (New York:

Harcourt, Brace, 1932).
John Tyndall, "Essay on the Scientific Use of the Imagination,"

Fragments of Science (London: Longmans, Green, 1871),

Vol. 2.
E. Rignano, Psychology of Reasoning (London: Kegan Paul, 1923),

Chap.VI.
C. Spearman, Creative Mind (New York: Appleton, 1931).
A. C. Benjamin, The Logical Structure of Science (London: Kegan

Paul, 1936), Chap. IX.

CHAPTER X

EXPLANATORY SCIENCE

If there are sciences which are empirical or descriptive in
character, it is none the less true that there are sciences which
are rational or explanatory in character. Mathematical
physics, rational mechanics, and geometry are the most
obvious examples of such sciences. It was stated at the
close of the preceding chapter that explanatory sciences
may be considered as the results of the techniques of dis-
covery and of verification in the same way that descriptive
sciences are the results of the techniques of classifying,
ordering, and correlating; when one endeavors to describe
nature he constructs an empirical science, and when he
endeavors to explain nature he constructs a rational science.
This places verificatory techniques on the same level as
techniques of discovery, i.e., as methods through whose
application explanatory science takes form. From this point
of view it would seem preferable to discuss these techniques
before an analysis of explanatory science itself is made.
However, the fact that an understanding of verificatory
techniques is impossible without an understanding of the
general nature of explanation lessens the advantage of this
manner of presentation. Consequently, the present chapter
will be devoted to an analysis of the meaning of explanation
and of the structure of explanatory science, leaving for the
ensuing chapter the consideration of the techniques by
which an explanatory science becomes corroborated and
substantiated.

Since the key to the understanding of explanatory science
lies in the meaning of explanation, this problem affords
the logical starting-point for the discussion. What, es-
sentially, does one do when he explains, and how is the
activity of explanation to be differentiated from that of

196

EXPLANATORY SCIENCE 197

description? The answer to this question will throw into
proper perspective the distinction between the two types of
science.

NATURE OF EXPLANATION

Though description and explanation are usually sharply
contrasted, there is reason to believe that the distinction
between them cannot be made in any absolute way. If one
takes the realistic attitude toward science and insists that
all explanatory entities exist in the same way as that which
they aim to explain, there can be no important difference
between description and explanation; description calls
attention to the more obvious properties and relations of
events, and explanation indicates those which are less
obvious. Hence one leaves descriptive techniques when he
begins to penetrate beneath the surface, or to get behind
apparent phenomena. But even if one takes the positivistic
attitude and insists that the task of science is the invention
of conceptual devices such as classes, series, and laws,
which render nature intelligible through simplification and
correlation, there is still no significant distinction between
description and explanation; employment of the less elab-
orate symbolic tools is called description, and of the more
elaborate tools, explanation. These two interpretations
suggest that description and explanation are strictly con-
tinuous, and that the drawing of any line separating the one
from the other is more or less arbitrary.

Yet there appears to be an important distinction between
the two with reference to verification. Both description and
explanation are, of course, in terms of symbols, and symbols
are verified by their referents. But symbols which describe
can be verified directly because their referents are given
clearly, while symbols which explain cannot be so verified
because the events to which they refer are 'beneath' or
"behind" the phenomena. Hence the verification of ex-
planatory symbols must be indirect. For example, the
description of copper in terms of its toughness, malleability,

198 INTRODUCTION TO PHILOSOPHY OF SCIENCE

red color, and bright metallic luster can be quite readily
verified by direct inspection and the performing of simple
experiments; but the explanation of its properties in terms
of atomic structure can be verified only by elaborate tech-
niques which are designed to show what properties copper
would exhibit if its structure were of a certain supposed
character. Hence verification of symbols for explanatory
entities is in terms of their logical consequents, not in terms
of the entities themselves as in the case of descriptive sym-
bols.

This affords a convenient foundation for the distinction
between description and explanation. An event is described
by those symbols which refer to it directly, and it is ex-
plained by those symbols which imply other symbols refer-
ring to the event directly. Description is thus the limit to
which explanation approximates when the events to which
it refers become more and more clearly given, and explana-
tion is the limit to which description approximates when the
properties to which it refers become more and more obscurely
given. The situation may be diagrammed as follows:

SYMBOLS

EVENTS

(Description)

o

• 1-4
■*->

q

13,

y ^ (Obscurely Given)

a

o

-t->
a
a

'a

Description

xw (Clearly Given)

In the strictest sense of the words 'description" and "ex-
planation," X may be said to describe x and Y may be said
to explain X; thus description is a relation of symbols to
events, and explanation is a relation between symbols. But
according to a more generous use of the word "explanation"
Y may be said to explain x, i.e., a symbol may be said to
explain an event. Now if one adopts the realistic view in
science and maintains that a symbol cannot explain an event

EXPLANATORY SCIENCE 199

unless it refers directly to some other event, then one may
employ the word "description" in an equally generous sense
and say that Y describes y even though y is a hidden event.
By virtue of this use it becomes possible to say that x is
explained by y, i.e., explanation is a relation between events.
It seems best to employ the words in the strictest sense be-
cause this seems more precise and because it is a use which
satisfies both the positivist and the realist, i.e., description
is at least a relation of a symbol to a clearly given event,
whatever else it may be, and explanation is at least a relation
between symbols, whatever else it may be. According to this
interpretation the essence of the explanatory relation is to be
found in the implicative relation between the explanatory
symbol and the descriptive symbol. Description is a matter
of extension, while explanation is essentially a matter of
intension. Descriptive or empirical science consequently
emphasizes the relations of symbols to events, while ex-
planatory or rational science emphasizes the relations of
symbols to one another. Descriptive science is primarily
concerned with reference outside of itself, explanatory
science is primarily concerned with internal consistency.
This is the foundation for the distinction, to which reference
will be made later in the chapter, that empirical sciences are
real or existential while rational sciences are ideal or non-
existential.

The character of these relations may be made clear by an
illustration. Suppose that X is the descriptive law, "Bodies
expand when heated." A strictly descriptive law would
never have this universal form, since all bodies could never
be observed, but this fact may be neglected for the present.
Then x symbolizes the actual fact of a large number of
associations between cases of the application of heat and
cases of ensuing expansion; the law may be said to describe
this fact. Suppose, now, that Y is a group of propositions
about molecules, viz., the group which would ordinarily be
said to reveal the defining characteristic of molecules. Since
this group of propositions implies the descriptive law, the

200 INTRODUCTION TO PHILOSOPHY OF SCIENCE

latter may be said to be explained by it. Hence one may say
that propositions about molecules explain propositions about
heat, and propositions about heat describe facts in which
heat occurs. A descriptive science is constituted by proposi-
tions of the kind X. An explanatory science would pre-
sumably be constituted by propositions of the kind Y;
however, for reasons to be disclosed later, it seems better to
characterize an explanatory science as including a descrip-
tive science, and, hence, as any science constituted by
propositions of the kind Y and the kind X in the relation
Y implies X. Though the Y propositions would not ordi-
narily be called descriptive, they may easily become so by
any techniques which permit y to appear in the more clearly
given; for example, in the Brownian movement one may be
said in effect to be observing molecules; hence through such
activities the propositions about molecules may be con-
sidered as approximating to descriptive propositions.

The essence of the explanatory relation, then, lies in the
relation of implication. Whenever there is a logical structure
consisting of premises and conclusion, the premises may be
said to explain the conclusion. The premises give the reasons
for the conclusion, the conditions which — if satisfied — will
determine the truth of the conclusion. Hence the relation of
explanation holds between any group of underived proposi-
tions (postulates, axioms, definitions, principles) and the cor-
responding group of derived propositions (theorems, corol-
laries, laws). The underived propositions need not be
ultimately underivable, but are simply, at the moment,
considered as underived. The theorems and corollaries of a
system of geometry may be said to be explained by the
corresponding postulate system, and the laws of empirical
science may be said to be explained by the proper set of
principles and theories.

However, although the implicative relation seems to ex-
press the essence of explanation, it does not exhaust that
relation. Implication is necessary for explanation, but is it
sufficient? According to Campbell, "Explanation in general

EXPLANATORY SCIENCE 201

is the expression of an assertion in a more acceptable and
satisfactory form." x He then goes on to show that a state-
ment is more acceptable and satisfactory when it expresses
ideas with which we are more familiar, i.e., "it invokes a
definite response in our minds which we describe by saying
that we understand the statement." Presumably one does
not explain, therefore, unless he knows more about the un-
derived propositions than he does about the derived proposi-
tions; one always explains the unknown in terms of the
known.

There is a measure of truth in this contention, and a
proper understanding of the logic of science demands that
the notion be clarified. What, precisely, is meant by saying
that in explanation one must know more about the ex-
planatory entity than about that which is to be explained?
Clearly there is a sense in which one knows more about that
which is to be explained, since this is given while the ex-
planatory entity is hypothetical and conjectural, i.e., the
datum is clearly given while the hypothesis is obscurely
given. Yet if the explanatory entity is to explain one must
know more about it than he does about that which he is
attempting to explain. This apparent paradox can be re-
solved if one recognizes the precise character of explanation.
The datum is always more familiar in the sense that it is
given observationally, but the hypothesis is always more
familiar in the sense that it is determined imaginatively.
Now the observational and the imaginative may differ both
quantitatively and qualitatively. Quantitatively, the hy-
pothesis contains less than the observationally given in
one sense, and more in another sense. No hypothesis at-
tempts to explain more than a selection from the total given,
hence every hypothesis asserts less than is contained in the
given; but every hypothesis attempts to make predictions
about the given, hence asserts more than is contained in
the given. For example, there are many thermal properties
of objects (the occurrence of melting and boiling at one

. l What Is Science?, p. 77.

202 INTRODUCTION TO PHILOSOPHY OF SCIENCE

temperature rather than at another, the fact of expansion
upon solidification in certain substances and contraction in
others, and so on) which are not explicable by the theory of
molecules; hence the explanatory conception accounts for
only a part of the known facts. But the theory enables one
to predict certain phenomena of diffusion, surface tension,
and solution, which are later verified ; hence the explanatory
conception accounts for more than the known facts. Conse-
quently one is obliged to say that the observational and the
imaginative partly overlap, each extending beyond the
other. Qualitatively, the observationally given would seem
to have an essential advantage over the imaginatively deter-
mined; the facts of perception have a brute character which
compels one's acceptance of them. Yet the imaginatively
determined has a vividness which cannot be denied. The
suggestion has already been made that the anticipations
which one makes of nature are founded upon analogies drawn
from the character of nature as known; hence the imaginative
retains some of the forcefulness of the perceptual. But,
what is more important, the imaginative is almost always
vivified through the extensive use of iconic symbols; mole-
cules are thought of as small billiard balls, the ether as a
jelly, and forces as elastic tubes. This gives a clarity to
these notions which would be lacking from a less pictorial
symbolism. That the clarity may be of a pseudo-sort, and
hence misleading, is not to be denied. But something of this
kind seems to be the interpretation of the fact that the
explanatory entity is ordinarily more clearly known than
that which is to be explained.

The emphasis upon familiarity as an attribute of ex-
planatory entities leads readily to the conclusion that ex-
planation is merely verbal, or linguistic. To explain a
proposition, according to this conception, is to express
another proposition to which the first can be reduced by
certain rules of transformation. Propositions are equivalent
if they may be substituted for one another in all contexts in
which they occur. Explanation is therefore essentially the

EXPLANATORY SCIENCE 203

same as translation from one language into another; for
example, all propositions about heat may be translated into
propositions about molecules, and if one happens to be
more familiar with the latter language than with the former
he succeeds by this act in explaining heat.

It is clear that this conception of explanation is in strict
accord with the positivistic conception that entities should
not be multiplied beyond necessity. Explanation is a lin-
guistic matter — of this one can be sure. Whether it is more
than a linguistic matter, i.e., whether there actually are
entities referred to by the explanatory symbols — of this one
cannot be sure. Hence the principle of caution demands that
one refrain from supposing anything which is not certainly
known to exist. It is also in strict accord with the positivistic
contention that logical deduction is itself merely verbal;
conclusion can be obtained from premises by the application
of the rules for substitution. Hence premise and conclu-
sion, underived proposition and derived proposition, state-
ment about explanatory entities and statement about data —
both propositions state the same fact, though in different
language.

The realistic reply to this contention follows the lines laid
out by Bavink in the quotations given in Chapter VIII, and
need not be discussed here. Suffice it to say that for the
realist explanation is not merely a matter of language, but an
activity involving the actual penetration into the hidden
recesses of nature. When one explains he is not exploring
language, but nature; nature reveals not only heat but
molecules as well, and the problem of science is to determine
the precise character of the correlation between these two
types of natural entity. This is sharply contrasted with the
positivistic attitude which insists that there is only one
thing, which may be spoken about either in the language of
heat or in the language of molecules. (It is also sharply
contrasted with an attitude of extreme realism which in-
sists that when heat has been explained it has been ex-
plained away, hence only molecules exist.) The realist quite

204 INTRODUCTION TO PHILOSOPHY OF SCIENCE

justly insists that there is as much of an assumption involved
in making the distinction between the explanatory entity
and the datum merely a linguistic one, as there is in making
it a real or a natural one. The fact that it is a linguistic
distinction affords no grounds for concluding either that it
is or that it is not also a real one.

The general conception of explanation here developed
permits of any number of more specific interpretations. It is
sometimes contended, for example, that explanation is
always in terms of causes, or that it is always in terms of
generalities, or that it is always in terms of microscopic
elements such as atoms and electrons. Nothing in the above
conception of explanation would forbid any of these types of
explanation. All that would be required in each case would
be that the propositions describing the causes, or the general
principles, or the minute elements, be such as to permit the
logical deduction of certain other propositions descriptive
of the data as actually known and as discoverable by further
exploration. Whether or not such can be done is dependent
upon the required logic. If there is a logic of cause-effect
relations, then from propositions making assertions about
causes one may infer propositions making assertions about
effects, and perhaps vice versa. Similarly with reference to
universal-particular relations, part-whole relations, and the
like. For example, one of the vital problems of modern
science is the legitimacy of inferring from the properties of
the parts to the properties of the whole which is made up of
these parts, and vice versa. Does determinism as exhibited
by the mass behavior of particles afford a basis for con-
cluding a corresponding determinism with reference to the
individual elements? Are there "emergent" or "holistic"
properties possessed by groups but not predictable from a
knowledge of the properties of the elements? Do molecules
in organic compounds possess properties different from those
which the "same" molecules possess in inorganic com-
pounds? Each of these problems is reducible to the general
problem of the validity of analysis or of synthesis, and as

EXPLANATORY SCIENCE 205

such it is a special case of the problem of explanation. What
is to be emphasized here is that explanation is not to be
limited to one type. It is just as possible for the biological
and social sciences to become explanatory — though they
may require hypotheses of final causes and purposes — as it
is for the physical and mathematical sciences through the
application of notions of efficient cause, abstraction, and
analysis.

Granting that explanation is approximately the sort of
thing which has been discussed, what may be said as to the
character of an explanatory science? Following the outline
of Chapter VII explanatory science may be considered from
the point of view (a) of extension, and (b) of intension.

EXTENSIONAL FEATURES OF EXPLANATORY SCIENCE

Extensionally explanatory science aims to represent both
(1) the clearly given events, and (2) those less clearly given
events which although conjectural as to status, are required
both for the purpose of rendering the clearly given events
" intelligible " and for the purpose of increasing the range of
our knowledge of such events.

(1) The basic feature of explanatory science to be insisted
upon here is that such a science, in becoming explanatory,
does not cease to be descriptive. Every explanatory
science consists of two parts: (a) the descriptive proposi-
tions which constitute precisely the empirical science upon
which the explanatory science is founded, and (b) the
hypothetical propositions which characterize all of the
explanatory entities in terms of which the descriptive
propositions are to be rendered intelligible. These con-
stitute, respectively, the derived and the underived proposi-
tions, the theorems and the postulates, symbols of the kind X
and of the kind Y, as given in the diagram on page 198.
Every explanatory science, therefore, retains its descriptive
reference; it contains a number of propositions which are
capable of empirical verification. It is precisely these propo-
sitions out of which the explanatory science in its broader

206 INTRODUCTION TO PHILOSOPHY OF SCIENCE

sense arose, and in terms of which it is to be accounted for.
Whatever else the explanatory propositions may do, they
must at least explain the descriptive propositions. Otherwise
they become purely arbitrary, subject to no criterion except
that of internal consistency.

What is maintained here may be clarified by pointing out
the thesis with which it is contrasted. It is usually asserted
that sciences are capable of being divided into two mutually
exclusive classes — the empirical, inductive, existential, real,
or a posteriori, and the rational, deductive, non-existential,
ideal, or a priori. The former, illustrated by experimental
physics, biology, and sociology, are derived from the realm
of events, and therefore refer to this realm; the latter,
illustrated by logic, geometry, and rational mechanics, are
not derived from the realm of events, and therefore do not
refer to this realm. Hence the former may be called real
sciences, while the latter must be called ideal. But since
the latter exhibit an important logical structure they may
be called deductive or necessary, while the former must be
called inductive or probable. A proposition which belongs
to one type of science cannot also at the same time belong to
another. Hence no proposition can be both logically neces-
sary and empirically true. Einstein has formulated this
thesis clearly in a statement which is frequently quoted:
"As far as the laws of mathematics refer to reality, they are
not certain; and as far as they are certain, they do not refer
to reality." 1

The unfortunate consequence of this dichotomy is that it
leaves inexplicable the problem of how the rational sciences
contribute to the understanding of the empirical sciences.
There is not only pure mathematics, but applied mathe-
matics; not only rational mechanics, but empirical mechan-
ics. If rational sciences have not been derived from and do
not talk about events, how can they have any application to
such events? The goal of science is neither propositions
having a maximum of necessity and a minimum of truth,

1 A. Einstein, Sidelights on Relativity (London: Methuen, 1922), p. 28.

EXPLANATORY SCIENCE 207

nor propositions having a maximum of truth and a minimum
of necessity; on the contrary science is seeking propositions
having a fair amount of both necessity and truth.

This goal can be attained if one recognizes that the ra-
tional sciences contain both empirical propositions and those
other propositions which have been formulated for the
purpose of explaining the descriptive propositions. Rational
sciences are simply empirical sciences which have expanded
into the realm of the theoretical. The theoretical proposi-
tions cannot be taken away from the total science in which
they occur, for apart from this setting they become purely
arbitrary, and responsible only to the imagination for both
meaning and truth. In the context of their origin, however,
they retain responsibility to the empirical propositions; they
are both meaningful and true to the extent to which one may
deduce from them propositions capable of empirical verifica-
tion. All of the entities of the so-called rational sciences,
therefore, must be considered merely as hypotheses in terms
of which empirical propositions are to be explained, and
from which further empirical propositions are to be derived.
This seems to be the status of all propositions about perfect
triangles and circles, frictionless motion and ideal gases, i.e.,
they refer to hypothetical events whose character is to be
determined by the events which they are called upon to
explain. It is unfortunate that when a descriptive science
becomes explanatory the interest of the investigator shifts
from the empirical propositions to the hypotheses. There is
reason for this shift of interest since the empirical proposi-
tions can all be deduced from the hypothesis and hence need
not be attended to explicitly. But what should be emphasized
is that the empirical propositions cannot be deduced unless
there is admitted into the postulate system a further proposi-
tion which states the relation of the ideal entities to the
actual entities. Apart from this there can be no "applica-
tions" of the postulate system, and it becomes arbitrary.

(2) An explanatory science also claims to contain symbols
for those less clearly given events which are required for

208 INTRODUCTION TO PHILOSOPHY OF SCIENCE

explanation. The contrast with descriptive science is here
somewhat obliterated. As has been mentioned repeatedly,
data are given with continuously varying degrees of clarity.
Hence if one attempts to point out the most clearly given
data, he may be said to be describing; but if he symbolizes
the less clearly given data, he must be said to be explaining.
Descriptive science, for example, insists that the task of
science is the symbolism of the classiiicatory, serial, and
correlational features of events. But it is noteworthy that
descriptive science limits itself to the most obvious of these
features, i.e., it does not describe in terms of highly abstract
properties or series, nor does it refer to universal correla-
tions. The presumption is that these features of events ap-
proach the obscure, and hence would lead into explanatory
science. Reference to such entities would, in fact, constitute
border-line cases, and one might say with equal justification
that he is describing or that he is explaining. A mature
explanatory science represents the continuation of this
process of symbolizing more and more obscure entities.
Hypotheses of the type mentioned earlier in the chapter
(causes and effects, ends, elements and wholes, etc.) indicate
sciences which have become definitely explanatory. Since
it is not known that all events possess causes, effects, ends,
elements, or wholes, one is plunging into the realm of the
conjectural. He runs the risk of populating nature with
entities of his own creation. Hence he has abandoned
description and resorted to explanation.

INTENSIONAL FEATURES OF EXPLANATORY SCIENCE

Intensionally every explanatory science (1) exhibits a high
degree of integration, whose essential feature is (2) the
explanation of all descriptive symbols by means of hypoth-
eses.

(1) An explanatory science is a system of symbols rather
than a mere aggregate. An explanatory science is a de-
scriptive science in which every symbol has found its
proper place. A descriptive science is one in which no

EXPLANATORY SCIENCE 209

symbol has important relations to any other symbol; any
symbol might be removed from the scheme or modified with-
out affecting the other symbols in any significant way. The
integration of a descriptive science is achieved by introduc-
ing hypotheses which serve to relate apparently discon-
nected propositions by showing that they are jointly im-
plied by the hypotheses. Hence an explanatory science
which is precisely the expanded descriptive science, exhibits
relations of super-, and sub-, and coordination of proposi-
tions. Every proposition is either an underived proposition
(axiom, postulate, hypothesis) or a derived proposition
(theorem, corollary, descriptive law); and every derived
proposition takes its place subordinate to the hypothesis
from which it can be derived, and coordinate with all other
derived propositions deducible from the same hypothesis.
The ideal of explanatory science is the construction of a
single system of postulates from which all other propositions
in the system may be derived. The special and general
theories of relativity approach the ideal of such a postulate
scheme in the field of physics.

The increased compactness of an explanatory science is
accomplished by the introduction of highly integrating
propositions. Such a science is distinguished from a descrip-
tive science by the presence of universal laws in place of
statements of occasional correlations, and by the presence
of mathematical functional relations in the place of qualita-
tive correlations. Since explanatory science is not tied down
to what is clearly given it may ^assert universal laws, even
though they may be hypothetical in character. Hence one
may generalize in explanatory science from what happens
in a few cases to what happens universally and without
exception. This becomes an important instrument of in-
tegration, for every future case is derivable from such a
law. Furthermore, mathematical techniques of measure-
ment and correlation may be introduced. Relations of mere
presence and absence are replaced by relations of degree of
quantitative manifestation. For example, the colors become

210 INTRODUCTION TO PHILOSOPHY OF SCIENCE

arrangeable on a scale through the numerical measures of
their wave lengths; chemical substances become arrange-
able in a table on the basis of atomic weights; circles, ellipses,
parabolas, and hyperbolas become related through a general
quadratic equation. As a result every symbol in the system
takes on important relations to other symbols, and signifi-
cant information about any symbol may be obtained merely
by exploring its intensional features. Definition plays a
predominant role, which replaces that of illustration in
descriptive science. For as the system takes on integration
the meaning of any symbol becomes increasingly a function
of its associated symbols, and decreasingly a function of its
referent.

In view of this fact there arises a peculiar duplicity in the
meaning and truth of those descriptive propositions which
have been explained by the postulates. A descriptive
proposition has two very important relations, both of which
may be considered as contributing to its meaning and truth :
It has a relation to the fact which it describes, and it has a
relation to the postulate group from which it can be deduced
and by which it is explained. For example, the proposition
2 + 2 = 4 is descriptively true, since it states a fact about
stones, leaves, and other physical objects; but the proposi-
tion is also deductively true since it can be deduced from a
series of postulates constituting the logical foundations of the
number system. There is no difficulty here, since the proposi-
tion is true in both senses. But there are propositions which
are descriptively false yet deducible from postulate schemes,
and the question arises in such cases as to whether the
propositions are true or false. The answer is to be found in
considerations of the kind suggested in Chapter VII in the
discussion of analytic and synthetic propositions.1 Whether
a proposition of the kind in question is to be considered as
true or false depends upon whether the intensional relations
are or are not to be taken as regulative over the extensional,
i.e., whether the deducibility of a proposition from a postu-

» Pages 142-143.

EXPLANATORY SCIENCE 211

late set constitutes a ground for severing its connection with
empirical data. So far as descriptive science is concerned,
the answer here is definite; intension is never regulative over
extension, hence a proposition is true or false according as
it is descriptively true or false, regardless of its deducibility
from a postulate system. But the tendency in rational science
is to make intension regulative over extension, and hence to
say that a proposition which is capable of being deduced
from a postulate set is true no matter what its descriptive
reference may be. This is essentially equivalent to con-
sidering the relation between the Y and the X proposition
as analytic, and as depending therefore upon linguistic
factors rather than upon data. If the postulates do imply
the propositions in question, it is part of their meaning that
they do so, hence nothing empirical could ever constitute a
refutation of this fact; the postulates imply the propositions
in exactly the same sense that the meaning of the word
"triangle'1 contains the meaning of the phrase "three-
sided figure." The only alternative is to consider the relation
between the Y and the X propositions as synthetic, and as
depending therefore upon empirical data rather than upon
linguistic factors. If the postulates imply the propositions
in question it is only an empirical fact that they do so, hence
nothing in the character of language or logic could legislate
this away; the postulates imply the propositions in exactly
the same sense that the meaning of the word "body' is
connected with the meaning of the phrase "possessing
weight." According to this latter conception a descriptive
proposition is always true or false in an empirical sense, and
nothing in the character of postulate sets could make a
descriptive proposition which is empirically true false, or one
which is empirically false true.

This results in the development of a peculiar sensitivity in
explanatory sciences. Being highly integrated, they suffer
extreme shocks when new information necessitates a change.
For a change in any one part of the system requires modifica-
tions in all other parts. Mathematics experienced such a

212 INTRODUCTION TO PHILOSOPHY OF SCIENCE

shock last century with the formulation of non-Euclidean
geometries, and physics passed through a similar crisis with
the advent of the theory of relativity. Descriptive science is
able to make readjustments by specific modifications in the
region where the error is discovered. But in such explanatory
science there are no isolated regions; every element has
determinate relations to every other element. An explanatory
science is organic in the same sense that the human body is; a
purely localized disturbance may "make one sick all over."
(2) An explanatory science explains. Here, again, as in
the case of descriptive science, this statement may be a pure
tautology unless one interprets it. Explanatory science
answers the question "Why?" and thus eliminates all brute
facts. A brute fact is one which is unrelated, and might
equally well have been otherwise. There are no such facts
in a highly developed explanatory science. For every de-
scriptive proposition is derivable from an hypothesis, and
if it were otherwise the hypothesis would of necessity be
otherwise; but if the hypothesis were otherwise all other
descriptive propositions deducible from it would be different.
Hence no descriptive proposition can any longer be said to
assert a brute fact, for it has found its place in a general
system of propositions which represents a general system of
facts. Every descriptive proposition in the scheme has two
definite relations — one extensional, to the events which it
describes, and the other intensional, to the hypothesis from
which it can be deduced. The extensional relation verifies
the proposition, and the intensional relation explains the
proposition. For example, the proposition "This metal bar
expands when heated' is verified by a simple experiment
which produces the event described in the proposition. The
proposition in question is explained when it is shown that
it can be deduced from a general theory stating that the bar
is made up of molecules which are put into rapid motion
when the bar is heated, and which tend by the violence of
their motion to separate one from another and thus to in-
crease the space which is occupied by their aggregate.

EXPLANATORY SCIENCE 213

But a genuine hypothesis explains also in a more far-
reaching sense. Every hypothesis is an instrument of dis-
covery. As such it must permit the deduction of propositions
not included in the list of known descriptive propositions,
but such as to be later verified. Every hypothesis must be
fruitful. It must direct the attention of the investigator to
realms of nature not yet explored, and it must suggest novel
experimental set-ups. This function of anticipation, as has
already been seen, is a result of acts of creative imagination.
The precise way in which it operates in science will be con-
sidered in the next chapter.

REFERENCES

C. J. Keyser, Thinking about Thinking (New York: Dutton, 1926).
Pastures of Wonder (New York: Columbia University,

1929).
R. D. Carmichael, Logic of Discovery (Chicago: Open Court, 1930).
J. RuefF, From the Physical to the Social Sciences (Baltimore: Johns

Hopkins, 1929).
Norman Campbell, What Is Science? (London: Methuen, 1921),

Chap. V.
Physics, the Elements (Cambridge: Cambridge University,

1920), Chap. V.
F. M. Chapman and Paul Henle, Fundamentals of Logic (New

York: Scribners, 1933), Chap. IX.
J. W. Young, Fundamental Concepts of Algebra and Geometry

(New York: Macmillan, 1927), Chaps. IV, V.
A. Wolf, Essentials of Scientific Method (New York: Macmillan,

1925), Chap. IX.
A. C. Benjamin, The Logical Structure of Science (London: Kegan

Paul, 1936), Chap. XIII.

CHAPTER XI
VERIFICATORY TECHNIQUES

The fact that explanatory science develops not only
through the use of the techniques of discovery but through
the application of the verificatory techniques as well, unites
the present chapter with the preceding one in an intimate
way. Properly speaking, no hypothesis is truly such until
it has been verified. Consequently, a discussion of the
techniques by which hypotheses are discovered or devised is
insufficient. A genuine hypothesis must contain implications
with reference to novel data, i.e., it must be fruitful in
predictions. To assert this is to say, simply, that every
hypothesis must be such that if it were true there would
exist a certain specifiable state of affairs. The verificatory
techniques are concerned with the ascertainment of what
this state of affairs would be, and whether it actually exists as
predicted. To the extent to which the anticipations are
verified by the proper techniques the hypothesis takes its
place as an integral part of the more inclusive explanatory
science. Hence an established explanatory science must be
presumed to contain a certain number of such hypotheses,
once conjectural in character but now verified.

In order to prepare the way for this discussion of verifi-
catory techniques, a brief resume of the essential methods
employed in the formation of a hypothesis may be given.
This will duplicate, to a certain extent, material already
presented in earlier chapters, but some features not yet con-
sidered will be introduced. The topic may be called the
development of a theory.

DEVELOPMENT OF A THEORY

A theory may be said to develop through four stages. The
first is the preparatory stage in which the theory is still

214

YERIFICATORY TECHNIQUES 215

embryonic. This is the stage in which the science from which
the theory is to emerge is still at the descriptive level. The
techniques employed up to this point have been directed
mainly at getting the data through the introduction of
physical, physiological, and psychological operators, and
describing the data through the introduction of classifica-
tion, ordering, and associating. Only the most obvious
events are attended to. At this level there is no mention of
hypotheses or theories, though the foundation upon which
the theoretical structure will be built is being established.

The second stage is one in which there is recognition of the
insufficiency of mere description. It is seen that the task of
science is not merely the description of that which is ob-
viously given, but the explanation of this in terms of some-
thing which is less obviously given. Hence it is admitted
that the problem of science lies in the more or less imagina-
tive extension of the given and the resulting introduction
into science of conjectural, hypothetical, and theoretical
entities. The essential technique which is employed at this
stage is the method of construction. It recognizes the danger
in the use of the uncontrolled imagination, and endeavors to
keep the explanatory conceptions as close as possible to the
range of data. It attempts, so far as this is feasible, to derive
explanatory conceptions from the data. The methods of
abstraction and of concretion are the two most important
techniques at this stage; they aim to give to the conjectural
notion only such content as is demanded by the data. Hence
they are considered to be essentially elaborative, and not
sharply differentiated from the strictly descriptive tech-
niques.

The third and fourth stages constitute the most significant
stages in the development of a theory. For only at these
levels does the theory become truly explanatory. The
theory explains because it implies propositions descriptive
of the data. Hence the data are explained if there can be
found the required propositions making assertions about
hypothetical and conjectural entities, and of such a char-

216 INTRODUCTION TO PHILOSOPHY OF SCIENCE

acter that all of the propositions descriptive of the data can
be deduced from them. But since this body of descriptive
propositions includes not only those which are known to
apply to the data but also those which constitute anticipa-
tions of data not yet disclosed to perception, it is readily
seen that, if this is to be possible, the explanatory entity as
obtained through the method of construction must be in-
creased through activities of the imagination. If the con-
struct is merely derived from the data it cannot be turned
about and used to explain the data, nor can it be used to
predict data not yet observed. Hence these two stages
represent the theory as it undergoes progressive expansion
through the tentative attribution to it of the desired content.
The distinction between the third and fourth stages is
relative. In the third stage one attempts to increase the con-
tent of the explanatory entity in such a way as to permit the
deduction of the propositions already known to be verified,
i.e., the propositions descriptive of the original data of the
problem. In this activity one finds it hard to avoid the feel-
ing that he is cheating. He is deliberately giving the ex-
planatory entity such content as will permit him to deduce
propositions which he already knows; he is making the
hypothesis do precisely what he wants it to do. He can be
sure that the explanatory entity will explain because he has
developed it in such a way as to make it do exactly that
thing. But in the fourth stage, into which the third merges
imperceptibly, the investigator is not proceeding in such an
obvious way. Here he attempts to increase the content of
the explanatory entity in such a way as to permit the deduc-
tion of propositions not yet known to be true, i.e., proposi-
tions descriptive of data still to be discovered. This stage
constitutes the essential moment in the development of the
theory. Only in this stage has it become a genuine theory,
fulfilling its predictive function. Only in this stage has it
become really novel, enabling one to anticipate nature. Here
one no longer feels that he is playing the game unfairly. On
the contrary he recognizes that the activity of imaginative

VERIFICATORY TECHNIQUES 217

expansion rests upon insight rather than rules, upon pene-
tration rather than superficial awareness, and upon genius
rather than techniques. Whether this activity is considered
to be "creative" involving the "invention" of explanatory
entities, or "penetrative" involving the "discovery" of ob-
scure features of nature, depends upon one's general theory
of science, and need not be decided — if it can be decided at
all — at this point. It may be that scientific genius is like
artistic genius, founded upon the activity of imagination
which freely transforms and modifies the given; if this is the
case the third stage would be differentiated from the fourth
in the fact that in the latter the given has been definitely
increased by contributions which are the product of human
inventiveness. On the other hand, it may be that scientific
genius is characterized only by a peculiar insight which
enables it to explore the hidden recesses of nature, i.e., it may
be that the mental act which is responsible for a theory is
nothing more than the vague awareness of the existence of
certain data, heretofore undiscovered. If this is the case the
third stage would be differentiated from the fourth only in
the fact that the data to be explained by the theory are
clearly recognized in the former and only vaguely grasped
in the latter. At any rate, the techniques of the third and
fourth stages are not differentiated; so far as they can be
formulated at all they are such indeterminate operations as
serial extension and interpolation, cause and effect infer-
ences, and analytic and synthetic operations. In all of these
operations, however, the hypothetical expansion is a matter
which is not susceptible of formalization; it reduces ulti-
mately to a matter of insight or genius, which is to say that
it is essentially a mystery.

A theory which has developed through the four stages is
ready for verification. Whether the verificatory operations
are considered as contributing to the development of the
theory and hence as constituting a fifth stage in its growth,
or whether they are considered to be techniques of testing
or of corroboration, is a matter of no great concern. It is

218 INTRODUCTION TO PHILOSOPHY OF SCIENCE

clear that a theory is not properly such until it has under-
gone at least a minimum of verification; inadequacies in the
theory can be detected only by examining the predictions
in the light of the facts, hence a false theory may be said to be
one which has developed improperly or incompletely. This
would seem to argue for the thesis that verification of a
theory is the fifth stage in its development. But the move-
ment of verification, on the other hand, is quite strictly the
reverse of the movement of discovery. The movement of
discovery is essentially a movement from data to symbols,
from the clearly given to the obscurely given; while the
movement of verification is essentially a movement from
symbols to data, from the obscurely given to the clearly
given. The former is a leap in the quagmires of conjecture,
the latter is a return to the hard ground of fact. The former is
inductive, receiving its motivation from insight and imagina-
tion, and carried on most readily by those types of mind
excelling in spontaneity and suggestion; the latter is deduc-
tive, deriving its impulse from criticism, and pursued most
actively by those types of mind excelling in logical rigor.
Hence the movements seem to be different in kind and to
offer support for the thesis that in the movement of verifica-
tion the attitude and direction of the mind have been changed.
In the broadest sense of the term, verification may be
considered as a double movement. It involves, first, the
actual drawing of the implications from the hypothesis after
it has been expanded through the hypothetical method. This
may be called the movement of prediction. But it involves also
the act by which the implied notions are compared either with
existing data or with data which are capable of creation through
experimental methods. This may be called the movement of
confirmation. Each of these will be discussed briefly.

PREDICTION

The movement of prediction is one of deduction, and, as
such, seems to offer no significant difficulty. There are
recognized techniques of formal deduction. Hence the prob-

VERIFICATORY TECHNIQUES 219

lem of prediction apparently lies simply in the derivation
of the required propositions, by means of the rules of logic,
from the body of propositions characterizing the theory.
But the problem is not so simple. What is important about
any hypothesis is not what it implies formally but what it
implies contentually. The formal implications of a postulate
system are those which can be drawn merely through the
applications of the principles of logic; they are not based
upon the content of the system, and are therefore independ-
ent of what the system is about specifically. They are
expressive only of the highly abstract features of events —
features which belong to all events indiscriminately, and
hence of no importance where reference is made to a limited
range of events. The contentual implications, on the other
hand, are those which are based on empirical generaliza-
tions; they are expressive of the content of the system, and
are therefore dependent upon what the system is about
specifically. They are expressive of the more concrete ways
in which particular kinds of events are associated in nature,
and they are true only of events correlated in these ways.

As Carnap points out,1 one must recognize the need in
physical science for drawing consequences of two different
kinds from a given proposition. On the one hand are the
transformations which are based on logical rules, such as
are found in Principia Mathematica. But one could add to
such a system "transformation rules of an extralogical char-
acter, for instance some physical laws as primitive sentences,
as, for example, Newton's principles of mechanics, Maxwell's
equations of electro-magnetics, the two principles of thermo-
dynamics, and such like." Carnap calls the former L-rules
and the latter P-rules, and the respective consequences
L-consequences and P -consequences, a distinction which may
be generalized here in terms of formal rules and consequences
and contentual rules and consequences. For example, the
proposition, " Matter is made up of molecules, and molecules
increase their rate of motion through the application of

1 Philosophy and Logical Syntax, pp. 50-54.

220 INTRODUCTION TO PHILOSOPHY OF SCIENCE

heat," formally implies a number of propositions. It implies,
"Matter is made up of molecules," "Molecules increase
their rate of motion through the application of heat,"
"Matter is made up of molecules or of atoms," "Molecules
increase or decrease their rate of motion through the ap-
plication of heat." But none of these propositions conveys
any very important new information about molecules. They
are all possible by virtue of the fact that the proposition
in question has the form "jo and 9," from which the proposi-
tions "jo," "g," "jo or r," and "g or s" follow without regard
to content. The contentual implications of the proposition
in question, however, are somewhat more informative. If
the application of heat to bodies increases the speed with
which the molecules are moving, it follows that bodies will
expand when heated. If matter is made up of molecules in
motion, it follows that gases placed in the same container
should diffuse, and that certain solids immersed in fluids
should dissolve. Only implications of this kind have any
value as instruments of verification; they follow from the
particular assumption about the molecular character of mat-
ter, and would not, presumably, follow from any alternative
theory. Hence they are implications which permit decision
to be made as to the adequacy or inadequacy of a theory.
Formal implications permit no such decisions to be made.

But whereas formal implications are of no great use in
verification, they are the only techniques for which there
are rules. There are no rules for the drawing of contentual
implications. No formal analysis of the notion of molecules
would enable one to predict what empirical phenomena
would exist if there were such things as molecules. The
only justification for a contentual implication is an empirical
generalization. 'Man' implies 'mortality' because all
men are mortal; "metal" implies "conductor of electricity'
because all metals are conductors of electricity; "increase in
pressure of a gas" implies "decrease in volume" because all
increases of pressure are accompanied by decreases in volume.
One proposition contentually implies another because the

VERIFICATORY TECHNIQUES 221

facts which they describe, respectively, are related in nature
in a specifiable way.

But this does not meet the difficulty which is involved
in making predictions from hypotheses. Only the contentual
implications of the hypothesis count. But empirical gen-
eralizations are of no avail in making predictions from
hypotheses. For every hypothesis designates an entity
which is not certainly known to exist. Hence, in the very
nature of the case there can be no descriptive generalizations
expressive of the behavior of hypothetical entities. Every
hypothesis, considered as a postulate for the drawing of
implications, represents a contrary-to-fact condition. It
has been debated by philosophers whether any consequence
follows from a contrary-to-fact condition. Certainly no
strictly contentual implication can be drawn. It may be
insisted that an hypothesis designates not a contrary-to-
fact condition but merely a different-from-fact condition.
But in either case the empirical foundation for the gen-
eralization has disappeared, for the hypothesis refers to a
state of affairs which has never been observed and which
therefore has never been described in generalizations.

It follows that there is no technique for prediction. Here,
again, resort must be had to more or less imperfect analogies.
If molecules have never been observed, one simply cannot
know how they will behave. But billiard balls in a bushel
basket can be observed and crude analogies can be drawn
from such behavior. Furthermore, operations of serial ex-
tension upon such objects, involving consideration of them
as getting smaller and smaller, and more and more elastic,
can be performed. To be sure, in this process of refinement
the objects will almost certainly lose many of their empirical
properties; but they will probably retain some of them, and
the nature of the operation of refinement should tell the
investigator roughly what these are. But every prediction
from the resultant entity can be no better than probable.
Necessary prediction from hypotheses seems impossible. All
that can be said is that predictions will be more or less

222 INTRODUCTION TO PHILOSOPHY OF SCIENCE

probable according as the realm of the clearly given exhibits
events more or less like the hypothesis in question. If there
are events of a closely similar character, the empirical
generalizations descriptive of the behavior of such events
may be taken as the foundation for predictions from the
hypothesis, and such predictions will have a certain plausi-
bility ; but if there are no events of a closely similar character,
the only foundation for the prediction is some less closely
related empirical generalization which is then imaginatively
modified through such activities as abstraction and idealiza-
tion. Predictions in such cases will have a correspondingly
lower degree of plausibility.

Reference should be made to a further feature of the pre-
dictive act. In order that the verificatory movement may
be carried out it is not sufficient simply that implications
be drawn from the hypothesis; the consequences must be
such as can be either confirmed or infirmed x empirically.
Ry this is meant not that the predictions must be such as
can be corroborated by data, though such must be the
character of the predictions if the theory is to be estab-
lished; what is meant is, rather, that the predictions must
be of the general kind which have relevance to empirical
data, i.e., they must be of the kind which can be unequivo-
cally confirmed or infirmed by experience. Hence the draw-
ing of an implication which demands the performance of an
impossible physical experiment, or the assuming of an im-
possible observational point of view, would be illegitimate.
Furthermore, the implications must be such as to refer to
the range of the more clearly given data; no verification of
hypotheses, which by their very nature refer to the obscurely
given events, can be made if the implications drawn from
the hypotheses do not take one out of the realm of obscurity.
From this it follows that verifications of highly abstract
hypotheses (e.g., the law of universal gravitation) cannot be

1 The term "infirm" may be used in what follows to designate negative verifica-
tion or negative confirmation. Thus the proposition "Today is hot" would be con-
firmed if the day is hot, but would be infirmed if the day is cold. This use is closely
similar to that of Nicod, though not identical with it. See Chapter XVI, p. 361.

YERIFICATORY TECHNIQUES 223

made in terms of further high abstractions but must be
made through concretions (e.g., balls rolling down inclined
planes); verifications of microscopic phenomena (e.g., mole-
cules) cannot be made in terms of further microscopic
phenomena but must be made through macroscopic objects
(e.g., expanding bodies); verifications of idealizations (e.g.,
perfect levers) cannot be made in terms of other idealizations
but must be made through actual objects (e.g., real levers).
In every case the language of the hypothesis must be
"translated" into the language of empirical data. Nor-
man Campbell 1 suggests that every theory contains a "dic-
tionary' by which ideas inside of the theory are related
to other ideas whose truths are determined independently
of the theory. It is by means of a dictionary that one passes
from mathematical equations containing only numbers to
the objects of which the numbers represent measured values.
This is merely an alternative formulation of the necessity
for providing a technique by means of which the essentially
unverifiable entities constituting the hypothesis can be re-
lated to more empirical entities. It is an additional corrobo-
ration of the thesis, already insisted upon in Chapter X,
that every rational science must retain its empirical refer-
ence; without the descriptive propositions from which it
has been derived and in terms of which it is verified it
becomes purely arbitrary; it has the same status as an
hypothesis which has not been verified.

CONFIRMATION AND INFIRMATION

Confirmation and infirmation are the operations by which
the predictions from hypotheses are established or dises-
tablished. The scientific procedure as a whole is essen-
tially a series of inductions and deductions, guesses and
corroborations, flights and perchings. The confirmatory-
infirmatory movement is that part of this total movement
by which the imagination is restrained and kept relevant
to the data. It is the act in which the scientist endeavors

1 Physics, the Elements, pp. 122 el seq.

224 INTRODUCTION TO PHILOSOPHY OF SCIENCE

to verify his imaginative efforts by returning to the realm
of data from which he departed in search of explanatory
conceptions.

It should be clear that the heart of this act lies in percep-
tion, which is, as was suggested in Chapter V, the essential
method for getting events. All that was said in that con-
nection may be repeated here, with a slight shift in empha-
sis. Whereas perception in the context of the movement
of discovery is aimed at the derivation of symbols, percep-
tion in the context of the movement of verification is aimed
at the verification of symbols. One perceives not merely
to get ideas but to establish conjectures. The significant
difference in the perceptual act in the two cases lies in the
greater emphasis on control in the latter case. In the
former, one observes anywhere and at any time for the
purpose of noting anything that might occur; in the latter,
one observes a specific spatio-temporal situation for the
purpose of noting whether a specific event occurs. There is,
consequently, in the latter case, a definite psychological
framework within which the perceptual act takes place;
attention becomes keener because of the functioning of the
psychological operators. But there is a corresponding prone-
ness to error, since the mind tends to read preconceived
ideas into the physical situation. Bacon was so conscious
of this fact that he placed undue emphasis on the movement
of discovery, hoping by this to eliminate the verificatory
act. It seems futile to argue whether facts precede hy-
potheses or hypotheses precede facts. Certainly at the stage
in which science emerges upon the scene both facts and
hypotheses are given. It is quite unlikely that a pure fact,
without an increment of interpretative material, is ever
perceived; and it is equally unlikely that a pure hypothesis,
without connection with any observed fact, is ever conceived.
Mind is not a tabula rasa, as Locke supposed, nor does it
approach the world with a bundle of fixed forms into which
facts are to be fitted, as Plato suggested. All that need
be recognized for science is that investigation into nature

VERIFICATORY TECHNIQUES 225

is sometimes primarily a search for forms, and at other
times primarily a verification of previously suggested forms.
Both movements are essential to science.

A similar distinction may be made between experiments
for discovery and experiments for verification. As was
pointed out in Chapter VI, the more usual sorts of experi-
ment belong in the latter class. The essential difference
between the two is that experiments for discovery are
unguided, while experiments for verification are guided. The
guiding factor in the latter case is a preconception as to
the nature of the outcome. In the inductive experiments
there is no foreseen knowledge of the result; manipulations
are made in a more or less random way, and the results of
the changes are noted and recorded. But in verificatory
experiments there is an anticipation of the result; it is
predicted that a change of a specified character should
bring about another change of a specified character. In
the former case one is merely learning from nature; in the
latter he is, in a sense, legislating for nature, since he is
using his acquired knowledge of her behavior in other realms
to predict her character in a given realm. He is saying to
nature, in effect, "If you have not been deceiving me you
must behave in such-and-such manner in the present sit-
uation." Verificatory experiments are therefore much more
complex than inductive experiments, for one's previous ex-
perience with nature suggests myriads of ways in which
changes may be introduced into it. In pure observation
one merely listens to nature, in -experiments for discovery
he prods nature to make it speak, in verificatory experi-
ments he asks nature questions — in fact, he asks questions
which are definitely leading, and he is justly surprised when
he receives negative answers. Consequently verificatory
experiments are much more decisive than inductive ex-
periments.

The distinction which is commonly made between ob-
servational and experimental verification is largely relative.
For example, it may be maintained that the proposition

226 INTRODUCTION TO PHILOSOPHY OF SCIENCE

''Sodium is silver in color' can be verified observationally,
but the proposition "Sodium burns with a yellow flame"
must be verified experimentally. However, if all perception
involves control the difference between these two situations
cannot be great. Both propositions can be expressed in the
following form: "If I place a piece of sodium in a certain
physical situation (characterized merely by certain condi-
tions of atmosphere and light in the one case, and by the
presence of a flame in the other), and if I focus my eyes
and attend to what is taking place, I shall perceive a cer-
tain event (a silvery luster in the one case, and a yellow
flame in the other)." The only difference between the two
situations is that the modification introduced into the first
situation is not presumed to transform the end-object, while
the modification introduced into the second is. If experi-
mentation is defined as the introduction into nature of
changes which would not have occurred without man's
intervention, the distinction between observation and ex-
perimentation becomes quite obliterated. For man is himself
a natural object, and whenever he observes in a controlled
manner he introduces changes into nature. None but the
most passive sort of observation, therefore, would be non-
experimental in character. As a working distinction between
the two, one may say that experimentation involves con-
trol over both the observer and the observed, while observa-
tion involves control only over the observer.

The so-called experimental methods of John Stuart Mill x
have application in this connection, though their use is
somewhat more limited than the prominence given to them
by logicians would lead one to believe. In their narrowest
scope they have reference to the problem of the ascertain-
ment of causes from effects, or of effects from causes. In
their broadest scope they may be considered as techniques
for the determination of laws, or correlations (of which
causal correlations are a species). They are not, properly

1 Svstem of Logic (7th ed., London: Longmans, Green, 1868), Book III,
Chaps. VIII, IX.

VERIFICATORY TECHNIQUES 227

speaking, methods for the discovery of conditions, as their
name implies, but rather methods of verification; they are
useless unless the investigator has some conception, how-
ever vague, as to what kind of event may be the condition
which is being sought after. They are not, therefore, prin-
ciples which enable one to infer conditions from consequents,
or the reverse; they are rather principles of location. Based,
as they are, upon the general kind of connection which
condition and consequent bear in nature, they guide ex-
perimentation in the sense that they instruct one where and
when to look for conditions, given consequents, and where
and when to look for consequents, given conditions. This
makes them important techniques, especially of infirmation.
What should be insisted upon with reference to them is
that their use is somewhat more limited than their name
implies.

An important problem in confirmation is that which
arises when the predicted consequences fail to receive cor-
roboration, i.e., when they are infirmed rather than con-
firmed. The usual procedure is to reject the hypothesis
from which the deductions were drawn. It is commonly
recognized that many confirmations are required to estab-
lish an hypothesis, but one single infirmation is sufficient
to disestablish it. This is based upon the fact that the
hypothesis is the sufficient, but not the necessary, condition
for the predictions. Hence the failure of the predictions
permits one to deny the hypothesis, but the occurrence
of the predictions does not permit one to affirm the hy-
pothesis, for there may be alternative hypotheses each of
which is sufficient.

But what has not been so commonly recognized is that
there are alternatives to the complete rejection of the hy-
pothesis in cases where infirmation occurs. In the first place,
the hypothesis need not be rejected but may require only
modification. Every hypothesis is merely an aggregate of
propositions characterizing the hypothetical entity, and as
such suffers no serious shock if some members of the ag-

228 INTRODUCTION TO PHILOSOPHY OF SCIENCE

gregate are eliminated and replaced by others. The infirmed
prediction may have followed from certain of the proposi-
tions, but not from others. All that is required, therefore,
is to remove the undesirable elements, and replace them by
propositions which will have other implications. It is a
noteworthy fact that in the history of science no hypothesis
seems ever to have been completely discarded; it may have
gone through such extreme modifications as to be hardly
recognizable, but there is usually a permanent core which
persistently resists inflrmation. This is probably that part
which has been derived through the method of construction.
Around this center there gathers through successive acts of
imagination, a variety of fringes, each of which determines
certain predictions, to be subjected to verification. Those
predictions which receive confirmation become incorporated
into the hypothesis as part of its essential core; those which
receive inflrmation are rejected and replaced by alternates.
In this way the hypothesis expands and contracts, meanwhile
growing progressively in such a way as to retain both past
successes and past failures. It is still convenient, at times,
to explain in terms of the geocentric theory of the heavens,
the caloric theory of heat, the fluid theory of electricity,
and the homuncular theory of the origin of life. All of
these theories did actually explain at one time, in spite of
misleading and erroneous implications which can be drawn
from them. Progress in science consists not in the complete
abandonment of infirmed theories, but in their modification
in such a way as to retain their positive explanatory features.
In the second place, inflrmation may require not modifica-
tion or rejection of the hypothesis itself but merely a re-
examination of the reasons for supposing that the hypothesis
did imply the proposition which was infirmed. It has already
been shown that there are no rules for the drawing of con-
tentual implications. When the hypothetical entities are
such as have never been observed, one is quite unable to
assert with certainty anything as to their consequences.
Hence an infirmed prediction may prove to have been er-

VERIFICATORY TECHNIQUES 229

roneously drawn from the hypothesis. The amateur detec-
tive often finds to his dismay that the concept "murderer"
does not strictly imply the many things which he sup-
posed it to imply, and consequently that the one who ac-
cording to his reckoning could not have committed the
murder is the one who really did. Even empirical generaliza-
tions are subject to exception, and these generalizations
which are founded on the imaginative anticipation of what
would occur from a state of affairs nowhere realized cannot
be expected to have a high degree of necessity. Hence it is
always advisable to reconsider the implicative relation before
rejecting the hypothesis.

In the third place, infirmation may be due to the failure
to exert proper control either over the experimental or over
the observational set-up. All verification, as was pointed
out earlier in the chapter, involves noting what happens
when certain conditions, partly in the observer, and partly
in the physical medium, are established. That sodium burns
with a yellow flame can be confirmed if the observer places
his body and mind in a certain state of readiness, and if he
places a piece of sodium in the physical situation which
will produce the burning. But through inadvertence the
observer may fail to realize one or more of these conditions;
he may fail to look when the flame occurs, or he may not
be attending to the event and thus he may fail to see it,
or he may not have been sufficiently careful in setting up
the physical situation. Under any of these conditions the
predicted yellow flame may fail to occur for the awareness
of the observer. Examination of these conditions should
therefore be made before the hypothesis is rejected. Such
examination involves, on the part of the observer, the as-
certainment of whether normal conditions of observation
prevail; the establishment of normal conditions in the case
of the movement of verification is more difficult than in the
case of the movement of discovery, for preconceived ideas
are important sources of error; the observer is prone to
read into the situation that which he expects to occur. But

230 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the examination also involves, so far as nature itself is
concerned, the ascertainment of whether the conditions
demanded by the experiment have actually been realized.
This is a complicated problem requiring both knowledge of
the situation and skill in manipulation of instruments. Only
those who have experienced the chagrin of a carefully pre-
pared experimental lecture-demonstration — which failed at
the critical moment to function as predicted — can appreci-
ate the complexity of conditions which are here relevant.
What is to be emphasized at this point is merely that in a
case of infirmation a careful examination of all of the ob-
servational and experimental aspects should be made before
the hypothesis is rejected.

With this discussion of verificatory techniques the con-
sideration of problems in the logic of science ends. The
attempt has been made merely to outline the structure of
scientific method and doctrine and to indicate the main
types of problem which arise. Concrete application of
many of the principles here disclosed will be made in Part
Two.

REFERENCES

A. D. Ritchie, Scientific Method (London: Kegan Paul, 1923),

Chap. VI.
Frederick Rarry, Scientific Habit of Thought (New York: Columbia

University, 1927), Chap. III.
J. S. Mill, System of Logic (London: Longmans, Green, 7th ed.,

1868), Rook III, Chaps. VIII, IX.
W. S. Jevons, Principles of Science (London: Macmillan, 1907),

Chaps. XIX, XX, XXIII.
J. A. Creighton, Introductory Logic (New York: Macmillan, 1922),

Chap. XIX.
A. Wolf, Essentials of Scientific Method (New York: Macmillan,

1925), Chap. VII.
E. A. Rurtt, Principles and Problems of Right Thinking (New York:

Harper, 1928), Chap. IX.

PART TWO

PROBLEMS IN THE ANALYSIS
OF THE CONCEPTS
OF SCIENCE

AS2S5 H^X<t

CHAPTER XII

PROBLEM OF THE ANALYSIS OF SCIENTIFIC

CONCEPTS

The problems which are associated with the analysis of
the basic scientific concepts are, perhaps, the most difficult
in the philosophy of science. There are several reasons for
this. In the first place, consideration of problems of such
an abstract character requires a skill in the analysis and manip-
ulation of highly general and highly technical notions which
is comparatively rare. In the second place, the problems
themselves demand for their solution a peculiar combination
of logical acumen and metaphysical insight; questions of
the nature of explanation are interfused with questions
of the nature of the given; and there arises the problem of
distinguishing that part of the meaning of any concept
which is due to operations of the mind performed upon the
data, and that part which is due to the data themselves.
In the third place, problems of this type demand a greater
familiarity with the content of science than is the case either
with problems of method or with speculative problems; in
order to analyze symbols as they are used in science one
must know how they are used in science. In the fourth
place, and most important, the problems themselves have
not yet received any precise formulation; authorities seem
to agree that there is a significant task to be performed
here, yet they seem unable to come to any agreement as
to the exact character of the task or how it is to be under-
taken. As a result, one is obliged either to fumble along
without any well-defined conception of the proper procedure,
or to formulate the problem according to his own ideas even
at the risk of being charged with an essential misconstruing
of the task.

As a consequence, no universality can be claimed either

233

234 INTRODUCTION TO PHILOSOPHY OF SCIENCE

for the formulation of the problem or for the illustrative
solutions which are presented in the following pages. What
is offered is merely a proposal. The attempt has been made
to define the problem in a way which will make intelligible
the many writings on the subject. A common conception
of the task is, I believe, discernible in the mass of material,
though the authors themselves are not always clearly con-
scious of its character ; the general problem and the outlines
of its solution seem to be implicitly rather than explicitly
recognized. The proposed formulation may be examined
immediately.

GENERAL CHARACTER OF PROBLEM

The terminology in which the problem is expressed is
unfortunate. Properly speaking, the question is not merely
one of concepts but one of propositions as well. Science is
based not only upon unexamined ideas but on uncriticized
beliefs. Hence the problem is to determine not merely what
the concepts of science mean but what the justification is
for the mass of assumptions about an external world, a
uniform nature, the existence of causes, and so on. Con-
cepts, of course, are neither true nor false; the only legitimate
problem in connection with them is one of meaning. But
propositions, or judgments, are both meaningful and either
true or false; hence questions of both kinds may arise in
connection with this type of symbol.

But from a more general point of view the differences
between these two types of problem are not great. For both
meaning and truth are determined by essentially the same
techniques. A concept is meaningful and a proposition is
both meaningful and true either extensionally, i.e., by refer-
ence to the realm of events, or intensionally, i.e., by refer-
ence to other symbols. Hence the problem is primarily one
of establishing the relationships which any given symbol
(concept or proposition) bears, on the one hand, to events,
and, on the other, to symbols.

A recognition of this common feature seems to place the

ANALYSIS OF SCIENTIFIC CONCEPTS 235

problem in its proper perspective. The problem of the anal-
ysis of the concepts of science is approximately as follows:
To clarify the meanings of vague concepts, and to establish
the truths of doubtful propositions by showing the relations
which they bear either to events, or to concepts whose meanings
are more clear and propositions whose truths are more certain.
It may thus be considered as a problem of "reduction,"
for something which exhibits important deficiencies or inade-
quacies is replaced by something else upon which it in some
sense depends and which lacks these deficiencies and inade-
quacies. It is obvious, for example, that meanings of words
can be clarified by pointing to the objects which they desig-
nate; the meaning of the word "time" can be understood
if one can discern from the background of events that gen-
eral feature which is time. Meanings can also be clarified
by the method of definition; the meaning of the word
"motion" can be understood if one points out that it is
equivalent to "change of space with respect to time."
Truths can be ascertained by referring to facts; for example,
the truth of the proposition "This substance is yellow" can
be determined by examining the substance. But truths can
also be ascertained from other truths; for example, the
proposition "2 + 2 = 4" is true by virtue of the postulate
system which defines the natural numbers and the operation
of addition. Thus one clarifies meanings and justifies truths
by disclosing relationships to other entities. Just why
this activity should be called "analysis" is somewhat hard
to see; it is probably not such in the vague sense in which a
whole is analyzed into its parts. But if one considers that
every symbol participates in a large complex of relationships,
both to events and to other symbols, he realizes that certain
of them must be more highly determinative of meaning
and truth than others. Analysis is the act by which those
relations which are significant in the ascertainment of the
meaning and truth of a given symbol are selected. A man
may have relations to his friends, business associates, wife,
and children, but when he is spoken of as a "husband" the

236 INTRODUCTION TO PHILOSOPHY OF SCIENCE

relation to his wife immediately becomes selected as essen-
tial. The problem of the analysis of the basic concepts of
the sciences is concerned with a similar selection of relation-
ships with regard to symbols in general.

However, if the problem is thus formulated it can be for
the purposes of science greatly simplified. Science is defi-
nitely empirical in its ultimate reference. As a consequence
the essential reference of any symbol is to the realm of
events, and both truth and meaning must be determined
by this route. The problem of truth and meaning cannot
be solved finally by reducing symbols to other symbols, for
the resultant symbols are themselves inadequate unless their
empirical reference can be readily ascertained. Hypotheses
are both defined and verified in terms of data, as has already
been seen. No hypothesis can be clarified by defining it in
terms of another hypothesis which is equally vague, and no
proposition can be justified by deducing it from other propo-
sitions whose truths are equally doubtful. The only alterna-
tive to this principle is the admission of innate ideas and
self-evident propositions — both of which are contrary to
the empiricism of science. Hence extension predominates
over intension in the ascertainment of truth and meaning,
and the ultimate reference of any symbol is to the realm of
events.

This is not, of course, to deny that the operations which
are employed in the determinations of both meaning and
truth may be very elaborate. In fact, it is the formulation
of these operations which is the core of the problem. An
important question to be asked with regard to every symbol
is, "To what events does it refer?' But a still more im-
portant question is, "How does it refer to these events?'
The meaning and truth of a symbol are a function not
merely of the events to which it refers but also of the manner
of referring to these events. Symbols are descriptions,
classifications, correlations, associations, generalizations, ab-
stractions, measurements, idealizations, limits, and interpola-
tions. All of these are descriptions of the way in which

ANALYSIS OF SCIENTIFIC CONCEPTS 237

symbols have been obtained from events, and, consequently,
of the way in which they refer to events. Hence to tell
what events a symbol refers to is to tell only a part of the
story.

The task of the analysis of scientific concepts can be
defined as the attempt to answer three questions with refer-
ence to each of the basic notions and each of the assumptions
of science. (1) To what, presumably, does the concept or
proposition in question ultimately refer in the realm of
events? This may be called the problem of the empirical
foundation, or of the descriptive reference of the symbol.
(2) What does science itself consider to be the meaning
and truth value of the symbol? This may be called the
problem of the scientific content, or the scientific status of
the symbol. (3) What is the character of the relation which
the symbol, considered in its scientific meaning and truth
value, bears to the realm of events? This may be called the
problem of the relation of the scientific content of the symbol
to its empirical foundation.

A quotation from CD. Broad illustrates the problem as
thus formulated. He is discussing the character of our
knowledge of space as obtained through common sense.
"We notice that all the information gained in this way is
extremely crude, as compared with the concepts that we
use in geometry and apply in physics. We see and feel
finite surfaces and lumps of complicated shapes, not the
unextended points and the lines without breadth of the
geometers. And the spatial relations that we can immedi-
ately recognize between outstanding patches in our fields
of view are equally crude. They are not relations between
points and straight lines, but between rough surfaces and
volumes. . . . These crude objects of sense-awareness do
have properties that are evidently spatial, and ... we
can see in them the germs of the refined notions of points,
straight lines, etc. The question is: 'How are the refined
terms and their accurately definable relations, which we use
in our mathematics and physics, but cannot perceive with

238 INTRODUCTION TO PHILOSOPHY OF SCIENCE

our senses, connected with the crude lumps or surfaces, and
their rough relations, which we actually do sense?' . . .
What we want to do is to analyse finite figures and their
fearfully complicated perceptible relations into sets of terms
with simpler and more manageable relations. If we can
do this successfully we shall have killed two birds with
one stone. We shall have done full justice to the spatial
properties of what we can perceive; for our analysis is sup-
posed to be exhaustive. And, on the other hand, we shall
be able to grasp these properties and to reason about them
in a way that was impossible while they remained in the
crude unanalysed state in which we meet them in sense-
awareness." * Though the three problems are not specifically
distinguished in this quotation, the threefold character of
the pursuit is clearly evident. One is obliged, first, to de-
scribe the rough surfaces and volumes of immediate ex-
perience; secondly, one must define the refined points and
lines of mathematics; thirdly, one should show how the
latter are derived from or reducible to the former.

An essentially equivalent formulation of the problem is
to be found in Russell. ' The first thing that appears when
we begin to analyse our common knowledge is that some
of it is derivative, while some is primitive; that is to say,
there is some that we only believe because of something
else from which it has been inferred in some sense, though
not necessarily in a strict logical sense, while other parts
are believed on their own account, without the support of any
outside evidence. It is obvious that the senses give knowl-
edge of the latter kind: the immediate facts perceived by
sight or touch or hearing do not need to be proved by argu-
ment, but are completely self-evident." 2 Data of this kind
may be called "hard," or psychologically primitive, and
are to be contrasted with "soft" data, which are psycholog-
ically derived. 'Psychologically, a belief may be called
derivative whenever it is caused by one or more other
beliefs, or by some fact of sense which is not simply what

1 Scientific Thought, pp. 35-36. 2 Our Knowledge of the External World, p. 68.

ANALYSIS OF SCIENTIFIC CONCEPTS 239

the belief asserts. Derivative beliefs in this sense constantly
arise without any process of logical inference, merely by
association of ideas or some equally extra-logical process." x
Hence it is possible for a belief to be psychologically derived
but logically primitive, since it is not the result of any
logical deduction. "We naturally believe, for example,
that tables and chairs, trees and mountains, are still there
when we turn our backs upon them. . . . The belief that
they persist is, in all men except a few philosophers, logically
primitive, but it is not psychologically primitive; psycholog-
ically, it arises only through our having seen those tables and
chairs, trees and mountains." 2 The basic problem then
becomes: "Can the existence of anything other than our
own hard data be inferred from the existence of those data," 3
i.e., can the existence of anything which is psychologically
derived be inferred from the existence of something which is
psychologically primitive? As applied to the field of physics
the problem is that of "bridging the gulf between the world
of physics and the world of sense." 4 The former reveals
" a set of indestructible entities which may be called particles,
moving relatively to each other in a single space and time" 5
while the latter reveals a mass of gross and changing objects,
located in private spaces and private times. The problem is,
then, "to show the kind of way in which, given a world with
the kind of properties that psychologists find in the world
of sense, it may be possible, by means of purely logical
constructions, to make it amenable to mathematical treat-
ment by defining series or classes of sense-data which can
be called respectively particles, points, and instants. If
such constructions are possible, then mathematical physics
is applicable to the real world, in spite of the fact that its
particles, points, and instants are not to be found among
actually existing entities." 6 The similarities between this
analysis and the threefold approach suggested above are
obvious.

1 Ibid., p. 69. 3 Ibid., p. 73. 5 Ibid., p. 104.

2 Ibid., p. 70. * Ibid., p. 101. 6 Ibid., p. 122.

240 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Since the discussion in the following pages will consist of
illustrations considered from the point of view of the three-
fold analysis, a brief consideration of each of the sub-
problems will be of value at this point.

(1) The first problem is essentially metaphysical, or, at
least, naturalistic. It is a problem of finding events of a
certain kind. Presumably, when the scientist uses such
words as 'time," "space," "substance," "number," and

'cause' and when he asserts that nature is uniform, he is
referring to natural objects. The events to which he refers
may be very elusive, and hence not open to direct inspection.
In fact the existence of a problem in connection with such
concepts and propositions suggests that their reference to
events is not of an obvious kind. Certainly one must not
be led to expect nature to reveal precisely the kind of thing
that science means by these terms, and it may prove to be
the case that nature reveals something which is only very
remotely like the scientific notion. One must recall that the
mind often operates upon empirically given entities and
introduces elaborate modifications and transformations. But
it seems likely that science does not begin with just noth-
ing. Perfect points, lines, and levers, ideal gases, friction-
less motion, isolated individuals, economic cities, Utopias,
and the like are not pure imaginative fancies but modifica-
tions of actualities. The mind is able to abstract, generalize,
pass to limits, and form associations, with a freedom which
is apparently very great, but it always seems to start with
something which is empirically given and which exhibits a
certain plasticity to modifications in these directions. Hence
the problem of primary importance is to determine what this
empirically given stuff is. The task is essentially descrip-
tive, though it often involves the discovery and clarification
of data which have been implicitly rather than explicitly
recognized. Consequently it is a problem which,* as will be
seen immediately, offers serious difficulties.

(2) Though the first problem is metaphysical, the second
is partly scientific and partly logical. It involves the exam-

ANALYSIS OF SCIENTIFIC CONCEPTS 241

ination of actual scientific doctrine and procedure with a
view to determining the meaning of certain concepts such as
"time," "space," "matter," "number," and "cause," and
the truth value of certain propositions such as the assertion
of the existence of a uniform and objective nature. Unfor-
tunately, however, this problem is also complicated by the
fact that the concepts and propositions in question function
in science in an implicit as well as an explicit way. Hence it
does not suffice merely to ask the scientist what he means
by these symbols, for he may never have taken the trouble
to think about them consciously. Consequently, he may
not be able to tell what they mean, or what he says about
them may be contradicted by the way in which he uses
them, or his description of them may involve a circular
process such as Eddington describes * as the cyclic method
in physics, in which potential is defined in terms of interval,
interval in terms of scale, scale in terms of matter, matter
in terms of stress, and stress in terms of potential again.
The point is that the problem of determining the meaning
of such symbols is not merely a scientific problem but also
a logical problem. It involves such considerations as the
analysis of assumptions and preconceptions, the examination
of the structure of logical systems, and ascertainment of the
function of measurement in the sciences. It should reveal,
for example, in combination with the problem of the em-
pirical foundation of scientific concepts, the essential dif-
ference between the time which is assumed by the physicist
and the time which is revealed in direct perception as the
actual going-on of events, or the space which is implicit in
geometry and the space observed as the relations of distance
and direction between natural objects. The fact that the
same word is used to describe the two notions in each case
does not imply that the notions are identical.

(3) The third problem is almost entirely logical, though
the border-line between the logical and the psychological
aspects is not sharply drawn. It may be formulated either

1 Nature of the Physical World, pp. 260-265.

242 INTRODUCTION TO PHILOSOPHY OF SCIENCE

as the attempt to determine the operational derivation of
symbols, or as the task of describing the techniques of the
verification of symbols. Both of these formulations consider
the symbols from the point of view of the routes by which
they are connected with events, and attempt to relate the
symbols as employed in science with their empirical founda-
tions. The object of this correlation is to reveal any dis-
crepancies between the two, and to prepare the way either
for showing how the scientific notion could be obtained from
its empirical foundation by the employment of certain de-
scribable operational techniques, or for showing how the
scientific notion could be verified in terms of its empirical
foundation by the use of certain techniques of verification.
The differences between the derivational techniques which
are psychological and those which are logical are not im-
portant. In general those which are unconscious, spontane-
ous, and varying from individual to individual are consid-
ered to be psychological, while those which are at least
partly reflective, more or less deliberate, and relatively
common to many minds are considered to be logical. The
logical in this connection is only the psychological which
has attained a certain standardization, deliberateness, and
social approval. Logical techniques are psychological tech-
niques which have achieved a certain formulation and thus
are available as tools for the attainment of ends. Verifica-
tion techniques may also, of course, be either psychological
or logical, though the logical techniques are usually em-
phasized. In the discussion which follows, the derivational
as over against the verificatory techniques will be empha-
sized. The justification for this approach to the problem lies
in the fact that verification is never possible unless some mean-
ing has already been given to the symbol in question. Hence
the derivational problem is not only temporally prior but also,
in a sense, logically prior to the problem of verification.

Though the proper formulation of the problem is an im-
portant step toward the determination of its solution, it is
only a first step; the difficulties to be encountered in the

ANALYSIS OF SCIENTIFIC CONCEPTS 243

various stages of the process are great. The remainder of
the chapter will be devoted to a consideration of the most
important of these difficulties.

DIFFICULTIES IN ASCERTAINMENT OF EMPIRICAL

FOUNDATION

The first difficulty is one to which reference has already
been made in connection with the difference between de-
scriptive and explanatory sciences, viz., the fact that the
empirically given is a variable, and fails to exhibit precise
boundaries limiting the range of "hardv data. Russell
himself admits that the distinction between "hard" and
"soft" data is one of degree.1 The given exhibits a strict
continuity with reference to the clarity or obviousness of
its elements. Some data are more clearly given than others,
but may be less clearly given than still others. Hence one
must admit something like levels in the empirically given.
For example, it seems certain that the private perceptual
space of the individual is more clearly given than the one
universal geometrical space presupposed by science. But
the application of analysis reveals the fact that the private
perceptual space of the individual is itself a construction
out of visual, tactile, and motor spaces; hence the private
space which was presumed to be psychologically primitive
turns out to be psychologically derivative. Similarly, the
scientific concept of order seems to have its empirical foun-
dation in the perceived relation of " betweenness " ; yet this
relation may itself be considered as a construction out of
more primitive data constituting the merely directional
features of events, e.g., right and left, above and below, etc.
The consequence of these facts is that the description of the
empirical foundation of a concept or proposition implies always
a conscious recognition that the level which is being chosen
as basic is only relatively so, and may prove upon further ex-
amination to be reducible to one still more primitive.

In the second place, one must be reconciled to the fact

1 Our Knowledge of the External World, p. 70.

244 INTRODUCTION TO PHILOSOPHY OF SCIENCE

that discourse about events on the empirical level is essen-
tially vague. This is due partly to the fact that all definition
must be in popular terminology, which is essentially obscure.
One must talk about time, for example, as the "going-on,"
or the "passage," or the "flow" of events; one must describe
space as the 'spread-out-character' of events; one can
explain a class only as a "heap," "aggregate," "collection,"
"pile," or "ensemble"; and one is obliged to characterize
matter by describing it as 'stuff," or "substance." But
the vagueness is due to a much more important cause.
Definition, in the strict sense, is not possible on the empirical
level. The clearness with which events are given is a per-
ceptual rather than a conceptual clarity, i.e., an extensional
rather than an intensional clarity. Definition is possible
only when symbols have been integrated into systems; but
on the empirical level this has not yet taken place. Symbols
must be clarified by the method of pointing, but not by the
method of definition. The function of discourse at this
stage is that of directing the attention to the place within
the realm of nature where the events in question can be
found, so that their characters can be determined by direct
inspection. Proper names, gestures, and pictorial symbols
are often more effective than abstract concepts. Discourse
is possible only in the sense that one may 'talk about''
the symbols in question. One must proceed as did Poinsot,
according to Claude Bernard: x "'If anyone asked me to
define time, I should reply: 'Do you know what it is that
you speak of?' If he said, 'Yes," I should say, "Very
well, let us talk about it." If he should say, "No," I should
say, "Very well, let us talk about something else."

But, in the third place, in addition to the ineffectiveness
of the method of definition and the consequent resort to
the method of pointing, one finds that the application even
of this latter method is not without difficulties. Pointing
is ambiguous. Events are highly complex entities and there

1 A. J. Lotka, Elements of Physical Biology (Baltimore: Williams and Wilkins),
p. 19.

ANALYSIS OF SCIENTIFIC CONCEPTS 245

is no way of directing one's gestures in such a way as to
indicate the phase or aspect of events to which he wishes to
call attention. For example, one cannot by means of point-
ing distinguish the smoothness from the hardness of an
object, or the shape from the size. One cannot, even by
means of proper names and pictorial symbols, direct the
attention of an individual unambiguously to the temporal
feature of the world, for time is a phase of objects and one
can never be assured that the listener has not confused the
temporal phase with some other with which it is associated.
Similar difficulties arise in the attempt to locate instances
of number and order. For example, the clarification of the
concept "twoness': may be attempted by pointing to a
pair of objects. But a pair of objects is a highly complex
event, of which not only the event as a whole but each of
the partial events exhibits spatial and temporal features,
shape, size, color, and so on; consequently there is no way
of indicating that it is the duality of the event and not one
or more of the associated aspects to which reference is being
made. As a result, the reduction of scientific concepts to
their empirical foundations and of assumptions to the em-
pirical facts which they presume to justify cannot be carried
out with any assurance of success. In case dispute arises
as to what is given, almost no means of settlement are avail-
able. It seems likely that the disagreement between positiv-
ists and necessitarians on the question of the empirical
foundation of causation is essentially of this kind; one group
maintains that nature exhibits only sequences, the other
insists that it discloses intrinsic connections as well. In a
case of this kind, resort to the method of pointing is useless,
yet similar difficulties arise in connection with the attempt to
point out the empirical foundations of all of the basic concepts.

DIFFICULTIES IN ASCERTAINMENT OF SCIENTIFIC

CONTENT

The second of the problems gives rise to further diffi-
culties. Analogous to the variability in the given there is a

246 INTRODUCTION TO PHILOSOPHY OF SCIENCE

variability in the levels of abstraction at which the scientific
concepts may be analyzed. For example, time and space on
the level of the Newtonian physics are not the same as the
time and space of relativity; and number may be defined
in such a way as to include only the positive cardinal num-
bers, or it may be generalized successively so as to include
the negatives, the fractions, the irrationals, and the imag-
inaries. The situation is even more confusing than this, for
by time and space may be meant simply the measured
values obtained by reading clocks and scales, and by num-
ber may be meant simply the rules according to which
certain arbitrarily chosen marks may be combined and
substituted for one another. At these extreme levels it seems
safe to say that the scientific concept has more or less com-
pletely lost its content; by attaining extreme generality of
application it has lost the features which distinguish it
from any other concept. The movement of science seems
to be always toward greater and greater abstraction. For
example, the attempt is made to identify the concepts of
mathematics with purely logical notions, the concepts of
mechanics with the concepts of mathematics, the concepts
of physics with the concepts of mechanics, and so on. Hence
one must recognize the importance of stating clearly at the
outset what stage of abstraction is being considered in his
analysis; conclusions which are applicable at one stage
may not be applicable at another.

Since this is an important difficulty, a few remarks may be
made relative to the position which will be taken in the
following chapters. Though much is to be gained by con-
sidering the concepts at a high level of abstraction, much
is also lost. Consider, for example, the use of measurement
techniques in science. By this process a qualitative event,
e.g., a force, a duration, or a motion, is replaced by a number
corresponding to the reading on an instrument; the force
is replaced, say, by the number 5 which represents so many
dynes, the duration by the number 2 which represents so
many seconds, and the motion by the number 3 which

ANALYSIS OF SCIENTIFIC CONCEPTS 247

represents so many centimeters per second. The presump-
tion of this view is that an entity can enter into physical
science only if it can be measured; physics talks only about
quantities, not about qualities. The outcome of the view is
that the subject matter of physics is pointer readings, a posi-
tion which has been made prominent in recent years by Ed-
dington. * Time then becomes identified with clock-readings,
space with readings on meter sticks, force with readings on
spring balances, and so on. But what should be remembered
is that this does not reduce time, space, and force to mere
numbers; time is the number obtained from a clock, but a
clock is different from a meter stick and a spring balance,
hence the nature of the instrument must be taken into con-
sideration in defining the measured value. This means
that the actual techniques of using the clock in an experimen-
tal set-up, and even the techniques employed in making the
clock in the first place, are part of the definitions of the
measured values. This makes the reduction of physics to
mathematics impossible. Physics is meaningless apart from
clocks, meter sticks, and spring balances, and all of these
instruments must be constructed and calibrated by percep-
tual differences in qualitative experiences. To lose these
qualitative aspects in the abstractions of science is to make
them essentially meaningless.

The problem here involved is very complex, and cannot
be solved at this point.2 What should be stated is merely
the point of view which will be taken in the ensuing chapters.
In what follows the concepts will not be taken at the high
level of abstraction which reduces them to mere numbers.
Recognition must always be made of the fact that the
number is a measured value of something, and this something
must be retained in a qualitative form. This is to deny not
the legitimacy of measurement, but only the exhaustiveness
of the reduction of quantity to quality. The distinctions

1 See below, Chapter XX.

2 See A. C. Benjamin, Logical Structure of Science (London: Kegan Paul, 1936),
Chap. XIV.

248 INTRODUCTION TO PHILOSOPHY OF SCIENCE

between time, space, and force remain in science even
though they are all "reduced' to measured values. Similar
considerations apply to that high abstraction of numbers
which generalizes them into meaningless marks manipulated
according to arbitrary rules.

In the second place, one must recognize the difficulties
which arise in the attempt to clarify the meanings of the
concepts and assumptions, even from the point of view of
the way in which they function in the science. Attention
has already been called to the fact that they are often im-
plicitly rather than explicitly present, and hence may never
have been consciously clarified even by the scientist himself.
In addition there are difficulties due to the technical char-
acter of the terminology which is often employed in the
definitions of these notions. But most important is the
recognition of what is involved finally in the very method
of definition itself. A definition is a statement of equivalence
between two symbols, one of which is better understood
than the other; hence definition involves the reduction of
an obscure symbol to a clear one. "Now, obviously the
process of definition can not be led back ad infinitum. It
must terminate in the undefined, or indefinable. Any dis-
cussion must begin with certain primitive concepts from
which it proceeds in an orderly way. Psychologically, it
would always be best to take as undefined those concepts
which are most clearly understood; but logically, such a
procedure might be very limiting indeed, being confined by
the circumference of the understanding to which we appeal.
What is best taken as primitive (or undefined) may there-
fore be some extremely complex idea, so far as understand-
ing is concerned. A glance at any mathematical system
easily convinces us that this is the case." : Thus definition
is not usually a reduction to the psychologically primitive
but to the logically primitive, as Russell uses these terms
in the quotation given on page 238. Broad points out that
what is logically most primitive in nature is not what is

1 R. M. Eaton, General Logic (New York: Scribners, 1931), p. 298.-

ANALYSIS OF SCIENTIFIC CONCEPTS 249

now most familiar to us.1 Hence we may find that the
techniques should be called logically rather than psycho-
logically elucidating. From this point of view there is rel-
evance in the following quotation from D'Alembert: 2
"The most abstract notions, such as the majority of man-
kind regard as the most inaccessible, are often those which
carry with them the greatest elucidating power: our ideas
seem to be blotted out by obscurity in proportion as, in
any object, we examine into its sensible properties." Unless
the distinction between logical and psychological elucidation
is kept in mind, this quotation is in essential conflict with
remarks made in connection with the problem of the empir-
ical foundation. Abstract ideas are logically clear but em-
pirically obscure; sense-data, on the other hand, are em-
pirically clear but logically obscure.

Finally, the clarification of the basic concepts and assump-
tions of science cannot possibly be made through the method
of pointing. Here the difficulty is not merely a matter of the
ambiguity in the denotative gesture, but a matter of the
inherent elusiveness of the entities in question. In fact
many scientists, as has already been seen, give to all such
entities a fictional status and refuse to find a place for them
in nature. They are essentially mental creations, and have
either no connection at all with the empirical realm or else
are so remotely related that it is absurd to look for their
empirical counterparts. One should not look for an infinitely
extended time in nature any more than he should look for a
perfect lever. Abstract space, number, order, and the like
are not natural entities but conceptual schemes for the
interpretation of nature, almost identical with the Kantian
forms of perception and understanding. While not all
scientists would go to this length in removing abstractions
from the realm of the given, most would agree that if such
entities do exist they must do so in a manner which is quite
different from that of ordinary events. Consequently they

1 Scientific Thought, p. 26.

2 Quoted by T. Ribot, Evolution of General Ideas (Chicago: Open Court, 1899),
p. 201.

250 INTRODUCTION TO PHILOSOPHY OF SCIENCE

cannot be easily located in space and time, and they do not
exhibit the ordinary sensible qualities. This is merely to
say that they are inherently obscure as empirical entities.

DIFFICULTIES IN ASCERTAINMENT OF OPERATIONAL

DERIVATION

The main difficulty in the ascertainment of the operational
routes by which the scientific symbols are derived from their
empirical foundations is the necessity for a previous knowl-
edge of the main types of operation which may be per-
formed. The techniques which have been employed in a
specific case can be more readily recognized if one knows
what the most common techniques are. But no satisfactory
classification of the operations of symbolic derivation has
ever been made. The list given in Chapter IX was merely
illustrative and made no pretension to completeness. As
will be recalled, the main types there mentioned were
abstraction (including measurement), concretion, serial opera-
tions, cause and effect inferences, and operations of analysis
and synthesis. It will be the task in the following chapters to
illustrate the uses of some of these methods with reference
to certain of the concepts. A more adequate classification
would insure a more accurate analysis.

Another difficulty is the fact that alternative operations
are often employed to derive concepts which are verbally
the same. The best known example of this is the two at-
tempts to derive the concept of the mathematical point.
According to the one method it is defined as the limit of a
series of gradually decreasing volumes; according to the
other it is defined as the enclosure property which is exhibited
by events through their capacity to extend over other
events and thus to generate a series. The former route is
that of serial extension, the latter is abstraction. Irrationals,

such as v 2, possess similar alternative routes of derivation;
they may be defined either as the limits of certain series of
increasing fractions, or as the class of such fractions. The
concept of force may be derived either as the cause of motion

ANALYSIS OF SCIENTIFIC CONCEPTS 251

or as the measure of motion; these suggest alternative routes
of derivation. The verbal similarity is a source of error, for
if the routes of derivation are different the concepts them-
selves would presumably be differently defined; at least
the concepts should be assumed to be different until the
routes of derivation have been demonstrated to be equiv-
alent.

In the third place, a proper understanding of the opera-
tional derivation of any symbol demands that one ascertain
whether the method has been that of construction or that
of hypothesis. The distinction between these two methods
has already been clarified.1 But the decision in any given
case is difficult to make. A symbol may be considered a
construction if it contains only such content as may be
derived from its empirical foundation through the use of
the required operation; but a symbol may be considered
an hypothesis if it contains such additional content as must
have been obtained through the use of creative insight.
The distinction is, of course, a fine one, and requires a pre-
cision in techniques which is not easy to attain. Further-
more, the difficulty is augmented by the fact that, although
one may know in a general way what the operational deriva-
tion has been, scarcely anyone knows specifically what the
rules for the employment of the operation are; hence he is
not in a position to estimate the operation as having been
correctly or incorrectly performed. The point is, simply,
that one does not know in any very precise way what ab-
straction, association, serial extension, and the rest are;
consequently he is not able to formulate any rules according
to which symbols should be given meanings through the
use of such techniques. As a further consequence, therefore,
one is not able to say when a symbol has been increased
through imaginative activities. This makes the discussion
of the operational derivation of scientific symbols essen-
tially unsatisfactory. The best that can be done is to throw
out certain suggestions, indicate obvious inadequacies, and

1 Chapter IX, pp. 185-186.

252 INTRODUCTION TO PHILOSOPHY OF SCIENCE

point out further directions for research. This represents
the condition of the problem today.

Since the following chapters are considered merely as
illustrative, they will be confined to the problem of the
meaning of the scientific concepts, and no reference will be
made to the problem of the validity of assumptions. The
procedures are essentially the same in the two cases. The
neglect of this latter problem is merely a convenience of
presentation, and should not be considered as a judgment
as to its unimportance.

REFERENCES

Th. Ribot, Evolution of General Ideas (Chicago: Open Court, 1897).
Bertrand Russell, Analysis of Matter (New York: Harcourt, Rrace,

1927), esp. Chap. I.
Our Knowledge of the External World (Chicago: Open Court,

1915).
C. D. Broad, Scientific Thought (New York: Harcourt, Brace,

1923), introd., Chap. I, also Part II.

E. W. Hobson, Domain of Natural Science (New York: Macmillan,

1923).
K. Pearson, Grammar of Science (New York: Macmillan, 1911).

F. Enriques, Problems of Science (Chicago: Open Court, 1914).

CHAPTER XIII
ORDER, NUMBER, QUANTITY

The concepts which will be subjected to analysis in this
chapter are those which are presumed to lie at the basis of
mathematics. Whether they are properly mathematical
concepts or not, however, need be of no concern. The point
of view seems to be gaining ground in recent years that
mathematics has no specific subject matter, but is consti-
tuted merely by its form. The famous definition of Benjamin
Peirce, "mathematics is the science which draws necessary
conclusions," 1 and the views of Russell, Wittgenstein,
Hilbert, and others are all in accord with this claim. For-
tunately, the dispute need not be settled here. All that is
required is the recognition that the concepts of order, number,
and quantity are implicitly present in a large part of scien-
tific investigation. They are thus basic in the sense that a
recognition of their natures is important to an understanding
of the sciences.

The order in which the concepts should be discussed is
more or less arbitrary. If one's concern were with the estab-
lishment of a postulate scheme in terms of which the con-
cepts could be defined, the decision as to order would be
important. The more complex of the terms should be de-
fined by means of the less complex, and the order of discus-
sion would therefore coincide with the order of logical
derivation. But since the present concern is also with the
problem of empirical foundation, the issue is not so important.
As has already been shown, the concepts which are empirically
most obviously given are not necessarily those which are log-
ically most basic. Hence it is of pedagogical convenience to
examine the concepts roughly in the order of psychological ac-
cession rather than in the order of logical deducibility.

1 American Journal of Mathematics, Vol. iv, 1881, p. 97.

253

254 INTRODUCTION TO PHILOSOPHY OF SCIENCE

order: empirical foundation

It seems obvious at the outset that nature does exhibit
situations which can be spoken of as orders, or arrangements,
and the initial problem is to select events of this kind and
examine their properties. Common sense is assured that
complexes such as the following should be spoken of as
series : the days of the week, the months of the year, points
on a line, the floors of a building, the colors in the spectrum
arranged in the usual way, individuals arranged according
to height, automobiles arranged according to cost, and so
on. Spatial and temporal relations are predominant in
serial situations, though they are not usually supposed to
define the orders in question. For example, the individuals
in a group may be said to have serial properties by virtue
of their differences in weight, yet individuals need not be
arranged in an actual order with the heaviest at one end,
the lightest at the other, and all intervening individuals
placed properly on the line joining the two. In the same
way, one may think of his pleasures as having an ordering
of intensity, though no physical arrangement of them would
be possible. Order, therefore, seems to be applicable to com-
plexes whose elements exhibit certain characteristic relation-
ships, and the problem is to determine the nature of these
relationships.

Agreement can be reached, in the first place, on the fact
that order is applicable only to events exhibiting a certain
complexity. A single, unitary event may not be ordered;
such an event may itself have position in a series, but it is
then considered in its relation to other events, and the total
group of events exhibits order. Serial arrangement is pos-
sible only with reference to the elements of a complex event.
But how great must the complexity be; e.g., would a two-
term complex suffice? The answer to this question depends
upon the level at which the empirical analysis has been
made. There is some justification for the contention that
order exists wherever there is an asymmetrical relation; l

1 For the definition of this notion see p. 123.

ORDER, NUMBER, QUANTITY 255

for example, Monday and Tuesday have an actual order
which would be different if Tuesday occurred before Mon-
day ; similarly father and son may be said to have a certain
order by virtue of the fact that the father begets the son
but the son does not beget the father. The question then
arises as to whether the asymmetrical relation is psycho-
logically more primitive than a three- termed relationship,
such as Monday-Tuesday-Wednesday, or father-son-grand-
son, and whether the greater complexity of this latter type
is essential to order. Since the question is largely a verbal
matter at this point it may be answered arbitrarily by sug-
gesting that order be denied empirical applicability to events
unless they exhibit a complexity which is at least threefold.

What is required, therefore, in the second place, is to
specify the character of the relational-structure which must
be exhibited by a three-termed complex in order to permit
the characterization of this complex as ordered. The re-
quired relational-structure may be described as one which
possesses betweenness. Betweenness may be defined as a
triadic relation in which there is a term such that (a) it has
an asymmetrical relation to each of the two other terms,
and (b) its relation to one of the terms is the converse of its
relation to the other.1 The element possessing this relation
would then be said to be between the other two. For exam-
ple, Tuesday is between Monday and Wednesday, since
there is a triadic relation characterizing the complex, of
such a kind that a certain element (Tuesday) is so situated
that it has an asymmetrical relation to Monday (succeeds)
and to Wednesday (precedes), and its relation to the one
is the converse of its relation to the other. A similar
relational-structure is exhibited by any three months in
the year, any three points on a line, any three floors of a
building, and so on.

The relational-structure may then be said to determine
the serial arrangement. Usually the arrangement which is

1 This is essentially equivalent to Russell's definition. See his Principles of
Mathematics (Cambridge: Cambridge University, 1903), p. 200.

256 INTRODUCTION TO PHILOSOPHY OF SCIENCE

adopted is one which is readily observable, i.e., one which
employs the relational-structure of time or space. Since
instants in time and points in space themselves exhibit
order, they become convenient instruments for the por-
trayal of orders which are not directly temporal or spatial.
For example, weights may be arranged by putting the least
heavy at the top of a column and the others below in order
of increasing weight; in this case the spatial relation of
'lying beneath' is taken as the equivalent of the non-
spatial relation of "being heavier than." Or pleasures may
be arranged by mentioning first the most intense pleasure
and then the less intense pleasures in order of decreasing
intensity; in this case the temporal relation of "succeeds" is
taken as the equivalent of the non-temporal relation of " being
less intense than." These are illustrations of empirical series.

order: operational derivation

However, it is not the task of science merely to discern
the obvious features of events. It is one of the functions of
the developing intelligence to disclose hidden relations
between events. But this requires greater precision in the
conceptual tools which are to be employed in the search.
Hence the scientist demands greater refinement in the
concept of order. This refinement is accomplished, as is
usually the case with the basic concepts, by an increase in
abstractness and generality. The ideal is to eliminate from
the empirical conception those features which are relatively
specific. The goal is to retain the relevance of the concept
to all of the empirical situations but to exclude all of those
aspects which tie the concept down to one situation rather
than another. The operation from empirical order to scien-
tific order is the same as that from redness to color, or from
color to quality in general. It is not an operation of neglect
in the sense that the specific qualities are merely dropped
out of consideration; rather the specific aspects are retained
in a feature which is generic to them. One does not pass from
redness to color or from color to quality in general by

ORDER, NUMBER, QUANTITY 257

dropping out something, so that what one ends with con-
tains less than what one started with; rather one retains
as a variable those features which were present as values.
The generalization of the concept of order may be exam-
ined from several points of view, all of which are essentially
equivalent. One is that of serial exlension. It seems obvious
that the relational-structure of an empirical series is not
changed by the discovery of an additional element; hence a
series does not become any less so by passing from a three-
termed series to an n-termed series. All that is required is
that the element designated as unique in the definition of
" betweenness v should no longer be considered as such; if
the series is ^-termed, where n is greater than 3, any ele-
ment except the first or the last may be the element which
was formerly spoken of as unique. Hence the attempt is
made to define the relation of betweenness in such a way
as to make it applicable generally to the series. An equiva-
lent result could be accomplished through an operation of
interpolation, i.e., by recognizing that an empirical series is
not changed by the discovery of a new element which would
presumably lie between two elements supposed to be adja-
cent; the notion of adjacency is not essential to the concept
of order. Through considerations of this kind many features
of the empirical series are seen to be essentially irrelevant
to the concept of order. It is seen that an order as such
involves no specific reference to the number of terms, except
that n must be at least 3 (or at least 2, if one wishes to in-
clude the directional features of nature under the concept
of order); this is to say that a series does not need a first
term nor does it need a last term in order to be a series. It is
also seen that an order as such involves no specific reference
to adjacency; this is to say that a series may have a term
between any two and still remain a series.

order: scientific content

The scientific concept of order, thus derived, is capable
of precise formulation. One of the most satisfactory of the

258 INTRODUCTION TO PHILOSOPHY OF SCIENCE

many descriptions of the concept is that given by E. V.
Huntington: x

If a class, K, and a relation, < (called the relation of order),
satisfy the conditions expressed in the postulates 0, 1-3, below,
then the system (K, <) is called a simply ordered class, or a series.
The notation a < b (or b > a, which means the same thing) , may
be read: "a precedes 6" (or "6 follows a"). The class K is said to
be arranged, or set in order, by the relation < , and the relation <
is called a serial relation within the class K.

Postulate 0. The class K is not an empty class, nor a class con-
taining merely a single element.

This postulate is intended to exclude obviously trivial cases. . . .

Postulate 1. If a and b are distinct elements of K, then either
a < b or b < a.

Postulate 2. If a < b, then a and b are distinct.

Postulate 3. If a < b and b < c, then a < c.

These three postulates may be called, respectively, the
postulate of connexity, the postulate of irreflexiveness, and
the postulate of transitivity.2 The logical independence of
these postulates, i.e., the fact that no one of them can be
derived logically from any of the others, is shown in Hunt-
ington by illustrations of systems which satisfy each two
of the postulates but not the third. As an example of a
series satisfying postulates 2 and 3 but not postulate 1, he
offers the class of all human beings throughout history, with
< defined as "ancestor of"; as an example satisfying 1 and
3 but not 2 he gives the class of all the natural numbers with
a < b signifying "a is less than or equal to 6"; finally, as an
example satisfying 1 and 2 but not 3, he suggests the class
of natural numbers, with < meaning "different from."

The generality of this postulate set is clearly seen in the
fact that nothing is said with reference to the number of

1 The Continuum (Cambridge: Harvard University, 1917), Chap. II.

2 The equivalence of this postulate set with the set given in Chapter VI, p. 122,
may easily be shown. The principle of connexity was not there stated as a specific
postulate, though it is equivalent to the assertion that an ordering relation must
exist between every two members; the principles of transitivity in the two cases
are identical; the principle of asymmetry which was given earlier as a specific
postulate may be shown to follow from the postulates 2 and 3 as given by Hunting-
ton. See ibid., pp. 10, 11.

ORDER, NUMBER, QUANTITY 259

terms, whether there is a first or last term, or whether the
terms of the series are adjacent. This permits the applica-
tion of the notion to infinite as well as to finite series, and
to varying types of compactness. The variation in degrees
of compactness is very important for science, consequently
the postulates as given by Huntington for the definition
of these specific types of order will also be given.

The postulates defining a discrete series are as follows:

Postulate AT. (Dedekind's postulate.) If Ki and K2 are any two
non-empty parts of K, such that every element of K belongs either to
K \ or to K2 and every element of Ki precedes every element of K2, then
there is at least one element X in K such that:

(1) any element that precedes X belongs to K\, and

(2) any element that follows X belongs to K2.

Postulate 7V2. Every element of K, unless it be the last, has an
immediate successor.

Postulate 7V3. Every element of K, unless it be the first, has an
immediate predecessor.1

This is the type of order which, if it has a first and a last
element, is that exhibited by the gross objects of perception;
observed objects are discrete and lumpy and stand adjacent
to one another, e.g., the houses on a street, the books on a
shelf, and the days in a week. If the series is defined as
having a first element but no last element, it is called a
progression, and is exemplified by the natural numbers.

The postulates defining a dense series are as follows:

Postulate HI. If a and b are elements of the class K, and a < 6,
then there is at least one element x in K such that a < x and x < b.

Postulate H2. The class K is denumerable; that is, the elements
of K can be put into one-to-one correspondence with the elements of a
progression.2

Postulate HI, called by Huntington the postulate of
density, forbids one to give empirical examples of this type
of series, unless one supposes that the numbers themselves
are empirical objects. This postulate requires that there

1 Ibid., p. 19. 2 Ibid., p. 34.

260 INTRODUCTION TO PHILOSOPHY OF SCIENCE

should always be at least one element and therefore an
infinity of elements between any two. Empirical events
could not constitute such a series, for at the limits of the
perceptually discernible adjacency would be an observed
fact. It is easy, however, at least with the techniques of
mathematics, to construct series satisfying these postulates.
One of the most useful is that of the class of proper fractions
arranged in the usual order.1

An even more compact type of series is that called the
continuum, which has important applications in the analysis
of time and space. Its postulates are as follows:

Postulate CI. (Dedekind's postulate.)

Postulate C2. (Postulate of density.)

Postulate C3. (Postulate of linearity.) The class K contains a
denumerable subclass R in such a way that between any two elements
of the given class K there is an element of R. 2

Some of the commonest examples of the continuum are the
points on a line, the instants in a duration, the real numbers,
and the non-terminating decimal fractions. It is clear that
these are not empirical orders in the strict sense of the word ;
they are definable by means of operations having empirical
application within a given range, but extended beyond that
range through a principle justifying indefinite repetition.

number: empirical foundation

That there are numbers, or at least numbered groups,
seems obvious; yet the problem of the precise empirical
foundation of the concept of number is one involving some
difficulty. This is due at least partly to the fact that the
concept of number in ordinary speech is ambiguous. It may
refer, on the one hand, to a certain property of groups, or
pluralities; in this sense it applies only to collections of
events, and not to a single event. But it may refer, on the
other hand, to the property of individuality, distinguishabil-
ity, or discreteness, which is possessed by an event; in this

1 Ibid., p. 14. *Ibid„ p. 44.

ORDER, NUMBER, QUANTITY 261

sense it applies only to simple events, and not to complexes
except as they themselves are distinguishable from other
complexes. The two notions are obviously interrelated, yet
they are not identical; for example, if a group has number
the members of the group must be numerically distinguish-
able, and if an event is numerically distinguishable (from
another event) there must be a group (of at least two) which
possesses number; but it is clear that the property which is
possessed by the individual members is not the same as the
property which is possessed by the group. Before one can
talk about empirical foundations, therefore, one must decide
which of these two notions is the proper meaning to be
given to the concept. Jevons, for example, defines number
as "the empty form of difference"; 1 but Russell defines it as
a property of similar classes.2

But, in the second place, contingent upon this fact a new
problem arises. Which of the two notions is psychologically
more primitive? In other words, is all recognition of num-
bered groups a synthetic act involving a very rapid counting
of individuals, or is all recognition of individuals an analytic
act involving selection from totalities? Expressing the
same idea crudely, does one build up the idea of "many"
by combining "ones," or does one build up the idea of "one"
by breaking up a "many "? It is not likely that this question
can be answered with any finality. The conclusions of the
recent Gestalt psychology suggest that there is such a thing
as an immediate recognition of wholes and patterns; this
would seem to argue for the fact that, in certain situations
at least, plurality is psychologically more primitive than
distinguishability. Yet the notion of number is so intimately
associated in one's mind with the notion of counting, and
the ascertainment of number in very large groups is so cer-
tainly a matter of counting, that plurality seems to occupy a
secondary place in the order of experiential derivation.

Since the issue is not important one may adopt, as in the
case of the concept of order, an arbitrary point of view.

1 Principles of Science, p. 158. 2 Introduction to Mathematical Philosophy, p. 18.

262 INTRODUCTION TO PHILOSOPHY OF SCIENCE

The notion of number as plurality seems to have a somewhat
more direct empirical reference than the notion of number as
distinguishability ; hence it seems best to suppose that the
immediate recognition of pluralities is possible without the
employment of counting. At least there are simple empirical
groups whose number seems to be discernible without a
conscious act of counting, and these may be taken at least
temporarily as on the primitive level of givenness. It may
be that counting can be shown to be logically more basic
than number, but this is an independent issue. The problem,
then, is to determine what kinds of events have numbers,
and what sort of thing number is when thus derived.

To say that number is a property of complexes or plurali-
ties is merely to state a first approximation to an empirical
definition of number; what is required further is a concep-
tion of the kind of property which number is. An under-
standing of the distinction between collective and distributive
properties is helpful in this connection. For example, the
word "all" is ambiguous in the English language; it may
refer to an aggregate taken as a whole as in the proposition,
"All the angles in a triangle are equal to two right angles,"
or it may refer to the individual members of an aggregate as
in the proposition, "All the angles in a triangle are less than
two right angles." This suggests that there are two kinds of
properties — collective, or "holistic," properties which are
applicable only to aggregates and not in general to the in-
dividual elements, and distributive, or elemental, properties
which belong to the members and not in general to the
totalities. Inference from a class to the members, as given
in the ordinary syllogism, is based upon distributive prop-
erties; the absurdity of an inference constructed after the
same pattern but with a collective property substituted for
the distributive property is illustrated in the following:
"Americans are numerous; since I am an American, I am
numerous." The general fact to be pointed out, then, is that
number is a collective property, applicable only to aggregates
or complexes. In this respect it belongs in the same category

ORDER, NUMBER, QUANTITY 263

as such words as "organization," "pattern," "structure,"
"complexity," "disorganization," and the like.

But it is important to determine the empirical foundation
not merely for the general fact of number but also for specific
numbers. Though all complexes possess number, they do not
all possess the same number. When do two complexes possess
the same number? Presumably, when they possess some-
thing in common. But this feature which they possess
jointly is nothing very obvious. As Russell says, "it must
have required many ages to discover that a brace of pheas-
ants and a couple of days were both instances of the num-
ber 2: the degree of abstraction involved is far from easy." x
Clearly, not just any sort of resemblance will suffice; a pair of
shoes and a trio of crows may both be black, but they will not
thereby possess the same number. The similarity must re-
side, rather, in the holistic properties. Yet how may this
similarity be determined? The method which first suggests
itself is to count the respective groups and determine the
number of each. But this will not do, for counting itself
presupposes that individual numbers have been recognized
and arranged into a series. What is required is an activity by
means of which the individual members may be selected
from the respective groups and correlated with one another.
This is called the activity of setting up a one-to-one correla-
tion, and two aggregates which can be thus correlated are
said to be similar to one another. Two classes may be said
to be similar when for every member of the first class there is
one and only one member of the second, and for every mem-
ber of the second there is one and only one member of the
first.2 By means of this technique it is possible to ascertain
that two groups have the same number without knowing
what number either group possesses. For example, in a room
in which every seat is occupied and there is no one standing,
the number of individuals is the same as the number of seats ;
the relation 'occupying'1 constitutes the correlating rela-

1 Introduction to Mathematical Philosophy, p. 3.

2 If the occurrence of the word "one" in this definition is considered objection-
able, it may be avoided by a different phrasing. See Russell, op. cit., p. 15.

264 INTRODUCTION TO PHILOSOPHY OF SCIENCE

tion. In a country where neither polyandry nor polygamy
is permitted, the number of husbands living at any moment
is the same as the number of wives. By means of this tech-
nique all pairs could be correlated, all triads, and so on.
The number 2 could then be empirically defined as the prop-
erty possessed in common by all classes similar to some given
class, say a pair of shoes; and the number 3 could be defined
as the property possessed in common by all classes similar to
another given class, say the sides of a triangle.1

This should suffice as an empirical definition of number.
By means of such a criterion one should be able to distin-
guish the various types of complex from one another, group
together all similar complexes, and devise the proper numeri-
cal symbol for the characterization of each type. But there
is also involved in the empirical conception of number a
feature which, I am convinced, must be considered as part
and parcel of it. The different types of complex are recog-
nized not only as being different in number from one another
but as being derivable from one another by certain mathe-
matical operations. It seems impossible that there should be
an awareness of the difference between a 3-group and a
5-group without a simultaneous awareness of the fact that
the 3-group would be similar to the 5-group if it had two more
members, i.e., if it were combined with a 2-group. This seems
to be the foundation for the notion of mathematical opera-
tion, which, in its general form, is a concept of great im-
portance for science. Reference has already been made to
the physical, biological, and psychological operations in-
volved in the perceptual act.2 In general an operation may be
defined as an act performed upon something given to produce
something else. Mathematically, the notion of operation is
somewhat more specific; "an operation upon the elements

1 This is in essence Russell's definition. He defines number as follows: "The
number of a class is the class of all those classes that are similar to it." The main
difference is that Russell places more emphasis on extension; since there may not be
any such property as number, while there obviously is such a thing as a class of
classes, he considers that the safest procedure is to adopt the extensional definition.
Ibid., p. 18.

2 Chapters V, VI.

ORDER, NUMBER, QUANTITY 265

a and b is defined, if, corresponding to the elements a and b
and to a certain order of those elements, there exists a certain
third thing c." 1 Thus the operation of addition upon a
3-group and a 2-group is defined, if, when the groups are
taken in the given order there is determined a third group,
viz., a 5-group; this operation is symbolized in the ordinary
way, 3 +2 = 5. It seems important to recognize that certain
elemental operations — addition, subtraction, and possibly
also multiplication — are intimately tied up with the recogni-
tion of the simple numbers. As such they come definitely
into the empirical picture, and are considered inseparable
from the descriptive concept of number. Unless this is
recognized a difficulty arises in the understanding of the
scientific concept, for the latter makes important use of the
concept of operation.

On the empirical level, then, numbers may be considered
as collective properties of certain complex events which can
be correlated with one another. What seems important to
recognize is that the pluralities here considered have a
complexity of not more than six or seven terms, and not less
than two terms. At least groups of greater complexity can
probably not be recognized by a simple act of attention,
but must be built up by counting or by operations upon
smaller groups. And groups of lesser complexity could not,
according to the empirical conception, be groups. This sug-
gests that the notion 1 is somewhat more abstract than the
notions 2 ... 6, and hence must be defined by logical
extension from the latter group. The notion 0 is clearly one
involving complicated acts, and arises only very late in the
psychological development. The notions of the negative
numbers, the fractions, and the irrationals arise by similar
extension, hence are not to be examined at this level of
analysis. Mention may be made further of the fact that the
aggregate of complexes which constitutes the empirical
reference of the concept of number has not yet been ordered;

1 J. W. Young. Fundamental Concepts of Algebra and Geometry (New York: Mao
millan, 1927), p. 88.

266 INTRODUCTION TO PHILOSOPHY OF SCIENCE

in other words, one does not yet have the series 2, 3, 4, 5, 6,
but merely the collection 2, 5, 4, 6, 3. One is, therefore, not
yet able to count.

number: operational derivation

The concept of number, like the concept of order, accom-
plishes its task in science through generalization of its
empirical foundation. But whereas this was attained in the
case of order through a direct generalization of the concept
itself, it is brought about in the case of number through a
generalization of the notion of operation.

It should be apparent that on the empirical level the no-
tion of mathematical operation involves the conception of
illegitimate operations. While addition may always be per-
formed, since it produces a further complex which may then
be presumed to exhibit number, subtraction often cannot be
performed; for example, a 2-group cannot be subtracted
from a 3-group, for what would remain would not be a group
at all, hence could not be numbered; furthermore, a 3-group
could not be subtracted from a 2-group for the act could
not be performed. Similarly, though multiplication is
always possible, division is generally impossible. Hence a
proper formulation of the empirical conception would re-
quire a classification of operations on the basis of legitimacy
and illegitimacy. It is this distinction which is abandoned
at the scientific level. The generalization of the concept of
number is accomplished primarily by the elimination of
illegitimate operations. If mathematical operations can
always be performed, the outcome of an operation will
always be a number. As a result of this act of generalization
place must be found for 1, 0 and the negative numbers,
which arise through subtraction; for the fractions, which
arise through division; and for the irrationals and the
imaginaries, which arise through extraction of roots. This is
accomplished, as will be seen immediately, through the
introduction of the notion of group.

But a further transformation is sometimes introduced

ORDER, NUMBER, QUANTITY 267

into the empirical concept of number through an operation
of ordering. In fact the negatives, fractions, and irrationals
may themselves be considered as serial extensions rather
than as the results of operational generalization. As was
pointed out, alternative routes of derivation are often
possible. But what is important is that some notion of order
is frequently considered essential to the definition of num-
ber, i.e., numbers are considered to be not merely a collection
of entities but an ordered collection. This gives rise to the
notion of ordinal numbers, and justifies the act of counting.
It gives rise also to elaborate techniques by which order
may be set up among fractions, for example, or among irra-
tionals. The general techniques for the establishment of
series have already been discussed ; the problem in each case
is the discovery of a relation which will satisfy the general
postulates defining order. For example, it is possible to
order the natural numbers on the basis of the relation "less
than"; all of the general postulates defining order would be
satisfied, and all of the special postulates defining the dis-
crete series; hence the result would be the ordinary number
system, 1,2,3,4,5, . . . , called earlier in the chapter the
progression. It is by means of this that counting is carried on.

number: scientific content

The generality involved in the scientific concept of number
suggests that it has become far removed from its empirical
foundation. With the introduction of 1, 0, the negatives,
the fractions, the irrationals, and the imaginaries, it seems
that mathematics is no longer concerned with events. "In
accepting these symbols as its numbers, arithmetic ceases
to be occupied exclusively or even principally with the
properties of numbers in the strict sense. It becomes an
algebra whose immediate concern is with certain opera-
tions . . . defined formally only, without reference to the
meaning of the symbols operated on." x Instead of defining
number as the property of groups, mathematics considers it

1 H. B. Fine, The Number-System of Algebra (Boston: Heath, 1907), p. 26.

268 INTRODUCTION TO PHILOSOPHY OF SCIENCE

essentially as the field of mathematical operations, i.e., num-
bers are any entities which may be operated upon in spec-
ifiable ways to produce other entities of a similar kind. But
if the operations are such as cannot be physically performed
upon empirical groups, there is no reason to suppose that the
resultant numbers will be empirically descriptive. Hence
mathematics becomes by this act of generalization more or
less removed from the empirically given. It is due to the
important part which acts of this kind play in mathematics
that it is commonly characterized as a strictly formal, or
non-existential, science. With the breaking away from
empirical groups the way is open for the development of
meaning along intensional rather than extensional lines;
hence the search is for formal postulate systems.

Clearly, the essence of the formal definition of number lies
in the notion of operation. As a result there arise various
levels of generality. One may define merely the positive
integers; or one may define the entire class of whole numbers,
positive and negative; or one may define the rational num-
bers; or one may generalize so as to include the irrational
numbers as well, and thus define the real numbers; or one
may reach a still higher stage and formulate postulates
descriptive of numbers as including also the imaginary
numbers. Each of these represents a higher stage of gen-
eralization, and each includes a wider range of different types
of number. For the purposes of illustration the set chosen
will be that which defines number in the highly general
sense which includes the real and the imaginary numbers.

In this connection the notion of group is important. A
group, in this technical sense, is a class of a certain kind,
viz., a class whose members satisfy certain laws with refer-
ence to operations which may be performed upon them.
Operations serve to correlate members of the group with one
another. Hence if one specifies a certain class of elements
whose natures are undefined except for the operations which
may be performed on them and the laws according to which
such operations must be performed, one has a group. One

ORDER, NUMBER, QUANTITY 269

might leave the operations themselves in an undefined form,
and thus define a highly abstract group. Or one might inter-
pret them in a manner which suggests certain empirical
operations performable on certain empirical objects, and
thus define a less abstract group. The postulate system which
is here offered as a definition of the field of numbers employs
the notions of addition and multiplication as the basic
operations. Then the number system may be defined by the
following postulates :

1. If a and b are numbers, then a X b and a + b are numbers.

2. (Associative law.) a X (b X c) = (a X b) X c, and a -j-
(6 + C) = (a + b) + c.

3. (Commutative law.) a X b = b X a, and a + b = b + a.

4. (Definition of identity element.) There exists a number 1 such
that aXl = lXa = a, and a number 0 such that a + 0 = 0 +
a = a, for every number a of the class of numbers.

5. (Definition of inverse element.) There exists, corresponding to
any number a, another — a such that a + — a = 0, and another
1 la such that a X 1/a = 1, except that no inverse of 0 is required.

6. (Distributive law.) If a, b, c are numbers, a X (b + c) =
a X b + a X c, and (b + c) Xa = bXa-\-cXa.1

Nothing is said in this postulate scheme concerning the
scope of the class of numbers; the only two elements whose
existence is assured are 1 and 0. But if one supposes, say,
that successive additions of 1 determine distinct elements,
the class becomes infinite. The operations of subtraction and
division may be defined, respectively, in terms of addition
and multiplication. Through ^these operations the class
becomes indefinitely extended to include the negatives, the
fractions, the irrationals, and the imaginaries. The prin-
ciples by which the class of numbers may be ordered are not
given in this set, though they may be added as further
postulates if they are required.

The important feature to be noted in connection with
this abstract definition of number is the discrepancy be-

1 This set is a modification of that given by J. W. Young, Fundamental Concepts of
Algebra and Geometry, p. 94. See also R. B. Lindsay and H. Margenau, Founda-
tions of Physics (New York: Wiley, 1926), pp. 9-10.

270 INTRODUCTION TO PHILOSOPHY OF SCIENCE

tween the scientific content of the notion and the empirical
content. There are two main differences — one pertaining
to the order of the elements, and the other applying to the
nature of the operations. The former is indicated by the
fact that that which is psychologically primitive at the
empirical level is the collection of numbered groups, 2, 5, 6,
4, 3, from which 1 and 0 are considered to be psychologically
derivative; but that which is logically primitive at the
scientific level is the class of elements, of which 1 and 0 are
given, and from which 2, 5, 6, 4, 3, and the rest of the num-
bers follow by logical derivation. Hence the number 5, say,
is psychologically primitive but logically derivative, while
the number 0 is psychologically derivative but logically
primitive. The distinctions in the meaning of the term
"operation" are illustrated in the fact that at the empirical
level an operation is a method for manipulating groups and
collections, while at the scientific level it is a rule for manipu-
lating symbols. In the present case this is not quite true,
since the operations have not been taken at the highest
possible level of abstraction; they retain a tinge of their
empirical reference which permits one still to speak of the
things which are operated upon as numbers. But the tend-
ency to the sharp separation between the extensional and
the intensional is clearly indicated. At a high level of gen-
erality emphasis shifts from extension to intension. Ab-
stractions are elusive features of the given, and cannot be
readily pointed to; hence symbols which describe them can-
not be defined by the denotative method but require the
connotative method instead. This leads to a formalization
of the concepts in question, and to a gradual elimination of
empirical content. It results in the conception that mathe-
matics is not an existential science but is concerned solely
with ideal objects. A recognition of the empirical content
of the notion, and of the operational routes involved in the
passage to the scientific content dulls the sharpness of this
dualism, and results in the conception that mathematics is
the same kind of study as empirical science, except that

ORDER, NUMBER, QUANTITY 271

operations play a somewhat larger part in the determination
of the meanings of its basic concepts.

QUANTITY : EMPIRICAL FOUNDATION

The greatest difficulty in connection with the concept of
quantity is a terminological one. Authorities disagree es-
sentially in the way in which "magnitude" and "quantity'
are to be used, and in the way in which these two notions
are to be connected with "number'1' and "measurement." 1
In the face of this confusion almost any use of terms is
justifiable. In what follows, the term "magnitude" will be
avoided, and the term "quantity" will be considered to be
empirically definable as a certain feature of groups, and
scientifically definable as the number which is attached
through the technique of measurement to such empirical
groups.

The fact that one speaks commonly of quantity of time,
quantity of space, quantity of light, quantity of pleasure,
and the like, suggests that there are events which exhibit
certain properties which may be defined as quantitative.
The problem is to locate such events and then endeavor to
select that property in terms of which they are identified.

The most obvious feature of quantities is that they are
always quantities of something — length, duration, motion,
weight, sensitivity, pain, wealth, etc. This is simply to say
that quantities are always qualities, i.e., events which exhibit
quantitative differences or resemblances also exhibit quali-
tative similarities. Thus if three lines differ quantitatively
they resemble one another qualitatively in the fact of one-
dimensional extension, and if three pleasures differ quanti-
tatively they resemble one another in being pleasures of the
same kind — say, of taste, or of musical appreciation.

The second feature of quantity is its relativity; an event
is called a quantity only by virtue of the existence of at
least two other events which exhibit varying degrees of the

1 See Bertrand Russell, Principles of Mathematics, Part III; W. E. Johnson, Logic
(Cambridge: Cambridge University, Vol. II, 1922), Chap. VII; A. Spaier, La pensSe
et la quantite (Paris: Alcan, 1927).

272 INTRODUCTION TO PHILOSOPHY OF SCIENCE

same quantity. This aspect of quantity is not apparent but
may be made clear after a moment's consideration. Quan-
tity is usually supposed to be relative in the sense that it
always involves a relation of greater or less, i.e., an event
is called a quantity only if it is greater or less in some respect
than some other quantity. For example, a line is called
long because of the existence of another line which is short,
and a stone is called heavy because of the existence of another
stone which is light, and so on. From this point of view
no event could be called a quantity unless there existed at
least one other event to which it bore a certain relation. It
seems, however, that quantity is relative in a somewhat
more complicated sense than this. Quantity, in fact, never
arises unless there is something akin to the notion of an
intermediate or "between'1 element, and this necessarily
involves at least three events. Suppose, for example, that
in a certain community every day were either hot, say 90°,
or cold, say 20°, and there were no days of intervening
temperature; it is not likely that in such a community the
notion of heat as a quantity would arise. Heat would be
considered as an absolute quality possessed by certain days
and lacking from certain other days; hot days would be
related to cold days as positive to negative, or the reverse.
Similarly, if all light was either very bright or very dim,
there would probably arise no conception of light intensity ;
and if all pleasures were of very great or very minute in-
tensity, there would probably arise no conception of quan-
tity of pleasure. Quantity arises only when there occur
three events similar in kind but so connected that the
relation of the first to the second is of essentially the same
kind as the relation of the second to the third, or, what
amounts to the same thing, when one event is between the
others and has a relation to one of them which is the con-
verse of its relation to the other. For example, so long as
propositions are considered to be either true or false, the
notion of degrees of truth cannot arise; but once the notion
of probability is introduced it is seen that the relation of a

ORDER, NUMRER, QUANTITY 273

somewhat probable proposition to a false one is of the same
kind as the relation of a true proposition to one which is
somewhat probable, i.e., a probable proposition lies in be-
tween a false one and a true one.

In view of the discussion of order these results may be
summarized by stating that it is essential to the notion of
quantities that they be orderable. Since this is still on the
empirical level one may define order in terms of the " be-
tween " relation. One may then say that quantity is a
property exhibited by any three-termed complex in which
there is a term such that (a) it has an asymmetrical relation
to each of the other two terms, and (b) its relation to one
of the terms is the converse of its relation to the other.
The relation "greater than," with its converse, "less than,"
would satisfy this criterion, and enable one to order any
three such quantities.

But if this were all that could be said about quantity,
there would be no means for distinguishing between quan-
tity and order. For example, a father, son, and grandson
could be ordered according to the relation "begets," yet
they would not be called quantities; events could be ar-
ranged in a causal chain by the relation "causes," but the
ordered events would not be considered quantities. What
is the unique feature which distinguishes a quantitative
series from a non-quantitative one?

This differentiating feature is to be found in the ordering
relation. In a quantitative series the essential feature is
that the between relation should be interpretable as "greater
than" and "less than." This itself is an empirically given
relationship which is probably irreducible to anything psy-
chologically more primitive. Logically one sometimes de-
fines a greater quantity as a lesser quantity to which some-
thing has been added. But this does not seem to constitute
a psychological simplification, and it is, moreover, applicable
only to extensive quantities and not to intensive quantities.
Often a greater quantity cannot be obtained from a lesser
quantity by any sort of addition, especially in those cases

274 INTRODUCTION TO PHILOSOPHY OF SCIENCE

where the greater does not seem to extend beyond the lesser
in any sense. For example, liquids may be arranged into a
quantitative specific gravity series on the basis of the rela-
tion "floats in," but this does not involve the notion that a
substance of high specific gravity extends beyond one of
low specific gravity. One simply decides that the relation
"floats in,: determines a quantitative distinction. Essen-
tially the same technique is employed in arranging sub-
stances according to hardness on the basis of the relation
'scratches," and in the arrangement of masses according
to weight on the basis of the relation "displaces on a bal-
ance." The relation "greater than" can be defined only
as the abstract feature which each of these ordering relations
exhibits.

It can be seen that at the empirical level the notion of
quantity is not dependent in any way either upon the notion
of number or upon the notion of measurement. Numbered
groups are, of course, quantities, since they may be arranged
in an order on the basis of the relation "greater than";
they are, in fact, one of the most basic quantitative notions
since they afford the pattern for the understanding of the
less clear quantitative notions. But it does not seem essen-
tial to a quantity that it be measurable, and it does not
seem advisable to define the notion in this way. On the
empirical level quantity may be roughly defined as the
property exhibited by the elements of an event of at least
threefold complexity when these elements are similar in
some respect and capable of being ordered according to a
relation which may be interpreted as "greater than."

QUANTITY : OPERATIONAL DERIVATION

Empirical quantity is incorporated into scientific con-
ceptual schemes through the technique of measurement.
Scientific quantity, as will be seen presently, is identified
with measured value. Hence the operational transformation
of empirical quantity is such as can be accomplished through
the application of measurement. The detailed description

ORDER, NUMBER, QUANTITY 275

of such techniques is far beyond the scope of this book.
In addition to what has already been said x a few remarks
may be made.

In the first place, measurement should be understood in
its true light as an operation which is essentially abstractive.
The attempt is made to consider only one property of an
event, and to portray this only in its quantitative aspect.
This is the foundation for the claim that quantitative meth-
ods in science lose the qualitative features of events and
reduce them to abstract structures. It is well to note that
although the measured values are numbers, and are manip-
ulated according to the rules of mathematical operations,
they are not purely such. A measured value is always a
qualitative entity, for it is a value of something, e.g., a
length, a mass, a duration, or a velocity. Thus quality is
not completely lost in the measurement, for there must
always be reference to the unit in terms of which the meas-
urement is made. But it is true that the measuring tech-
niques serve to preserve not the individual features of the
quality but only its abstract quantitative aspects, such as
its position in a series of similar quantities, and its reduci-
bility or irreducibility to other quantities.

In the second place, brief recognition should be made of
the essential measurement techniques. They may be roughly
divided into three types. The first and most common sort
is the direct measurement by scales and clocks of extensive
quantities, such as lengths, areas, volumes, angular spreads,
and durations. This may require the actual physical ma-
nipulation of certain devices such as tapelines and pro-
tractors. Or the operations may be incorporated into re-
cording machines which require nothing more of the observer
than the reading off of a number. The second kind of
measurement is applicable to quantities which are not ex-
tensive but which have convenient extensive correlates; in
cases of this kind the intensive variations of the quantity
to be measured are associated through physical laws with

1 Chapter VI, pp. 112 et seq.

276 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the extensive variations in certain other quantities, and the
measured values of the latter become the measured values
of the former. For example, heat intensities are measured
by variations in the length of a column of mercury, weight
intensities by the distortions in a coil spring, and electricity
intensities by the spatial deflection of a coil in a magnetic
field. Similarly, though much more crudely, the intelligence
of an individual may be measured by counting the number
of questions of a certain kind which he is able to answer
correctly, and pleasures may be measured by the amount
of money required to produce them. Finally, measurement
of intensive quantities which have no extensive correlates
involves an application of the principle of order; the quan-
tities to be measured are arranged in a series by virtue of
some ordering relation; one member of the series is then
selected more or less arbitrarily as the standard element
and given a number, such as 1 or 0; finally, the remaining
members of the series are numbered, and values are as-
signed to them in terms of their distance in the series from
the standard element. This is essentially the way in which
hardness and specific gravity are measured, and it is com-
monly employed in the measurement of various commercial
products such as the coarseness of sandpaper, the quality of
coal, and the delicacy of canned fruits and meats.

quantity: scientific content

Scientific quantity is measured value. Hence the field
of scientific quantity is the field of numbers. But this
statement requires clarification. Measuring and counting
are both activities of attaching numbers to events, and they
should not be confused. In the first place, number is prop-
erly an attribute only of pluralities, hence always applies
to classes or aggregates; measured value, on the other hand,
applies to a single event by virtue of its position in a series.
Number, therefore, applies not to the simple events them-
selves but to the aggregate in which they occur; measured
value, however, applies directly to the simple events them-

ORDER, NUMBER, QUANTITY 277

selves. In the second place, as was pointed out a moment ago,
measured values are always numbers of something. Hence
what is properly attached to events in measurement is not a
number but a ratio, i.e., a fraction whose denominator is
the standard used and whose numerator is the number of
times that standard is contained in the quantity measured.
A length is not 5 but 5 inches, a weight is not 10 but
10 pounds, and an angle is not 30 but 30 degrees.

With these reservations it becomes possible to say that
the field of scientific quantity is the field of numbers. As a
consequence, no specific set of postulates is required to
define quantities. Quantities are simply numbers with
which some qualitative notion is associated. It follows that
the features of the abstract postulate set defining numbers
have their correlative interpretations when applied to quan-
tities. Operations upon quantities are subject to specific
interpretations for different quantities. For example, the
product of two lengths is an area, the quotient of two lengths
is an angle, the quotient of space over time is a velocity,
and the product of mass and acceleration is a force. In
this way new quantities may be introduced by definition
in terms of elemental quantities. The identity elements,
1 and 0, are given correlative interpretations, the former
signifying usually the unit value of the quantity, and the
latter indicating the complete absence of intensive or ex-
tensive manifestation. The negatives, fractions, and irra-
tionals are sometimes subject to quantitative interpretation
and sometimes not. As quantities, however, they are subject
to more extensive empirical reference than as mere numbers.
It is, in fact, their applications as devices of measurement
which account for their importance in the natural sciences.
Some difficulty is found in trying to grasp the empirical
reference of fractions, negatives, irrationals, and even 1 and
0, so long as these are considered as numbers. But as quan-
tities, fractions have an interpretation which is almost uni-
versal; negatives have certain noteworthy interpretations,
as in the case of negative velocities, accelerations, spaces

278 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and times; and even irrationals are subject to empirical
reference in the ascertainment of the length of the diagonal
of a square. The techniques of measurement serve to
establish these empirical connections.

REFERENCES

Bertrand Russell, Principles of Mathematics (Cambridge: Cam-
bridge University, 1903).

Introduction to Mathematical Philosophy (London: Allen

and Unwin, 1920).

T. Dantzig, Number, the Language of Science (London: Allen and
Unwin, 1930).

J. W. Young, Fundamental Concepts of Algebra and Geometry (New
York: Macmillan, 1927).

A. N. Whitehead, Science and the Modern World (New York: Mac-
millan, 1925), Chap. II.

E. V. Huntington, The Continuum (Cambridge: Harvard Uni-
versity, 1917).

E. W. Hobson, Domain of Natural Science (New York: Macmillan,
1923), Chap. V.

CHAPTER XIV

SPACE, TIME

The concepts of space and time are among the most ob-
scure to be found in the philosophy of science. There are
many reasons for this. Not the least of these is the long and
venerable history which the concepts have had in philo-
sophical literature; this has tended, unfortunately, rather
to confuse than to clarify their natures. Of importance,
also, is the fact that the concepts have been intimately
associated with developing science, and have influenced and
been influenced by theories of the continuity and discon-
tinuity of matter and by views as to the nature of growth,
decay, and change. Of greatest importance, however, is the
complexity of the concepts themselves. Though they are
high abstractions, they are not empty of content but are
highly complex, exhibiting features of dimensionality, order,
structure, and extent, and intricate relations to events which
they "contain." For these reasons the discussion in this
chapter will be hardly more than an outline of the features
to which reference should be made in an examination of the
concepts.

In order to avoid later difficulties, mention must be made
at the outset concerning the meaning which is to be given
to the concepts at the empirical and the scientific levels.
The obvious fact, which confuses the entire problem, is
that there are several empirical and several scientific levels.
To consider space only, for example, there is not one space
which can be called empirical; on the contrary there are
visual, auditory, tactile, motor, and possibly olfactory, and
gustatory spaces as well, each of which claims a certain
psychological primacy. The problem then arises as to
whether these are psychologically primitive, and, if so,
whether one of them is more so than the others. Similar

279

280 INTRODUCTION TO PHILOSOPHY OF SCIENCE

difficulties arise at the scientific level. Prior to the discovery
of non-Euclidean geometries, about a century ago, no one
had seriously questioned the accuracy of the Euclidean
system as a description of the space of nature; scientific
space was Euclidean space. But since the advent of the
theory of relativity suspicions have begun to arise that an
alternative space might serve better as the background for
the explanation of certain phenomena. Yet Euclidean space
still remains adequate upon a certain level. Hence one
finds himself in the peculiar position of being obliged to
examine two scientific concepts, each having a certain range
of application. Some authors recognize this ambiguity,
and insist even that there may be three spaces, viz., psy-
chological or individual space, public or physical space,
and geometrical space.1 Similar difficulties arise in connec-
tion with time.

Since the discussion in this chapter aims at mere illustra-
tion rather than comprehension, an arbitrary point of view
may be taken. Empirically, space and time may be con-
sidered on that level at which the synthesis of the spaces
and times of the separate sense organs has already been
made; hence there will be for each individual only one space
and only one time. Scientifically, the concepts may be
considered at the pre-relativity level, at least for the major
part of the discussion; a brief consideration of the difference
between the absolute space and time of Newtonian physics
and the space- time of the special theory of relativity will
conclude the chapter, and will, perhaps, compensate for the
over-emphasis on the Newtonian conception. As a conven-
ience of terminology, pre-relativity space and time may be
called simply Euclidean space and Newtonian time; together
they constitute the background of the classical physics.

For obvious reasons, a variation in the order of discussion
of the three basic questions will be introduced in this chap-
ter. Contrary to what was found to be true in the case of
the concepts of mathematics, scientific space and time are,

1 R. B. Lindsay and H. Margenau, Foundations of Physics, Chap. II.

SPACE, TIME 281

in a sense, closer to the individual than are empirical space
and time; at least the average individual, if called upon to
describe space and time, does so in the Euclidean-Newtonian
terminology rather than in more empirical terms. Apparently
he has become so habituated to the scientific conception,
which has infiltrated into the common sense point of view,
that he finds it difficult to remove himself to a level which
is psychologically more primitive. For this reason a discus-
sion of scientific space and time advisedly precedes a dis-
cussion of the more empirical notion; only when the former
is contrasted with the latter is it seen to be hypothetical
and to be itself derivable from the empirical conception by
certain operational techniques. Hence in what follows, the
order of discussion will be: scientific content, empirical
foundation, operational derivation. Because of the obvious
similarity between space and time the two concepts will be
considered together throughout the chapter.

NEWTONIAN TIME AND EUCLIDEAN SPACE

The space and time of classical physics may be described
as objective, single, continuous, infinite, homogeneous, and
isotropic. A few remarks concerning each of these features
will serve to characterize them briefly.

Objectivity. By the objectivity of space and time is meant
their independence of events. They are considered to be
containers which may or may not be full. Events, presum-
ably, cannot exist without spEiee and time, but space and
time can exist without events. Events make no difference
to space or time. The independent character of time is
summed up in such adages as, "Time and tide wait for no
man," and in the words from Macbeth,

Come what come may,

Time and the hour run through the roughest day.

Newton described time and space in the following words:
"Absolute, true and mathematical time, of itself, and from
its own nature, flows equably without regard to anything

282 INTRODUCTION TO PHILOSOPHY OF SCIENCE

external. . . . Absolute space, in its own nature, without
regard to anything external, remains always similar and
immovable." x One of Euclid's basic assumptions was the
legitimacy of moving figures from place to place; this pre-
sumed an independent character for space, and made its
nature in no way an effect of its occupant. Hence space and
time are considered from this point of view to be the back-
ground or stage-setting for events. Events may come and
go but time goes on forever; similarly events may be here
and there but space extends everywhere.

Singleness. The singleness of space and time follows,
perhaps as a corollary, from their objectivity. If space and
time are independent of events, they are in no way tied up
with the peculiar content of my experience as over against
yours. Hence I have no right to conclude that my space and
time are different from yours. Though I always experience
spatial events as relative to my own body, and though I
always experience temporal events as relative to the stream
of my own individual consciousness, space and time as
such are subject to no such relativity. There is, in fact, only
one space, which is the space of all experiences, and only
one time, which is the tune of all experiences. We live,
therefore, in a common world whose structure is that of
space and time. The time which is here (say, on the earth)
is the same as the time which is there (say, on the moon) ;
the 'right" time is everywhere the same. Similarly, the
space which is now (say, 1937) is the same as the space
which will be at some later time (say, 2037): the "true"
space is always the same. Negatively, no individual is
isolated in his own spatial or his own temporal system.
Communication is possible precisely because of the inter-
section of private systems in a common space and common
time.

Continuity. The notion of continuity as applied to space
and time is somewhat ambiguous. There are at least three
senses in which these aspects of nature may be said to be

1 Newton's Principia, tr. by Motte (New York: Adee, 1846), p. 77.

SPACE, TIME 283

continuous. In the first place, they exhibit no natural
divisions; time does not pass in pulsations or in rhythms,
and space possesses no fences. Though space and time are
both quantitative, i.e., they permit the comparison of incre-
ments according to the relation greater than, there is nothing
in either space or time to suggest that they prefer one unit
to another. Time does not proceed by jumps or ticks, but
without rhythms; and space is unbroken by any natural
lines of division. In this sense space and time may be said
to be amorphous, since they offer no metrics; they exhibit
no structure by which one part of space may be compared
with another, or an earlier duration compared with a later
one. Hence measurement in both space and time must
take place by means of material objects and processes,
more or less arbitrarily selected from a wide range of candi-
dates. And their use implies measurement not of space
and time as such, but merely of further material objects
and processes located elsewhere in space and time. By the
continuity of space and time in this sense is meant simply
their unbrokenness ; they are continuous in the same way
that a London fog or a tropical sky is continuous. Any point
represents a potentiality of division, but no such actual
divisions are to be found.

In the second place, space and time may be said to be
continuous in the technical sense of the linear continuum,
defined in the preceding chapter. The order of instants in
time and of points in space is that of the continuous rather
than that of the discrete series. A discrete series is lumpy
and atomic, with minimum elements between which strict
adjacency holds; a continuum exhibits no such indivisibles,
for between any two there is an infinity of others. A dis-
crete series is empirically illustrated by a chain; but a
continuum has no empirical illustration, for perceptual events
exhibit only a finite divisibility. Hence one is obliged to
resort to conceptual examples. The continuity of space
and time are of the same kind as that exhibited by the
series of real numbers. Accordingly, one may say that space

284 INTRODUCTION TO PHILOSOPHY OF SCIENCE

is a three-dimensional continuum of points, and time is a
one-dimensional continuum of instants, each of which series
is capable of correlation with the series of real numbers.
The applications of this correlation to measurement are
obvious.

According to the third meaning of "continuity' space
and time may be said to be continuous in the sense that
they exhibit no gaps. There is no time when time does not
pass, and there is no extent where there is no space. It is
obvious that the notion of a gap in time would be incon-
ceivable without the conception of another time stream by
which the gap could be defined; for the notion of a gap in
time implies a separation of two instants in time, and this
would be possible only with reference to a background which
would itself be a time stream. Another way of expressing
this same feature is to say that at no point in the temporal
series could one make a cut which would produce an ele-
ment outside of time. Similar remarks apply with reference
to the notion of a gap in space.

Infinity. By the infinity of space and time is meant the
impossibility of designating any element as the end-element
(either first, or last, or both). It is intimately tied up with
the notion of order, and therefore requires reference to the
dimensionality of space and time. Space is three-dimensional
and time is one-dimensional. By this is meant simply that
in order to locate an event in space three independent bits
of information are required, while in order to locate an
event in time only one is required. The notion of dimension
is technically defined in terms of a cut.1 Roughly, a series
is n-dimensional when in order to cut it a series of (n — 1)
dimensions is required; for example, a plane must be cut
by a line, and a line must be cut by a point. Space may
then be considered as constituted by three intersecting
linear series, while time is simply a single linear series.
By the infinity of space and time is meant the absence of
first and last points in each of the spatial series and the

1 H. Poincare, Foundations of Science, pp. 240-241, 256-257.

SPACE, TIME 285

absence of first and last points in the temporal series. Tech-
nically a series is infinite when, given any element, there is
available a principle by which another element may be
found. It is clear that the only argument for the infinity
of space and time is of the rational type similar to that
employed a moment ago when space and time were shown
to be without gaps. It is obviously impossible to ask "When
did time begin?" or "Where does space end?" since the
very use of the words 'when" and ' where " implies a
temporal and spatial background. Thus the question,
"When did time begin?' means "At what instant in (an-
other) time did time begin?" and the question, "Where does
space end?" means "At what point in (another) space does
space end?"

Homogeneity. To assert that space and time are, respec-
tively, homogeneous is to say simply that they are every-
where alike. No point in space, and no instant in time bears
any qualitative feature by virtue of which the general en-
vironment of space or of time from which it has been selected
could be ascertained. Space and time do not exhibit any
hummocks or irregularities, any compressions or expansions,
any twis tings or deformations. A mile selected from the
line joining Chicago and New York would be indistinguish-
able from a mile selected from the line joining Paris and
London; a ten-minute section drawn from the hours of the
morning would be indistinguishable from a ten-minute sec-
tion drawn from the afternoon. Neither the 'here'' nor
the "now" is unique; no physical law describing the change
in state of a system prescribes the time of day or the time
of year when the law holds. The equations of the pendulum,
for example, "c/o not contain t explicitly. The state of the
system varies at any stage in a way dependent only on the
instantaneous state itself, but not on the date of this state,
not on the indication of the clock." 1 "Now" points and
"here" points are determined by observers; but observers
are of no importance so far as abstract time and space are

1 L. Silberstein, Causality (New York: Macmillan, 1933), p. 129.

286 INTRODUCTION TO PHILOSOPHY OF SCIENCE

concerned. As Newton said, "time flows equably," and it
makes no difference whether the individual is busy or idle,
amused or bored. Though the last mile may seem the longest,
abstract distances are always the same.

Isotropy. Some difficulty arises in connection with the
concept of isotropy, due to the ambiguity in the notion of
"direction." By the isotropy of space is meant its sameness
in all directions. Poincare describes space as isotropic in that
" all straights which pass through the same point are identical
with one another." 1 This suggests that by isotropy is meant
the similarity in all dimensions. If this is the correct in-
terpretation no question arises with regard to time, for
time is one-dimensional. But by "direction" is also meant
the asymmetry of a relation; for example, Chicago is in a
different direction from New York than New Y ork is from
Chicago, and the direction of time from 1936 to 1937 is
different from the direction from 1937 to 1936. In this sense
time may or may not be isotropic; but since there are two
possible "directions" for time the question becomes at least
relevant. One may call the former sense of isotropy its
dimensional interpretation, and the latter its directional in-
terpretation. Separate discussions of space and time are
then necessary.

According to the dimensional interpretation Euclidean
space is isotropic. By this is meant that the up-down,
right-left, and here-there dimensions of space are identical.
Since one's movements in the first of these dimensions are
somewhat restricted, he tends to assign to that dimension a
peculiar place in space; but this individual character must
be seen to be merely relative to the observer, and hence
not a feature of space as such. So far as space itself is con-
cerned, rotation of objects makes no difference, i.e., an
object is not compelled to suffer a deformation merely by
virtue of rotation through ninety degrees. According to
the directional interpretation Euclidean space is also iso-
tropic. By this is meant that the up-down direction is the

1 Foundations of Science, p. 67.

SPACE, TIME 287

same as the down-up direction, the right-left is the same as
the left-right, and the here- there is the same as the there-here.
Spatial lines have no arrows. Directional passage in space
is not affected by the character of space. Isotropy in both
of these senses is required for measurement. Though it is
properly the material object, i.e., the scale, which is presumed
to be unchanged by any movement in space, corresponding
properties are attributed to space itself. "For example,
it is assumed that the interval associated with any two
points on a rigid rod (used as a scale) is independent of
any motion of the rod; that is, no matter how the rod is
moved about as a measuring instrument, the interval re-
mains the same. This is a natural assumption; it is difficult
to see how measurement could be carried out at all simply
without it. Yet we must recognize its postulational nature.
As soon as we have transferred it from its status as a postu-
late about operations with physical objects to a postulate
about 'space,' it becomes equivalent to the assumption of
isotropy and homogeneity (or free mobility, as we shall
later call it) which are then considered characteristics of
physical space." *

In the directional sense time may or may not be consid-
ered isotropic, depending upon the level of abstraction at
which it is examined. From the empirical point of view,
as will be seen later, time has an obvious arrow; events
which are now future become present and then past; time
"flows" from the future to the past and not from the past
to the future. From the scientific point of view, however,
the story may be different. At least if one asks what the
symbol t means, as it occurs in physical equations, he may
receive a different answer. If one limits himself to the equa-
tions of mechanics, "the equations are just as valid for
negative values of / as they are for positive values. If the

1 Reprinted by permission from Foundations of Physics by R. R. Lindsay and
H. Margenau, published by John Wiley and Sons, Inc. Professor Carl Eckart
has pointed out to the author that this "assumption" of Lindsay and Margenau
should be taken either as a definition of "rigidity" or as a definition of "interval."
To make it an assumption involves a needless multiplication of undefined terms.

288 INTRODUCTION TO PHILOSOPHY OF SCIENCE

equations predict future events, they predict past ones as
well. Time in mechanics is then completely reversible or
two-way time." * Eddington expresses the same fact by
saying that the laws of nature are indifferent as to the doing
or the undoing of an event, hence "they must be indifferent
as to a direction of time from past to future. That is their
common feature, and it is seen at once when (as usual)
the laws are formulated mathematically. There is no more
distinction between past and future than between right and
left. In algebraic symbolism, left is — x, right is + x\
past is — t, future is + £." 2 The laws of mechanics enable
us to compute the time-difference between one event and
another, but they do not assign an absolute value to this
difference and hence do not enable us to determine which
event is earlier and which is later.3

The question hinges upon the meaning of reversible proc-
esses. "All processes, the effects of which can be completely
annulled, are called reversible. Irreversible processes are
such that, with the use of all possible physical means, a
complete restoration of the initial state everywhere cannot
be achieved." 4 The problem, then, is to determine the
actual character of physical processes. Are all reversible,
all irreversible, or some reversible and some not? In the
first case the laws should contain a two-way time, in the
second case a directional time, and in the third case distinct
laws for the two types of process would be required. But
when the problem is formulated in this way the solution
is readily seen to be quite arbitrary. Whether nature is
considered to be reversible or irreversible depends upon the
level of abstraction at which one looks at nature. At the em-
pirical level, as will be seen in the next section, time pos-
sesses an obvious directional feature, and any accurate
description of physical processes must portray this fact.
But if one neglects sufficient of the empirical features,
e.g., friction and heat conduction, any physical process

1 R. B. Lindsay and H. Margenau, Foundations of Physics, p. 76.

2 Nature of the Physical World, p. 66.

3 Ibid., p. 296. * R. B. Lindsay and H. Margenau, op. cit., p. 196

SPACE, TIME 289

can be described by laws which are invariant under the
substitution of + t for — t. To take a particular instance,
the motions of the planets can be described by reversible
laws if one chooses to ignore tidal friction, but such a law
would be more abstract than one which includes reference
to this important fact. Hence a classification of natural
processes into reversible (movements of perfectly rigid bodies
and of incompressible fluids, oscillations of a simple pendu-
lum, movements of the planets) and irreversible (heat con-
duction, heat generation by friction, diffusion, explosions),
such as that given by Lindsay and Margenau,1 is based
upon a difference of degree rather than one of kind. In the
former the temporal aspects seem unimportant, and we feel
justified in neglecting them, while in the latter the temporal
aspects seem important, and we recognize the artificiality
which results in our symbolic scheme if we fail to include
them. The whole issue, in fact, is essentially one of con-
venience. "We can at any rate safely say that, in the actual
use of the time concept in physics, the physicist will consult
his convenience with respect to reversibility or irreversi-
bility. The situation here is precisely that encountered in
connection with other concepts. If the demands for clarity
and simplicity cannot be met by the more intuitive notions,
the physicist has no hesitation in modifying these notions
and subliming them into more abstract concepts.'

»?

EMPIRICAL SPACE AND TIME

Empirical space and time may be described as relative,
plural, discrete, finite, non-homogeneous, and anisotropic. Cor-
responding remarks may be made with reference to each
of these features.

Relativity. By the relativity of space and time is meant
their inseparability from events. Space and time, from the
empirical point of view, are simply features of happenings
in space and time. At this level there is no empty space,
and there is no unoccupied time.

1 Ibid., p. 197. 2 Ibid., p. 76.

290 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Consider space first. At the perceptual level space is a
relational feature of events. Space reduces to position.
But position is meaningless apart from relations of distance
and direction, and these must always lie between events.
An event has position because it can be reached from an-
other event by a movement through a certain distance and
in a certain direction. As an ultimate point of reference
one always has his own body, and this tends to give to the
"here," as will be seen later, a privileged position. Elim-
ination of events from space, as in a perfectly dark room,
results in a weakening of one's spatial sense; ascertainment
of distance is conspicuously unreliable at sea; and the di-
rectional aspects of space easily become confused when one
is riding an airplane through a fog. Space, thus, is for the
individual a feature or aspect of events — essentially like
color or weight, except that it is relational in character.
Space must be occupied by events, otherwise it is not
space.

Time exhibits in a more pronounced manner a dependence
upon events. Time is, in essence, change, and change is
always an aspect of events. For there to be change, some-
thing must change. Change, in fact, reduces to three aspects:
It involves, first, "the coming in, rise or emergence into
existence of something new, something which was not be-
fore. Every alteration or development is an illustration: a
body moves into a new point; an organism passes into a
stage which was hitherto not its own." But this requires a
second aspect. "Plainly the new which comes to be does
not rise into a void, but into a space already there, into a
world already old. Here is the second moment of change —
the persistence of a core of reality upon which the new is
grafted. This abiding aspect of the changing thing is usu-
ally called ' the thing which ' changes. . . . Third and last,
change involves disappearance from existence, disintegra-
tion, loss. If we did not know this independently, we could
deduce it from the moments of change already cited. For
the new, by breaking in upon the old situation and giving

SPACE, TIME 291

to it a new element, necessarily destroys it." * Time also,
therefore, is considered by the individual to be a feature
or aspect of events — essentially like color or weight. Time
must be occupied by events, otherwise it is not time.

Plurality. The plurality of space and time follows from
their relativity. That event which is always given, and with
which space and time become most intimately associated, is
the observer himself. His body is always present to deter-
mine location in space, and his consciousness, if not nature
itself, gives content to the temporal process. But just for
this very reason space and time come to be built around
him as a center. Space is for him the totality of relations of
distance and direction connecting the events of his experi-
ence; time is for him the totality of relations of before and
after, connecting the events in his experience. But no two
individuals live the same lives, nor experience the same
range of events. Hence, at the empirical level one may say
that there are as many space systems and as many time
systems as there are individuals. What I see at this moment
is not identical with what you see, even though we are
located at approximately the same point in space; if we are
widely separated our experiences may be quite diverse.
But my memories and expectations also differ from yours,
even though we are contemporaries; if we are widely sep-
arated in time our total experiences may be quite diverse.
The only means of linking our spatial and temporal systems
together is through the medium of a common event, i.e.,
an event which is approximately "here-now" for both of us.
Clearly, only by means of the discovery of such an event
can the common space and the common time of science be
derived. Hence arise the difficulties of the relativity theory,
to which reference will be made later.

Discreteness. The characterization of empirical space and
time as discontinuous is subject to the same ambiguity
which appeared in the characterization of scientific space

1 D. H. Parker, Self and Nature (Cambridge: Harvard University, 1917), pp. 96-
97.

292 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and time as continuous. According to the first meaning of
"continuity," viz., 'unbrokenness," it seems safe to say
that empirical space and time are continuous rather than
discontinuous. In other words, in this aspect empirical
space and time do not differ from scientific space and time.
But whereas the unbrokenness at the scientific level was
due to the absence of demarcations and pulsations, at the
empirical level it is due to the multiplicity of divisions
arising from the intimate association of space and time with
events. Any event has such a variety of spatial relations
to other events that no single one stands out as the char-
acteristic metric; one does not find that space favors, say,
the meter unit as over against the yard unit, since events
are just as likely to be separated by the one distance as by
the other. Similarly, time exhibits no subdivisions at all
unless one associates it with clocks or other processes, and
in such cases the processes selected are soon seen to be
relative. For example, the rising and setting of the sun
might seem to contribute a definite metric to time itself,
indicating, so to speak, definite lumps in the temporal
process. But these events are soon seen to be varying as
measured according to certain other processes, such as the
number of swings of a pendulum. Hence time seems to ex-
hibit only such a metric as is obtained by a completely
arbitrary selection of processes. This seems to indicate that
empirical space and time are, like scientific space and time,
simply unbroken potentialities of division.

But according to the second meaning of "continuity,"
viz., "linear continuity," the situation may be different.
There seem to be definite limits in our ability to distinguish
spatial extents and temporal durations in the direction of
the very small. Perceptually one finds neither indefinitely
smaller distances nor indefinitely shorter durations; points
and instants, in the scientific sense, are not empirically
given. Space and time are lumpy, consisting of atoms
which represent the minimum discernibles. Nor does one
find on the empirical level that space and time exhibit an

SPACE, TIME 293

indefinite number of elements between any two ; in perceptual
space and time the atoms are adjacent to one another. All
of this may be summarized by saying that empirical space
and time are describable rather as discrete series, in the tech-
nical sense defined in the preceding chapter, than as linear
continua.

According to the third sense of "continuity," viz., "ab-
sence of gaps," empirical space and time may be said to be
discontinuous, provided, of course, one recognizes the legit-
imacy of using scientific space and time as referential sys-
tems. From the strictly empirical point of view neither
space nor time exhibits gaps, for an empty space would
not be space and an empty time would not be time. When
one spends the night in a deep dreamless sleep, the moment
of going to sleep is strictly contiguous with the moment of
waking in the morning; the time of the night's passage does
not exist for the individual. In the same way, when one
spends the night in a Pullman the view from the window on
retiring is strictly contiguous with the view on arising; the
space intervening does not exist for the individual. But
through communication with others who remained awake
all night the individual learns of the occurrence of inter-
vening temporal and spatial events. He is then obliged to
separate the contiguous events of his experience, and to
insert empty time and empty space between them. This
gives rise to gaps in his space and time. None of this occurs,
of course, at the strictly empirical level, for at this stage
space and time for the individual are simply his events,
and an empty space and an empty time would be mean-
ingless. It is only at the higher stage in which there is a
growing recognition of a common space and common time
that the notion of gaps has any significance.

Finitude. If space and time are intimately associated
with events, they will exhibit definite limits. The last point
in space is, for the individual, the most remote point which
he has visited; the first moment in time is his earliest re-
membered experience. Strictly, of course, the notion of first

294 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and last elements implies a more extensive series taken as
the referential system; hence there must be the vague
recognition of scientific space and time in order that the
finitude of empirical space and time may be rendered clear.
But the individual easily recognizes that the events of this
more extensive spatial-temporal system are not in his ex-
perience, hence do not constitute his space and his time.
The question as to whether empirical time is infinite in both
directions depends upon the attitude which one takes toward
the existence of the future in his own time scheme. If the
future is defined in terms of expectations just as the past
is defined in terms of memories, then the most remote
future instant will be determined by that event of which
there are definite expectations, just as the most remote
past instant is determined by that event of which there are
definite memories. But if the future is considered to be
non-existent, the empirical temporal series may be considered
as ending at each present moment. Whether this would be
considered a finite series would depend upon considerations
too profound to be examined here.

Non-homogeneity. By virtue of the close association of
empirical space and time with events, they take on the ir-
regularities of the events. It seems unquestionable that the
"here" in space and the "now' in time have privileged
positions in the series. Since the "here''1 is the location of
my body it becomes the ultimate standard of spatial refer-
ence, and qualitatively distinguishable from all other points.
"Here" has immediacy, "there" has remoteness. Similarly,
since the "now' is the moment of my consciousness, it
becomes the ultimate standard of temporal reference, and
qualitatively distinguishable from all other instants. In
fact, some would say that only the "now' exists, and that
all "thens" are non-existent; if so, the "now' occupies a
distinctly privileged position in the series. By virtue of
these features one should always be able to tell from what
environment a given section of empirical space or time has
been taken; it bears its qualitatively distinguishing features

SPACE, TIME 295

in itself. This is unquestionably due to the intimate associa-
tion of both space and time with events, and applies also
to extents of space and to durations of time. A mile which is
"full," i.e., contains a great variety, seems shorter than a
mile which is "empty"; and an hour which contains exciting
events seems shorter than an hour which is filled with monot-
ony. From the empirical point of view the inch on the end
of the nose is actually longer than the inch on the yard-
stick; and the one second interval before some impending
catastrophe is really longer than a one second interval
drawn from ordinary life. Events vary in importance and
significance, and space and time take on corresponding
heterogeneities. Empirical space and time exhibit hummocks
and irregularities, compressions and expansions, twistings
and deformations.

Anisotropy. According to the dimensional interpretation
empirical space is probably not isotropic. The conclusion
here depends partly upon whether one concerns himself
with visual, tactual, auditory, or motor space. Due to the
fact of eye convergence, the near-far dimension is probably
qualitatively distinct from the up-down dimension or the
right-left dimension. The omnipresence of gravitation gives
to the up-down dimension a qualitative distinctness. The
essential freedom in one's right-left and near-far movements,
as compared with the limitations in his movements up
and down, contribute further to the anisotropy. Much of
the difficulty in one's visualization of the other side of the
earth is due to the anisotropy of the up-down dimension.
According to the directional interpretation, empirical space
is not so clearly anisotropic. It is doubtful whether there
is any fundamental distinction between the near-far and the
far-near directions, and between the left-right and the right-
left. The up-down direction is, I believe, sharply distin-
guished from the down-up — due, again, to the fact of gravi-
tation; one moves up with great effort, but one moves down
with ease. Probably the directional features of space are
intimatelv associated with movement; to the extent to

296 INTRODUCTION TO PHILOSOPHY OF SCIENCE

which movement is reversible space may be considered
isotropic.

If time is anisotropic, it can be so only in the directional
sense, for time is one-dimensional. In this sense there seems
little reason to doubt the fundamental anisotropy of time.
Time has a definite direction, or arrow; it passes from the
future into the past, and not from the past into the future.
The directional character of time is intimately connected
with one's conception of causal influences, hence a reversal
of time would be essentially unthinkable. A life in which
one first dies, then is married, and finally is born, could
hardly have any kinship with the present mode of being.
To be sure, this is a series of events, not time itself. Yet from
the empirical point of view time is inseparable from change
of events, and it is because changes of one kind always
occur, and changes of another kind never occur that a
reversibility of time becomes unthinkable. It seems hard to
doubt that an awareness, more or less vague, of the going-on
of time is present at all levels of consciousness. Eddington
identifies this basic recognition of time's arrow with one's
feeling of "becoming." * The notion of time as something
which "flows," or "passes" is essential to it at the empirical
level; but "flow' and "passage' are both directional in
character. Hence time must be described as asymmetrical,
or irreversible.

SPACE AND TIME: OPERATIONAL DERIVATION

The analysis of space and time has thus far revealed an
important fact. There are at least two conceptions of space
and two conceptions of time, which are sharply to be dif-
ferentiated from one another. In general the properties
possessed by the one are contradicted by those possessed by
the other. Immediately the question arises as to which is
more adequate as a description of the space and time of
nature, i.e., which is real space and which is real time.
Although this formulation of the problem is essentially

1 Nature of the Physical World, p. 69.

SPACE, TIME 297

misleading, since there is probably a sense in which each
of the alternatives is real, it indicates the direction in which
one must look for the answer. Obviously empirical space
and time are in some sense closer to the facts, and hence
less open to conjecture, than scientific space and time.
Scientific space and time, on the other hand, are in a sim-
ilar sense hypothetical or constructional. The problem,
then, is to show how scientific space and time, as derivative,
are obtainable from empirical space and time, as primitive.
If scientific space and time are constructional in character,
they can be given content only in terms of their operational
derivations. Hence one has not properly understood what
scientific space and time mean until he has described the
techniques by which they are obtainable from more obvious
data.

From relativity to objectivity. Empirical space and time
are transformed from relativity to objectivity by an act of
abstraction, or of neglect. What is given is always a complex
consisting of an event in space and time. Through an act
of isolation the spatial and temporal aspects of the complex
are singled out for attention, since they seem permanent
while events vary in content. From this it is but a short
step to the realization that the essence of the complex is its
spatial and temporal features, and that these are not in
any way affected by the events. All of this is accomplished
through an act of generalization, by which space and time
are presumably given a wider range of application; empty
space and empty time, which at the empirical level are
impossible, become possibilities at the scientific level. Hence
arises the notion of large containers, of a spatial and a
temporal kind, in which events may be located. This is
the objective space and time of science.

From plurality to singleness. The many spaces and times
are united into a single space and time by an operation of
correlation. The problem is to eliminate the privacy of
my space and my time by finding an event which is in my
space and time but also may be in yours as well. Correlation

298 INTRODUCTION TO PHILOSOPHY OF SCIENCE

is therefore accomplished by finding common events, i.e.,
events which are 'now' and "here' both for myself and
for someone else. Practically, this can be easily done. My
friend and I meet in a certain room. I then tap on a table
and we agree that the event which is his hearing of the tap
is to be considered as contemporaneous with the event
which is my hearing of the tap. Thus by means of coexistent
events our two time schemes become linked together. Events
which are past in my friend's time system become correlated
with events which are past in mine, and a common time
begins to emerge. By extension the time systems of others
are introduced. Finally, a moment of absolute time becomes
defined as that property which is possessed in common by
all coexistent events; this property is called presence, past-
ness, or futurity, depending upon its location in some one
time scheme. Then, to say that an event happens at a
certain moment t is simply an abbreviated way of saying
that the event coexists with the mutually coexistent events
ei, e2, e3, . . . en. Similarly, I can correlate my friend's
space system with mine if we can agree on an event, say
the table, which we shall both call "here." By means of
this, events which are remote in his scheme become remote
also in my scheme, and a common space begins to emerge.
As more and more time schemes are included I begin to see
the arbitrary character of the "here' point which has been
selected, and willingly replace it by the equator or one of
the fixed stars. Then a point of absolute space becomes
defined as that property which is possessed in common by
all events lying at a certain distance and direction from
some agreed-upon event; this property is called nearness,
or remoteness, depending upon its location in some one space
scheme. Accordingly, to say that an event happens at a
certain point p is simply an abbreviated way of saying
that the event has the relation R to a certain event E. In
this way arise the single space and the single time systems
which are so fruitful for science. The important point to
recognize, since reference will be made to it later, is that the

SPACE, TIME 299

correlation of the private spaces and private times is pos-
sible only through the discovery of common events. The
theoretical difficulties arising in this discovery constitute
one of the foundations for the theory of relativity.

From discreteness to continuity. Only one of the meanings
of "continuity' will be considered here, viz., 'linear con-
tinuity." The problem is to determine the operational route
by which a finitely divisible space and time are made infi-
nitely divisible. This problem is sometimes formulated in
terms of the empirical derivation of points and instants.
Two closely similar views as to the nature of this derivation
may be presented. One is that of Russell and is called the
method of logical construction; the other is that of White-
head and is called the method of extensive abstraction.

Russell's illustration is taken from time, but a similar
procedure is applicable to space. 'Let us take a group of
events of which any two overlap, so that there is some time,
however short, when they all exist. If there is any other
event which is simultaneous with all of these, let us add it
to the group; let us go on until we have constructed a group
such that no event outside the group is simultaneous with
all of them, but all the events inside the group are simul-
taneous with each other. Let us define this whole group as
an instant of time." 1 A somewhat less empirical point of
view would be inclined to define 'point" not as the class
of such events but rather as the property possessed in com-
mon by all of the events.2 This method of defining "point"
seems preferable to the traditional one which considers it
as the limit of a series of gradually decreasing volumes.
Since the limit cannot be certainly known to exist, an opera-
tional route which defines the construct in terms of an
abstract feature which is known to exist retains a closer
empirical reference.

Not altogether unlike this is Whitehead's method of

1 Our Knowledge of the External World, p. 118.

2 This empirical tendency has been noted before in connection with Russell's
definition of number as the class of all classes rather than as the properly of classes.
See above, p. 264 n.

300 INTRODUCTION TO PHILOSOPHY OF SCIENCE

extensive abstraction. Consider it with reference to time.
"Durations can have the two- termed relational property of
extending one over the other. Thus the duration which is
all nature during a certain minute extends over the duration
which is all nature during the 30th second of that minute." l
"Every event extends over other events, and every event
is extended over by other events. Thus in the special case
of durations which are now the only events directly under
consideration, every duration is part of other durations;
and every duration has other durations which are parts of it.
Accordingly there are no maximum durations and no min-
imum durations." 2 "Such a set . . . has the properties of
the Chinese toy which is a nest of boxes, one within the
other, with the difference that the toy has a smallest box,
while the abstractive class has neither a smallest event nor
does it converge to a limiting event which is not a member
of the set." 3 The abstractive set serves to "guide thought
to the consideration of the progressive simplicity of natural
relations as we progressively diminish the temporal exten-
sion of the duration considered. Now the whole point of the
procedure is that the quantitative expressions of these
natural properties do converge to limits though the abstrac-
tive set does not converge to any limiting duration. The
laws relating these quantitative limits are the laws of
nature 'at an instant,' although in truth there is no nature
at an instant and there is only the abstractive set. Thus an
abstractive set is effectively the entity meant when we con-
sider an instant of time without temporal extension. It
subserves all the necessary purposes of giving a definite
meaning to the concept of the properties of nature at an
instant." 4 As in the case of Russell, the notion of "point"
is defined not as the limit of the series but as the series
itself, or an abstract feature of it.

From finitude to infinity. The limits of empirical space
and time are extended through correlation. The essential
feature of an infinite series is the existence of a principle

1 Concept of Nature, p. 58. 2 Ibid., p. 59. 3 Ibid., p. 80. 4 Ibid., p. 61.

SPACE, TIME 301

by means of which, given an element of a series, an adjacent
element may always be found. At the empirical level space
and time are finite, for there is no such principle which is
universally applicable; my space extends to the most remote
point of my experience, and I have no principle for going
beyond this; my time begins with my first remembered
event and I have no principle for determining anterior
events. But if I admit the legitimacy of correlating the
events of my experience with those of another individual,
I find myself provided with just the principle required.
For example, my first remembered event may be a spanking
administered by my mother for some misdeed, though I
may not remember the misdeed; but by talking with my
mother I may learn what the cause of the spanking was,
since this is a remembered event in her experience. By
multiplying correlations I extend my time system indefinitely
into the past. Similarly, I correlate my spatial system with
that of another by locating an event which is the boundary
of my system with an event in the space of another who
has traveled more widely than I; again by multiplying
correlations I extend my space system indefinitely in three
directions. The activities involved in both of these processes
are those of serial extension; a principle presumed to hold
only in the series is discovered to hold beyond its supposed
limits.

From non-homogeneity to homogeneity. The irregularities
in empirical space and time are eliminated by the abstractive
act which rids space and time of events. Only because
space and time are tied up with happenings do they seem
to exhibit heterogeneity. The "here" is different from the
"there" only so long as I think of my body as a unique
point of reference; when by correlation I discover that my
"here' is another's "there" and my "there'' is another's
"here" I realize the arbitrary character of this distinction;
the "here" and "there" lose their qualitative distinctness.
Similarly, when I realize that a space which for me is "full"
may be correlated with a space which for another is " empty,"

302 INTRODUCTION TO PHILOSOPHY OF SCIENCE

I recognize the essential irrelevance of spatial occupants;
space then begins to exhibit a permanent structure which is
independent of events. Analogously, through a recognition
of the fact that messages take time I realize that what is
' 'now' for me may be "then': for another, and what is
"then' for me may be 'now' for another. Furthermore,
when I find that an hour which for me was very exciting and
therefore very short can be correlated with an hour which
for another was very dull and therefore very long, I recognize
the essential irrelevance of temporal occupants; time then
begins to exhibit a permanent structure which is independent
of all processes. In some such way the hummocks, twistings,
and compressions of space and time are eliminated, and a
strictly homogeneous space and time result.

From anisotropy to isotropy. Both the dimensional and
the directional features of isotropy are introduced into
empirical space and time through abstraction. The dimen-
sional anisotropy of empirical space is lost with the abandon-
ment of events. The uniqueness of the up-down dimension,
for example, lies, as was seen, in such things as gravitation,
our upright positions, the limitations of our movements
in this direction, etc.; when reference to one's body
and to other events is abandoned the uniqueness disappears.
The peculiarity of the near-far dimension can be eliminated
by the simple device of placing individuals in such a way
that what is for one a near-far dimension is for the other a
right-left dimension. The directional anisotropy can be
eliminated in a similar manner. To show the arbitrary char-
acter of the distinction between right-left and left-right, all
that is required is one individual facing another. By similar
techniques all directional features of space can be shown
to be dependent merely upon coordinate systems, and hence
arbitrary. The directional anisotropy of time is eliminated
when causal concerns are abandoned. Causation does not
seem to be inherent in the time scheme, but merely a feature
of events. The unthinkable character of a world in which
death precedes birth is not a matter of time itself but of

SPACE, TIME 303

events; events in this world simply do not occur that way.
An earlier instant does not cause a later instant; rather, an
earlier event causes a later event. Hence with the elimina-
tion of events from time there is no longer any obstacle
to the view that time is reversible. Time becomes a series,
and a series has no unique directional features.

SPACE-TIME

In conclusion, brief reference may be made to the modifi-
cations which have been introduced into the scientific notion
of space and time through the discoveries which eventuated
in the theory of relativity. From the limited point of view
of the treatment in this chapter the differences between the
two views may be explained in terms of difficulties which
arise in connection with the operational derivation from
empirical space and time. It has already been suggested
that Newtonian time and Euclidean space are constructs.
By this is meant that they do not describe obvious features
of nature but are derived from them by certain logical
techniques. Immediately the question arises as to whether
the techniques are legitimate. There are two ways of answer-
ing this question. One is to examine the techniques them-
selves, and ascertain the assumptions upon which they are
based. This is the more difficult task, since the techniques
are not certainly known, and most of the assumptions are
implicit. The second way is to employ the ordinary tech-
niques of verification; Newtonian time and Euclidean space
evidently function not only as constructs but as hypotheses
as well, hence their adequacy may be determined by draw-
ing the implications from them and subjecting these to
empirical corroboration. If the predicted consequences are
not verified, presumably the techniques of derivation have
not been correctly employed, and abandonment or revision
of the hypotheses is necessary. This is the easier task, but
it unfortunately does not tell us precisely in what respect
the hypotheses are wrong, nor precisely where the error in
operation has been committed.

304 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Now it seems to be a fact in recent physics that the
inadequacy of absolute space and absolute time has been
disclosed through both methods. It has been shown that
the existence of such entities is highly conjectural, on the
one hand, because there is no technique by which they
could be derived; by operations which are relative it is
hardly possible to derive something which is absolute. But
it has also been shown, on the other hand, that such entities
must be conjectural because the deductions from them do
not always coincide with facts; the outstanding illustration
is, of course, the famous Michelson-Morley experiment.
Hence through both routes attention has been called to the
possible inadequacy of the classical space and time systems.

Reference will be made here only to the former of these
routes, since the concern throughout the chapter has been
with derivation rather than with verification. From this
point of view it seems possible to say in general that a
reexamination of the operational techniques employed in the
passage from empirical space and time to classical space and
time discloses certain questionable assumptions. As a result,
a modification of the classical point of view seems advisable.
The outcome of this modification is the space-time of rela-
tivity, whose outstanding feature is a "closer" connection
with empirical space and time. The justification of this
assertion will be found in the following paragraphs, which
will conclude the present chapter.

Relativity. It seems obvious that the space-time of rela-
tivity will exhibit relativity as its most characteristic feature.
Yet a word of caution is necessary. To show that a thing
is relative is to show that it possesses certain of its features
by virtue of something else with which it is connected.
For example, A may possess the property p not in itself
but only in relation to B ; in relation to C it may possess the
property q. But this determines something absolute, viz.,
the law according to which the properties of A change from
p to q as it is considered successively in its relations to B and
C. There are two senses in which space-time is relative.

SPACE, TIME 305

One, to be considered immediately, is the relativity of space-
time to events. The other, to be considered under the dis-
cussion of the serial properties, is the relativity of space and
time to one another. But in both of these cases there is some-
thing absolute. In the one case it is the law according to
which measuring devices vary with changing systems of
reference; in the other it is the abstract structure by which
space and time unite into a four-dimensional whole. Hence
there is a strict sense in which the theory of relativity in-
volves the assumption of an absolute structure. But this
absolute structure is different in important ways from the
absolute structure of the classical physics, and reference will
be made in what follows primarily to these differences.

The outstanding sense in which space-time is relative is
in its dependence on events. But whereas at the empirical
level the insistence is on events of any kind, at the level of
the relativity theory the insistence is on measuring devices.
Time and space are identified with measurement of time
and space. This involves an inevitable reference to clocks
and to scales. The result is that time and space both become
relative to the techniques by which they are measured.
Not only is time meaningless apart from the readings of
clocks, but the setting up and reading of clocks is all that
can be meant by time. Not only is length meaningless apart
from the readings of scales, but the application and reading
of scales is all that can be meant by length. This leads
immediately to a consideration of the second aspect of space-
time.

Plurality. If space and time are nothing apart from
measurement techniques, they will vary in character accord-
ing to the variation in the methods of applying and reading
recording devices. The most important feature of measure-
ment is that someone always measures; reference is therefore
necessary in every case to an observer. However, this fact
does not make space and time relative to the individual in
the same sense that empirical space and time are; it does not
make them private and relative to any subjective experience.

306 INTRODUCTION TO PHILOSOPHY OF SCIENCE

For the relativity theory, the important thing about the
observer is that he is located in a certain frame of reference.
Space and time are therefore plural in the sense that they
are determined by systems of reference; "length and duration
are not things inherent in the external world; they are rela-
tions of things in the external world to some specified ob-
server." 1 "A length is . . . but the expression of a rela-
tionship between the observer and the observed, and the
two partners of the relationship must be specified before the
length can have any meaning. . . . Duration and time
are mere relatives, mere expressions of relationships, and
have no absolute significance per se" 2 Hence there are as
many values assignable to any given length and to any given
duration as there are possible systems of reference. In this
sense space-time may be separated into space and time in
an infinite number of ways. Yet in a more abstract sense
space-time may still be said to be one, for there is a constant
manner in which measuring devices are affected by changes
in systems of reference. Though space and time are relative
in their measured aspects, the law of the change of measuring
devices is absolute. The old absolute of the Newtonian-
Euclidean system of a space and a time has merely been
transferred to the relation between space-time and measur-
ing devices.

Continuity and infinity. Nothing in the operational
derivation of classical space and time suggests that the
assumptions of continuity and infinitude are illegitimate.
Both of these have to do with the serial properties of space
and time, and these are essentially irrelevant to considera-
tions of relativity. Hence space-time of the relativity theory
is continuous in the three senses discussed earlier in the
chapter. It is amorphous, i.e., it exhibits no metric. It is
describable in terms of the linear continuum, the most im-
portant feature of which is the absence of adjacency with

1 A. S. Eddington, Space. Time, Gravitation (Cambridge: Cambridge University,
1920), p. 34.

2 A. d'Abro, Evolution of Scientific Thought (New York: Boni and Liveright, 1927),
p. 151.

SPACE, TIME 30'

regard to its elements, i.e., space-time is capable of infinite
subdivision. It is unbroken, i.e., there are no holes. Con-
cerning the question of infinity, nothing in the operational
derivation, so far as the special theory of relativity is in-
volved, would lead one to call it into question. From the
point of view of the general theory, however, certain con-
siderations suggest that space-time should be considered as
finite. The topic is too extensive to be discussed here.1

But reference should be made in this connection to the
fact that the three-dimensional space and one-dimensional
time of the classical physics have now become merged into
a four-dimensional whole. The reason for this intimate
union of what seem to be independent entities lies in the
difficulties which arise in the attempt to correlate the
various private space systems and private time systems.
This is done, as was seen, through the medium of common
spatial events and coexistent temporal events. Consider
for illustration the process of determining the coexistence
of two events which are located at points A and B, widely
separated in space. They may be said to happen at the same
time if they do so according to the readings of the respective
clocks located at the events. But how can one know that
the clocks have been properly set with reference to one an-
other? One might carry the clock located at point A to
point B and compare it with the clock at B. But the move-
ment would almost certainly change its reading. Instead,
one might send a light signal from A to B, and adjust the
clocks accordingly. But this supposes that one knows what
the velocity of light is. This difficulty might be avoided by a
somewhat more complicated operation of sending a signal
from A to B where it is immediately reflected back to A.
Then if one records the time of leaving A (ti) and the time
of returning to A (t2), the fraction (t2 — ti)/2 would repre-
sent the time of the light's journey from A to B. If one
started the clock at B when the signal reached this point,
and then set it back by an amount (t2 — U)/2 the clocks

1 See d'Abro, op. cit., Chap. XXXIV.

308 INTRODUCTION TO PHILOSOPHY OF SCIENCE

would then be parallel. But suppose that the whole system
A-B is moving toward A or toward B ; in either of these cases
the time required to go from A to B would presumably not
be one-half of the total, since in one case B comes to meet
the signal and in the other case B must be overtaken by it.
Further difficulties arise if the system is considered to be
moving perpendicularly to the line from A to B. A situa-
tion of this kind determined the set-up for the Michelson-
Morley experiment, whose results are too well known to
require examination here. The point of this discussion is
simply to show that the determination of coexistence is a
highly complicated operation involving the use of messages.
But the introduction of messages involves the introduction
of motion, which itself brings space into the problem. The
result is that measurement of time is seen to be impossible
unless reference is made to space. Analogous considerations
show that the measurement of space is impossible unless
reference is made to time. Hence time and space are inter-
woven in a manner which defies separation.

This constitutes the second sense in which space-time
may be said to be relative. Space measurements are relative
to time measurements, and vice versa. But it is well to note
here also that something absolute is implied in the concep-
tion. The abstract structure by which space and time are
united into a four-dimensional scheme is not relative but
absolute. 'According to the Galilean system of reference x
we may adopt, we divide space-time into space and time in
one way or in another. Hence the resolution of the drawings
of phenomena into space and time components is effected
in various ways. We thus obtain variations in the spatio-
temporal appearances of phenomena. Notwithstanding
these variations, dependent on our relative motion, the
absolute space-time drawings themselves, with their inter-
sections, remain unchanged, and a direct study of the abso-
lute world would consist in a study of these absolute draw-

1 A system of reference is Galilean if it is in uniform rather than accelerated or
rotational motion.

SPACE, TIME 309

ings without reference to their varying spatio-temporal
appearances." * Hence space- time is an absolute four-
dimensional scheme. This is simply to say that the location
of an event requires four independent values, of which three
are spatial and one is temporal.2

Homogeneity. Whether space-time is considered to be
homogeneous or non-homogeneous depends upon whether
it is examined in its abstract form, without regard to systems
of reference, or in its more concrete form, relative to systems
of reference. As has already been seen, the character of
space and time is determined by the systems of reference;
space may be shortened or lengthened and time may be
slowed down or speeded up by properly chosen systems of
reference. In this sense space and time may be said to be
non-homogeneous, for the "here" and the "now' of the
systems of reference determine the character of the space
and time which is measured. But, again, if one recognizes
that there is a constancy in the way in which space and time
"appear" from given systems of reference he is obliged to
conclude that the irregularities disappear if by space and
time are meant not their "appearances" but the law accord-
ing to which their "appearances'' change for varying sys-
tems of reference. If space and time are defined not in terms
of given manifestations but in terms of the potentiality of
all possible manifestations, the hummocks, condensations,
and other heterogeneities disappear. Abstract space-time
exhibits a permanent structure of which all deformations
are due to selected perspectives. Space-time is therefore
homogeneous.

Isotropy. The dimensional isotropy of space-time is not
perfect. So far as the spatial dimensions are concerned com-
plete isotropy exists, i.e., there is no distinction between the
up-down, the near-far, and the right-left dimensions, but

1 d'Abro, op. cit., pp. 197-198.

2 It is not to be denied, of course, that the pre-relativity system of Euclidean
space and Newtonian time was also a four-dimensional system. Graphs of space
against time were used long before Einstein. But the structure of the relativity
system is different from that of the pre-relativity scheme. Roughly, the former
involves a greater "interfusion" of space and time than the latter.

310 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the now-then dimension refuses obstinately to become
identified with any of the spatial dimensions. In a strictly
Euclidean space the dimensions would be interchangeable.
Furthermore, in a four-dimensional Euclidean system the
additional dimension would be interchangeable with the
other three. For example, the hypotenuse of a right triangle
is represented by the formula,

s2 = (x2 - Xi)2 + (y2 - yi)2.

Analogously, in a four-dimensional world the equation would
be

s2 = (x2 - x,)2 + (y2 - y02 + (z2 - z,)2 + (t2 - ti)2.

But it turns out that space-time is not strictly Euclidean,
though only a slight modification is required. If the / is
changed from positive to negative, the required alteration
is introduced. Hence the formula for distance in the theory
of relativity becomes

s2 = (x2 - x,)2 + (y2 - y02 + (z2 - z,)2 - (t2- t,)2.

This expresses the lack of homogeneity in the space-time of
relativity; the before-after dimension is always distinguish-
able from the spatial dimension.

From the directional point of view, space- time is isotropic
as to its spatial dimensions but not as to its temporal dimen-
sion. "The common impression that relativity turns past
and future altogether topsy-turvy is quite false." l Rela-
tivity, in fact, makes a distinction between past and future
which is quite as fixed as it was for the classical physics. The
basic notion is again that of causal influences, which is
associated with the idea of messages. Since the maximum
speed of messages is that of light, which is finite, causal
relations are possible only between events so located that a
message may be sent from one to the other. If an event B
occurs at such a time that it may receive a message from
another event A, then B may be the effect of A, and B must
succeed A. Two such events lie absolutely in the past and

1 A- S. Eddington, Nature of the Physical World, p. 48.

SPACE, TIME 311

future with reference to one another. But if the events are
so situated that a message from one to the other would be
required to travel faster than light, causal influences could
not pass from one to the other. Two such events could have
no absolute time order; A might be contemporary with B,
A might precede B, or B might precede A, according to the
system of reference of the observer. Hence relativity insists
upon an absolute directional feature for time, but specifies
in what sense it applies to events and in what sense it does
not.

REFERENCES

E. W. Hobson, Domain of Natural Science (New York: Macmillan,
1923), Chap. VI.

C. D. Broad, Scientific Thought (New York: Harcourt, Brace,

1923), Chaps. I, II, XII.
H. Poincare, Foundations of Science (New York: Science, 1921),
Science and Hypothesis, Part II; Value of Science, Chap. II.

D. H. Parker, Self and Nature (Cambridge: Harvard University,

1917), Chaps. V, VII.
A. d'Abro, Evolution of Scientific Thought (New York: Boni and

Liveright, 1927).
Bertrand Russell, Our Knowledge of the External World (Chicago:

Open Court, 1915), lect. V.
A. N. Whitehead, Concept of Nature (Cambridge: Cambridge

University, 1920), Chaps. Ill, IV, V.

CHAPTER XV

MOTION, FORCE, MATTER

As one approaches the concepts at this level, measurement
techniques become increasingly important. The view that
qualitative events are not properly a part of the subject
matter of science unless they can be replaced by quantities,
i.e., by measured values, has already been presented.1 Such
a view would entitle one to examine the present concepts
at their highest level of abstraction and to say that by them
one means simply numbers obtained by reading measuring
devices; e.g., by force is meant simply the number obtained
by reading a spring balance. Since numbers are properly
the subject matter of mathematics, this view involves the
reduction of physics without remainder to mathematics.
The danger in this position has already been pointed out.
If qualitatively different events in science are reduced ex-
haustively to numbers, all possibility of differentiation dis-
appears for there is no mathematical difference between the
number 2 which represents a force and the number 2 which
represents a motion. Numbers which are measured values
are always measured values of something, and they function
in the equations of science not as mere numbers but as
5, /, v, etc., i.e., as qualitatively distinct entities. The view
of science which reduces quality to quantity neglects the
fact that measuring instruments must be devised in the first
place, must be calibrated by reference to judgments of per-
ception, and must be manipulated in any given situation.

Hence the attempt will be made in the present chapter to
avoid that extreme abstraction which reduces motion, force,
and matter to pure numbers. This is not to deny that they
are quantitative. But it is to recognize that the process of
attaching numbers to them involves specific instruments

1 Chapter XII.

312

MOTION, FORCE, MATTER 313

and specific techniques, and hence that the meanings of the
concepts cannot be isolated from these physical events and
processes. Scientific motion, force, and matter are definable
as measured empirical motion, force, and matter but in that
one word lies a significant distinction which it will be the
task of this chapter to elucidate.

motion: empirical foundation

At the empirical level, motion may be described as a quan-
titatively variable change in the spatial relations holding be-
tween two events. The terms in this statement which require
clarification are "relation," "change," and "quantity."

Relativity. Empirical motion is relative in two very obvi-
ous senses: It is relative to something which moves, and it is
relative to a point of reference. Consider the former of these
two senses. Motion is a property of objects or events; trains,
baseballs, clouds, raindrops, and planets move. Motion is
capable of analysis into (a) the motion itself, and (6) the
mover. What is given empirically, therefore, is not motion
as such but rather moving objects. All that seems to be
involved in this notion of objects is something which retains
a qualitative identity through the change. The notion
readily develops into the conception of an underlying "sub-
stance," existing beneath the observable qualities of the
object. There seems to be nothing, however, in the empirical
data that demands this hypothetical development. All that
is involved is the possibility of identifying the object which
moves throughout its history by comparing the object which
began the motion with the object which completed the
motion and noting enough similarity to permit them to be
designated as the same object. The conception of empirical
motion is closely allied to the conception of empirical space
and time. Just as there can be no empty space or time, for
space and time would then melt away, so there can be no
"empty' motion. Motion is not mere change of space
through a given duration, but change of something in space;
from the empirical point of view mere change of space is

314 INTRODUCTION TO PHILOSOPHY OF SCIENCE

meaningless, for it represents a change in something which
has its form determined only by its content. What
moves is indifferent; but that something moves seems
essential.

But, in the second place, motion is meaningless apart
from a point of reference. Motion is something which is
descriptive of a relation between events, and not of a single
event. As has already been seen, empirical space reduces to
position, and position reduces to relations of distance and
direction. Motion, therefore, which is change in position,
reduces to change in distance and direction — relations which
hold only between events or objects. On the empirical level
it is arbitrary whether one says that A moves and B remains
at rest, or B moves and A remains at rest. The air of paradox
which one finds in a concrete illustration of this, e.g., the
case of a train moving past a station, is dissipated when
one recalls two facts: (a) The scientific theory of absolute
motion has become so completely a part of the background
of the individual's experience that he tends to think of
motion in these terms rather than in terms of perceptual
data. The situation here is precisely what it was in connec-
tion with space and time. (6) Empirical motion is in some
way intimately associated with the feeling of effort which is
required to move objects; small objects are easier to move
than large objects, hence the former are more likely to move
than the latter. In the case of the train, the station is un-
consciously associated with all other objects with which it
has no relative motion and which have no motions relatively
to one another; the inherent difficulty involved in moving
so extensive a system suggests that it is at rest while only
the train is in motion. When the reference system is reduced
in extent and becomes, for example, another train on a
parallel track, the strict relativity of the motion again
emerges; it is a noteworthy fact that if an observer in the
latter case cannot see the ground and cannot feel the motion,
he is quite unable to decide whether his train or the one on
the parallel track is really moving.

MOTION, FORCE, MATTER 315

Change. It seems clear, moreover, that motion is a change
of some kind. The definition of the concept of change is a
task of some difficulty, and can hardly be undertaken here.
Reference may be made to the preceding chapter where a
brief analysis of the notion was made in connection with the
empirical foundation of time. It was there suggested that
change always involves something coming into being, some-
thing passing out of being, and a permanent background
within which these events occur. An alternative description
is that of Russell, who defines change as "the difference in
respect of truth or falsehood, between a proposition con-
cerning an entity and a time T and a proposition concerning
the same entity and another -time T', provided that the two
propositions differ only by the fact that T occurs in the one
where T' occurs in the other." 1 For example, if of the two
propositions, "x is white at time T," and " x is white at time
T"," one is true and the other is false, then x may be said
to have changed. This is to define "change'' in terms of
"truth" and "falsity " — a procedure which may involve one
in further difficulties when the definitions of these latter con-
cepts become necessary. The point is, however, that motion
is change. Rut it is a kind of change. An object may be said
to move when its spatial relation to another object passes
out of being, another spatial relation comes into being, and
there remains an identical feature which is the objects them-
selves. Or, in Russell's terms, motion arises when the com-
mon feature of the two propositions is a spatial relation,
e.g., if "x is five miles northeast of y at time T" is true (or
false), and "x is five miles northeast of y at time T"' is false
(or true), then x and y may be said to have moved relatively
to one another.

Of these two formulations of the concept of change, the
former has an advantage from the empirical point of view,
for it permits the description of motion as taking place,
while the latter, without the addition of further propositions
about the continuity of T and T', describes only the fact of

1 Principles of Mathematics, p. 469.

316 INTRODUCTION TO PHILOSOPHY OF SCIENCE

motion as having taken place. Now it seems that motion on
the empirical level is properly described rather as something
taking place than as an inference to something which must
have taken place by virtue of the evidence afforded by cer-
tain data. " If a body is moving at all fast, we see its motion
just as we see its color. A slow motion, like that of the hour-
hand of a watch, is only known ... by observing a change
of position after a lapse of time; but, when we observe the
motion of the second-hand, we do not merely see first one
position and then another — we see something as directly
sensible as color." ! Motion, therefore, is an empirical datum,
and, moreover, one which resists analysis into anything
which is psychologically more primitive. There are motions
which are not reducible to a series of positions, but are per-
ceived as single facts. It is these which give the concept of
motion its empirical content.

Quantity. To say that motion is empirically a quantity
is to characterize it in terms of a concept whose analysis
has already been made. Quantities are events which may be
ordered on the basis of the relation "greater than." Mo-
tions are, therefore, also velocities, and may be compared to
one another according to degree. Perceptual discernment en-
ables one to make crude judgments as to relative velocities,
e.g., that an express train travels faster than a horse-drawn
vehicle. In doubtful cases measurement is introduced. This
involves correlating the two motions either with the respec-
tive changes in space over a given time, or with the respective
times required to accomplish a given change in space. Fur-
thermore, motion, in addition to exhibiting variations in
intensity, manifests also variations in direction. Movement
of A and B toward one another is not the same as motion of
A and B away from one another, nor the same as motion of
A obliquely to a line joining A and B. Rotational and
"squirming" motions also exhibit features peculiar to them-
selves. These can be described as complicated functions of
changes in distance and direction.

1 Bertrand Russell, Our Knowledge of the External World, p. 137.

MOTION, FORCE, MATTER 317

motion: scientific content

There is not one concept of motion which functions in
science, but two. Corresponding to the Newtonian-Euclidean
absolute space and time there is an absolute motion, and
corresponding to the space-time of relativity there is a
relative motion. For purposes of illustration emphasis will
be placed on the former, with concluding remarks showing
the changes that must be introduced when the facts of
relativity are taken into consideration.

Dependence on particles. The abstractive operation in-
volved in the passage from empirical motion to scientific
motion is not so great as that involved in the passage from
empirical space and time to absolute space and time. Abso-
lute motion cannot be empty; it is defined as "the occupa-
tion, by one entity, of a continuous series of places at a con-
tinuous series of times." l Abstractly, any correlation of the
spatial continuum with the temporal continuum is possible;
but only certain of these correlations are motions. The cor-
relation desired is accomplished through the notion of the
particle. This is merely a refinement of the notion of event,
or object, which is demanded in the empirical conception of
motion. For science, as for common sense, there is always
something which moves. For the purposes of defining motion
a particle may be considered to be any entity which can be
at a point in space at an instant in time. The more precise
characterization of this notion will be given later in the
chapter. For the present, however, one may say that a par-
ticle is any entity which through the notions of "being at a
point," and "being at an instant" brings about the correla-
tion between space and time by which motion is to be de-
fined. Absolute motion, therefore, is dependent on the con-
cept of the particle.

Dependence on measurement. Motion as it functions in
science is more closely tied up with activities of measure-
ment than is empirical motion. Empirical motion is a given

1 Bertrand Russell, Principles of Mathematics, p. 469.

318 INTRODUCTION TO PHILOSOPHY OF SCIENCE

fact, exhibiting quantitative variations, but not reducible
to readings of speedometers, clocks, and meter sticks. For
science, however, motion is inseparable from the measure-
ment of motion, since it is defined as the quotient of space
divided by time, and these are in turn expressible only as
numbers. Hence, scientific motion takes on its meaning only
through a description of the activity of constructing, setting
up, and reading clocks, meter bars, and other instruments
of a more complicated sort. It is still empirical motion with
which the scientist is concerned, except that he is able to
measure unobservable motions, and to measure observable
motions more accurately. The fact that motion exhibits not
only features of magnitude, or intensity, but direction as
well, places it in the class of vector quantities, and permits it
to be handled according to the special laws determining the
addition, multiplication, and other operations of this kind
of quantity. The ordinary representation of a vector quan-
tity as a straight line with an arrow attached, exhibits
clearly the magnitude and directional features of motion.
Absolute character. The precise sense in which Newtonian
motion is absolute must be made clear. If, for the moment,
one calls the Newtonian theory the Absolute Theory, and
the empirical theory the Relational Theory, the differences
between the two points of view may be made clear by a quo-
tation from Rroad. "Absolute motion is the passing of a
body from one point of Absolute Space to another. Absolute
rest is the remaining of a body at a point of Absolute Space.
Relative motion has the same meaning on both theories; it
is just a change in the relative positions of two bodies. The
difference about it is that the Relationists say that all
motion simply is a change in the spatial relations of one
body to others, whilst the Absolutists say that there is
absolute as well as relative motion and that the two must be
distinguished from each other. On the Absolute Theory all
relative motion implies absolute motion, and is the appear-
ance of it to us, but a knowledge of relative motion does not
suffice to determine unambiguously the absolute motions

MOTION, FORCE, MATTER 319

involved. Thus, suppose that A and B are two bodies, and
that u is the rate at which the distance between them is in-
creasing. Then u is a relative velocity. The Absolutist says
that it must be due to absolute motions in A or in B or in
both, and that all that we can say about them is that their
difference is equal to u." 1

The difficulties inherent in the conception of the Absolute
Theory are apparent. What is that ultimate frame of ref-
erence according to which all motions are, in the final anal-
ysis, absolute? Newton's formulation is not particularly
helpful. "If a place is moved, whatever is placed therein,
moves along with it. . . . Wherefore entire and absolute
motions can be no otherwise determined than by immovable
places; and for that reason I did before refer those absolute
motions to immovable places, but relative ones to movable
places. Now no other places are immovable but those that,
from infinity to infinity, do all retain the same given posi-
tions one to another; and upon this account must ever re-
main unmoved; and do thereby constitute immovable
space." 2 Absolute space seems thereby to be entirely postu-
lational. Attempts have been made in the history of science
to locate this absolute system of reference in terms of a
material entity. C. Neumann, for example, assumed the
existence somewhere in physical space of a completely im-
movable body called the "body Alpha," 3 to which all
motions are to be referred. Alternative choices for this
ultimate point of reference are certain of the "fixed" stars,
and (until fairly recent times) the ether. The arbitrary char-
acter of all such systems of reference is obvious.

Correlational character. Motion is commonly defined as
the time rate of change of position, or as the first derivative
of space with respect to time. The correlational character of
this definition is clear; motion is incapable of definition
without at least the notions of "space" and "change," the

1 Scientific Thought, pp. 97-98. 2 Newton s Principia, p. 80.

3 Ueber die Principien der Galilei- Newtonschen Theorie (Leipzig: Teubner, 1870),
p. 15.

320 INTRODUCTION TO PHILOSOPHY OF SCIENCE

latter of which is essentially involved in the notion of
"time." Hence, motion may be defined as the correlation of
two continuous linear series, as these notions were defined in
Chapter XIII, one of which is space and the other of which
is time. But not every correlation of space and time is
motion. By virtue of the notion of particle, by which the
correlation is achieved, certain types are excluded. Ab-
stractly, four general types would be possible: taking the
two series in the order space-time, the correlation of the
points of the former with the instants of the latter may be
many-one, many-many, one-one, or one-many. But by
virtue of the definition of "particle" the first two are impossi-
ble; a particle cannot be at two different points at the same
instant. A many-one correlation of space and time defines
instantaneous extension, and a many-many correlation de-
fines enduring extension. The one-one and the one-many
correlations then define, respectively, motion and rest. A
particle is said to be in motion at an instant if it is possible
to find an interval of time including that instant such that
at every instant within the interval the particle is at a dif-
ferent point in space. A particle is said to be at rest at an
instant if it is possible to find an interval of time including
that instant such that at every instant within the interval
the particle is at the same point in space.1

Two features of this definition may be called to attention.
The first is the fact that a correlation of this kind gives the
desired continuity to motion. "In a continuous motion . . .
at any given instant the moving body occupies a certain
position, and at other instants it occupies other positions;
the interval between any two instants and between any two
positions is always finite, but the continuity of the motion is
shown in the fact that, however near together we take the
two positions and the two instants, there are an infinite
number of positions still nearer together, which are occupied

1 Compare Russell's definitions of these notions in his Principles of Mathematics
(pp. 472-473). Difficulties with regard to end-points, i.e., points of change from
motion to rest, or from rest to motion, can be handled by introducing the proper
technicalities into the definition.

MOTION, FORCE, MATTER 321

at instants that are also still nearer together. The moving
body never jumps from one position to another, but always
passes by a gradual transition through an infinite number
of intermediaries." * The second feature of the definition
is that both motion and rest require the notion of "interval"
for definition. There is no such thing as motion or rest
at an instant; in order to ascertain what the particle is doing
at an instant one must know something as to what it was
doing before that instant or what it will be doing after that
instant. Motion and rest require comparison of the positions
of a particle at two instants; if the particle is at the same
position at the two instants, it is at rest; but if it is at dif-
ferent positions at the two instants, it is in motion. If one
has given only one instant, no such comparison is possible.
The importance of the notion of interval in the definition of
motion and rest is obvious in the ease with which it enables
one to avoid Zeno's paradoxes.

motion: operational derivation

The operational passage from empirical motion to scien-
tific motion is essentially that involved in the transition
from empirical space and time to the space and time of the
classical physics. Empirical motion is an aspect of empirical
space and time in much the same way that scientific motion
is an aspect of scientific space and time. However, the degree
of abstraction is not quite so great. Whereas scientific space
and time are empty, scientific motion retains the notion of
particle; hence although for science space and time need not
be occupied, motion demands occupants, i.e., motion and
rest would be meaningless in an empty world. To be sure,
in the scientific concept of motion there is an element of
abstraction, for reference to specific spatial frames has been
lost. Nevertheless, there is a general frame. The fact that
even this general frame of reference tends to take material
form in the "body Alpha," one of the fixed stars, or the
ether, suggests the abstractness of the conception and the

1 Bertrand Russell, Our Knowledge of the External World, pp. 135-136.

322 INTRODUCTION TO PHILOSOPHY OF SCIENCE

reluctance of the human mind to leave the empirical realm.
Similarly, the generalization of the scientific concept of
motion to include velocities beyond the limits of observa-
tion may be described as an operation of abstraction, or, if
one prefers, of serial extension. An instantaneous velocity
could be defined either as the limit of velocities of con-
tinually decreasing durations, or as the series itself of such
velocities, as in the case of Whitehead's definition of " point."
The distinction between the concept of motion as it func-
tions in the classical physics, and the notion as it plays a
part in the recent relativity theory is based upon a recog-
nition of the elusiveness of absolute velocity through space.
Newton himself, apparently, realized the hypothetical char-
acter of absolute motion, since he pointed out that the laws
of mechanics have the same form in all reference systems
moving with respect to each other with constant velocity.
This was equivalent to admitting that by no mechanical
experiment could absolute motion of this kind be deter-
mined. "No mechanical experiment that can be performed,
for example, on a train moving at constant speed can
divulge to us that the train is really moving, for the results
of all such experiments relative to the train are precisely the
same as those which would have been obtained by the
performance of similar experiments at the station or on the
roadside." 1 It was supposed, however, that such absolute
velocity, i.e., velocity relative to some absolutely fixed point
such as the ether, could be detected by other experiments,
e.g., optical ones. The Michelson-Morley experiment was
designed to verify precisely such a supposition. But its
negative results, and the negative results of similar experi-
ments performed upon electro-magnetic phenomena in
general, have suggested that perhaps absolute velocity
cannot be detected by any means; and the suspicion im-
mediately arises that absolute velocity may be meaningless.
At least if absolute motion cannot be established by any
instrumental techniques, and if it cannot be logically derived

1 R. B. Lindsay and H. Margenau, Foundations of Physics, p. 331.

MOTION, FORCE, MATTER 323

through any formal techniques, there is no longer any
reason to suppose that it functions in science in any sig-
nificant way. It must therefore be replaced by a more fruit-
ful notion, viz., that of relative motion. This becomes the
foundation for relativity mechanics just as the Newtonian
conception became the foundation for the classical mechan-
ics. The complications which are introduced when general-
ization is made to accelerated and rotational motions in-
volve extension to the general theory of relativity and are
too great to be discussed here.

Hence, in summary of the concept of motion, one may
say that at the empirical level it designates a quantitatively
variable change in the spatial relations holding between two
events. But at the scientific level, it designates a certain
correlation between points of space and instants of time,
accomplished through the medium of a particle, and ex-
pressible in terms of measured values; for the absolute
theory this correlation is between an absolute space and an
absolute time, and hence determines an absolute motion;
but for a relative theory the correlation is recognized as being
relevant always to coordinate systems, and hence as in
some sense arbitrary. Since motion is defined in terms of
space and time, the operational derivation of scientific
motion from its empirical foundation is such as is involved in
the passage from empirical space and time to scientific space
and time.

FORCE : EMPIRICAL^ FOUNDATION

The confusion which is to be found in recent literature
with reference to the concept of force makes a satisfactory *
discussion of it impossible. The obscurity bears not only on
the empirical notion, but on the scientific concept, and,
as a result, on the operational derivation as well. That there
is empirically revealed some such thing as force seems hard
to deny, in spite of Russell's statement that "force is a
mathematical fiction, not a physical entity." l Yet, on the

1 Principles of Mathematics, p. 482.

324 INTRODUCTION TO PHILOSOPHY OF SCIENCE

other hand, the term "force' is applied to so wide a range
of experiences — weight, inertia, energy, mass, momentum,
and work — that one wonders whether any definition of the
term which would include such a variety of connotations
would be possible. On the side of science itself, the confusion
is of another kind. There seems to be little doubt but that
Newton's laws of motion constitute the essential postulate
system for the definition of 'force" as it is used in science.
But the task of determining which among these postulates
is to be considered as definitive of the nature of force, and
which merely as making assertions "about force," is not at
all easy. Furthermore, dispute arises as to whether force is
itself a basic notion for a system of mechanics, or must be
defined in terms of a more fundamental notion, e.g., mass,
or momentum. Hence one cannot be sure what is meant by
force, even for contemporary science. As a result, the prob-
lem of logical derivation from its empirical foundation be-
comes essentially insoluble; logical techniques cannot be
made precise if there is no clear-cut knowledge of that with
which they start and that with which they end. At this
level the problem is very much complicated by the ideal
character of the laws of mechanics; they describe not actual
but theoretical situations, hence their derivations from em-
pirical situations must always be by involved routes. In the
face of these difficulties the more or less systematic analysis
of the preceding pages must be abandoned, and a somewhat
random series of comments must take its place.

Attempting to ascertain the empirical foundation of the
concept of force, one is compelled to recognize that forces
have their loci in situations provoking in us feelings of effort.
"Unquestionably the sensational basis of the scientific con-
cept of force is the feelings of strain that we experience when
we drag a heavy body along, or throw a stone, or bend a
bow." x It seems hard to deny that there is a wide range of
situations which give rise in us to feelings of a similar kind —
stretching an elastic band, stopping a swiftly thrown ball,

1 C. D. Broad, Scientific Thought, p. 162.

MOTION, FORCE, MATTER 325

carrying a heavy valise, lifting ourselves by our arms from
a rigid bar, pressing upon a table-top, and so on. These are
facts of experience, and anyone with a feeling for reality
could hardly deny that they must be reckoned with in any
comprehensive scientific theory. Just how they exist is not
important. Some writers, for example, insist that forces are
resident merely in our muscles, hence do not have a part
in the physical world but only in the physiological, or perhaps
the psychological, world. Others, Broad for example, insist
that we must distinguish between our feeling of strain and
the strains which we feel. "Force is not supposed to be
our feelings of strain; it is simply supposed that the strains
which we feel are forces, or are indications of forces." 1
Again, still others may dispute as to whether force is a purely
relative aspect of events, depending for its existence upon
the presence of the observer, or an objective feature, wholly
independent of the observer; for example, is it correct to
say that the sun attracts the earth through a force of gravi-
tation, or is such a conception meaningless unless one sup-
poses that the sun is in some respect like a human observer,
and hence is able to feel the force? These are some of the
most representative of the alternative views. But whatever
status is given to forces, a recognition of their unanalyzable
character seems basic. One cannot say what forces are, for
to do so would imply the existence of something which is
psychologically more basic than they are. To call them
"efforts," "resistances," "strains," "tensions," etc., is not
to define them but to attempt through alternative designa-
tions to point to them. Here, as in the case of all empirical
concepts, one's only method of clarification is through deno-
tation.

Furthermore, it seems undeniable that forces exhibit
themselves always as attached to events. There are no dis-
embodied forces; forces always manifest themselves as
properties of things which push, pull, weigh, resist, impel,
attract, and press. To say that force always certifies the

1 Ibid., pp. 162-163.

326 INTRODUCTION TO PHILOSOPHY OF SCIENCE

presence of matter does not help, for this places an extra
burden on the concept of matter. In fact, as will be seen
later, there is reason to believe that force is one of the essen-
tial features of matter and hence to be used in its definition;
but this would then forbid one to define force by means of
matter. Accordingly it may be said, for the present, merely
that forces are always attached to events which exhibit a
certain qualitative identity. Even the wind which fans one's
cheeks is hot or cold, fragrant or foul-smelling; and one
promptly materializes as 'unseen hands' any very subtle
forces which seem to cause him to act without effort. Dis-
embodied forces, like disembodied spirits, are not found so
long as one limits himself to the most clearly given data.

This leads promptly to a consideration of a further aspect
of force — its intimate association with motion. In this
regard the concept of force is intimately tied up with the
concept of causation, to which reference will be made in a
later chapter. At the empirical level, force is commonly
defined as the cause of change in motion. Whether the cause-
effect relation is reducible to mere succession, or whether
there is something of "production" involved, are questions
which must be postponed. However, the feeling of force
seems to be an important part of all situations in which
one is himself active in bringing about a change in nature.
But that the force is the cause of change of motion rather
than the effect is not too obvious. When I instigate move-
ment, e.g., push an automobile, I feel the force before I
notice the motion, hence I conclude that the force has caused
the motion. But when I stop movement, e.g., endeavor to
hold a coasting automobile, I notice the motion before I
feel the force, hence I conclude that the motion caused the
force. It seems arbitrary, therefore, to say that force causes
motion rather than that motion causes force. What can be
said with a fair degree of certainty upon the empirical level
seems to be merely that in all situations in which there is
change of motion, i.e., initiation or acceleration, and stopping
or slowing, force is present. In other words, nature reveals

MOTION, FORCE, MATTER 327

not causal connection but mere concomitance; force and
change of motion coexist in events of certain kinds, but no
invariable temporal relation and no relation of causal efficacy
seem to be indisputably present. Furthermore, concomitance
does not mean identity. Though force and motion are pre-
sumed to be coexistent features of certain events, they are
distinguishable. In this respect they are analogous to cer-
tain other sense qualities, e.g., spatial extent and color; all
extensions are colored and all colors are extended, yet one
has no difficulty distinguishing these qualities from one
another. Hence at the empirical level force is neither the
cause nor the effect of change of motion, nor is it to be
identified with change of motion; the two are simply con-
comitants.

Finally, as in the case of motion, force is quantitative.
This is simply to say that forces may differ from one another
in a way which permits the observer to say that one is
greater in intensity than another. The force felt in bending
a bow is greater than that felt in stretching a small rubber
band, and the force imparted by a moving baseball is greater
than that imparted by a tennis ball moving with the same
velocity. Forces also exhibit differences in direction. A
force up differs from a force down, and a force to the left
from one to the right.

force: scientific content

As a first approximation to a scientific definition of force,
one may say that force means 'whatever is asserted about
force in any propositions of science in which the word or
symbol occurs. Whatever may be asserted as a true proposi-
tion about force says something about force, and the totality
of such assertions constitutes the meaning of the concept.
Furthermore, since the important statements about force
in science are mathematical, force may be defined as the
totality of mathematical equations in which / occurs.

What is required in science, however, is not primarily a
knowledge of everything that may be said about force but

328 INTRODUCTION TO PHILOSOPHY OF SCIENCE

only a knowledge of the basic properties of force. The pre-
sumption is, in other words, that certain statements about
force may be taken as fundamental, and others taken as
derivative, with the latter capable of logical deduction from
the former. What is demanded is a set of postulates de-
fining force, which will imply a set of theorems giving addi-
tional information about force. Then the postulate set
may be considered as giving the essential meaning of the
concept.

In spite of very general disagreement among writers on the
philosophical foundations of the concepts of mechanics,
there is apparently a common recognition of the necessity
for defining force approximately in terms of Newton's three
laws of motion. Whether these three laws are consistent
and independent, and whether there is a more basic system
from which they may all be deduced, are questions concern-
ing which there seems to be some dispute. The reduction
of these laws to their empirical foundations is a problem
which, as will be seen immediately, involves some difficulty.
But an examination of these basic laws will afford a satis-
factory method for determining approximately what is to
be understood by force as it functions in science.

"Every body preserves in its state of rest, or of uniform
motion in a right line, unless it is compelled to change that
state by forces impressed thereon.

"The alteration of motion is ever proportional to the
motive force impressed; and is made in the direction of the
right line in which that force is impressed.

'To every action there is always opposed an equal reac-
tion: or the mutual actions of two bodies upon each other
are always equal, and directed to contrary parts." x

The first refinement to be introduced into this conception,
so far as modern science is concerned, is the replacement of
the crude notion of "body' by the more precise notion of
"particle." This concept was defined earlier in the chapter.
The essential property of particles, for the purposes of this

1 Newton's Principia, p. 83.

MOTION, FORCE, MATTER 329

discussion, is motion; since particles exhibit motion and rest
they also exhibit changes of motion, and hence any other
property intimately connected with this phenomenon.

The second refinement concerns the elimination of the
notion of compulsion which plays so prominent a part in the
first law. As has already been shown, there is some doubt
whether even at the empirical level the notion of causation
or necessity is an essential part of every force-experience.
The whole question is tied up with the idea that force in-
volves muscular action, and that changes in nature are
analogous to those found in acts of will. That this notion
played a prominent part in the thinking of primitive man
seems unquestionable, but that it should be eliminated so
far as possible from scientific thinking seems equally certain.
"The idea ... of enforcement, of some necessity in the
order of sequence, remains deeply rooted in men's minds, as
a fossil from the spiritualistic explanation which sees in will
the cause of motion. This idea is unfortunately preserved
in association with the scientific description of motion, and
in the materialist's notion of force as that which necessitates
certain changes or sequences of motion, we have a ghost of
the old spiritualism. . . . The necessity in a law of nature
has not the logical must of a geometrical theorem, nor the
categorical must of a human law-giver; it is merely our
experience of a routine, whose stages have neither logical
nor volitional order." x Furthermore, "though there is no
sense in saying that anthropomorphism is wrong," since
"we can never get away from it in at least a diluted form,"
nevertheless this conception of force "is of doubtful value
for mechanics." 2 Recognizing, therefore, the necessity for
eliminating the notion of compulsion from Newton's first
law, one may restate it in such a way as to avoid this feature,
and to indicate more clearly that the law states merely a
correlation between force and change of motion. 'Every
particle in a state of change of motion (i.e., neither at rest,

1 K. Pearson, Grammar of Science, pp. 119-120.

2 R. B. Lindsay and H. Margenau, Foundations of Physics, p. 87.

330 INTRODUCTION TO PHILOSOPHY OF SCIENCE

nor in uniform motion in a straight line) exhibits force."
The law then states merely that force may be defined with
reference to something with which it is uniformly associated.
In other words, it is part of the meaning of force that it
should be associated with change of motion.

But although this law tells one essentially what is meant
by force in terms of one of its important correlates, it does
not afford a means for measuring force. If the important
scientific statements about force are expressed in mathe-
matical equations, the notion must function in science not
as a quality but as a quantity. The quantitative character
of force is described in the second and third laws. These
state that force is capable of intensive variation, and that it
exhibits a directional feature. Hence force, as motion, is a
vector quantity. Forces then become numbers of certain
kinds and can be operated upon according to the laws of
vectoral calculation.

Specifically, the second law is presumed to afford a tech-
nique for measuring force intensity in terms of change of
motion. Change of motion is capable of measurement
through meter rods and clocks, and does not require the
observer to be in contact with the moving object. Hence
precision can be achieved, and anthropomorphism avoided.
Change of motion is a somewhat more complicated function
of space and time than mere motion. Just as the latter is
the quotient of space over time, the former is the quotient
of this quotient over time, i.e., the time-rate of change of
velocity. This is called acceleration. The third law affords
no technique for measuring force. It does state, however, an
important fact about forces, viz., that they always occur in
pairs, not singly. Though these two forces are equal in
magnitude, they are opposite in direction; hence they are
different vectoral quantities.

However, although the second law states a proportionality
between force and acceleration, it does not state an eguiva-
lence. It affords a means for comparing two forces through
the respective accelerations with which they are associated,

MOTION, FORCE, MATTER 331

but the comparison may be presumed to hold only in case
there is no other factor of variation. However, there is just
such a factor. To refer a moment to the empirical level,
where there is contact with an observer and where forces
may therefore be felt, acceleration is not an accurate measure
of force. Greater force is exerted by a moving baseball than
by a moving tennis ball, though they have the same velocity;
and greater force is required to set an automobile in motion
than a bicycle. This further property of particles is called
mass, which Newton endeavored to clarify by calling it
"quantity of matter." Force, then, may be defined as
equivalent to the product of the mass by the acceleration,
f = m a. This is the basic equation of mechanics.

In summary, then, force as it functions in science may be
described as a property of particles; its measured value is a
vector quantity, and it is universally correlated with (a) a
similar property, equal in intensity but opposite in direction,
and (b) two other properties known as mass and acceleration
by means of which it is measured.

force: operational derivation

The search for a definition of force which will meet the
needs of science has been the attempt to find a satisfactory
criterion for locating and measuring forces. However realistic
one may be in his attitude toward forces, he is compelled to
admit that their empirical definition in terms of pushes,
pulls, pressures, resistances, and the like — all of which imply
contact between an observer and an object — is both too
vague and too narrow to function adequately in science. Such
a definition is especially vague because it offers no technique
for measuring accurately the intensity and direction of
forces. But it is vague also because it confuses a large group
of "forces" all of which, to be sure, exhibit common features,
but which show also important differences and require
therefore to be distinguished. Furthermore, the definition is
too narrow because it implies, indirectly at least, that forces
can be known to be present only when the objects to which

332 INTRODUCTION TO PHILOSOPHY OF SCIENCE

they are attached are touched by observers, and, conse-
quently, that the study of force is a matter for physiology
rather than for physics. The scientific definition of force
must, therefore, satisfy two criteria: It must enable one to
measure force and to differentiate between the various kinds
of "forces"; but it must enable one to locate and to measure
forces in situations not involving the immediate contact of
the observer.

The essential operational act, therefore, by which the
scientific notion of force is derived from its empirical founda-
tion is measurement. This, as has been seen, is a type of
abstraction. But it differs from other types of abstraction
in that it attempts to devise a physical correlate for itself.
Measuring instruments are physical events, and they are
related to the events which they measure by physical con-
nections. Hence the "mental'' operation of generalizing a
qualitative event so as to retain only its quantitative features
has a parallel in the "physical' operation of inventing,
setting-up, and reading recording instruments. Both proc-
esses begin with qualitative events and end with numbers.
But whereas the former has no recognized principles or rules
for its guidance (it is usually described simply as the "neg-
lect" of individual features with the "retention" of common
features), the latter is capable of accurate formulation in
terms of certain recognized techniques determined by the
character of the event to be measured, the nature of the
recording device and its calibration, and its application in a
specific situation. There are rules for measuring, and the
meaning of any physical concept must not be separated from
its techniques of measurement. ' In general, we mean by any
concept nothing more than a set of operations; the concept is
synonymous with the corresponding set of operations. If the
concept is physical, as of length, the operations are actual
physical operations, namely, those by which length is meas-
ured; or if the concept is mental, as of mathematical con-
tinuity, the operations are mental operations, namely those
by which we determine whether a given aggregate of magni-

MOTION, FORCE, MATTER 333

tildes is continuous." * But where a recognized physical
technique is available it is always to be preferred to a mental
technique, even in those rare cases where the latter is to be
found. Hence the attempt to define the scientific concept of
force is the attempt to find a technique for the measurement
of force.

The scientific notion of force presumes to include in its
definition precisely such a technique ; force is measured by the
product of the mass and the acceleration. The necessity for
this conception resides in the fact that there seems to be no
way of measuring force directly. One cannot detach forces
from objects and move them about as one can clocks and
meter rods. One cannot even add and subtract forces in
quite the same way that one can spaces and times. Force is
an intensive quantity, like motion. Hence, like motion, it is
measured not directly but through correlation with events of
another kind which, in turn, are susceptible of more direct
measurement. Motion, it was noted, is measured in terms
of space and time, both of which are extensive quantities and
readily measurable. Acceleration is measurable in terms of
motion and time. But what may be said of mass? Is this
also directly or indirectly measurable? If it is directly
measurable, what is the qualitative experience of which it is
the measure? If it is not directly measurable, with what
qualitative experience is it correlated?

The answers to these questions are crucial. For if the
meaning of the scientific concept of force is identified with
its measured value, no analysis of this meaning is possible
without a recognition of the techniques of measurement.
What, then, is the empirical foundation of the concept of
mass?

There are two main attempts to solve this problem. The
first involves the search for a clearly given qualitative datum
to which the term refers. The presumption is that mass is
one of the psychological simples of experience, and if one can
only locate it and measure it he will have the information

1 P. W. Bridgman, Logic of Modern Physics, p. 5.

334 INTRODUCTION TO PHILOSOPHY OF SCIENCE

through which the concept of force may be clarified. Un-
fortunately, this attempt seems to fail. To describe mass, as
Newton did, by the phrase "quantity of matter'' does not
help one to locate it unless the meaning of this phrase is made
clear. To describe it in terms of inertia is inadequate, as
Lenzen points out, for "the status of inertia as a property
is very dubious ; it seems evident that we are not acquainted
with inertia in the sense in which we are acquainted with
redness, extension, etc." l Furthermore, even if there is
something empirically given which can be called "inertia,"
this datum is one of the general kind called "force," and
unless the features which distinguish it from all other
"forces" can be made clear, one has made no progress. What
is worse, unless there is some technique for measuring
inertia, one has not advanced the problem. To suggest, as
Newton did, that mass is measured by the product of the
density by the volume is of no help, for density is measurable
only as the mass per unit volume. Similar difficulties arise
in the attempt to define mass through gravitation. For
example, a recent writer 2 asserts that "the mass of a body
cannot be more definitely described than to say that it is the
quality to which are due both its inertia and its gravitational
action." Apart from the difficulty associated with the notion
of inertia and gravitation being due to mass, there is a further
obscurity associated with the notion of gravitational action.
The presumption is that this term is to be employed as a
designation for the fact of weight; but if so the circular char-
acter of the designation becomes apparent, for weight, like
inertia, is a datum of the general kind called 'force," and
unless the features which distinguish it from all other
"forces " can be made clear one has made no progress. Hence
the attempt to locate a qualitative datum to which "mass"
directly refers, seems to lead up a blind alley. All such data
appear to be merely force-experiences of certain kinds.
Hence one finds that in the attempt to measure force by

1 Physical Theory, p. 111.

2 F. H. Saunders, Survey of Physics (New York: Holt, 1930), p. 61.

MOTION, FORCE, MATTER 335

means of mass, he can do so only by means of certain forces.
The humiliating outcome is that one can measure force only
by measuring force.

The second attempt involves, if not a complete abandon-
ment of the empirical reference, at least the recognition
that mass may be a somewhat obscure and complex prop-
erty of events. From this point of view mass is considered
not to refer descriptively to any clearly given type of force-
experience. It is defined, rather, as a construct from the data,
and can be said to be given only in the sense that it is re-
quired to make certain experimental situations intelligible.
It is a property which "is ascribed to a body in order to
represent the results of experiments on the body. We are
acquainted with the phenomenon in the experiment, and
know the measure which we assign to the body, but we do not
appear to be acquainted with the property ascribed to the
body." 1 If the extreme conventionalism of Poincare's
position can, for the moment, be neglected, the view which
is here being maintained can be formulated in his words:
"Masses are coefficients it is convenient to introduce into calcula-
tions" 2 The fact of convenience prevents this from being a
purely nominal definition. It can be restated so as to elimi-
nate the tinge of arbitrariness by saying that masses are
coefficients determined by certain complicated experiments
on bodies, and by means of which other important prop-
erties may be demonstrated. The best example of this
attempt to define mass is that first given by Mach,3 and
reproduced with some modifications by Lindsay and Mar-
genau.4 In this approach mass is defined in terms of accelera-
tion, but in terms of a complicated function of the latter.
Given two bodies, A and B, each exhibiting an acceleration
toward the other, one may set up the function represented
by the quotient of these accelerations; experiment shows this
to be a constant, and it may therefore be presumed to be
some sort of property possessed by the bodies; this property

1 V. F. Lenzen, Physical Theory, p. 111. 2 Foundations of Science, p. 102.

3 Science of Mechanics (Chicago: Open Court, 1893), pp. 216-222.

4 Foundations of Physics, pp. 91-94.

336 INTRODUCTION TO PHILOSOPHY OF SCIENCE

may be called mass. For example, the mass of B with
respect to A is defined as the acceleration of A with respect
to B divided by the acceleration of B with respect to A, viz.,
Q>ab! — clba = Mb A> The mass of A with respect to B is the
reciprocal of this. If the accelerations are equal the masses
are equal, and if they are unequal the masses are unequal.
By arbitrarily defining one of the bodies, say A, as a unit
body, the mass of B becomes a fixed number. By this method
numbers can be found which may be attached to all bodies.
These numbers constitute the measured values of masses,
and function accordingly in the equations of mechanics.
All that should be emphasized here is that mass does not,
according to this approach, refer descriptively to any
immediately given force-experience. A quotient of accelera-
tions is hardly one of the psychological simples of percep-
tion. Alternative definitions of mass, which are essentially
constructive like the one given, are the attempts of Lenzen l
and Broad 2 to define mass through certain constant prop-
erties of bodies as they behave under impact.

In conclusion, then, the most significant feature of the
operational derivation of the concept of force is the invention
of a technique for measuring force. This requires the con-
struction (or the somewhat obscure discernment in the given)
of a property of bodies called "mass," which is capable of
measurement and affords the required technique. Force is
then measured by the product of mass and acceleration,
both of which are independently measurable. Many of the
complications of this technique have, of course, been omitted.
For example, the proportionality of mass to weight permits
one to substitute the direct measurement of the latter by
means of balances for the indirect measurement of the former.
But this method could not be employed as a definition of
mass, for then the difference between mass and weight would
be lost. Complications of this kind require more detailed
analysis than has been possible in this somewhat superficial
treatment.

1 Physical Theory, pp. 107 el seq. 2 Scientific Thought, pp. 169 el seq.

MOTION, FORCE, MATTER 337

The result of this rather disorganized discussion of the
concept of force is approximately as follows: Force at the
empirical level is a vague name for a great variety of data,
unquestionably present, yet incapable of precise char-
acterization; these data seem to be always associated with
events, often associated with motion, and capable of quan-
titative differentiation. Force at the scientific level is what
is obtained when the attempt is made to determine pre-
cisely where forces are, and how intense their manifestations
are, i.e., their loci and their measured values. But the at-
tempt to measure force reveals the fact that there is nothing
among the psychological simples of experience by which
this can be done. However, there is revealed a somewhat
obscure feature of nature, viz., a certain quotient of accelera-
tions, which seems to afford the required empirical basis;
this is called "mass," and is defined as proportionate to
force. Then force becomes measurable in terms of mass. This
makes mass psychologically derivative, but logically basic.
The operational derivation of the concept of force is therefore
simply the route by which its measured value is determined.

matter: empirical foundation

It is likely that the concept of matter is both the most
obscure of the basic physical concepts and the most ambig-
uous of philosophical notions. This is due partly to its long
and controversial history. But it is to be explained also by
the fact that the term "matter" has been employed to
designate features of nature which are widely different from
one another. An examination of the great variety of con-
texts in which the term has been used demonstrates this
ambiguity quite clearly. For example, " matter' : may be
used as synonymous with "thing," "body," or "substance,"
to be contrasted with "property," "aspect," or "quality";
or it may be used as equivalent to "particular," as opposed
to "universal"; or "content," as opposed to "form"; or
"physical," as opposed to "mental" or "spiritual"; or
"real," as opposed to "unreal" or "imaginary." It seems

338 INTRODUCTION TO PHILOSOPHY OF SCIENCE

obvious that no progress can be made in the analysis of the
concept unless there is an organized attempt to differentiate
these meanings sharply from one another.

Fortunately, not all of these meanings are equally relevant
for science and philosophy, and, as a consequence, a discus-
sion of the scientific meaning of the concept may be prefaced
by a definite rejection of certain of the philosophical mean-
ings as having no importance. On the basis of this principle
it is possible to limit one's consideration somewhat. Probably
most scientists would agree that their task is not to explain
matter either in the sense of the physical as opposed to the
mental or spiritual, or in the sense of the real as opposed to
the unreal or imaginary; both distinctions, they would
insist, may be legitimate, and must be recognized by science
provided they can be expressed in verifiable terms; but the
problem of finding such distinguishing criteria is one be-
longing to philosophy and not to science. Similarly, the
majority of scientists would be of the opinion that the dis-
tinction between content and form can be reduced to the
distinction between substance and quality if form is con-
sidered in the sense of shape or figure, and to the distinction
between particular and universal if form is considered in
the sense of type, or abstract character. Finally, most
scientists would presumably be in agreement that the dis-
tinction between particular and universal, while it must be
recognized by the scientist, does not constitute a scientific
problem as such but a logical and metaphysical problem.
Without doubt everything that the scientist observes is a
particular, whether it be a thing, a process, a happening, a
duration, an extent, a relation, or even a number. The
concept "particular'' is therefore approximately synony-
mous with the concept "event," as this latter term was
described in Chapter III and has been used throughout the
discussion. But it hardly seems the job of the scientist to
determine the nature of this basic scientific entity. Every
scientific entity is an event but certain events are material
and certain events are not, and it is the task of the scientist

MOTION, FORCE, MATTER 339

to determine the character of these more concrete types of
entity. The scientific problem of matter is the problem of the
ultimate stuff of nature, not in the sense of the most abstract
natural entity, but in the sense of that type of event to
which all other events can be related as attributes, relations,
processes, happenings, or changes. Material events are funda-
mental only in the sense that all other events are referential
toward them.

The scientific problem of matter, therefore, reduces to the
first of those given above. Matter is that which is most
adequately described by such vague common sense words
as "thing," "body," "object," and "substance." The
further problem, then, is to determine as precisely as possible
what these terms reduce to at the empirical level, what
content the scientist gives to them when he employs them as
tools in his investigation, and by what operational tech-
niques the latter may be derived from the former.

When one turns to the problem of the empirical founda-
tion of the concept of matter he is impressed with an im-
portant feature. Things are complexes of properties and
aspects. A table, for example, is a complex of shape, color,
weight, hardness, gloss, smoothness, warmth, etc. Further-
more, it appears at the empirical level that by the substance
or material of a thing one can mean only this complex or
some selected part of it. There is nothing given in observa-
tion that can be called the substratum of the qualities. One
can observe only the qualities, not "that which possesses the
qualities." At this level matter must be defined not as that
which explains the given, but as the given itself. Locke's
conception of substance as the unknowable substratum,
Berkeley's conception of substance as God, Mill's conception
as the Permanent Possibility of Sensation, and all historic
atomisms, are not descriptions of the given but interpreta-
tions of it through constructs and hypotheses. On the
strictly empirical level a thing must be defined simply as a
certain togetherness of sense-data; the object is the totality
of its manifestations or attributes.

340 INTRODUCTION TO PHILOSOPHY OF SCIENCE

However, although matter is capable of definition only
as a complex of qualities and relations, certain of the latter
are considered more basic than others, and hence as affording
the defining properties of matter. The empirical properties
of matter are approximately as follows :

1. Location and continuous endurance through time. A
complex of properties which is called " matter v seems to
have at least an approximate location in time, i.e., one is
able to say that there are certain complexes which it precedes
and certain others which it follows. This involves no more
precision than is possible upon the empirical level. Further-
more, the complex seems to endure, usually through a longer
rather than a shorter time; hence there is no such entity as an
instantaneous thing, and a complex of properties is more
certainly characterizable as matter if it lasts for a relatively
long time. Finally, matter seems to have a temporal identity;
it endures continuously and exhibits no breaks in its life.

2. Relative permanence. A complex which is called "mat-
ter" is usually relatively unchanging. When the change is
rapid the complex is commonly spoken of as a happening
rather than as a thing; a flash of lightning, the fall of a leaf,
an explosion, and a fire are not matter but happenings. Here,
again, there is nothing empirical corresponding to "that
which changes" except as one means by this phrase simply
the complex itself. " Consider, say, a wall-paper which fades
in the course of years. It is an effort not to conceive of it as
one ' thing ' whose color is slightly different at one time from
what it is at another. But what do we really know about it?
We know that under suitable circumstances — i.e., when we
are, as is said, 'in the room' — we perceive certain colors in a
certain pattern: not always precisely the same colors, but
sufficiently similar to feel familiar. If we can state the laws
according to which the color varies, we can state all that is
empirically verifiable; the assumption that there is a con-
stant entity, the wall-paper, which 'has' these various colors
at various times, is a piece of gratuitous metaphysics. We
may, if we like, define the wall-paper as the series of its

MOTION, FORCE, MATTER 341

aspects. These are collected together by the same motives
which led us to regard the wall-paper as one thing, namely a
combination of sensible continuity and causal connection." 1

3. Location and continuous extension in space. The com-
plex exhibits relations of distance and direction in space to
other complexes. This feature of matter is commonly con-
sidered as one of its most basic properties. Furthermore,
at the empirical level matter is also extended, and therefore
exhibits shape and size. Moreover, it has spatial identity;
i.e., it occupies an unbroken extent. Finally, by virtue of its
location in space it is capable of motion, since it is not tied
down to one point in space rather than to another.

4. Force. One element of the complex is that property
which is empirically revealed as force. This shows itself
both in a relative impenetrability, exhibited in the resistance
which the complex offers to pressure, and in weight, ex-
hibited in the resistance which the complex offers to move-
ment away from the earth. The property of force is also
considered to be one of the most basic properties of matter.
Matter is what one bumps against in the dark, and what one
experiences when he carries a heavy suitcase.

5. Secondary qualities. In addition, matter is presumed to
possess certain qualities such as heat, color, sound, taste,
and odor, which, because of their great variability, are not
taken as defining properties. Some of them may, on occa-
sions, be completely lacking.

matter: scientific content

Matter as it functions in science is a refinement of em-
pirical matter. The common practice in science involves the
substitution of more precise terms for the essentially vague
terms applicable at the empirical level. Lenzen uses the
term "body' to designate this basic entity of physical
science. "A thing considered merely from the point of view
of physical properties will be called a body; that is, a body
is something which has general measurable properties and

1 Bertrand Russell, Our Knowledge of the External World, p. 106.

342 INTRODUCTION TO PHILOSOPHY OF SCIENCE

relations." x An alternative term is "particle," which has
already been employed earlier in the chapter. A particle
may then be defined as that which exhibits certain measur-
able spatial, temporal, and force properties. A particle may
be defined by approximately the following postulates :

1. Every particle exhibits location in time. This is simply
the refinement of the corresponding empirical property of
things. It asserts that a particle occurs in the temporal
stream, though it does not state that the particle endures.

2. Every particle exhibits location in space. This, again,
asserts not extension but mere location. Spatial location is
considered one of the basic properties of particles.

3. Every particle is at some point or other at all instants.
This expresses the enduring feature of particles, and justifies
the principle of the indestructibility of matter. It demands
that every particle have a certain recognizable identity
through its history ; this persistent property is, as will be seen
immediately, its mass. Whatever changes in space or time a
particle undergoes, its mass remains constant (subject to
certain corrections due to the general theory of relativity).

4. No particle can be at two different points at the same in-
stant. This states definitely that a particle is not extended, a
refinement which is introduced by science to avoid complica-
tions of size and shape. In many mechanical transactions a
thing acts as though it were located at a point, hence varia-
tions of extent and shape are of no significance.

From these postulates the property of motion may be
deduced as a corollary. If a particle occupies and endures
through time, and if it occupies one but not more than one
point in space at an instant, it is capable of motion and rest
as these notions were defined earlier in the chapter.

5. No two particles can be at the same point at the same
instant. This is the justification for the principle of the
impenetrability of matter.

6. Every particle exhibits mass. This is the scientific sub-
stitute for the vague empirical notion of force. It is de-

1 Physical Theory, p. 19,

MOTION, FORCE, MATTER 343

manded, as has been seen, by the necessity for finding a
method of measuring the latter. Mass as a property of
particles is preferable to weight, since this varies from point
to point on the earth's surface and limits the generality of
one's system of mechanics. Mass is the one property of
particles which is preserved throughout mechanical trans-
formations, hence it becomes their identifying feature. From
this point of view matter is commonly defined in science as
that which exhibits mass.

By means of some such postulate scheme as this, the
scientific notion of matter receives definition. It is to be
noted that all of its properties are expressible in terms of
numbers which are obtainable through the medium of clocks,
meter rods, and coordinate systems. Time, space, and mass
are, in fact, the three basic quantitative notions in physics.
Together they define matter, and in various combinations
afford the foundation for all other physical measurements.
It should be noted, further, that the scientific conception of
matter involves no reference to the so-called secondary
qualities; particles do not exhibit heat, color, sound, taste, or
odor. These are not features in which things act as though
they were located at points ; on the contrary they are proper-
ties known to be related to qualitatively distinct parts of
things, e.g., molecules, atoms, electrons, and neutrons, etc.
They are therefore to be accounted for in terms of hypotheses
of matter, not in terms of idealized constructions.

matter: operational derivation

As in the case of force, matter functions in science only as
measured matter. The operational transformation of the
empirical concept of matter therefore consists in the introduc-
tion of the refinements which are necessary in order to permit
the basic properties of matter to be measured. These funda-
mental qualities are of three kinds: space, time, and force.
Hence the operational route from empirical matter to
scientific matter involves the passage from empirical space
to geometrical space, from empirical time to scientific time,

344 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and from empirical force to mass. These routes have already
been examined. They involve the attempt to replace the
crude and complex qualities of empirical data by the more re-
fined and simpler quantities of science. The result is the defini-
tion of " particle" which was given in the preceding section.

But it should be noted that there is an alternative defini-
tion of the concept of particle which claims to be more
empirical. Instead of defining it as that which possesses these
measured values, one may define it merely as the complex of
these measured values, together with the functional relations
connecting them. If empirical matter is to be defined in
terms of the totality of its qualitative manifestations,
scientific matter should be defined in terms of the totality
of its quantitative manifestations. Now the difficulty with
the former conception of particle is that it retains the un-
justifiable empirical notion of a substratum as that in which
the qualities inhere; a particle is defined as that which pos-
sesses the measured values rather than as the mere collection
6f the measured values. But if there is no evidence at the
empirical level for this underlying substance, there can be
no evidence at the scientific level. Hence the alternative defi-
nition claims to be more empirical. Matter should be defined
merely as it can be made known to the scientist, viz., as a
cluster of measured values having a certain constancy as a
group and having a certain functional interdependence
among themselves. Scientific matter, as empirical matter,
is the class of its manifestations; but for science these
manifestations occur in the form of numbers on recording
devices, not in the form of qualitative data. Hence a particle
should be defined not as something which possesses certain
measurable properties but as the complex of laws stating the
interrelations of certain measured values.

An examination of actual scientific treatises, however,
reveals the fact that the more empirical definition of sci-
entific matter has not been achieved in fact. It is clear that
the closer empirical reference is retained only at a great
cost to simplicity. The scientist finds it much more con-

MOTION, FORCE, MATTER 345

venient to talk in terms of bodies and particles as though
they were at points, and at instants, and exhibited forces.
Upon the basis of careful operational derivation one should
say, rather, that the collection of measured values exhibits a
dominant spatial value, or temporal value, or force value. As a
result of the awkwardness of this expression the scientist still
retains the terminology of the substratum, though he may ad-
mit that this terminology is a mere convenience and is not to
be taken at its face value. Scientific matter may consequently
be defined in terms of the particle, as that which exhibits cer-
tain measurable spatial, temporal, and force properties.

In summary, matter at the empirical level is simply a
group of qualities, or aspects, which seem to act essentially
as a unit; fundamental among these aspects are those
associated with space, time, and force. At the scientific level
matter is simply the refinement which is introduced into this
concept when the attempt is made to determine precisely
what its spatial and temporal locations are, and how intense
is its force manifestation. This results in the definition of
particle, either as that which exhibits a number of measured
values, or as the complex itself of these measured values.
The operational route employed in this transition is such as is
involved in the passage from empirical space, time, and force
to the scientific refinements of these notions.

REFERENCES

C. D. Rroad, Scientific Thought (New York: Harcourt, Rrace,

1923), Chaps. Ill, IV, V, VII, XI.
Victor Lenzen, Physical Theory (New York: Wiley, 1931),

Chaps. IV, XV.
R. R. Lindsay and H. Margenau, Foundations of Physics (New

York: Wiley, 1936), Chap. III.
E. W. Hobson, Domain of Natural Science (New York: Macmillan,

1923), Chap. VIII.
Rertrand Russell, Analysis of Matter (New York: Harcourt, Rrace,

1927), Chaps. XXIII, XXVII.
Our Knowledge of the External World (Chicago: Open Court,

1915), lects. IV, VI.
Philosophy (New York: Norton, 1927), Chap. XXVI.

346 INTRODUCTION TO PHILOSOPHY OF SCIENCE

H. Poincare, Foundations of Science (New York: Science, 1921),

Science and Hypothesis, Part III.
B. Bavink, The Natural Sciences (New York: Century, 1932),

Part II, Chap. IV.
A. N. Whitehead, Principles of Natural Knowledge (Cambridge:

Cambridge University, 1919), Part II.

CHAPTER XVI

LAW, CAUSE

The concepts to be discussed in this chapter occupy a
slightly different position in the table of the sciences. They
function not explicitly, as do the concepts already examined,
but implicitly. Number, order, quantity, time, space, force,
motion, and matter — each of these concepts constitutes,
with the possible exception of time, the subject matter of
one or more of the special sciences. Hence, in each of these
cases the scientist tells — not always in clear terms, to be
sure — what he means by the concept in question. A con-
tinuation of this type of discussion would require similar
examination of the concepts of life and mind, which con-
stitute the basic notions of the biological and psychological,
or humanistic, sciences. Since the present book makes no
claim to completeness, and since the concepts in these more
complex sciences are even more controversial as to meaning
and empirical reference than in the cases of the concepts
already examined, the analysis of the explicit concepts will
stop at this point. But there runs through the sciences a
certain group of basic concepts expressive rather of the
structure than of the content of the investigations — concepts
which are not, as a rule, subjected to critical examination
by the scientists who use them. Typical among such con-
cepts are the following: event, quality, relation, operation,
uniformity, objectivity, change, symbol, hypothesis, experi-
ment, law, and cause. Some of these concepts have already
been subjected to critical examination in Part I, and the
present chapter might well have occurred in that context.
However, the concepts of law and cause, intimately associated
as they are with such notions as measurement, time, space,
and force, are better examined in the discussion context of
these latter notions. The present chapter will approach these

347

348 INTRODUCTION TO PHILOSOPHY OF SCIENCE

concepts from the point of view of the triadic pattern em-
ployed in the preceding chapters.

However, the interrelation of the two concepts makes a
separate examination of each of them unnecessary. A causal
correlation of events is obviously a special type of repeated
association; hence if a law represents the repetition of con-
nections between events, a causal law will represent a
specifiable kind of connection. The notion of cause enters
into science — if it enters into science at all — only in associa-
tion either with causal laws as stated in symbols, or with
causal ties as holding between events. But in either case the
notion of law is directly involved. Consequently, the dis-
cussion in the present chapter will center about the notion of
law, of which causal laws will be shown to be a special case.

law: empirical foundation

However nominalistic one may be in his attitude toward
scientific law, considering it merely as "conceptual short-
hand" or "convention," he is obliged to recognize that there
is something at the empirical level to which it has direct or
indirect reference. Nature, even to the most skeptical, ex-
hibits approximate uniformities, repeated associations, re-
current sequences, or something of an equivalent character.
As was pointed out in Chapter VI,1 events have the property
of occurring together — occasionally, frequently, or univer-
sally. While the events themselves do not properly recur,
since an event is unique in any situation in which it occurs,
nevertheless approximately similar events do occur in other
situations and often with approximately the same asso-
ciates. This fact demands recognition in any symbolic
scheme, for it suggests that the repeated association of an
event of one kind with an event of another kind is an im-
portant bit of information about the character of each of the
events. As a consequence, the symbolic statement of this
repeated correlation, which is called a law, has informative
importance with reference to the meanings of the concepts

1 Page 123.

LAW, CAUSE 349

functioning in the law. A law may be tentatively described
at the empirical level, then, as a statement of a repeated
association of events. The examination of this formulation
will require a more detailed consideration (1) of the kinds of
events which may be correlated, (2) of the nature of the
correlation, and (3) of the meaning of "repeated."

(1) In general, any event whatsoever may be correlated
with any other event. The coming of spring is associated
with the appearance of robins; the ring around the moon
with stormy weather; the excessive size of an elephant with
excessive weight; freezing weather with bursting water
pipes; drinking arsenic with death; the equality of angles
in a triangle with equality of sides; black hair with dark
skin; and so on. Events, in other words, tend to gather into
clusters, and the clusters tend to repeat. In fact, as was seen
in the last chapter, the ordinary conception of "thing'' is
precisely such a cluster of events, having a certain unitary
character which permits inference from one of its aspects to
another. The statement of the correlation of these aspects
constitutes a law. Whether it is events or aspects which
are correlated is of no importance, since the difference is
merely in mode of speech. Strictly speaking, only events are
correlated, though when events are united into complexes
one tends to describe the elemental events as aspects of the
complex event.

What requires special mention at this point is the fact
that on the strictly empirical level the events which are
correlated are usually described in qualitative rather than in
quantitative terms. It should not be insisted dogmatically,
however, that an empirical law cannot be quantitative.
Much of the literature of science, for example, distinguishes
between two types of quantitative law. On the one hand are
empirical laws which are expressed not as functional rela-
tions between variables but as tables of crude measured
values which seem to exhibit a semblance of proportionate
variation, as in the measured values of the spaces covered
by a ball rolling down an inclined plane correlated with

350 INTRODUCTION TO PHILOSOPHY OF SCIENCE

durations. On the other are theoretical laws which are ex-
pressed as functional relations between variables. The latter
type of law is strictly scientific, and an analysis of it will be
made in the proper place. The question at issue is whether
the tables of values (or the plottings of them on coordinate
schemes) constitute laws at the strictly empirical level. The
question is not important since, as has already been seen,
there are many levels of the empirically given. Throughout
the discussion thus far the point of view has been taken that
the recognition of precise quantitative features of the given
involves the beginnings of the transition to the scientific
point of view. At the lowest of the empirical levels, though
quantitative differences are obscurely recognized, measure-
ment techniques have not yet been employed; hence at this
level a law states merely the fact of presence or absence, with
little or no awareness of the possibility of degrees of presence
or absence. For this reason a table of measured values,
though it is often called an empirical law, will be considered
from the point of view of this discussion as a rudimentary
scientific formulation.

(2) The structure of correlations is the structure of space
and time, hence the types of laws will be determined by the
types of spatio-temporal relations. Events occur at the same
or at different times, and they may exist at the same or at
different spatial locations. This fact determines two general
types of laws: laws of coexistence and laws of succession,
each of which may describe the correlation of events which
occupy the same space or different spaces. If the world were
a perfect system, and if one's knowledge of its laws were
complete, then from a knowledge of an event here and now
one could determine by means of laws of coexistence what is
happening now everywhere, and by means of laws of succes-
sion what will happen and what has happened. Such a state
of affairs is not at all apparent on the empirical level, how-
ever. All that seems to be given is the clustering of events
into spatial groups and into historical continuities; the
persistence of this associative character leads to the formula-

LAW, CAUSE 351

tion of laws of coexistence and laws of succession. A law of
coexistence states that an event of a certain kind is repeatedly
found at the same time as an event of another kind. A law
of succession states that an event of a certain kind is re-
peatedly found preceding (or succeeding) an event of an-
other kind.

It seems clear that causal laws constitute a special type of
law of succession. Whatever else may be said as to the nature
of the cause and effect correlation, certainly the cause must
always precede the eifect. But the problem in this connec-
tion is to determine precisely what it is that constitutes the
unique feature of a causal law as distinguished from a law of
mere succession. Can it be maintained, as Hume, Mill,
Mach, Pearson, and the contemporary positivists have
insisted, that causal connection is indistinguishable from
mere succession? Or must it be insisted, as Whitehead has
claimed, that a causal succession exhibits a peculiar feature
which must be recognized? The importance of this issue
warrants a brief examination of it.

Hume's analysis of causal connections has become classic
in the history of philosophy. "When we look about us to-
wards external objects, and consider the operation of causes,
we are never able, in a single instance, to discover any power
or necessary connexion; any quality, which binds the effect
to the cause, and renders the one an infallible consequence
of the other. We only find that the one does actually, in fact,
follow the other. The impulse of one billiard-ball is attended
with motion in the second. This is the whole that appears
to the outward senses. The mind feels no sentiment or inward
impression from this succession of objects. Consequently,
there is not, in any single, particular instance of cause and
effect, any thing which can suggest the idea of power or
necessary connexion." l Furthermore, argues Hume, no idea
of necessary connection can be derived from feelings of

internal power." "An act of volition produces motion in

i«

1 An Enquiry Concerning Human Understanding (Chicago: Open Court, 1912),
p. 64.

352 INTRODUCTION TO PHILOSOPHY OF SCIENCE

our limbs or raises a new idea in our imagination. This
influence of the will we know by consciousness. Hence we
acquire the idea of power or energy ; and are certain that we
ourselves and all other intelligent beings are possessed of
power." But this does not demonstrate the existence of a
necessary connection between will and motion. "This
influence, we may observe, is a fact, which, like all other
natural events, can be known only by experience, and can
never be foreseen from any apparent energy or power in the
cause, which connects it with the effect, and renders the one
an infallible consequent of the other. The motion of our
body follows upon the command of our will. Of this we are
every moment conscious. But the means, by which this is
effected; the energy, by which the will performs so extraor-
dinary an operation; of this we are so far from being imme-
diately conscious, that it must for ever escape our most
diligent enquiry." 1

Sharply opposed to this is the claim of Whitehead. Sup-
pose that in the dark an electric light is suddenly turned on
and a man's eyes blink. "The sequence of percepts, in the
mode of presentational immediacy, are flash of light, feeling
of eye-closure, instant of darkness. The three are practically
simultaneous; though the flash maintains its priority over
the other two, and these two latter percepts are indis-
tinguishable as to priority. According to the philosophy of
the organism [Whitehead's own philosophy], the man also
experiences another percept in the mode of causal efficacy.
He feels that the experiences of the eye in the matter of the
flash are causal of the blink. The man himself will have no
doubt of it. In fact, it is the feeling of causality which
enables the man to distinguish the priority of the flash ; and
the inversion of the argument, whereby the temporal
sequence 'flash to blink' is made the premise for the 'cau-
sality' belief, has its origin in pure theory. The man will
explain his experience by saying ' The flash made me blink ' ;
and if his statement be doubted, he will reply, 'I know it,

1 Ibid., p. 66.

LAW, CAUSE 353

because I felt it.' ' 1 Effect arises out of cause because the
future is immanent in the present. "The future is immanent
in the present by reason of the fact that the present bears in
its own essence the relationships which it will have to the
future. It thereby includes in its essence the necessities to
which the future must conform. The future is there in the
present, as a general fact belonging to the nature of things.
It is also there with such general determinations as it lies in
the nature of the particular present to impose on the partic-
ular future which must succeed it. All of this belongs to the
essence of the present, and constitutes the future, as thus
determined, an object for prehension in the subjective
immediacy of the present." 2

If Whitehead's statement is obscure, that of one of his
followers is unambiguous: "In examining my experiences I
discover cases of causal efficacy: for example, I may be
angry at one moment and calmer at the next. I not only
perceive that the moment of calm follows the moment of
anger, but I perceive the moment of calm rise out of the
moment of anger. In the very moment of calm I perceive
the influences of the previous feeling. The experience not
only follows but inherits the emotional tones of past experi-
ence. In general, I perceive genuine causal influence when I
become conscious of the relations of emotions and feelings.
Regarding each feeling or emotion as an event, there is here
an indubitable experience of the causal relation of events." 3

The decision between these sharply opposed points of
view is a difficult one. From one point of view the issue is
irrelevant to science. As will be seen later, regardless of
what may be the case at the empirical level, at the scientific
level nothing like causal efficacy seems to play an important
part; for science a purely descriptive view is adequate. But
from another point of view the issue is relevant. Though
science does not require the notion of causal efficacy it does

1 Process and Reality (New York: Macmillan, 1929), pp. 265-266.

2 Adventures of Ideas (New York: Macmillan, 1933), p. 250.

3 Mortimer Taube, Causation, Freedom, and Determinism (London: Allen and
Unwin, 1936), p. 155.

354 INTRODUCTION TO PHILOSOPHY OF SCIENCE

require, at least according to the prevailing view, the notion
of necessity, and the problem arises as to what can be the
empirical foundation for this notion. Is necessity a property
of scientific law merely because, as Hume maintained, the
correlation occurs repeatedly? If so, it is hard to see how
necessity can be found in a collection of cases if there is
not the slightest hint of necessity in the individual case.
Or is necessity a property of scientific law because, as
Whitehead maintains, each individual case exhibits neces-
sity? If so, it is hard to see how one can ever be mistaken
as to a causal connection. The view which will be taken on
this issue can be more clearly indicated by turning to the
third aspect of law, viz., that which is involved in the notion
of repetition.

(3) It seems unquestionable that a single correlation or
association of events does constitute a fact about each of
the events. An event is not merely what it is "in itself
but what it is in its associations with all other events.
Hence to know with what events a given event is once
associated, occasionally associated, frequently associated, uni-
versally associated, and even never associated, contributes to
the understanding of the nature of the given event. Further-
more, it seems hard to deny that the information contributed
in each of these cases is different in degree. One may call
this feature of an association its empirical necessity. An as-
sociation which occurs only once has a low degree of empirical
necessity; associations which occur occasionally, frequently,
and universally have continuously increasing degrees of
empirical necessity.

At the empirical level little or no attention is paid to the
degree of empirical necessity involved in any association.
Unless a specific problem is involved cases are not counted,
and exceptions are not noted. Presumably no attention is
paid to any association unless it occurs at least occasion-
ally. This accounts for the fact that a law is customarily
described as a repeated association of events. The opera-
tional transformation of the notion of empirical law involves,

LAW, CAUSE 355

as will be seen later, the refinement in the recording of the
number of associations, the ascertainment of the degree of
similarity holding between them, the noting of exceptions,
if any, and consequently an assignment of the degree of
probability to the scientific law. Degree of probability and
necessity constitutes the scientific refinement of variations
in empirical necessity. The further complications in this
problem will be discussed in the proper place. Here all
that is required for emphasis is that a single correlation
involves a finite degree of empirical necessity. Whether
this is to be reduced, as in the case of Hume, to a subjective
factor such as expectation, or whether it is to be considered
as existing in the association itself as an objective property
capable of additive increase through multiplication of cases —
these are questions which are perhaps not important for a
philosophy of science.

In summary, an empirical law is a repeated association of
events. The events so associated are usually qualitative
rather than quantitative in character, and the association
itself is either of coexistence or of succession. Causal laws
are the most important type of law of succession, and may
designate either mere sequences which occur repeatedly, or
connections which exhibit causal efficacy. Every empirical
law possesses a greater or lesser degree of empirical necessity,
depending upon the frequency with which the association
occurs.

law: operational derivation

An empirical law becomes a scientific law through three
significant operations: (1) measurement, which replaces qual-
itative events by quantitative ones, (2) a highly complex
operation involving generalization, interpolation, and ap-
proximation, which replaces special types of empirical cor-
relation by timeless logical interrelationships, discontinuous
values by continuous variables, and highly complex
correlations by simple functions, and (3) ascertainment of
frequencies and degrees of analogy, which replaces vague

356 INTRODUCTION TO PHILOSOPHY OF SCIENCE

recognition of empirical necessity by more or less precise
statements of necessity and probability. Each of these will
be examined in greater detail.

(1) Although, as will be shown in the next section, the
question as to whether all scientific laws are quantitative
rather than qualitative in character is debatable, never-
theless from the point of view of operational techniques
measurement is the most important method by which pre-
cision is introduced into science. If one agrees, for the
moment, that most scientific laws are expressible in terms
of measured values, the meaning of the notion of scientific
law must depend on an analysis of the operational techniques
employed in procuring measured values. This implies that
the meaning of scientific law is tied up with measurement
and all of the assumptions on which it is based. It implies,
further, that from this point of view a scientific law states
not a correlation between events in the strict sense of the
term but rather a correlation between numbers on measuring
instruments and recording devices. For example, the law of
falling bodies replaces spaces by numbers on meter sticks,
and times by readings of clocks; what it states is that the
numbers obtained from one recording device vary in a cer-
tain way as compared with the numbers obtained from
another device. And in a deeper sense the meaning of the
law is a function not only of the methods of obtaining the
numbers, but also of the methods of constructing and cali-
brating the instruments. This dependence of law upon the
techniques by which it is derived is in complete harmony
with the dependence of scientific concepts in general upon
the methods by which they are measured. Repeated refer-
ence to this feature of scientific concepts has been made
in the preceding chapters.

(2) The operational techniques which are involved in the
transformation of empirical correlations into precise func-
tional relations are highly complex in character. They may
be discussed briefly as (a) generalization, (b) interpolation,
and (c) approximation, (a) Generalization, or abstraction,

LAW, CAUSE 357

is the method by which the difference between laws of co-
existence and laws of succession is lost in science. Empirical
necessity becomes generalized into logical or mathematical
necessity. Empirical laws state the dependence of the oc-
currence of one event upon that of another; scientific laws
state the dependence of one measured value upon another.
In the case of causal laws one may say that science generalizes
the notion of cause and effect into the notion of reason and
consequence — an operation which involves loss of the tem-
poral features of the empirical correlation. The outcome of
this operation, and its justification, will be discussed further
in connection with scientific law. (b) Interpolation is the
serial operation by which the discontinuity of measured
values is replaced by a continuous function. The presump-
tion is that the measured values obtained are an adequate
indication of the general type of serial order involved, and
hence that interpolation of probable values between any
two actual values is justified. In the case of a ball rolling
down an inclined plane, for example, the discrete values
representing the positions of the ball at successive moments
may be replaced by a variable which changes continuously,
since the reasonable assumption is that the ball behaves in
between any measured points in essentially the same way
as it does at the measured points, (c) Approximation is
the method of idealization by which a simple mathematical
function is substituted for a table giving parallel columns
of measured values. Such a complex table is, of course, a
scientific law in the most general sense of the term. But
simplicity of correlation is much to be desired in the inter-
ests of intelligibility ; consequently simple rather than com-
plex relations are sought in every case. Approximation is
the method by which discrete values are replaced by points
plotted on a coordinate system. Due to the inaccuracies of
measurement the points seldom lie on a smooth curve. But
by increasing the number of points one can obtain a general
notion of the path of the curve, and the line may be drawn
even though it does not pass through all of the points. If

358 INTRODUCTION TO PHILOSOPHY OF SCIENCE

this line can be expressed in a simple functional formula,
the desired approximation has been achieved. Examples
of this process can be found in almost any elementary
textbook of science.

(3) Since scientific laws state repeated associations of
events, an analysis of this important notion is required.
Whether a law is asserted as true without exception, or
merely as true in general, is a question of its derivation or
justification, i.e., a question of the logical techniques by
means of which it was obtained, or by means of which it
must be verified. A problem of this kind is usually called
inductive according to one of the many meanings of this
ambiguous word. A few remarks may be made on the in-
ductive problem.

The character of the problem is not hard to discern.
Empirical correlations are, as was seen, of various kinds —
single, occasional, frequent, and universal. Such correlations
exhibit increasing degrees of empirical necessity, and hence
increasing degrees of relevance in the problem of under-
standing the structure of nature. It seems clear that science
is more interested in correlations possessing a high degree of
necessity than in those possessing a low degree. Hence it is
one of the important aims of science to express scientific laws
with as wide a scope of generality as the evidence permits.
The occurrence of a given correlation creates a finite proba-
bility that it will repeat, and the common assumption of
science is that, as the number of situations in which the
correlation occurs increases, the probability that it will be
found in still further situations also increases. There is
always a tendency, therefore, for the scientific formulation of
laws to run ahead of the evidence, i.e., for laws to be asserted
with wider generality than the actual situations justify. This
determines the inductive problem, which may be formulated
approximately as follows: On the basis of an association known
to hold in a finite number of cases, what may be asserted either
as to other cases not examined or as to all possible cases?

Though the problem has had a long and venerable history,

LAW, CAUSE 359

the developments since John Stuart Mill are of particular
importance. Mill and his predecessors seem to have believed
that universal laws could be logically justified if one could
only find the proper premise. This premise was commonly
located in a feature of nature which was called its uni-
formity. Granted that nature is uniform, then what is true
in a few cases will be true in all cases, provided the cases in
question are typical. But this is precisely the difficulty; how
can one determine whether the cases are usual or unusual?
The fact seems to be that nature exhibits disuniformity as
well as uniformity, and one cannot tell in any given case
which is revealed. What is required, therefore, for the
logical deduction of the principle of induction, is not merely
the principle of the uniformity of nature but a further
principle which will tell whether the cases observed are such
as to come under the general assertion of uniformity.

This need seems to have turned the attention of investi-
gators into new directions. The focal center of the problem
of induction has shifted, particularly in the present century,
from necessity to probability. It is now seen that the prin-
ciple of the uniformity of nature, being itself an inductive
generalization, can hardly afford a basis for grounding any
particular law. Attention is therefore turned to the actual
cases, with a view to determining whether they are such as
to permit generalization. Progress on the inductive problem
can be made if principles can be formulated describing the
effect which such evidence as the number of instances of the
association and the degree of similarity of the various in-
stances has upon the probability of the law. No law is stated
to be necessarily true. Every law has a higher or lower
degree of probability, and probability is meaningless without
reference to the evidence on which it is based. The two most
important contributors to the problem in recent years have
been Jean Nicod and J. M. Keynes. A brief reference may be
made to the essential contribution of each.1

1 J. Nicod, Foundations of Geometry and Induction (New York: Harcourt, Brace,
1930); J. M. Keynes, Treatise on Probability (London: Macmillan, 1929).

360 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Keynes insists that the problem of induction is intimately
connected with two problems, both of which are important
in the determination of the probability of a generalization.
On the one hand is the likeness which holds between the
several cases; this is called Analogy. On the other hand is
the number of cases; this is called Pure Induction. But
Keynes insists that "an increase in the number of experi-
ments is only valuable in so far as, by increasing, or possibly
increasing, the variety found amongst the non-essential
characteristics of the instances, it strengthens the Negative
Analogy." x By Negative Analogy Keynes means the dis-
similarity in non-essential characteristics of the instances.
Hence in the supposition, say, that metals conduct elec-
tricity, the probability of the law is increased by finding
more and more cases in which it holds ; but the effect of these
instances is not in their number but rather in the fact that
by increasing the variety of the cases one is able to narrow
the scope of the generalization. By this method the known
negative analogy is increased. But the positive analogy must
also be increased. This can be done both by decreasing the
determinateness of the predicate-term and by increasing the
determinateness of the subject-term of the law. By this
method the cases which do not properly come under the
law are excluded, and possible exceptions are thus avoided.
Symbolically stated, a law of the form "all A is XY ' is less
probable than one of the form "all A is X" and this, in
turn, is less probable than one of the form "all AB is X."
For example, that all Irishmen are red-headed and quick-
tempered is less probable than that all Irishmen are quick-
tempered; and this, in turn, is less probable than that all
Irishmen from Cork are quick-tempered. Hence probability
can be increased by defining less narrowly the known re-
semblances as expressed in the predicate-term, and by de-
fining more narrowly the known resemblances as expressed
in the subject-term.

Nicod agrees with the greater part of this analysis, but

1 Op. cit., p. 219.

LAW, CAUSE 361

feels that Keynes has neglected the effect on the probability
of a law due to the mere increase in the number of cases.
Nicod is responsible for the introduction of the convenient
terms "confirmation' and "infirmation." 1 A law "all
A is Br is confirmed by any case in which A and B occur
together, and infirmed by any case in which A occurs in the
absence of B. It is generally recognized that infirmation
definitely decreases probability but not that confirmation
increases probability. Nicod, however, insists upon the
fact that mere multiplication of instances does increase the
probability of a law, entirely apart from the fact to which
Keynes referred that such multiplication increases the nega-
tive analogy. Such a contention, however, rests upon two
assumptions which Nicod states explicitly. "It is at first
necessary that the law possess, from the very start, a prob-
ability that is not null no matter how small it may be."
And 'it is necessary, besides, that on the hypothesis that
the law is false, its successive verification in an infinite
number of cases is infinitely improbable; or in more precise
terms, that its improbability exceeds any limit for a suffi-
ciently large number of cases." 2 According to Nicod 's
thesis, therefore, if one grants that a single instance of an
association contributes a finite probability to the law (or
possesses a minimum of empirical necessity, in the termi-
nology employed earlier in the chapter), and if one grants
that the multiplication of such instances to infinity would
be infinitely improbable if the law were false, then each new
instance even though it introduces no differing factor does
increase the probability of the law. For example, the illus-
tration of the Irishmen may be formulated, somewhat in-
accurately, in the following terms: If the existence of a
single Irishman who is quick-tempered makes it at least
slightly probable that all Irishmen should be so character-
ized, and if it is highly improbable that one should continue
to find Irishmen possessing this feature if the law that all

1 These words have already been introduced, though in a slightly different sense.
See above, Chapter XI, p. 222.

2 Op. cit., p. 274.

362 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Irishmen are quick-tempered is false, then the finding of a
single additional case does increase the probability of the
law. Under such conditions the probability of the law is
increased by the mere number of cases, without regard to
the element of variety which these cases contribute.

Still another approach to the problem of the operational
derivation of scientific laws, closely associated with the
work of Keynes and Nicod, is the attempt to determine
probabilities on the basis of frequencies. Techniques of
this kind become especially applicable when the correlation
is known not to hold universally. The problem then centers
about the attempt to determine the proportion of favorable
cases as measured against the totality of cases, favorable
and unfavorable, in order to determine the probability that
the correlation will occur in any given case. The probability
of any given case is then determined by the limiting value
of the ratio of the number of favorable cases to the total
number of cases, when the total number becomes very
large. The probability of throwing a two on a die is J since
in the long run a two will be thrown once in every six throws.
A law derived in this way is called a statistical law since it
has meaning only if applied to large numbers. If it were
known, for example, that there are Irishmen who are not
quick-tempered, the probability of any given Irishman pos-
sessing this quality would be determined by counting the
cases of Irishmen who exhibit this feature and then dividing
by the total ascertained number of Irishmen, i.e., those
possessing the property and those not possessing it.

It is well to be as clear as a brief discussion of this kind
permits concerning the distinction between probabilities of
the kind sought by Keynes and Nicod, and those which are
based on frequencies. The former are universal laws which
are only probably true, while the latter are statements of
frequencies. In the former the evidence is only affirmative,
in the latter it is both affirmative and negative. Both state
only probabilities with reference to any individual case,
but the former forbid certainty because the universality of

LAW, CAUSE 363

the law is not assured, while the latter forbid certainty be-
cause the specific features of the individual are not known.
Universal laws are distributively applicable to individual
cases, while statistical frequencies are collectively applicable.1
When one states that all Irishmen are probably quick-
tempered he means that there is a certain probability that
each Irishman is quick-tempered; but when one states that
the frequency of quick-tempered Irishmen is 86 in 100 he
is attributing a certain number, a ratio, to a group as a
whole, and this states nothing whatsoever with reference to
each Irishman, except that he is a member of a group possess-
ing a certain collective property. Statistical frequencies
state distributions, and distributions are applicable, basi-
cally, only to collections.

The summary of these various operational approaches to
the problem of scientific law will be made in connection
with the analysis of the scientific content of law. The
purpose of this reference to the work of Keynes and Nicod,
and to the problem of statistical correlations, has been to
show that the problem of induction is no longer concerned
with the establishment of necessary laws. The operational
techniques are directed to the ascertainment of probability,
either in the law itself or in the behavior of an individual
case. Probability depends on evidence, and the ascertain-
ment of evidence depends on the establishment of laws
connecting evidence of certain kinds either with laws of
certain degrees of probability or with predictions of certain
degrees of probability concerning individual cases. The
problem is one of great complexity, and is not likely to be
solved in the immediate future. The present discussion has
attempted merely to locate the problem in its proper context.

Reference must be made, however, to an alternative
operational technique by which universality in a scientific
law may be achieved. Though this method is employed in
science with great frequency, there is some question as to
whether it should be called an operational technique. It

1 See Chapter XIII, p. 262.

364 INTRODUCTION TO PHILOSOPHY OF SCIENCE

accomplishes its end by mere fiat. Any law may acquire
universality by a simple act which denies the possibility
that the law should have exceptions. This does not deny
the existence of the so-called exceptional cases, but merely
that they are properly to be called exceptions; they are
asserted as lying outside the scope of the law. The law
that unsupported bodies fall is not violated by balloons,
since these are supported bodies and hence do not come under
the scope of the law. A law which has been observed to be
true in a large number of cases may be asserted as legislative
over all future cases, and incapable of violation. Such a law
may be said to be nomically necessary, i.e., true by an arbi-
trary fiat. In empirical laws the events are first character-
ized, and the association is then asserted to hold between
the characterized events; but in nomically necessary laws
the characterization of at least one of the events is deter-
mined by the existence of the association. If it is an empirical
law that water boils at 100°, there must be some means for
identifying a substance as water independent of its boiling
point; but if this law is nomically necessary then whatever
boils at this temperature must be water, and whatever boils
at some other temperature cannot be water, for water is
identified by this property. Nomically necessary laws func-
tion as definitions, since they cannot be refuted.

It seems clear that the necessity which is a feature of such
laws is obtained only at the cost of objectivity. Though one
can know that the law is incapable of refutation, he can
never know whether it is any longer descriptive of events.
Considerations of the kind raised in Chapters VII and X
become relevant. The intensional features dominate over
the extensional. Meaning and truth are determined not
by illustration but by definition. Interest has shifted from
events to symbolic systems. Knowledge is passing from
description to explanation. Hence the appearance of nomic
necessity in a scientific law is a signal for the passing of the
science from the descriptive to the rational or explanatory
stage. Nomic necessity can always be achieved through the

LAW, CAUSE 365

devising of a postulate system, for any law which can be
derived from such a system becomes true no matter what;
i.e., its truth becomes of an intensional kind which is de-
pendent merely upon a symbolic scheme, and independent
of empirical reference. All laws of pure mathematics, all
laws of rational mechanics, and many of the laws of physics
are necessary in this sense. Since the attribution of nomic
necessity to a law is an arbitrary act, any law in any science
may become nomically necessary. V. Stefansson * argues
that the definition of an ostrich as a bird which buries its
head in the sand when pursued, even though there is no such
bird as this, has some advantage over the definition in terms
of biological properties. Since most people believe that the
ostrich does this, such a definition would have social ap-
proval. A new term could then be invented to name the
biological specimen. This illustrates clearly the relation
between a law which is empirically necessary and one which
is nomically necessary. Usually, however, the development
of a postulate system is required to give sufficient stability
to the intensional definition of the concept entering into the
law. The future of the biological and humanistic sciences
presumably lies in the development of postulate systems
and the emergence of more and more laws which are nomi-
cally necessary.

The operational derivation of scientific law may be sum-
marized in the following terms: An empirical law becomes
scientific through measurement, which replaces vaguely
described qualitative events by precisely designated quanti-
tative events; through a complex operation involving gen-
eralization, interpolation, and approximation, which results
in a further refinement; and, finally, through such activities
as the multiplication of cases, the ascertainment of the degree
of analogy applying to them, the determination of frequen-
cies, and certain acts of arbitrary fiat — all of which replace
a vaguely grasped empirical necessity by more or less pre-
cise statements of probability and necessity. These state-

1 The Standardization of Error (New York: Norton, 1927), p. 17.

366 INTRODUCTION TO PHILOSOPHY OF SCIENCE

merits are scientific laws, and their character may be exam-
ined immediately.

law: scientific content

Law, at the scientific level, is simply a refinement of
empirical law. A scientific law also states a repeated associa-
tion of events. But greater attention is paid to precision and
accuracy of formulation. This feature of scientific law may be
discussed from the point of view of the three aspects con-
sidered in the previous section: (1) the kinds of events
correlated, (2) the nature of the correlation, and (3) the
meaning of "repeated."

(1) The important problem in this connection is asso-
ciated with the question of measurement. Is there such a
thing as a qualitative law, or must a scientific law be quanti-
tative? Many would insist that qualitative laws are not
laws at all. Yet this seems hardly fair to the non-physical
sciences. The biological and the humanistic sciences are
not in a position to use techniques of measurement as suc-
cessfully as are the physical sciences, since the character of
the subject matter does not always permit it. Presumably
all that can be required of them is the introduction of
methods of measurement where the content of the science
permits, and the use of other techniques of precision — such
as accurate definition and ascertainment of frequencies —
where the subject matter does not permit measurement.
Qualitative correlations occur even in physics, and the
question as to whether these are properly to be called physi-
cal laws is debatable. "Shall we classify in the list of physi-
cal laws such purely qualitative observations as the proposi-
tions: copper conducts electricity, the melting point of ice
is lowered by pressure, a grating forms a spectrum, etc., or
such numerical statements as that there are three states of
matter, there are two types of waves possible in an elastic
medium — compressional and distortional, etc.? It is con-
ceivable that a difference of opinion may be honestly enter-
tained here. Some authors take the view that these really

LAW, CAUSE 367

are examples of physical laws. No one doubts that they
express physical facts, i.e., routines of experience. Never-
theless they do appear in a different category from the
mathematical relations among symbols to which numbers
may be attached by means of operations performed in the
laboratory. These relations are the ones which we shall
consider as forming the class of real physical laws in the
sense in which the term is used in the present text." x How-
ever adequate such a view may be for the purpose of writing
a book on physics, it is hardly proper for a general logic of
science. One may well admit that a functional correlation
represents the ideal of all science, but one need not admit
that only ideal science is science. Clearly, carefully stated
qualitative laws are scientific laws in the most general sense
of the term.

Furthermore, if the scope of science is limited to quantita-
tive laws, there is no place for those peculiar laws which
describe the technique of measurement itself. In a specific
case, for example, one may perform certain operations, the
outcome of which would be expressed in the judgment,
"The length of a certain line is 2 centimeters." This states
a correlation between something qualitatively given — a
length — and something quantitatively given — a number.
The generalization of this process results in a number of
statements which would be called the laws for the measure-
ment of lengths. They state the general type of correlation
which holds between lengths and their measured values.
Laws of this kind are implicit in the functioning of all auto-
matic measuring devices. They are not properly quantita-
tive laws since qualitative events enter into them. Hence it
seems preferable to define "scientific law" in such a way as
to permit the inclusion of laws of this kind.

(2) However, although qualitative laws may occur in
science, they differ from empirical laws not in the character
of the correlation but in the care and precision with which
the respective elements of the law are defined and identified.

1 R. B. Lindsay and H. Margenau, Foundations of Physics, p. 20.

368 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Hence the main difference between scientific laws and em-
pirical laws lies in the fact that functional correlations con-
stitute an important type of the former, while they occur
rarely or not at all as instances of the latteT. For this reason,
an analysis of the notion of function is important in the
understanding of scientific law. One may define a function,
of which the simplest type is a single-valued function, as
follows: "A single- valued function of a variable # is a second
variable y so related to x that whenever a value is assigned
to x from the z-range, a corresponding value of y is uniquely
determined in the y-range." 1 A variable represents any
qualitative event which is capable of quantitative variation.
Hence a scientific law, from this point of view, states not
mere presence or absence but degree of presence or absence;
it states not merely that two events are found frequently
together, but how much of one is found with how much of
the other. This involves recognition of the dependence of
the law upon measured values, to which reference was made
in the previous section. A law states a functional relation
between variables which are qualitatively distinct from one
another, and which are qualitatively distinct from variables
symbolized in other ways and occurring in other laws. The
fact that kinetic energy is equivalent to i mv2 and the space
of a falling body is equal to \gt2 does not make the laws
identical; for m, v, g, and t represent different variables
whose values are determined by different techniques of
measurement. Though the general form of the function is
the same, neither the entities measured nor the techniques
employed are the same; hence the laws mean something
different in the two cases. This fact is often lost from view
in theories which attempt to reduce science to mathematics.
By virtue of the establishment of functional relationships
the distinction between laws of coexistence and laws of
succession becomes obliterated. Mathematical laws state
merely the logical dependence of one measured value upon

1 Quoted by G. A. Bliss from Dirichlet in J. W. A. Young, Monographs on Modern
Mathematics (New York: Longmans, Green, 1924), p. 266.

LAW, CAUSE 369

another, and no attention is paid to the spatial or temporal
locations of the events concerned. This is accomplished, in
the case of temporal laws, by inserting the value giving
the temporal duration into the equation as one of the inde-
pendent variables; instead of saying that a certain value of
y is followed by a certain value of x it states that a certain
value of y is a function of a certain value of x and a certain
value of t — the value of /, of course, being properly expressible
as (ti — to) since it represents a duration, i.e., the difference
between two clock times. Similar considerations apply to
laws of coexistence, in so far as they involve spatial intervals.
The reduction of laws of succession to this purely logical
form is more important since these laws " allow us to predict
in advance a certain course of events; much less frequently
do we need those which allow us to conclude from a state
of affairs at one point or another, what is happening simul-
taneously elsewhere. But in principle, these two cases of
'dynamic' and 'static' causality, as we might call them,
have no priority one over the other. The essential feature,
the conclusion from a determined A to a co-determined B,
is in both cases exactly the same, only that in one case time
occurs among the necessary variables, and not in the other
case." 1 Hence one may say that the difference between
laws of coexistence and laws of succession lies not in the
character of the functional relation itself, but in the charac-
ter of the variables which are thus related; the former con-
tain no time variable while the latter do.

But the matter cannot be dismissed too lightly, for it is
tied up with the question of causal laws in science. Many
believe, for example, that whatever may be said as to the
existence of causal connections at the empirical level nothing
of the kind is required for science. There are in science no
causal laws if one means by these certain unique types of
correlation differing from functional relations. For there
are only two respects in which such laws could differ from
the more general types of mathematical correlation — in

1 B. Bavink, The Natural Sciences, p. 75.

370 INTRODUCTION TO PHILOSOPHY OF SCIENCE

their reference to the property of causal efficacy, or in their
reference to the property of temporal asymmetry. But the
former of these properties is not a datum, and the latter is
not required hi the statement of a law. For example, "in
the extension of a wire by weight or other force (Hooke's
law), the force has popularly been called the cause of the
extension, and the extension then figures as the effect of the
force, the idea being that with the force in operation the
extension takes place, and that without it the extension
would not take place. . . . Now there may be a certain
advantage to this popular version: certainly, it is an in-
stinctive stand taken in everyday life. But on careful exam-
ination it must be confessed that the view has little value
for physics. Thus, in the example of Hooke's law, as far as
the law itself is concerned in its symbolic form, it is just as
sensible to call the extension the cause and the force the
effect as vice versa. . . . All that the laws state is a relation
among symbols which represent well-defined operations in
the laboratory, and no notion of precedence or antecedence,
or dynamic enforcement is involved in them." l If. as
Hume maintained, causal efficacy cannot be discovered, it
cannot appear in the law as an empirical datum. Further-
more, even granting that something like "compulsion" is
discoverable, certainly it cannot be measured and hence
cannot occur as a variable in the mathematical statement of
the correlation. On the other hand. if. as has just been seen,
laws of succession can be reduced to functional relations in
which tune occurs as an independent variable, then even
the unique before-after character of cause and effect correla-
tions is lost. One can infer just as readily from an effect and
a time to a cause as from a cause and a time to an effect,
since each is the ground of which the other is a consequent.
The sole differentiating features of causal laws are therefore
lost, and laws of this type may be replaced by statements of
functional relations.

This presumed reducibility of causal laws to functional

1 R. B. Lindsay and H. Margenau, Foundations of Physics, p. 18.

LAW, CAUSE 371

relations may be indicated in another way. As Bacon, Mill,
and most other writers on causality have indicated, a causal
connection can be assured only when some sort of concomi-
tant variation has been noted with reference to the cause
and effect. This is tested by introducing a variation in the
intensity of the cause and noting whether there is also a
variation in the intensity of the effect. If this variation
can be noted, and if it is of a comparatively direct sort, the
causal correlation may be presumed to be a genuine one.
For example, if as the cause increases the effect increases
at the same rate, the situation is judged to be truly causal.
In fact, even if the cause increases more rapidly than the
effect, or the effect more rapidly than the cause, there is
still a reasonable ground for concluding that a causal con-
nection exists. These would be considered direct variations.
But as the variation in the values of cause and effect, re-
spectively, becomes less and less direct, the conclusion to a
causal connection becomes more and more conjectural. If,
for example, a succession of changes in the cause in some
interval produces no changes in the effect, the conclusion as
to a causal correlation becomes relatively precarious.

Now if this feature of direct and concomitant variation
in cause and effect may be presumed to characterize the
causal situation definitively, there can no longer be any
objection to the reduction of causal correlations to mathe-
matical functions. For the series of proportionate values
can be expressed through the method of approximation as a
simple function, e = f (c). In the well-tested cases e must
be a single-valued function of c; otherwise a variation in e
could occur without a variation in c. Now this looks very
much like a causal law in the sense that it asserts a depend-
ence of e upon c. But the distinction between dependent
and independent variables in a functional relation is purely
relative; consequently the law can also be represented in
the form, c = f (e), in which c is also a single- valued func-
tion of e. However, this no longer looks like a causal law,
for it presumably expresses a dependence of c upon e.

372 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Yet one should note that a cause which is both sufficient
and necessary does depend upon its effect in the sense that
from the existence of the effect one could infer both the fact
and the degree of the cause. It must be admitted, therefore,
that a causal law is reversible in the sense that from the
cause one can infer the effect and from the effect one can
infer the cause. As a consequence, if one admits that con-
comitant variation characterizes the causal correlation defini-
tively, he finds it hard to deny the legitimacy of reducing the
causal law to a functional relation.

But this is just what many would deny. For in eliminating
from causal correlations everything but concomitant varia-
tion, they would insist, one is rejecting precisely that feature
which is essential, and which was described a moment ago as
"causal efficacy' and "temporal asymmetry." In other
words, there is a peculiar asymmetry in the relation of cause
and effect; in the general correlational sense cause may be
inferred from effect, and effect may be inferred from cause.
But because of this uniquely asymmetrical feature effect
depends upon cause in a way in which cause does not de-
pend upon effect. It thus appears that nature exhibits in
still another form a factor which vitiates the reduction of
causal connection to functional relation. Causal laws can
be expressed as functional laws only if one neglects the fact of
causal efficacy, or temporal asymmetry, or one-way dependence.
It may be that this unique and elusive feature cannot be
described or located at all. But if it can, the reduction of
causal laws to functional relations can be accomplished only
by neglecting it.

Can this unique feature be neglected? Certainly it can
upon grounds of method. Science is admittedly abstract; it
employs the principle of isolation and ignores those features
of the given which are presumed to be irrelevant. If the
scientist considers the asymmetry of the causal relation to
be unimportant, one cannot object if he chooses to exclude
it in the formulation of descriptive laws — provided one recog-
nizes that the resulting laws are abstract. As was suggested

LAW, CAUSE 373

in Chapter XIV,1 time is often considered at that level of
abstraction which neglects its arrow. The question can be
settled, therefore, largely on the grounds of convenience.

Can this peculiar asymmetric feature of nature be located
and symbolized ? Clearly, of the three candidates — causal
efficacy, temporal asymmetry, and one-way dependence —
the second appears most likely. Is there any scientific
technique by which the directional feature of time may be
ascertained? Is there any method by which the distinction
between earlier and later may be recorded? Is there any
device by which the scientist is able to distinguish between
what Eddington calls a "becoming''' and what he describes
as an "unbecoming?" 2 The mere fact that the passage of
time can be measured does not suffice. It is true, of course,
that t may appear as an independent variable in the func-
tional statement of a law. But it occurs in such an equation,
in general, only as a lapse of time, i.e., a duration, and one
may substitute for it indifferently a positive or a negative
value. But if the functional statement is causal, i.e., of the
form e = f (c, t), substitution must be made subject to the
condition: "t must be positive," or "if t is given a negative
value this law describes an unbecoming." The question
involves considerations which lead into the very heart of
physical science, and hence cannot be raised here.3 Many
believe that in the phenomenon of entropy one has precisely
what is required. Nature seems to exhibit a one-way proc-
ess which may be described as the increase of randomness.
Differences of energy tend to become equalized, hence energy
passes from an available to an unavailable form. This is
expressed in the second law of thermodynamics by saying
that entropy continually increases. For example, if a hot
and a cold body are placed in proximity, and the difference
in their temperatures immediately recorded, the hot body
will cool and the cold body will become warm with the result

1 Page 288. 2 Nature of the Physical World, p. 94.

3 See A. S. Eddington, Nature of the Physical World, Chaps. IV, V; R. B. Lindsay
and H. Margenau, Foundations of Physics, Chap. V; J. Jeans, New Background of
Science (New York: Macmillan, 1933), Chap. VIII.

374 INTRODUCTION TO PHILOSOPHY OF SCIENCE

that the difference in their temperatures will become less;
hence a thermometer reading which exhibits great differ-
ence will always be earlier than one which exhibits small
difference. Any physical process in which a reading of this
kind is significant must be called an irreversible process.
Examples of such phenomena were listed in Chapter XIV.1
In situations of this kind, at least, the directional feature
of time must be retained.

Hence the state of causal laws in science seems, at present,
to be about as follows: Science recognizes the distinction
between two types of process — reversible and irreversible —
both of which seem to be exemplified in nature. Reversible
correlations are capable of adequate representation in sci-
ence through functional relations in which t occurs as an
independent variable, indifferently positive or negative.
Irreversible correlations are incapable of such represen-
tation, and require description in the general form S2 —
Si > 0, where Si and S2 represent measured values indicative,
respectively, of an earlier and a later state of a certain closed
system. If S2 — Si = 0 the process is reversible. If S2 —
Si < 0 the process represents an "unbecoming," hence is not
empirically found. Whether or not this difference in scientific
law represents adequately the difference in empirical proc-
esses, cannot perhaps, at this stage in the development of
science, be decided. Only two remarks may be made. In
the first place, there is no certainty that the fact of entropy
is the essence of irreversible processes; hence there is no
assurance that in the scientific formulation of irreversible
processes the important feature of causal sequences has been
retained. In the second place, the notion of causal efficacy
has been lost in the scientific formulation, unless by this
awareness of the immanence of the effect in the cause one
means simply the temporal irreversibility of the association.
These remarks are merely suggestive of further problems.

(3) Scientific laws state repeated associations of events.
As was shown in the operational derivation, the question as

1 Page 289.

LAW, CAUSE 375

to whether a law is universal or less than universal is inti-
mately associated with the problem as to whether the law
is necessary or probable. An examination of the operational
techniques suggested that the search for laws which are both
universal and necessarily true has been more or less com-
pletely abandoned; in its stead has appeared an operational
route which endeavors to base universal laws — where such
laws are at all possible — on probabilities, and to substitute
for universal laws — where such laws are not possible —
statistical frequencies. The result of this approach is the
diversification of scientific laws into somewhat the follow-
ing types:

(a) Laws which are universal and necessary, but whose
universality and necessity are determined intensionally
rather than extensionally. This is the status of all nomic
laws, which include the propositions of all "rational" sci-
ences, especially those laws which are called "ideal." Such
laws are necessary and true by virtue of the postulate sys-
tems from which they can be deduced, rather than by virtue
of empirical reference.

(b) Laws which are universal, but only probably true.
This is the status of most scientific laws which are not nomi-
cally necessary. Such laws have a definite empirical reference
to examined cases through routes which describe the number
of instances, and the degrees of similarity and dissimilarity
exhibited by the instances.

(c) Laws which state statistical correlations only, and are
based on examined frequencies. This is the status of all
scientific laws which are not of the other two types. These
laws also have a definite empirical reference, but to collec-
tions or aggregates rather than to individuals, and deter-
mined through routes which are descriptive of the counting
and sorting of cases.

Such a classification is at least suggestive of the main types
of law. It is probably not exhaustive. For example, no refer-
ence has been made to the distinction between microscopic
and macroscopic laws, which has played an important part

376 INTRODUCTION TO PHILOSOPHY OF SCIENCE

in recent discussion of the foundations of science. Whether
this distinction is purely relative and therefore not deter-
minative of distinctions between kinds of laws, or whether
it is more basic than this, is not easy to state. Unquestion-
ably the problem is intimately tied up with the distinction
between individual and statistical laws, for if an event is
considered to be constituted by microscopic elements it
behaves both as an individual and as an aggregate. But the
problem is too involved to be examined here.

Furthermore, these classes of laws are not mutually ex-
clusive. It is possible, for example, that a law should be
both nomically necessary and empirically probable. Any
law which is an empirical generalization but which is be-
ginning to take a place in a rational symbolic scheme would
be such a law. And, as has just been seen, a law which is
descriptive of an aggregate (and is therefore statistical) may
also be descriptive of that aggregate acting as a unit, hence
laws of the type (c) are not sharply distinguished from those
of the type (b). Again the problems are too complex to be
examined in an elementary treatise.

Reference may be made in a final section to a problem
intimately connected with this, viz., the problem of inde-
terminacy in nature.

INDETERMINISM

Recent approaches to the problem of induction differ
from earlier approaches, as has been seen, in an increased
interest in probability. It has been recognized that there
exists no principle called the uniformity of nature by which
inference to universal scientific laws may be justified. But
this does not involve an abandonment of the belief that
there are strains of uniformity in nature. Even probable
inferences are based on certain assumptions of constancy,
and it is the task of science to select these features of uni-
formity and to formulate them in laws.

One of the simplest and most pervasive of the types of
uniformity is that exhibited in the system of classical me-

LAW, CAUSE 377

chanics. Until a few years ago the laws descriptive of the
movements of particles acted upon by forces were presumed
to be the most perfect illustrations of purely deterministic
systems. Though the systems were known to be ideal, since
particles are portions of matter without extension, never-
theless the presumption was that any actual system could
be made to approximate as closely as one wished to such
ideal systems by progressive refinement. The law descriptive
of behavior in such a system took the form of a functional
relation between one variable representing the state of a
system (its position and velocity) at one time and another
representing its state at an earlier or later time. This law
was presumed to be universal. It was, of course, nomically
necessary in the sense that it was deducible from the basic
postulates of mechanics and therefore could not possibly
be violated. But it was also empirically verified in all cases in
which a high degree of refinement could be introduced. It was
therefore presumed to represent a basic structure of nature.
Hence nature was supposed to be a deterministic system, at
least so far as its mechanical features were concerned.

The generalized mechanical view of nature which arose
out of this conception has been accurately formulated by
Laplace. "We ought then to regard the present state of the
universe as the effect of its anterior state and as the cause
of the one which is to follow. Given for one instant an intel-
ligence which could comprehend all the forces by which
nature is animated, and the respective situation of the
beings who compose it — an intelligence sufficiently vast to
submit these data to analysis — it would embrace in the
same formula the movements of the greatest bodies of the
universe and those of the lightest atom; for it, nothing would
be uncertain and the future, as the past, would be present
to its eyes. The human mind offers, in the perfection which
it has been able to give to astronomy, a feeble idea of this
intelligence. Its discoveries in mechanics and geometry,
added to that of universal gravity, have enabled it to com-
prehend in the same analytical expressions the past and

378 INTRODUCTION TO PHILOSOPHY OF SCIENCE

future states of the system of the world. Applying the same
method to some other objects of its knowledge, it has suc-
ceeded in referring to general laws observed phenomena
and in foreseeing those which given circumstances ought to
produce." *

It seems safe to say that some such view as this was held
by most scientists prior to the discoveries which eventuated
in the quantum theory. The recent interest in indeterminacy
in nature can therefore be traced to those scientific dis-
coveries which suddenly threw this whole conception into
confusion. In outline, these facts were approximately as
follows: In the attempt to apply the general functional
equation stating the relation between two states of a given
system to very small particles such as electrons, certain
obstacles appeared. According to the Heisenberg principle,
the two values — position and velocity — which indicate the
state of a particle at a time cannot both be determined with
a high degree of accuracy. Since the particle is very small,
a very short wave must be used to determine its position.
But a radiation of short wave length has a high momentum,
since wave length and momentum are in inverse ratio to
one another. Consequently, the electron when struck by
this wave will be pushed from its position, and its motion
changed. If this difficulty is avoided by using a radiation
of long wave length, the momentum is decreased and there
is less recoil, but now it is no longer possible to tell precisely
where the electron is. Hence there arises an interdependence
in the measurement of the position and velocity. If A x
be used to express the possible error in fixing position, and
A v to express the possible error in fixing velocity, this
interdependence may be formulated,

Ax-At) > h/m

where h is Planck's constant (magnitude 6.55 X 10~27 erg-
seconds) and m is the mass of the particle. Since m functions
in the denominator of the fraction, the indeterminacy for

1 Philosophical Essay on Probabilities (New York: Wiley, 1902), p. 4.

LAW, CAUSE 379

masses of appreciable size is very small, hence is practically
equal to zero. This accounts for the fact that no difficulties
of the kind here indicated are noticed in connection with
gross objects. But for particles of the size of electrons the
indeterminacy becomes larger. The essential meaning of
this principle for the deterministic view of nature is that
position and velocity (the necessary and sufficient condi-
tions for ascertainment of state) cannot be determined at
the same time with a high degree of accuracy. Position can
be determined accurately, but then velocity is measured
only very inaccurately; or velocity can be determined accu-
rately, but then position is measured only very inaccurately.1

The inferences from this fact to a general view of nature
are of two kinds, and physicists seem to be divided about
equally into two classes on the basis of their views as to
these consequences. On the one hand are such men as
Eddington and Compton, who conclude that the world
cannot be a rigidly deterministic system; on the other, such
men as Planck and Einstein, who insist that the difficulties
lie merely in our techniques of observation and not in nature
itself. A brief examination of these contrasting views may
be made.

The former view, which may be called objective indeter-
minism, argues essentially as follows: The meaning of any
physical concept is determined by the operations which
are employed in locating the object to which the concept
refers. Concepts, to be meaningful, must refer to events
which can be produced in observation by describable tech-
niques. If the operations purporting to locate an event are
self -contradictory, or such as cannot be carried out without
violating recognized physical laws, the concepts which

1 Professor Carl Eckart has called the author's attention to a very important
feature of the principle of indeterminacy. There is actually no way of measuring
the position and momentum of an electron or any other small particle accurately
enough to confirm or infirm this inequality. On the other hand there are actual
experiments that confirm the classical theory and thus contradict the principle of
indeterminacy. This is, indeed, a noteworthy fact, and weakens to a very great
extent the positions of all of those who argue for an objective indeterminacy upon
the basis of the principle. It is surprising that some of the popularizers of the theory
(Eddington, Compton, and Planck) have not chosen to emphasize this fact.

380 INTRODUCTION TO PHILOSOPHY OF SCIENCE

require definition through such operations are strictly mean-
ingless. This means, in effect, that "only those aspects of
the world have reality which are capable of showing them-
selves in some way to the observer." x The operational
theory insists "that the meaning of position amounts to a
specification of a method of reaching the particle." 2 Ref-
erence to this point of view has been made repeatedly in the
course of the preceding pages; according to this theory, for
example, motion means measured motion, scientific mass
means measured mass, and so on. Hence the meaning of any
quantitative notion in science involves explicit reference
to the techniques employed in obtaining the measured value
which is attached to it.

What, then, on the basis of this theory is the meaning of
the mechanical principle which asserts a functional relation
between two states of a system — state being indicated by
position and velocity? Such an equation is meaningless
unless the processes to be employed in measuring a state can
actually be carried out. Rut according to the Heisenberg
principle this is just what cannot be done if the state in
question is that of an electron. For accurate measurement
of position is incompatible with accurate measurement of
velocity. The obvious conclusion is that the notion of state
is meaningless in such a case, and the law stating a relation
between states must also be meaningless. This seems a safe
conclusion on the grounds of the operational theory. If by
causal determination one means predictability, then causal
determination must be abandoned. For if one cannot know
both position and velocity — which are the sole grounds for
prediction — one cannot predict the behavior of any particle.

Rut the objective indeterminist is not satisfied with this
somewhat conservative conclusion. He takes another step,
which is much more important in the determination of his
outlook. He insists that if a concept is meaningless it cannot
designate any natural entity. Hence there cannot be any

1 A. H. Compton, The Freedom of Man (New Haven: Yale University, 1935), p. 40.

2 R. B. Lindsay and H. Margenau, Foundations of Physics, pp. 80-81.

LAW, CAUSE 381

event in nature which is of such a character that it must be
located and measured by operations which are self-contra-
dictory or physically impossible. The application of such a
principle in the case at hand is obvious. Since there can be
no joint determination of position and velocity, there can be
no joint fact of position and velocity. The difficulty is not
merely one of prediction. For if the particle cannot be known
to have both position and velocity at the same time, it
cannot have them at the same time, hence "it cannot itself
know' what its behavior is to be. Not even Laplace's
omniscient intelligence could predict its behavior, for the
conditions of its activity are non-existent. This is, in effect,
a complete denial of uniformity in certain ranges of nature.
It is an insistence upon the fact of objective indeterminism.
The opposing view, while recognizing the importance of
operations, denies that they function in so legislative a
way in science. To be sure, argues this position, knowledge
is a function of knowing techniques, but it is also a function
of that which is known. Knowledge cannot reduce to mere
knowing, for there is an object as well, and there are alterna-
tive routes for knowing a given object. Objective indeter-
minism makes the mistake of supposing that obstacles in
knowing are obstacles in nature, and that incompatibilities
in knowing techniques justify legislating natural objects out
of existence. It projects features of knowing into the known
without justification. It reduces to the absurdity of sup-
posing that being half-conscious that one's brother is present
is the same as being conscious that one's half-brother is
present. Such implications are not justified by the principle
of indeterminacy. All that this important principle argues
for is the breakdown of prediction in certain situations in
nature. It shows that science was wrong in supposing that
from a knowledge of position and velocity a future state
could always be predicted. However, this is erroneous not
because there is no functional relation between the two
states — one has no justification for arguing this feature out
of nature — but because one cannot know the required state.

382 INTRODUCTION TO PHILOSOPHY OF SCIENCE

If the principle of indeterminacy is true, prediction is no
longer possible upon the grounds disclosed by the traditional
physics. But unpredictability is a limitation in our knowing
and cannot reasonably be employed as a basis for arguing
to the character of that which is known.

Planck argues in somewhat this vein. The only indeter-
minism which is demonstrated by the Heisenberg principle
is a subjective indeterminism. He admits that the quantum
hypothesis has introduced a disturbance into the classical
theory of physics, and that "one cannot yet definitely say
what influence the subsequent development of the hypoth-
esis may have on the formulation of physical laws. Some
essential modification seems to be inevitable; but I firmly
believe, in company with most physicists, that the quantum
hypothesis will eventually find its exact expression in certain
equations which will be a more exact formulation of the
law of causality." l On the same question Einstein reports:
"I am entirely in agreement with our friend Planck in
regard to the stand which he has taken on this principle,
but you must remember what he has written. He admits
the impossibility of applying the causal principle to the
inner processes of atomic physics under the present state of
affairs; but he has set himself definitely against the thesis
that from this Unbrauchbarkeit or inapplicability we are to
conclude that the process of causation does not exist in
external reality." 2 "The indeterminism which belongs to
quantum physics is a subjective indeterminism." 3

It is likely that the time is not yet ripe in physics for the
final solution to this controversy. More careful formulation
of the operational point of view is necessary before any
reconciliation is possible. In particular, the assumptions
involved in measurement must be brought to light. Empha-
sis has been placed earlier in the book on the necessity for
recognizing that an operational theory which admits meas-
urement techniques but denies measuring instruments is
insufficient. Measuring instruments are devised to measure

1 Where Is Science Going?, p. 143. 2 Ibid., Epilogue, p. 210. 3 Ibid., p. 202.

LAW, CAUSE 383

something, and they must be calibrated over against that
something. Hence the method of measuring a given entity
cannot be exhaustive of the meaning of the symbol for that
entity. By position is meant not merely the method of
reaching the particle, but the qualitative feature of the par-
ticle which has been reached by this route ; by force is meant
not merely the method of reading indicators on spring bal-
ances and scales, but that qualitative feature of nature
which is correlated in a constant way with springs and
movements of beams; by motion is meant not merely the
quotient of a meter rod reading and a clock reading, but
that qualitatively given correlation of space and time which
exhibits itself to observation. Whether this refined notion
of operation has any important implications for the con-
clusion which may be drawn from the principle of indeter-
minacy remains to be seen. The importance of the principle
lies in the fact that it has compelled the scientist to pay
attention to operations ; no longer can the method of knowing
an event be neglected in the characterization of that event.
But, on the other hand, the principle has had the unfortunate
consequence of leading the scientist to believe that opera-
tions are exhaustive of meaning, and hence that the charac-
terization of the event is simply what is involved in knowing
the event. Both of these facts are important. What must
be decided now, before any ultimate reconciliation of the
opposed points of view can be achieved, is the precise ex-
tent to which one's knowledge of events is determined by
operations upon events and the extent to which it is de-
termined by the events themselves. This is the problem of
the future.

REFERENCES

R. B. Lindsay and H. Margenau, Foundations of Physics (New

York: Wiley, 1936), Chap. X.
Victor F. Lenzen, Physical Theory (New York: Wiley, 1931),

Chap. XVI.
Norman Campbell, What Is Science? (London: Methuen, 1926),

Chaps. Ill, IV, VII.

384 INTRODUCTION TO PHILOSOPHY OF SCIENCE

E. W. Hobson, Domain of Natural Science (New York : Macmillan,
1923), Chap. II.

K. Pearson, Grammar of Science (New York: Macmillan, 1911),
Chap. III.

A. D. Ritchie, Scientific Method (London: Kegan Paul, 1923),
Chaps. Ill, IV.

David Hume, Enquiry Concerning Human Understanding (Chicago:
Open Court, 1912), Sect. VII.

C. J. Ducasse, Causation and Types of Necessity (Seattle: Uni-
versity of Washington, 1924).

C. S. Peirce, Chance, Love, Logic (London: Kegan Paul, 1923),
Part II, Chap. II.

L. Silberstein, Causality (London: Macmillan, 1933).

J. Nicod, Foundations of Geometry and Induction (New York: Har-
court, Rrace, 1930), sect: "The Logical Problem of Induction."

J. M. Keynes, Treatise on Probability (London: Macmillan, 1929),
Part III.

A. S. Eddington, Nature of the Physical World (New York: Mac-
millan, 1929), Chap. XIV.

PART THREE

SPECULATIVE PROBLEMS

CHAPTER XVII

GENERAL CHARACTER OF SPECULATIVE

PROBLEMS

Those problems in the philosophy of science which are
called "speculative" constitute a rather miscellaneous group
which defies precise demarcation from other problems and
permits almost no systematization or organization. One
might almost say that problems of this character are what
remain in the philosophy of science when the strictly logical
problems, and the problems of the meaning of the basic
concepts — both of which are capable of fairly precise formu-
lation— are removed. Speculative problems of the type to
be here discussed constitute a part of the field of the philos-
ophy of science, for they draw their data, at least apparently,
from the content and the methods of the sciences. They thus
build upon the sciences, and if the sciences were different
either as to content or as to procedure the speculative prob-
lems would also demand new solutions. Hence they require
a knowledge of the sciences for their solutions, yet they are
not themselves scientific problems in the strict sense of the
word.

The essential reason why the classification of speculative
problems is difficult is that the systematization of such prob-
lems is itself a solution to the speculative problem. One of
the most important of the speculative problems, as will be
seen immediately, is that which revolves around the attempt
to classify and organize the sciences and thus to construct
a total picture of the various aspects of the universe in their
interrelations. If each of the sciences is a specialized ap-
proach to the world of events, a totalitarian view which
integrates the sciences into a systematic whole is clearly
required. But such an integrated view would be precisely
a classification of speculative problems, for it would attempt

387

388 INTRODUCTION TO PHILOSOPHY OF SCIENCE

to show what the possible problems are, and why their
solutions are required for a satisfactory view of things in
general. One cannot legislate as to what the possible types
of problem are and as to the way in which they are inter-
connected unless he has already had that inclusive view of
the universe which is precisely the solution to one of those
problems. One must solve the speculative problem in order
to know what the possible speculative problems are.

As a consequence, one is compelled to resort to the empir-
ical approach in the consideration of problems of this kind.
Instead of saying, "Here is an exhaustive list of the possible
speculative problems," one is obliged to say, "An examina-
tion of the literature in this unique field of overlapping
philosophy and science discloses the fact that such and such
problems have been considered most frequently by writers,
and may therefore be presumed to be both important and
capable of solution." Such an approach gives one not a
classification of problems, but merely a listing of them. It
does not show an interdependence of solutions upon one
another, nor does it establish the fact that the given prob-
lems are exhaustive of the field. It does not attempt to show
that there is one type of solution which is most plausible,
nor even that there is a general method which is common
to all of the problems. In fact, the great diversity in solu-
tions offered — though often based upon what appear to be
the same data — suggests rather the absence of any common
method. For example, it is not far from the truth to say
that from the mathematical character of scientific symbols
Jeans infers that God must be a mathematician, and Edding-
ton infers that He cannot be.

THE MAIN SPECULATIVE PROBLEMS

Adopting the empirical approach, one finds at least three
problems lying within this field. They may be characterized,
respectively as (1) the problem of the classification of the
sciences, (2) the problem of human freedom, and (3) the
problem of the nature of reality.

CHARACTER OF SPECULATIVE PROBLEMS 389

Certain remarks may be made at the outset with reference
to this list. It is not, of course, meant to be exhaustive.
There is, for example, the problem of the social implications
of science, which has been treated extensively by such men
as Julian Huxley, J. B. S. Haldane, and Bertrand Russell.
Closely connected with this is the problem of the general
effect of science in any historical period in determining the
"value outlook" of that period; for example, what is to be
understood when a given epoch — such as the present one —
is characterized as an "age of science"? Neither of these
problems is included in the list here given, yet they are
genuine problems. Nor are the problems here mentioned
presumed to be mutually exclusive. Often the attempt to
solve one of them demands data which are properly relevant
only to one of the other questions. The problem of the
relation between science and religion illustrates this over-
lapping clearly. Presumably science has information relevant
to the problem of the existence of God; this is an aspect of
the problem of the nature of reality. Yet there can be no
justification for using this information in the sphere of
religion until the problem of the precise interrelation of the
fields of science and religion has been solved; but this is an
aspect of the problem of the classification of the sciences.
Accordingly, one may consider the three types of problem
here listed merely as illustrative of the kind of speculative
problem on which scientists and philosophers have chosen
to express themselves in recent years. The omission of
certain problems should not be taken as implying a judg-
ment of their unimportance, nor should the apparently sharp
character of the classification of the problems be taken as
implying a judgment of their mutually exclusive reference.

The general character of all speculative problems is essen-
tially the same. Each of them attempts to show how, start-
ing from data all or most of which are disclosed by science,
one may, by an inference having a certain plausibility, con-
clude as to the existence of facts which are not themselves
directly revealed by science. The assumption in each case

390 INTRODUCTION TO PHILOSOPHY OF SCIENCE

is that science gives hints of facts which are not themselves
scientific. Accordingly, by a careful examination of the
data within science, one may be led by an inference of
greater or lesser cogency to a conclusion applying outside
of science. In all of the problems, therefore, three features
must be made explicit: (a) What, precisely, are the data
from which the inference starts? (b) What is the nature of
the inference itself? (c) What is the character of the con-
clusion inferred? With reference to (a), it will be found that
the data, in so far as they are drawn from the sciences, are
not usually the specific facts of science itself. For example,
it seems unlikely that the fact of gold melting at 1075°
would have any important implications outside of science.
It is rather the more general facts which seem to have this
inferential value, e.g., the general usefulness of mathematical
symbols in physics, or the inevitably analytic character of
scientific symbols, or the fact of an unavoidable uncertainty
in the precise location of very small particles. Yet the line
of demarcation between the general facts and the specific
facts cannot be drawn sharply, and it is likely that certain
relatively specific facts may have important speculative
implications. For example, the permanent deformations in
structure which certain metals undergo when subjected to
excessive strains — the phenomenon known as hysteresis —
may afford justification for the contention that there is in
the inorganic realm something analogous to memory, and
hence that the line between the organic and the inorganic
cannot be sharply drawn. With reference to (6), the char-
acter of the inferential route must be made clear. Is the
conclusion a definite implication of the data, i.e., deducible
from them, or is it merely an hypothesis having a greater
or lesser degree of probability? Is it obtained through the
method of construction, or through the method of hypoth-
esis? If it is obtained by the latter method, is it based upon
analogy, interpolation, serial extension, or some other recog-
nized inductive technique? With reference to (c), the
nature of the inferred entity must be made as clear as it can

CHARACTER OF SPECULATIVE PROBLEMS 391

be in view of the fact that it lies outside the field of science
and is therefore presumably not demonstrable by recognized
scientific techniques.

A brief analysis of each of the types of problem from the
point of view of these three features will be helpful as an
introduction to the discussion which is to follow. A more
detailed examination will be given in the specific chap-
ters.

(1) The classification of the sciences, (a) The data in this
problem are drawn exclusively from the sciences, except in
so far as they must include the studies of the religious,
esthetic, and moral aspects of human life — which are usually
presumed to lie outside of science. The point is, merely,
that any classification of the sciences must include not only
the sciences proper, e.g., the mathematical, physical, biolog-
ical, social, and psychological sciences, but the historical
disciplines and all those normative pursuits which examine
man's valuational responses. The data may be, as will be
seen, either the subject matter of the various disciplines, or
the methods. But unless they are drawn from a sufficiently
inclusive realm the resulting picture will be partial rather
than complete. (6) The inference is inductive in character,
and endeavors by synthetic operations to ascertain the char-
acter of the whole into which the individual sciences may be
presumed to unite. The whole is commonly taken to be an
hypothesis rather than a construct, since it is employed for
the purpose of explaining the individual sciences. The infer-
ence is from parts to whole, or from parts as unrelated to
parts as interrelated, (c) The inferred fact is the classifica-
tory scheme itself, which shows the precise interrelations
of general, special, and coordinate sciences, pure and applied
sciences, historical and non-historical sciences, composite
and simple sciences, concrete and abstract sciences, experi-
mental and non-experimental sciences, and so on. The aim
of such a scheme is to reveal those relations between the
sciences which are the most fruitful hypotheses for the
understanding of the sciences themselves.

392 INTRODUCTION TO PHILOSOPHY OF SCIENCE

(2) Human freedom, (a) The data in this problem are
any facts relevant to the existence or non-existence of
causal connections in nature. Presumably the most signifi-
cant data would be found in the realm of the humanistic
sciences themselves. But the value of such data is decreased
by the double fact that they are incapable of any precise
formulation and they are hopelessly entangled with intro-
spective phenomena such as the "feeling of freedom," or
the "feeling of causal efficacy"; consequently, in the fields
of the humanistic sciences themselves the problem seems
insoluble. Recent approaches to the problem have en-
deavored to solve it in terms of data drawn almost exclu-
sively from the realm of physical events. Here, at least,
precision is possible. Unfortunately the problem is com-
plicated by the fact that the data, even in this field where a
maximum clarity can be achieved, do not speak unambig-
uously. Reference has already been made to the fact that
the greatest disagreement exists among the physical scien-
tists themselves on the question as to whether even the
physical world is a deterministic scheme. The data revealed
by quantum physics suggest that it is not; macroscopic
data, on the other hand, suggest that it is. Consequently
one's inference as to whether human freedom is or is not a
fact is determined bv his answer to this still more basic
question. (6) The actual inference is, of course, merely
probable, since it is based upon the legitimacy of inferring
from what is true in the physical world to conditions in the
realm of human behavior. If man is a part of nature the
inference becomes deductive, for what is true of natural
objects in general must be true of man as a specific kind of
natural object. But if man is something superadded to
nature the inference becomes analogical and inductive, for
man may be an exception to natural objects and exhibit
properties peculiar to himself, (c) The inferred fact is, at
least in the present case, human freedom, though the alter-
native position of human determination is equally a solu-
tion to the general problem. The assertion of human freedom

CHARACTER OF SPECULATIVE PROBLEMS 393

may mean either that man is free in the sense that his actions
do not violate any of the laws of physics (Eddington and
Compton) or that he is subject to causal laws but unpre-
dictable in his behavior (Planck). Both views permit man
to do as he pleases, and this seems to be the demand of
human freedom.

(3) The nature of reality, (a) The data in this problem
are of the greatest variety. For three of the writers who will
be considered, the data are features of method; for the
fourth, they are a feature partly of subject matter and
partly of method. The most common solution to this prob-
lem takes its origin in the recognition of the essentially
limited character of science; the scientific method is shown
to predetermine the sort of object which the scientist will
find and to prevent him from finding an object of another
kind; for example, because the scientist employs mathe-
matical techniques he discovers only mathematical objects,
and because he excludes preferential judgments he fails to
find values. Accordingly, there is almost always drawn into
this problem, as an essential datum, the fact of an inde-
pendent knowledge of the non-scientific objects. Though
the scientist does not find God in his laboratory he does find
him when he leaves the laboratory and begins to live his
life in the broader sense of the term. Hence the problem in
this case often consists in showing the compatibility of the
conclusions of science with the convictions derived through
intuition, mystic insight, and revelation, (b) The inferences
are correspondingly various. In three of the cases to be
examined they proceed from the character of scientific sym-
bols to the character of that which is symbolized; but in
two of these cases the referent of the symbol is considered
to be essentially unlike its symbol, and in the third case
essentially like its symbol. In all three cases the inference
has some plausibility only because it is based upon an inade-
quate theory of the nature of symbols. In the fourth case
the inference is analogical, and passes from series which
have limits to other series which appear to have no limits

394 INTRODUCTION TO PHILOSOPHY OF SCIENCE

but are presumed to have by virtue of their similarity to
those which do; this permits inference to a realm of the
superrational. (c) The inferred fact is a realm of Reality,
which is presumed to lie beneath, behind, or above the data
of science. Often this is identified with God, though it need
not be; an atheistic materialism is frequently adopted as
the solution to the problem of the nature of Reality. The
solutions to be offered for examination may be called Spirit-
ual Idealism (Eddington), Mathematical Idealism (Jeans),
Logical Realism (Keyser), and Creative Evolution (Berg-
son). They must be considered as a very limited selection
from a wide range of metaphysical positions claiming to be
founded on science.

CHARACTERISTIC FEATURES OF SPECULATIVE PROBLEMS

An examination of the typical solutions to these three
main speculative problems discloses certain features which
may be considered as characteristic of them. In the first
place, they are not such as to require solution for science
itself; hence they are pursued by the investigator not as
scientist but as philosopher. This does not, of course, make
the pursuit of the problems unimportant. Sir James Jeans
says, for example, with reference to the general speculative
problem of the nature of reality, "I believe, in common
with most scientific workers, that without a background of
this kind we can neither see our new knowledge as a con-
sistent whole, nor appreciate its significance to the full." l
Eddington insists that such excursions into extra-scientific
territory afford the scientist a better view of his own domain.2
But the search for the view of the whole, and the apprecia-
tion of significance, are not strictly part of science in the
narrow sense. Accordingly, one may say that these problems
are of interest not to the critical philosopher who is con-
cerned with the foundations of science, but to the specula-
tive philosopher interested in the larger issues of life. As

1 New Background of Science (New York: Macraillan, 1933), p. vii.

2 Nature of the Physical World, p. vi.

CHARACTER OF SPECULATIVE PROBLEMS 395

such, problems of this type are distinguished from questions
of pure method, and from questions of the meanings of the
basic concepts, for in both of these latter cases there is
reason to believe that the philosophical problems are in
some very intimate way tied up with the scientific problems,
and hence to be looked upon as their logical development.
A good scientist must be a logician and a critical philosopher.
But a good scientist need not be a speculative philosopher.
Many, in fact, would insist that a scientist who pursues
speculative enterprises ceases thereby to be a scientist, for
he abandons critical methods. This may be true, but at
least the scientist is under no obligation to occupy himself
with these problems so far as the strict demands of his
science are concerned. It is still true, as Laplace remarked
to Napoleon, that the astronomer does not need the hypoth-
esis of God. The chemist, as chemist, need not concern
himself with the possible social applications of poison gas
and high explosives. Nor should the physicist refrain from
his investigations until he has succeeded in proving ab-
stractly that he is free to do as he pleases, or that there
really is a world outside of himself which is there to be
known. Science goes on its happy way independently of
these more speculative considerations. They belong, as
many would maintain, rather to the frills of science, to be
pursued as an entertaining and harmless pastime by those
whose minds turn readily to such speculative enterprises.
In the second place, speculative problems seem to depend
for their solutions upon the more critical problems of the
philosophy of science. Speculative philosophy, in other
words, presupposes either the logic or the metaphysics of
science. This seems to be due to the fact that the more
synoptic problems are founded, properly speaking, not
upon science itself but upon certain general features of its
method or certain general properties of its concepts. These
more philosophical aspects of science must be recognized
before the step to speculative considerations is possible.
For example, a classification of the sciences is based either

396 INTRODUCTION TO PHILOSOPHY OF SCIENCE

on method or on subject matter; in the former case reference
must be made to such methodological features as the dif-
ferences between rational and empirical sciences, experi-
mental and non-experimental sciences, statistical and indi-
vidual sciences, quantitative and non-quantitative sciences,
etc. ; in the latter case reference must be made to such meta-
physical problems as the classification of the categories,
"levels'" of reality, dependence and independence of the
sciences, etc. The solution to the problem of human freedom
presupposes that generalization has already been made as
to the existence or non-existence of causal determinations in
the inorganic realm. Problems of the nature of reality are
based either upon logical considerations pertaining to the
character of scientific symbols and the general nature of
scientific explanation, or upon metaphysical considerations
reflecting the interrelations of the sciences. Thus the solu-
tions to speculative problems approach a higher degree of
adequacy to the extent to which they are based upon careful
analyses of the more critical problems. The strict nature
of this dependence will be brought to light in the illustra-
tions to be given in the following chapters.

In the third place, since the inference in the case of each
of these problems is to a realm which is extra-scientific,
there is reason to doubt whether the criteria of scientific
verifiability are strictly applicable. Just because the infer-
ences extend out into that wider realm in which man reacts
morally, religiously, and esthetically, one may not be justi-
fied in estimating the results in the cold light of reason.
Broad suggests that conclusions in speculative philosophy
are almost certain to be influenced by the condition of one's
liver and one's bank account. Many of the inferences are
clearly little more than rationalizations of beliefs held upon
grounds other than those afforded by science. Eddington
suggests that we must avoid the "tendency to use 'reality'
as a word of magic comfort like the blessed word ' Mesopo-
tamia'" ;x we are continually confusing "reality' with

1 Nature of the Physical World, p. 327.

CHARACTER OF SPECULATIVE PROBLEMS 397

"reality (loud cheers)." 1 Many of the conclusions of R. A.
Millikan with reference to problems of religion, though
they are hardly to be called wishful thinking, are so little
based upon the data of science and so significantly founded
on a deep, personal religious experience, that they are hardly
to be classed as attempts at speculative philosophy in the
narrow sense in which the term is here being used. The
scientist who becomes enraptured by the beauty of a deduc-
tive scheme, who marvels at the grandeur of the heavens,
who wonders at the complexity of life — and concludes
therefrom a Spirit behind nature, is not making a judg-
ment of fact based upon the data of science but a judgment
of value based upon an esthetic experience. But if it is the
emotional man who is speaking, is one justified in using
the abstract, rational man as the judge of what is being said?

It seems important to recognize, therefore, in the fourth
place, that speculative problems almost always involve
implicit recognition of data which are other than those
offered by science. Eddington cannot conclude anything
as to the existence of a Spirit behind nature from the facts
of science alone, for scientific symbols are absolutely incap-
able, on his own grounds, of providing such. information;
it is rather the mystic experience and the introspective
experience which justify the inference. Bergson concludes
to the mobile and enduring character of reality not through
science, for science can reveal only the static and discon-
tinuous, but through intuition. Compton talks about
problems of religion not as a scientist but as a man attempt-
ing to guide his own individual life.2 It often turns out,
therefore, that the essential inference to the extra-scientific
domain is based upon data which are also extra-scientific,
and the speculative problem then reduces to one of showing
that the existence of such a domain is compatible with the
data of science. The inference is, consequently, not from
science to philosophy, but entirely within philosophy (or,
at least, entirely outside of science). The result is that the

1 Ibid., p. 287. 2 The Freedom of Man, pp. ix-x.

398 INTRODUCTION TO PHILOSOPHY OF SCIENCE

problem reduces to an attempt to show that nothing in
science is incompatible with the conclusion thus established.
Eddington, for example, expresses himself as opposed to
any attempt to base religion on scientific discovery; all
that can be concluded is "that the recent changes of scien-
tific thought remove some of the obstacles to a reconciliation
of religion with science." 1 This destroys, definitely, the
intimacy of the relation between science and the larger
problems, and suggests that perhaps no inference from the
one to the other has any measure of justification.

For this reason, finally, one should recognize the pre-
carious and conjectural character of the solutions to the
speculative problems. They are not certainties, nor are
they even very high probabilities — if one attempts to
measure them according to scientific criteria. There is
reason to doubt whether they ought even to be called
hypotheses. Logical positivism has denied that problems
of speculative metaphysics are philosophical problems; they
are either pseudo-problems, indistinguishable from poetry,
producing emotional responses but not asserting anything,
or else problems lying within the fields of the sciences, and
hence scientific problems.2 This probably represents an
attitude as extreme as its opposite, which insists that prob-
lems of this kind can be answered with a definiteness and
finality which negates the possibility of debate. Both posi-
tions are probably wrong. It seems likely that speculative
problems are genuine problems, though their terms are
extremely obscure as to meaning, and the evidence on which
they are based very elusive. The fact that such problems are
being linked up with science, if not actually based upon
scientific data, argues both for the fact that they are mean-
ingful and for the fact that there are data relevant to their
solutions. These are important conditions for increasing
the probability that one solution rather than another is cor-
rect in each case.

1 Science and the Unseen World (London: Allen and Unwin. 1930), p. 45.

2 See above, pp. 11-12.

CHAPTER XVIII

THE CLASSIFICATION OF THE SCIENCES

It was pointed out in the preceding chapter that the
problem of the classification of the sciences occupies a pecu-
liar position among the speculative problems. Although it
is itself one of these problems, it is nevertheless synoptic in
character and thus, in a sense, determines the limits and
interrelations of all of the problems. As will be illustrated
by Peirce, a properly constructed classification of the
sciences must contain as one type of legitimate discipline a
study whose task is precisely the construction of such a
classificatory scheme. If the making of surveys and reviews
is a legitimate enterprise, it must have its place in a general
survey and review of legitimate enterprises.

GENERAL CHARACTER OF THE PRORLEM

The designation of the problem as the classification of the
sciences is somewhat misleading. Though there is such a
problem, it is obviously only a small part of a more extensive
problem of the same kind which is the classification of human
intellectual disciplines. The scientific method is not the
only way of knowing, and lines of demarcation between
science and philosophy, science and history, science and
technology, science and art, etc., are far from clear. It is
almost impossible to say, for example, where mathematics,
which is quite obviously a science, passes into logic, which
is just as obviously a philosophical discipline; it is difficult
to discern the line separating anthropology as a science from
anthropology as a historical study; it is hard to say whether
medicine is a pure or an applied science; it is absurd even to
attempt to state at what point a dissertation on a scientific
topic ceases to be a treatise on science and becomes an exam-
ple of literary art. Hence the problem of the classification

399

400 INTRODUCTION TO PHILOSOPHY OF SCIENCE

of the sciences, properly conceived, is rather a problem of the
organization of knowledge.1 It is defined in Baldwin's
Dictionary of Philosophy2 as "the systematic arrangement
of the various branches of knowledge or of positive science,
in order to fix their definitions, determine their boundaries,
bring to light their interrelations, and ascertain how much
of the task of science has been accomplished and what
remains to be done." Accordingly, it includes not only what
are ordinarily called the sciences, but also the philosophical
disciplines, historical studies, trades and technologies, and
even religion and the fine arts in so far as these presume to
assert facts and convey messages.

With the problem thus conceived, a question arises as to
what can be the possible motive for carrying on speculations
of so extensive and conjectural a character. As is common
to all speculative problems, there seems to be nothing within
the special disciplines themselves that demands such con-
siderations. It is rather the encyclopedic or synoptic interest
of the human mind that appears to be the determining factor.
Organizations and systems are always to be preferred to
mere aggregates and collections. Sometimes, to be sure,
more specialized interests prevail. The individual pursuits
must be placed within a general scheme if one is to avoid
conflicts and hostilities, if one is to organize tasks upon coop-
erative lines, and if one is to avoid duplication of labor.
But a more basic interest is commonly to be discerned in the
long list of historical attempts to wrestle with this problem.
The speculative philosopher seems to feel that a classifica-
tion of intellectual disciplines somehow reveals important
information about reality itself. The various ways in which
one talks about the world at least indicate the various kinds
of things which may be talked about. "The system of the
sciences is broadly a synthesis of concepts and conceptual
relations, believed to be correlative to objective realities and

1 This is the title of a book by H. E. Bliss, to which more specific reference will be
made later in the chapter. It is probably one of the oiost satisfactory and com-
prehensive treatments of the problem in contemporary literature.

2 New York: Macmillan, 1901, p. 188.

THE CLASSIFICATION OF THE SCIENCES 401

real relations. Conversely, the systems of nature are dis-
covered and synthesized by science, and the real universe
is revealed, though imperfectly, to human intelligence. The
system of verified knowledge progressively reveals reality.
The intellect aspires ultimately to comprehend the universe.
This intellectual tendency is in some minds consciously
purposive. In religious minds the purpose is regarded as
related to a universal purpose that is causative, or teleolog-
ical, creative or divine." *

It is not likely that a problem of this scope will receive a
solution which is anything like final. The complete data
are all of the facts of method and subject matter as related
to the various disciplines, and are obviously too extensive
for a single mind to grasp. No man can know all things.
Accordingly, there must be a generous reliance upon the
method of authority and other indirect methods. One is
entitled, for example, to rely more or less completely upon
the specialized investigator for information pertaining to
his particular field. This method has its obvious disadvan-
tages. The specialized investigator is seldom in a position
to see his field in perspective; the man who is in love cannot
analyze love, the man who is immersed in the religious
experience cannot study religion, and the physicist cannot
say clearly what physics is. But this is the only method by
which the philosopher can hope to comprehend the great
mass of necessary data. As an alternative to this procedure
he must infer as to the character of the specialized disciplines
from what the individual investigators say and do — a method
which is open to dangers that are equally obvious. But even
after the philosopher has been provided with the necessary
data, many of which are conflicting among themselves, he is
confronted with the precarious task of assigning the special
studies to their places in the total scheme, a task founded upon
estimates of importance and unimportance, generality and
speciality, dependence and independence, all of which are al-
most certain to be reflections of an individual value outlook.

i H. E. Bliss, The Organization of Knowledge (New York: Holt, 1929), p. 409.

402 INTRODUCTION TO PHILOSOPHY OF SCIENCE

The most convenient form for the representation of such
a synoptic view is a Logical scheme of genus-species relations
like the following:

r AKX

(AK (aKY

AL
AM

AMR

AMS
AMT

This affords a general structure within which the various
disciplines may be located as superordinates, subordinates,
or coordinates. A table of this kind should provide a place
for highly general studies, such as science, philosophy, and
history; for the more specific disciplines, such as physics
and chemistry; and for the highly specialized investigations,
such as optics, acoustics, and electricity. The principle of
division need not be that of dichotomy, nor of trichotomy,
but will be determined, in each case, by the nature of the
subject matter. It would seem advisable to introduce the
principle of serial arrangement as well as mere classification
wherever the material permits, i.e., if the species of a given
genus exhibit ordinal properties they should take on a form
which clearly indicates this fact. The different levels of sub-
ordination may be indicated in a tabular form either by
means of columns or by means of rows. Where cross-classifi-
cation exists, i.e., where a species lies in two different genera,
this may often be represented by a two-dimensional pattern;
for example, the two divisions of biology into physiology
and morphology and into botany and zoology might be
indicated as follows:

10 °^y I Morphology

Botany Zoology

A table in which this principle is employed, however, takes
on a high degree of complexity, and loses its schematic form.
No convenient tabular representation is possible when the
dimensional variations exceed two. Elaborate geometrical

THE CLASSIFICATION OF THE SCIENCES 403

figures consisting of intersecting triangles, circles, etc.,1
which aim to indicate the highly complicated relations be-
tween the various disciplines may prove helpful, though
they are definitely limited in scope. It seems better to omit
some of the detail, even at the expense of accuracy, in order
that the more significant relations may be clearly indicated.

DIFFICULTIES IN THE CLASSIFICATION OF THE SCIENCES

Though the difficulties experienced in constructing a
classification of the intellectual disciplines are not insur-
mountable, they are great and a frank consideration of some
of the most important of them is a valuable preliminary to
the examination of the actual problem. In many cases they
must be met by arbitrary acts, as in the classification of
mathematics under the form of an independent discipline in
spite of its obvious use in most of the sciences; in other cases
the obstacles must be overcome by admitting defeat, as in
the mere attempt to list the various trades, occupations, and
avocations; in still other cases the difficulties must be met
by open compromise, as in the attempt to make any classifi-
catory scheme represent all of the ramifications of natural
relations. Some of the most obvious of the difficulties will
be considered in the following paragraphs.

The most superficial examination of the problem con-
vinces one that any classification must be highly schematic
in character. It seems clear that no such table can represent
all of the interrelations which nature itself exhibits. In fact,
it is questionable whether one would wish a classification
of the sciences to do this ; if a map of nature were as detailed
as nature itself, it would lose most of its advantages. The
construction of tabular schemes proceeds, as does all science,
by the method of abstraction; the attempt is made not to
mirror the complexity of nature but to simplify it by select-
ing only those events and relations which seem important.
Every science bears to other sciences relations which are
essential and relations which are unessential. The decision

1 Such as those given by Bliss, op. cit., pp. 402-403.

404 INTRODUCTION TO PHILOSOPHY OF SCIENCE

between these two types of relations is, of course, not easy
to make; hence an element of arbitrariness always enters.
But, granting that it has been correctly made, the neglect
of the unessential is presumed not to introduce any impor-
tant element of artificiality into the tabular representation.
The point which is here emphasized may be well illustrated
with reference to mathematics. This science has relations
to almost all of the other sciences, but the relations are so
various in character that no conceptual scheme could ade-
quately represent them. By virtue of its deductive structure
and its concern with highly abstract notions, mathematics
is closely affiliated with logic; by virtue of its application as a
technique of measurement, it is connected with physics;
by virtue of its non-experimental character, it tends to be
grouped with the sociological sciences; and by virtue of the
"mental" and idealized character of its subject matter, it
becomes closely associated with the psychological sciences.
The problem in this connection has to do not merely with
representing the fact of the various relations, which could be
easily indicated merely by the drawing of lines, but with
representing the fact that each of these relations is different
in kind from the others and would therefore require a dif-
ferent type of connecting link. As soon as the classificatory
scheme adapts itself to these highly complicated and in-
volved elements, its diagrammatic character is destroyed.
Hence it seems preferable to neglect all but one of these
relationships, even at the risk of introducing artificiality
into the representation. A classificatory scheme must
reveal nature in the same way that a well-fitting garment
suggests the underlying figure, not by portraying clearly all
details of its form but by neglecting or hiding some of its
features, and emphasizing and exhibiting others. A table of
the sciences represents a compromise between an ideal form
and the gross complexities of nature.

As a consequence, one must be continually on his guard
against constructing a scheme which is in accord with an
a priori philosophical point of view rather than with the

THE CLASSIFICATION OF THE SCIENCES 405

existent sciences. Peirce condemns certain classifications on
these grounds. "Many of these schemes introduce sciences
which nobody ever heard of; so that they seem to aim at
classifying, not actually existent sciences, but possible
sciences." 1 He says of his own scheme, on the other hand:
"This classification which aims to base itself on the principal
affinities of the objects classified, is concerned not with all
possible sciences, not with so many branches of knowledge,
but with sciences in their present condition, as so many
businesses of groups of living men." 2 Both the Kantian
and the Hegelian schemes strike one as attempts to force
the existent sciences into preconceived forms. Equally
artificial are the classifications which legislate for the future.
The problem seems to be essentially an empirical one, and
demands the techniques which are adapted to this type of
problem.

It follows, however, that a classificatory scheme is relevant
to the historical scene out of which it emerges, and its ade-
quacy should be measured in these terms. "If Plato's
classification was satisfactory in his day, it cannot be good
today; and if it be good now, the inference will be that it
was bad when he proposed it." 3 The development of thought
exhibits both the origination of new disciplines, and the
disappearance of pseudo-disciplines. One should hardly
expect the medieval scheme to have a place for psychology
and anthropology, and one should rightly condemn any
modern scheme which included alchemy and astrology on
the same level as chemistry and astronomy. There is reason
to believe that the future will witness the combination of
disciplines now thought to be independent, and the separa-
tion of disciplines now thought to be united. It seems inev-
itable that there should be a continued emergence of inter-
connecting sciences, such as physiological psychology and
bio-physics, and a progressive specialization such as has
already given rise to quantum physics, parasitology, and
ophthalmology.

» Collected Works, Vol. I, par. 1.203. 2 Ibid., par. 1.180. 3 Ibid., par. 1.203.

406 INTRODUCTION TO PHILOSOPHY OF SCIENCE

A difficulty which is somewhat more specific arises in
connection with the attempt to locate the sciences which
are themselves synoptic in character. One of the best
examples of these is geography. This science is obviously
composed of material drawn from geology, biology, and
sociology, to mention only the most important. The ques-
tion may be argued as to whether it contains any unique
subject matter, or is merely a study of the interrelations
of these fields. In either event it cannot be placed on the
same level as the other sciences, for the result would be a
cross-classification. The difficulty may be avoided by mak-
ing an initial distinction between the special sciences and
the synoptic, or complex, sciences, but this only creates a
new problem, for every science except the most highly
specialized may be considered as composite with reference
to its parts. For example, physics may be considered as
composite relatively to optics, acoustics, electro-dynamics,
etc. Similar difficulties arise in the attempt to place dis-
ciplines which cut across the more basic lines of demarca-
tion, e.g., in the location of mathematical logic, which is
both science and philosophy, and in the placing of geology,
which is both science and history.

Even more serious are the obstacles which are encountered
in the form of disciplines about disciplines. Recent thought
has compelled the recognition of such studies as the history
of science, the philosophy of science, and the history of
philosophy. The location of such pursuits creates obvious
difficulties. The situation is not helped any by the appear-
ance of such disciplines as the history of history, and even
the history of the philosophy of science and the philosophy
of the history of science. These are apparently legitimate
enterprises, each of which is acquiring a literature and de-
fining its problems. It is part of the task of the classifica-
tion of the sciences to assign each of them to its proper place.

A difficulty to which Rliss calls attention is important
since it injects an element of arbitrariness into the problem.1

1 Organization of Knowledge, Chap. XII.

THE CLASSIFICATION OF THE SCIENCES 407

Sciences may be arranged in alternative orders, and the choice
of order is essentially a matter of purpose and interest.
Bliss distinguishes five orders: the order of nature, the
developmental order, the pedagogic order, the logical order,
and gradation by speciality. There is reason to believe that
this classification of orders could itself be improved upon,
but this is not the concern at the moment. The point is
that those sciences which are most basic from the logical
point of view — in the sense that all of the sciences depend
upon them — are not necessarily those which emerged first
in the history of thought, nor are they those studies which
should be taught to the child in the elementary stages of
his education; that which is logically first need not be tem-
porally first either for the race or for the individual. Further-
more, the ways in which the sciences are used are not nec-
essarily a reflection of their inherent characters, hence a
classification of the arts and technologies need not parallel
a classification of the theoretical sciences. It follows that
a library classification of books about nature — which is
Bliss's main problem — need not reflect accurately the struc-
ture of nature itself, though it should clearly conform as
closely as this is possible. The agreement which Bliss finds
among the four alternative orders is somewhat surprising.
There is reason to believe that there should be an essential
conformity so far as the order of nature, the logical order,
and the gradation by speciality are concerned. But there
seems to be no reason why this order should agree either
with the pedagogic or the developmental orders. Neither
man nor the race grows logically. Hence the speculative
philosopher must recognize the possibility of alternative
schemes, and the relativity of any given scheme to the
intention of the classifier. This makes classificatory schemes
arbitrary but not whimsical.

Finally, certain terminological difficulties may be men-
tioned. The fact that the term "natural philosophy' has
often been employed historically for "physics" does not
mean that physics should be classified as philosophy rather

408 INTRODUCTION TO PHILOSOPHY OF SCIENCE

than as a science. The same consideration applies to the
use of "mental philosophy' for "psychology." The older
term "political economy' has been quite generally sup-
planted by the term "economics." The use of suffixes such
as "-ology," "-osophy," and "-ography' cannot be taken
as infallible indications of the characters of the disciplines
to which they are applied. Nor does it assure one of the
legitimacy of the studies, as witnessed by astrology and
theosophy. Disagreements among authorities as to the
proper scope of a given term are not uncommon, and they
create difficulties of classification. For example, epistemology
is sometimes included in metaphysics and sometimes in
logic; social studies such as sociology and economics are
sometimes called sciences and sometimes not; and the in-
clusion of ethics and esthetics in most colleges and univer-
sities in departments of philosophy does not make them
philosophical disciplines. Many disciplines which are ordi-
narily called sciences, such as archaeology, paleontology,
epigraphy, and heraldry, are just as significantly to be
classed as histories. All of these facts suggest that the con-
struction of a classificatory scheme must be preceded by
accurate definitions of the main disciplines; ambiguity and
vagueness in terminology is no less a vice in the speculative
problem than it is in the problems of the special sciences.

HISTORICAL ILLUSTRATIONS

History abounds in examples of classificatory schemes.
Most . philosophers and many scientists and literary men
have felt the urge to solve this synoptic problem.1 Many
of the historical instances, while no longer entirely adequate
to the modern scene, exhibit important lines of cleavage
and linkage. The division into ethics, physics, and dialectics,
usually attributed to Plato, suggests the parallel division
into problems of human life, problems of nature, and prob-

1 The availability of several good books devoted to the history of this problem
obviates the necessity for a more detailed consideration at this point. See H. E. Bliss,
op. cit.; E. C. Richardson, Classifications, Theoretical and Practical (New York:
Scribners, 1901); R. Flint, Philosophy as Scientia Scientiarum (London: Blackwood,
1904).

THE CLASSIFICATION OF THE SCIENCES 409

lems of knowledge — a classification which would be not
without value today. Aristotle's threefold division into the
theoretical, the practical, and the productive has much
to commend it. Though the medieval division into the
trivium (grammar, logic, rhetoric) and the quadrivium
(geometry, arithmetic, astronomy, music) seems somewhat
artificial today, it throws a certain light on the possible
affiliations of these studies. Bacon's division into history,
poesy, and philosophy, based on the three fundamental
"faculties" in man — memory, imagination, and reason —
would no longer be accepted in view of the general abandon-
ment of the faculty psychology. The classification of Hobbes,
which divided studies into those dealing with fact (history)
and those dealing with relations between antecedents and
consequents (science), offers a suggestive manner of dis-
tinguishing between these main types of discipline. Locke's
division into physics (knowledge of things), practics (skill
of right action), and semeiotics (doctrine of signs) is im-
portant in its recognition that the study of symbols is a
legitimate and important enterprise. Comte's hierarchy
consisting of mathematics, astronomy, physics, chemistry,
biology, and sociology is important because of the serial
principles employed in its construction; the arrangement
exhibits a progressive decrease in generality and an increase
in complexity and dependence. The classification of Bliss,
which will be examined in a moment, is based upon it.

For the purposes of more detailed examination, two classi-
ficatory schemes have been selected from contemporary
writings. One is that of the philosopher, C. S. Peirce, and
the other is that of the librarian, H. E. Bliss. These have
been selected from a host of candidates for several reasons.
The two men are drawn from the contemporary scene, and
one may therefore examine their products in the light of
the existent sciences. They include in their classificatory
schemes not merely the sciences in the narrower sense, but
philosophy, history, and the practical arts as well. They use
the characteristic modes of classification — the one (Peirce)

410 INTRODUCTION TO PHILOSOPHY OF SCIENCE

employing a form which is essentially that of logical subordi-
nation and not obviously one of serial arrangement, the
other (Bliss) employing a form which is predominantly
ordinal. Though Peirce is motivated by the philosophical
or theoretical interest, and Bliss is concerned with the prac-
tical desire to construct an adequate classificatory scheme
for books, nevertheless Bliss is convinced that such a scheme
will be adequate to the extent to which it corresponds closely
with the order of nature; hence the problem is similarly con-
ceived by both writers.

PEIRCE

Peirce's classification is predominantly trichotomic, most
of the studies being divisible into three species according
to a repeating plan, "the First of the three members relating
to universal elements or laws, the Second arranging classes
of forms and seeking to bring them under universal laws,
the Third going into the utmost detail, describing individual
phenomena and endeavoring to explain them." * This type
of division can be illustrated by psychical science, which is
subdivided into nomological psychics or psychology, classi-
ficatory psychics or ethnology, and descriptive psychics
or history. "Nomological psychics discovers the general
elements and laws of mental phenomena. . . . Classifica-
tory psychics classifies the products of mind and endeavors
to explain them on psychological principles. . . . Descrip-
tive psychics endeavors in the first place to describe indi-
vidual manifestations of mind, whether they be permanent
works or actions; and to that task it joins that of endeavor-
ing to explain them on the principles of psychology and
ethnology." 2

All studies are either sciences of discovery, sciences of
review, or practical sciences. Elsewhere 3 he groups the
first two under the general heading, theoretical science. The
science of discovery consists of mathematics, philosophy,
and idioscopy (the special sciences). The subdivisions of

1 Collected Works, Vol. I, par. 1.180. 2 Ibid., par. 1.189. 3 Ibid., par. 1.239.

THE CLASSIFICATION OF THE SCIENCES 411

these general disciplines will be clearly evident from the
following table:

PEIRCE'S

CLASSIFICATION «

' Mathematics of Logic

- Mathematics •

Mathematics of Discrete Series
k Mathematics of Continua

Phenomenology

' Ethics

Science of

Description

Philosophy

Normative Sc. •

Esthetics

rSpec. Grammar
Logic \ Critic

I Methodeutic

' Ontology

Metaphysics

Religious Metaphysics

k Physical Metaphysics

f Molar

Genl. \ Molecular

I Ethereal

( Crystallography

' Physical Sc.

Class. \ Chemistry
I Biology

Desc. / Geognosy

1 Astronomy

' Introspective

[ Idioscopy

, /""^—l

Experimental

Physiological
! Child

( Special

Psychical Sc.

Class. -

Linguistic

. Ethnology

' e.g., Comte's

' History Proper

Science of

Philosophie positive,

> Desc. •

Biography

Review

Spencer's

> Criticism

Synthetic Philosophy

Practical

4

Science

- e.g., Pedagogics, Gold-beating,

Etiquette, Pige

son-fancying,

Peirce asserts that "by ' science of review ' is meant
the business of those who occupy themselves with arranging

1 Constructed from Collected Works, Vol. I, Bk. II, Chap. I.

412 INTRODUCTION TO PHILOSOPHY OF SCIENCE

the results of discovery, beginning with digests, and going
on to the endeavor to form a philosophy of science. Such is
the nature of Humboldt's Cosmos, of Comte's Philosophie
positive, and of Spencer's Synthetic Philosophy. The classifi-
cation of the sciences belongs to this department." * Hence
Peirce might himself label his classification of the sciences
by calling it an instance of a science of review. Peirce does
not tell us what he means by his third great division —
practical science. In this, as in the case of sciences of review,
he offers not a classification but illustrations. He finds
himself somewhat bewildered by the motley crowd of prac-
tical sciences, but comforts himself in the belief that the
classification of this branch is of no logical importance.

BLISS

The basic principle which Bliss employs is that of grada-
tion by speciality. "It may be comprehensively defined as
the principle by which the several sciences and studies, dis-
tinguished by their conceptual scope and their relations to the
real order of nature, are arranged in serial order from the most
general to the most special. . . . The generalizations and
laws of each more general science are true in some measure
of all the more special sciences. . . . But the laws or truths
of the more special sciences rarely apply to the more general
sciences or solve their problems. The special sciences, how-
ever, supply materials to which the generalizations and laws
of the more general sciences are generally applicable, and
by which they may be verified. Here are involved the
principles of the dependence of the special sciences on the
general, the interdependence of the several sciences, general
and special, and filiation of the more special sciences in suc-
cessive derivation from and dependence upon the more
general." 2

Combined with the principle of gradation by speciality,
however, there is a further principle. It permits the four-
fold division of studies into philosophy, science, history, and

1 Ibid., par. 1.182. 2 H. E. Bliss, op. cit, pp. 217-218.

THE CLASSIFICATION OF THE SCIENCES 413

applied science. Each of these constitutes a class of disci-
plines within which there is gradation by speciality. Fur-
thermore, the gradations in the four fields parallel one
another, with certain minor exceptions. Thus the scheme
of the intellectual disciplines is two-dimensional, the vertical
dimension representing progressive specialization as one
passes from the top of the column to the bottom, and the
horizontal dimension representing parallel philosophies, sci-
ences, histories, and applied sciences, as one passes from the
left to the right.

The four main divisions are described as follows: "Sci-
ence is verified and organized knowledge, rationally and
methodically proceeding from empirical and experimental
data, simple concepts, and perceptual relations to generali-
zations, theories, laws, principles, and explications, and to
more comprehensive conceptions and conceptual systems." l
"Abstract conceptions that by rational processes are reared
too remote from empirical bases, with regard rather to ethi-
cal, religious, and esthetic implications, Science assigns to
Philosophy. . . . True philosophy, however, as a super-
structure resting on the foundations of common knowledge
and science, proceeds to more abstract conceptions, more
transcendent relations, and more metaphysical implica-
tions." 2 "By generalization science is more positively dis-
tinguished from history than it is from philosophy. History
for the most part deals with concrete, or discrete, objects
and individuals, with particular events, parallels, move-
ments, tendencies, and developments, as antecedents and
consequents, though it also considers the determinative, or
causal, relations, or 'forces.'" 3 Finally, as to applied sci-
ences, "there are certain fields of study or research that are
cultivated more in solving practical, technical, or economic
problems, are more concerned in applying known data and
principles by means of known methods, or methods readily
derived from those known, than they are in discovering
new data, relations, and principles. ... It is these sciences

» Ibid., p. 190. 2 Ibid., p. 193. 3 Ibid., p. 195.

414 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and studies that may provisionally and for convenience be
termed applied." 1

The construction of the table proceeds, then, with the
arrangement of the philosophies, sciences, histories, and
applied sciences in parallel columns, each exhibiting grada-
tion by speciality. The column of the sciences is taken as
the pattern. "Our point of view being dominantly that of
natural science, the main divisions of our system are likewise
consistent with the fundamental sciences as graded by spe-
ciality, and the correlative, or parallel, branches of philoso-
phy and of history are there accordingly placed under the
respective main divisions, and so also are the more scientific
branches of technology. This is the schematic statement for
the most comprehensive and fundamental structure of our
system.'' 2

The tabular arrangement which Bliss proposes is as
follows :

BLISS'S CLASSIFICATION 3

Philosophy

Science

History

Technologies and j

Principles

Science in gen-

History of

eral

Philosophy

Metaphysics

and Science

i

Abstract Sciences

and general methods

Logic

Mathematics

Philos. of

Natural Sciences

Applied Science

Nature

Physical Sciences

Technology :

Physics

Physical ;
Engineering;

Chemistry

Chemical

Special Natural Sciences

and descriptive Natural History

Cosmology

Astronomy

Geology

Historical

Economic Geology

Geology

Economic Geography

Geography

Meteorology

1 Ibid., p. 213. 2 Ibid., p. 252.

3 H. E. Bliss, A System of Bibliographic Classification (New York: H. W. Wilson,
1935), p. 75.

THE CLASSIFICATION OF THE SCIENCES 415

Philosophy
Philos. of Life

Philos. of Hu-
man Life

Science History

Biological Sciences
Biology

Botany

Zoology
Anthropological Sciences

Anthropology History of Man-
Physical kind and of

Human Life
Archeology
Psychological Sciences

Technologies and Arts

Humanities and

Humanitarian Studies

Medical Sciences and
Hygiene

Mental Philos.

Psychology
General and Comparative
Individual Psychology

Applied Psychology

Abnormal Psychology

Psychiatry

Social Philos.

Social Psychology
Social Sciences

Education

Sociology Social-political

Applied Social Science

Ethnology History

Theology

Religion History of Re-

ligions

Church-work

Mythology

Ethics

Morals

Applied Ethics

Political Philos.

Political Science

Government

Philos. of Law Jurisprudence History of Law Practice of Law

Philos. of Econ.

Economics Economic

Economies

History

Industries
Business
Arts:

Aesthetics

History of Arts
Philology

;: Technic of Arts:
Industrial;
Fine Arts, etc.
Music

Linguistics and Languages;

Rhetoric, Oratory, etc

Literature

Drama and Theatre

GENERAL COMPARISONS

Although the two classifications given exhibit apparent
discrepancies, they are not altogether unlike so far as
underlying structure is concerned. Peirce's threefold divi-
sion into nomological, classificatory, and descriptive sci-
ences is essentially identical with Bliss's division into philoso-
phy, science, and history; for the first group represents the

416 INTRODUCTION TO PHILOSOPHY OF SCIENCE

study of the most general laws without any direct reference
to specific phenomena, the second represents the study of
laws as applied to the phenomena, and the third represents
the study of the individual phenomena. Furthermore,
Peirce, in making the trichotomic division a repeating form,
accomplishes essentially the same end as Bliss does in his
use of columns, though he does not succeed so clearly in
representing the parallelism of the main disciplines. Though
Peirce 's scheme is not obviously ordinal it exhibits serial
properties by virtue of the repetition of the trichotomic
divisions. For the nomological divisions of nomological
studies are the most definitely nomological, and the descrip-
tive divisions of descriptive studies are the most definitely
descriptive; hence the former head the series as the most
abstract of the studies, and the latter terminate the series
as the most concrete. The parallelism of mathematics near
the top, and of literature, biography, and criticism near the
bottom in the two tables cannot easily escape notice. The
Peircean table has the advantage of affording a definite
place for synoptic sciences, though the author's failure to
introduce classification at this point prevents one from know-
ing whether this division is limited to the all-inclusive synop-
tic studies which are usually called philosophies, or extends
also to the less inclusive sciences, such as anthropology and
geography. The parallel representation of the practical
sciences, as in the table of Bliss, is to be preferred to the
plan of Peirce, for it seems likely that they are reflections of
corresponding theoretical studies, and hence may be tabu-
lated by virtue of the latter.

Both classificatory schemes are defective in the represen-
tation of disciplines about disciplines. No doubt studies of
this character are puzzling, for they require that the scheme
should be reentrant, e.g., if there are not only philosophies
and sciences but philosophies of science, it follows that
science must occupy a double place in the table — it must be
both a type of study and a subject matter. An adequate
classificatory scheme must indicate, therefore, that philoso-

THE CLASSIFICATION OF THE SCIENCES 417

phy may study science in essentially the same way that sci-
ence studies nature. Similar difficulties arise in connection
with such studies as the history of philosophy and the
history of history. One way of meeting this difficulty is to
make the classificatory scheme perfectly general, i.e., to
formulate it not in terms of science, or philosophy, or
history but in terms of studies, meaning by this concept
an abstract pursuit which may be interpreted according to
any one of the three disciplines. Then studies of studies
may be considered as indicating the history of philosophy,
or the philosophy of science, or the history of history,
according to the interpretation desired. This representation
complicates the table greatly, but it results in a more ade-
quate scheme.1

REFERENCES

R. Flint, Philosophy as Scientia Scientiarum (London: Blackwood,

1904).
H. E. Bliss, The Organization of Knowledge (New York: Holt, 1929).
C. S. Peirce, Collected Works (Cambridge: Harvard University,

Vol. I, 1931), Book II, Chap. I.

E. C. Richardson, Classifications, Theoretical and Practical (New

York: Scribners, 1901).

F. R. Tennant, Philosophy of the Sciences (Cambridge: Cambridge

University, 1932).
J. A. Thomson, Introduction to Science (New York: Holt, 1911),

Chaps. IV, V, VI, VII.
A. C. Benjamin, The Logical Structure of Science (London: Kegan

Paul, 1936), Chap. I.

1 The author has attempted to solve the problem along these lines in his book
mentioned in the bibliography given immediately above.

CHAPTER XIX

HUMAN FREEDOM

The problem of human freedom labors under two impor-
tant difficulties. In the first place, it is, perhaps, the most
pressing of the speculative problems. Many have felt that
both morality and religion must disappear unless it can be
solved — solved, that is, in such a way as to make human
freedom possible. For this reason most speculation on the
problem suffers from an initial partiality. Both because of
the urgency of the solution and because of the odds in favor
of one solution rather than another, reflection on the prob-
lem has been tinged with emotion. Fallacies of non sequitur
and begging the question abound. Frequently the conclusion
is drawn from an implicit premise, such as the unbearable
character of a world in which strict determinism prevails, or
the futility of striving after the Good in a world which is
governed by Fate.

But, in the second place, the problem is — perhaps because
of the emotional associations — inaccurately formulated.
The essential terms employed in its definition and solution
—"freedom," "determinism," "volition," "self," and "self-
determination" — are vague and ambiguous, and little
effort is expended toward their clarification. As a result, one
cannot always tell whether what is demonstrated on the
grounds of science is freedom in the sense of absolute de-
terminism or in the sense of self-determinism; nor can one
ascertain whether it is man's behavior or man's volition
which is proved to be free, or whether freedom consists in
the complete absence of causes or merely in the unpredicta-
bility of behavior. Terminological difficulties of this kind
make it possible for Planck and Compton both to demon-
strate human freedom, though the former considers nature
to be causally determined and the latter believes that the

418

HUMAN FREEDOM 419

Heisenberg principle argues for breaks in causal determina-
tion; for what Planck demonstrates is freedom in the sense
of unpredictability, and what Compton demonstrates is
freedom in the sense of the absence of physical determina-
tion.

The problem is not, of course, in its broadest sense, neces-
sarily solved on the grounds of data offered by science alone.
Presumably there may be data drawn from a wide range of
experience which would be relevant to it. But, considered
as a problem of speculative philosophy, it is limited for its
data to material offered by the subject matter or method of
science. Science, in its very fundamentals, is built around
the problem of the ascertainment of uniformities. Whether
the regularities are presumed to lie in nature itself, or whether
they are supposed to be merely techniques of explanation
is unimportant at this point; in either case they are the
sine qua non of science. For science attempts to assert
generalizations, and generalizations are impossible without
uniformities. Uniformities imply repeated connections and
the consequent absence of spontaneity. Thus the success
of science in its search for regularities is a measure of the
existence of regularities, or, at least, of the availability of
principles of regularity as techniques of explanation. But
man is obviously a part of nature. Whether he is merely a
part and therefore manifests the characteristic features of
the rest of nature, or an exceptional part and therefore
exhibits properties not common to nature as a whole — these
are questions which must be answered. But the legitimacy
of inferring the nature of human behavior from the behavior
of events in general seems never to have been called into
question.

It is interesting to note that the attitude on the question of
human freedom or human determination has been through-
out the course of history an accurate barometer of the status
of science in any given period. Ages in which science has
been quiescent have usually been periods in which man
forgot the regularity and uniformity of natural processes

420 INTRODUCTION TO PHILOSOPHY OF SCIENCE

and conceived of himself as master of his fate. On the other
hand, ages in which science has been active have been
periods in which man became conscious of the lawfulness of
nature and of his consequent ineffectiveness. This parallelism
suggests that there is some connection between the two
facts, at least for the popular mind. The absence of law is
associated with human freedom, and the presence of law is
associated with human determination.

The best historical illustration of this is to be found in the
contrast between the world-view which was characteristic
of the Middle Ages — a period which according to all records
was especially deficient in scientific achievements — and the
scientific world- view which followed it. 'For the Middle
Ages man was in every sense the centre of the universe. The
whole world of nature was believed to be teleologically sub-
ordinate to him and to his eternal destiny. . . . The pre-
vailing world- view of the period was marked by a deep and
persistent assurance that man, with his hopes and ideals,
was the all-important, even controlling fact in the uni-
verse. . . . An explanation in terms of the relation of things
to human purpose was accounted just as real as and often
more important than an explanation in terms of efficient
causality, which expressed their relations to each other.
Rain fell because it nourished man's crops as truly as be-
cause it was expelled from the clouds. Analogies drawn
from purposive activities were freely used. . . . The whole
universe was a small, finite place, and it was man's place.
He occupied the centre; his good was the controlling end
of the natural creation." x

Sharply contrasted with this was the world- view which
developed with the advent of science and its discovery of
the mechanical character of natural processes. "Just as it
was thoroughly natural for medieval thinkers to view nature
as subservient to man's knowledge, purpose, and destiny;
so now it has become natural to view her as existing and

1 E. A. Burtt, Metaphysical Foundations of Modern Physical Science (New York:
Harcourt, Brace, 1925), pp. 4-6.

HUMAN FREEDOM 421

operating in her own self-contained independence, and so
far as man's ultimate relation to her is clear at all, to con-
sider his knowledge and purpose somehow produced by her,
and his destiny wholly dependent on her." 1 Nature is no
longer teleological but causal. Man, instead of being the
controlling factor in the universe, does not even have con-
trol over his own destiny ; he is the innocent victim of blind
forces operating according to mechanical principles. Rain
falls not only to nourish his crops but to drench him in
tornadoes and floods, and to wipe out his home and family.
The universe is infinite, and man occupies a minute spot
which is but local and temporary, soon to be eradicated by
the irresistible march of unseeing forces. Man cannot be
free.

The recent interest in the problem of human freedom is,
similarly, a direct reflection of a state of affairs in the phys-
ical sciences. However, the situation is somewhat different
because the agitation for human freedom which has charac-
terized much of the contemporary literature in the philos-
ophy of science has been the result of a period not of scien-
tific quiescence but of scientific activity. The point is that
this activity has itself disclosed within the very field of
science a fact which is incompatible with the assumption
of a strictly lawful nature. Attention has already been called
in Chapter XVI to the formulation by Heisenberg of the
principle of indeterminacy. Whether or not this principle
argues for an actual break in the causal structure of nature
is, as has already been seen, debated by scientists. Rut even
if it does not demonstrate the existence of actual spontaneity,
it at least establishes the impossibility of making predictions
with regard to certain types of phenomena which had been
presumed to be causal in character. As a consequence, the
principle has been enthusiastically welcomed by the advo-
cates of human freedom. It is not always maintained by
these advocates that the principle actually demonstrates
human freedom; but it is commonly asserted that the prin-

1 Ibid., pp. 10-11.

422 INTRODUCTION TO PHILOSOPHY OF SCIENCE

ciple at least leaves room for a human freedom which may
perhaps be demonstrated on other grounds. At any rate
there is no longer any conflict between the assumptions of
physical science and the demands of the moral consciousness.
Even granting, therefore, that science is entitled to legislate
for human life, it cannot destroy human freedom, for some-
thing analogous to this is manifest even in the physical
world. Nature exhibits loopholes in uniformity; hence, if
man is a part of nature he may still be free. This is approx-
imately the state of affairs which has given rise to the recent
interest in the problem. The problem itself may now be sub-
jected to analysis before an examination is made of the
views of certain contemporary writers.

GENERAL CHARACTER OF THE PROBLEM

What, then, is the problem of human freedom considered
in the context of science? It may be formulated somewhat
as follows: The complete act of behavior may be analyzed
in two ways. On the one hand there is the physical analysis,
which breaks up the total act into the movement itself,
such as raising the hand, or speaking, the brain-state which
is presumably its cause, then the brain-state which is pre-
sumably the cause of this, and so on backward in time. The
brain is the central organ of control with regard to bodily
processes, and is responsible for the instigation of all activity
which is not purely reflexive. On the other hand there is
the psycho-physical explanation, which breaks up the total
act into a similar bodily movement, the brain-state which
is presumably its cause, and the volition or mind-state which
is the cause of this. This analysis also admits that the brain
is the central organ of control and is responsible for the
instigation of all activity, but it insists that the brain is
only the instrument of the volition. Here, in fact, is the
origin of the problem of freedom versus determinism. The
physical and the psycho-physical explanations are identical
with regard to the movement and the brain-state. But the
problem lies in the exact status of this brain-state. Is it the

HUMAN FREEDOM J23

effect of an earlier brain-state, or is it the effect of something
which is not a brain-state (though it may have a parallel
brain-state), viz., the volition or decision?

It seems clear that the deterministic solution to the prob-
lem of human behavior will follow the lines laid down by
the physical analysis. An act may be said to be determined
if there is an anterior state which, being known, would en-
able one to predict the act. This is at least determinism in
the sense in which Laplace supposed the world to be deter-
mined. If act, brain-state, anterior brain-state, and so on,
are all well-defined bodily states, the causal chain is clearly
evident. Like Laplace the determinist would be able to say
that if a being of sufficient intelligence knew the condition
of every particle in the brain of an individual he could pre-
dict all of the individual's future behavior. Determinism of
this type which involves no reference to mind or volition is
commonly characterized as materialistic, or epiphenomenal-
istic.

But it seems equally clear that the psycho-physical anal-
ysis may also eventuate in a determinism. Determinism
need not be materialistic. Even if at some point in the
regress from act to brain-state and brain-state to its cause
volition enters as a causal factor, there is no reason to
abandon determinism. All that is required is the recognition
of volition as a legitimate anterior state, knowledge of which
would permit prediction of activity. If mind-states are
effective, the Laplacian being could predict just as accu-
rately on the basis of such knowledge as he could in the
former case on the basis of knowledge of brain-states.

However, for some reason, a determinism of this kind does
not appear so distasteful as the materialistic kind. In fact
psycho-physical determinism reduces to self-determinism,
and this is what is commonly meant by freedom. For if the
volition is itself the outcome of a previous mind-state, this
of a still anterior one, and so on, what this amounts to in
effect is the progressive building up of the personality, or
self. I do not object to the supposition that my volition was

424 INTRODUCTION TO PHILOSOPHY OF SCIENCE

determined by a number of factors which I call motives,
reasons, desires, past experiences, etc.; in fact I insist that
my volition is precisely the outcome of the survey of just
such factors. But this examination of motives, reasons, etc.,
is nothing other than the act of making the decision. My
decision is not independent of these factors ; it is these factors
themselves blended into a harmonious whole. Hence when
I say that my decision has been determined by a previous
mind-state, all that I am asserting is that I myself have
determined the decision, for by my self at any moment I
mean simply the mind-state at that moment, which includes,
of course, the effects of all previous mind-states. But to
act according to the dictates of my self is not to be deter-
mined but to be free. Self-determinism is freedom.

Apparently, therefore, the differences between the phys-
ical and the psycho-physical analyses of the act of behavior
are two in number : (a) The latter theory permits a physical
state to be caused by something which is non-physical, i.e.,
by a mind-state, (b) The latter theory permits a mind-
state to be caused only by something which is non-physical,
i.e., another mind-state. The former theory permits neither
of these to be true. Both theories are causal, for they
both insist that the eventual movement is the outcome of
previous events. In fact both theories claim that the move-
ment is the immediate outcome of an event in a brain. The
difference arises when the analysis is pushed back further.
What is to be done with this brain-state which is the imme-
diate cause of the actP Is it caused by a previous brain-state,
and only by such? If so, the act of the individual is part of a
physical causal chain and is determined. Is the brain-state
caused by a previous mind-state, and only by such? If so, the
individual is part of a causal chain which is not wholly physi-
cal in character, and this is partly what is meant by saying
that the individual is free. He is free in the sense that his
behavior follows from his decisions. In this sense the indi-
vidual is free to act as he wills. But is he free to will as he
wills, i.e., is the individual's volition itself an event in a causal

HUMAN FREEDOM 425

chain? As has been seen, the fact that volition is the out-
come of earlier events does not destroy the freedom of the in-
dividual provided the causal chain is kept entirely in the
realm of mind-states. Hence the further demand of the con-
cept of freedom is that the volition be nowhere an immediate
or indirect effect of a brain-state. There is only a one-way
causal action, from mind-state to brain-state, but not in the
reverse direction. These two demands of a theory of freedom
may be stated as follows: There is no law which asserts that
a volitional state is a function of an earlier physical state.
There are laws which assert that physical states are functions
of earlier volitional states.

It is not likely that such an analysis of the problem of
freedom and determinism is a fruitful one for the ultimate
solution of the problem. Recent philosophy and psychology
have become convinced of the dangers inherent in the use
of the terms 'mind'' and "body," and have attempted to
avoid them. Rut the writers whose positions are to be exam-
ined in the following pages have used this terminology, and
it is for this reason that the words and the dichotomy based
upon them have been used. The analysis which is here given
may be taken merely as a general matrix to be used for the
clarification of certain contemporary views on the problem
of human freedom.

EDDINGTON

Eddington has been among the boldest of those who draw
speculative conclusions outside of the realm of physics upon
the basis of indeterminacy revealed in physical phenomena.
Eddington's data are of two kinds. On the one hand are
those conclusions of physical science to which reference has
already been made in Chapter XVI. The realm of physical
entities can no longer be looked upon as a strictly deter-
ministic scheme since small-scale phenomena, by virtue of
the principle of indeterminacy,- are unpredictable as to
behavior. "Strict causality is abandoned in the material
world. Our ideas of the controlling laws are in process of

426 INTRODUCTION TO PHILOSOPHY OF SCIENCE

reconstruction and it is not possible to predict what kind of
form they will ultimately take; but all indications are that
strict causality has dropped out permanently. This relieves
the former necessity of supposing that mind is subject to
deterministic law or alternatively that it can suspend deter-
ministic law in the material world." x Thus in the realm of
physical phenomena there is no longer any reason for assert-
ing that nature is completely causal in character.

But on the other hand there are important data which
are not strictly in the field of physics. These are discerned
by an examination of the methods of knowing objects. When
one examines the character of our knowledge of physical
objects he is impressed by an important fact. We know them
not directly but through the medium of symbols — pointer
readings. Our knowledge of space, time, motion, force, and
so on is merely that of numbers on recording instruments.
The inner nature of objects — if they have any inner nature
at all — is forever hidden from our awareness. Now one of
the physical objects which we know in this way is the human
brain. Our knowledge of the brain is such as is obtained by
measuring its volume, its duration, motions exhibited in it,
its heat, its energy, and so on. But in this "one case —
namely, for the pointer readings of my own brain — I have
an insight which is not limited to the evidence of the pointer
readings. That insight shows that they are attached to a
background of consciousness." 2 Introspection therefore
comes into the picture, and affords a method for getting at
the inner nature of the brain. Thus we can know the inner
nature of our own brain in a way in which we cannot know
the inner natures of ordinary physical objects. Hence,
"there is nothing to prevent the assemblage of atoms con-
stituting a brain from being of itself a thinking object in
virtue of that nature which physics leaves undetermined
and undeterminable." 3 Introspection reveals something
which cannot be revealed by science, and yet cannot be
gainsaid by science. The traditional solution to the problem

1 Nature of the Physical World, p. 332. 2 Ibid., p. 259. 3 Ibid., p. 260.

HUMAN FREEDOM 427

of human freedom has been one-sided, since it has recognized
the conclusions of science but disregarded the dictates of
introspection. The modern solution demands that these
data be admitted as of equal significance.

From these premises only one conclusion follows. When
I examine my own consciousness I find that its essential
feature is volition. "We may now feel quite satisfied that
the volition is genuine. The materialist view was that the
motions which appear to be caused by our volition are
really reflex actions controlled by the material processes in
the brain, the act of will being an inessential side phenom-
enon occurring simultaneously with the physical phe-
nomena. But this assumes that the result of applying
physical laws to the brain is fully determined. ... If the
laws of physics are not strictly causal the most that can be
said is that the behavior of the conscious brain is one of the
possible behaviors of a mechanical brain. Precisely so; and
the decision between the possible behaviors is what we call
volition. ... At some brain center the course of behavior
of certain atoms or elements of the physical world is directly
determined for them by the mental decision — or, one may
say, the scientific description of that behavior is the metrical
aspect of the decision." *

Unfortunately the meaning here is none too clear. Appar-
ently what Eddington has in mind is something like the fol-
lowing: By virtue of the principle of indeterminacy the
occurrence of a particle in a given state is unpredictable,
i.e., the anterior state is ascertainable only by knowing both
position and velocity of the particle — which is impossible.
If one argues from this fact to objective indeterminism he
concludes that any state of a particle may occur without
cause, i.e., without physical cause. Now let us suppose that
the particle in question is a brain particle. Any given state
of this particle may occur without physical cause, i.e., with-
out anterior brain-state. But introspection is a witness to
the fact that a brain particle has an inner nature which

» Ibid., pp. 311-312.

428 INTRODUCTION TO PHILOSOPHY OF SCIENCE

is not measurable by physical techniques. Consequently
there is nothing opposed to the supposition that this inner
nature which we call volition is effective in the determination
of the state of the particle. A particle may then take on a
certain state without violation of the laws of physics, yet
in response to the dictates of volition. This permits an
action of "mind' on " matter v without necessitating any
interruption of physical processes, for "mind' enters only
when there is an inadequacy in physical explanation.

This seems to guarantee the desired freedom of the will.
The will is effective over the brain, yet is not itself affected
by physical processes. It has the advantage, therefore, over
all materialisms and epiphenomenalisms which either deny
the reality of mind or else reduce it to the mere afterglow of
brain processes. Yet it does not violate the law of conserva-
tion of energy since volition is not an intrusion into the
physical realm. Hence on the grounds of scientific data and
introspection the freedom of the will is demonstrated.

COMPTON

The position of Compton in this issue is essentially the
same as that of Eddington, though its details are more in-
tricately worked out. For Compton the problem is not one
of deducing the fact of human freedom from the laws of
nature. This places human freedom in a derivative position
whereas, in fact, it is fundamental. "It seems unfortunate
that some modern philosopher has not forcibly called atten-
tion to the fact that one's ability to move his hand at will
is much more directly and certainly known than are even
the well-tested laws of Newton, and that if these laws deny
one's ability to move his hand at will the preferable con-
clusion is that Newton's laws require modification." x Such
a step, however, is not necessary, for physical science has
itself shown that "natural phenomena do not obey exact
laws." 2 Science, in other words, must itself "abandon its
cherished law of causality." 3 'I should consider it more

1 The Freedom of Man, p. 26. 2 Ibid., p. 7. 3 Ibid., p. 23.

HUMAN FREEDOM 429

likely," insists the author, "that the principle of the con-
servation of energy or the second law of thermo-dynamics
would be found faulty than that we should return to a system
of strict causality." * Hence for Compton the problem is one
of constructing a theory from which it will be possible to
deduce both the fact of human freedom and the fact of a
non-causal nature.

The unpredictability of natural events means that in
connection with small particles "knowledge of the initial
conditions does not enable us to predict what will happen,
for with the same initial conditions we cannot consistently
produce the same effect." 2 Hence a particle which chooses
one path would be physically indistinguishable from a par-
ticle which chooses another. The question then arises as to
whether there would be any distinction at all between two such
particles. The principle of operationalism demands that " only
those aspects of the world have reality which are capable of
showing themselves in some way to the observer." 3 It ap-
parently follows from this that a distinction which is physi-
cally undetectable is non-existent, and this seems to be the only
conclusion which we can draw as physical scientists.

But this point of view "is not broad enough to cover all of
our experience." 4 Hence we must extend our postulate in
such a way as to permit the discerning of differences where
there are no physical differences. This is apparently done
by assuming that physical events have properties which are
not detectable by physical techniques. On the one hand
such an assumption allows for the possibility that two
physical particles should differ, say, in "goodness" and
'badness." 5 Such a distinction would not be open to
physical inspection, but it would not be therefore non-
existent. On the other hand such an assumption asserts
"that the matter in our brains may occur in conditions
which though physically indistinguishable nevertheless cor-
respond to distinguishable states of consciousness." 6 Hence

1 Ibid., p. 23. » ibid., p. 40. 6 Ibid., pp. 39-40.

2 Ibid., p. 39. * Ibid., p. 43. 6 Ibid., p. 44.

430 INTRODUCTION TO PHILOSOPHY OF SCIENCE

two brain particles may be physically identical, yet they
may correspond to different states of mind. We are presum-
ably aware of this non-physical difference in brain particles
through introspection, though we are not informed of the
channels through which we become aware of such properties
as the "goodness" and "badness'1 of non-brain particles.

It follows that what is for physical science random action
may be for introspection caused and predictable action.
Given a brain particle in a certain state, physical science can
make no definite prediction as to its behavior, since the
ascertainment of both position and velocity of the particle
may be impossible. But introspection, being provided with
additional information about the particle, can anticipate its
behavior. Through introspection one can know whether the
physical state of the particle is associated with a decision of
one kind or with a decision of another kind; hence one can
predict what the behavior of the particle will be. Physics
must here admit its definite limitations. For, "if true free-
dom is postulated, with a knowledge of motives, a more
accurate prediction of the actions of a living being is possible
than can be made from a knowledge of the physical condi-
tions alone." x

Two further features are required in order to complete
the theoretical structure. One is the volitional act itself. A
brain particle must be subject to control by will. Here it is
important to refer to Compton's figure of the mind as pro-
vided with a shutter by means of which it controls the orifice
through which the electrons pass, allowing only the "good'
electrons to pass and preventing the "bad'' electrons from
entering. Thus mind is able both to distinguish between the
"good" and "bad" particles, and to control their move-
ments. Now it is clear that such a selective and controlling
act will be possible provided it does not conflict with any
physical law. But here one need have no fears. Physical
science can predict only on grounds of probability, i.e., it
can assert that of the possible behaviors of a particle one is

1 Ibid., p. 28.

HUMAN FREEDOM 431

more or less probable than another. But under such condi-
tions the intervention of an act of will is physically unde-
tectable. If the selective acts of volition were so adjusted
that over a long period the probability distribution of the
paths of particles were interfered with there would be a
physically observable effect, and the act of intervention
could be inferred. But in a single case, or in a limited run
of cases, the presence of an act of decision could not be de-
tected. Hence one's direct consciousness of freedom con-
flicts in no way with the conclusions of physical science.

The second feature required is the assumption that organic
behavior is such as to permit large-scale results to follow
from small-scale causes. There must be something like
"trigger action" in the human body. For the indeterminism
in nature is applicable only to minute particles, hence the
selective action must be applicable only to small-scale phe-
nomena. But "the living organism, in turn, acts as an ampli-
fier of very great power, which may be set in operation by
events on a scale comparable with the elementary events
which we know to be indeterminate. Considering the com-
plexity of the small scale events associated with any of our
deliberate acts, one may say with assurance that on a purely
physical basis the end result must have a relatively great
uncertainty." x

By means of some such theory as this our intuitive aware-
ness of freedom may be justified and shown to be perfectly
compatible with modern science. Physical laws "serve to
define the limits within whiclr action is possible. Within
these limits there may be a wide range wherein a man may
do as he pleases without violating any physical law. That
he actually does as he pleases is a matter of everyday experi-
ence. A man's pleasure, in other words consciousness, is
thus an additional determining factor which supplements
the physical laws in defining his actions." 2 Such a theory
clearly satisfies the theoretical demands of freedom. For,
in the first place, volition is not itself determined by any

1 Ibid., pp. 50-51. 2 Ibid., pp. 64-65.

432 INTRODUCTION TO PHILOSOPHY OF SCIENCE

physical features of events. It may be said, in a sense, to be
controlled by a non-physical property of events, since voli-
tion is affected by the "goodness" or "badness" of events.
Hence volition is causally responsible not to the physical
realm, which would destroy freedom, but merely to an
anterior mind-state which includes the recognition of moral
qualities of events; this, however, as was seen, reduces to
self-determinism, which is equivalent to freedom. Accord-
ingly, the theory allows for freedom in the sense that it
retains the aloofness of volition from the physical processes.
But, in the second place, volition is effective over physical
processes ; brain particles are under the control of will. How-
ever this causal efficacy involves no interruption of the
physical course of events, since it occurs only in those situa-
tions where physics is unable to ascertain causes. Conse-
quently the theory allows for freedom also in the sense that
it permits the formulation of the laws which state the func-
tional dependence of a physical state upon an earlier voli-
tional state.

PLANCK

The main difference between Planck and the two writers
just considered is that the former argues for human freedom
independently of the principle of indeterminacy. As was
shown in Chapter XVI, Planck insists that the principle of
indeterminacy has no objective implications. To conclude
to a complete breakdown of the law of causality seems to him
premature. "It is far more natural to avoid the difficulty
by another method, a method which has often rendered good
service in similar cases and which consists in assuming that
it is meaningless, with respect to physics, to ask for the
simultaneous values of the coordinates and of the velocities
of a material point or for the path of a photon of a given
color. Evidently the law of causality cannot be blamed
because it is impossible to answer a meaningless question;
the blame rests with the assumptions which lead to the
asking of the question, i.e., in the present case with the

HUMAN FREEDOM 433

assumed structure of the physical world image." 1 It seems,
however, that any system which is substituted for the clas-
sical one must exhibit a causal structure, though "causal"
may require some modification for alternative schemes.2
"In my opinion, therefore, it is essential for the healthy
development of Physics that among the postulates of this
science we reckon, not merely the existence of law in general,
but also the strictly causal character of this law." 3 On such
an unequivocal assumption there would seem to be no hope
that freedom could be demonstrated by evidence drawn
from the principle of indeterminacy. Yet Planck does just
this, though his use of the principle is somewhat indirect.

He begins by insisting that there is no question as to the
fact of causal laws in the realm of human affairs. "The
highest types of human intelligence are subject to the causal
law in the processes that result in even their greatest achieve-
ments." 4 "We must admit that the mind of each one of
our greatest geniuses — Aristotle, Kant or Leonardo, Goethe
or Beethoven, Dante or Shakespeare — even at the moment
of its highest flights of thought or in the most profound inner
workings of the soul, was subject to the causal fiat and was
an instrument in the hands of an almighty law which governs
the world." 5

The surprise which one experiences in the presence of such
a statement, argues Planck, is due to his failure to distinguish
between the validity of the causal principle and the practi-
cability of its application. "Under all circumstances the law
of causation is valid, because of its transcendental char-
acter." 6 But "it must be remembered that we ourselves
are only common mortals, and that we could never hope to
be in a position to follow out the delicate play of cause and
circumstance in the soul of a genius. . . . The whole point
lies in the inadequacy of the observer. Just so the macro-
scopic physicist is entirely unable to pursue microscopic
workings in natural phenomena, yet, as we have seen, this

1 The Philosophy of Physics, pp. 63-64. 2 Ibid., p. 73.

3 The Universe in the Light of Modern Physics (New York: Norton, 1931), p. 89.
« Where Is Science Going?, p. 158. B Ibid., pp. 157-158. 6 Ibid., p. 157.

434 INTRODUCTION TO PHILOSOPHY OF SCIENCE

does not mean that the law of causality is not valid for these
microscopic happenings." x

What is the sense, then, Planck asks, in speaking of causal
relations in cases where the difficulties of observation render
their applications impossible? The analogue of the quan-
tum phenomena 2 is enlightening here. The principle of in-
determinacy shows the impossibility of measuring both the
position and the velocity of a particle with the necessary
accuracy. This involves the conclusion that prediction of the
behavior of a particle is impossible, since it depends on knowl-
edge of state and this can never be obtained. Now if this view
is combined with the operational theory, the impossibility
of knowledge becomes the ground for the impossibility of
existence; hence there is an objective indeterminism. But
this step Planck will not take. He insists that the difficulties
in the ascertainment of position and velocity of a particle
are due to the techniques of measurement, i.e., to the rela-
tion of the observer to his phenomena. They are not diffi-
culties of the validity of the causal principle but of the prac-
ticability of its application. The virtue of the principle of
indeterminacy is that it has shown us the importance of
recognizing the observer and the methods which he employs
in observing. More specifically, it has shown us the general
principle to be used in determining the applicability of a
causal law: "The smaller the distance between the investiga-
tor and the object . . . the more uncertain and fallible will
be the causal and scientific treatment." 3 "Laplace held
that if there were a super-intelligence standing entirely out-
side of the facts occurring in the universe, this intelligence
would be able to see causal relations in all happenings of the
world of man and nature, even the most intricate and micro-
scopic. It is only by aiming at this sort of distance that the
individual could establish the required detachment of the
perceiving subject from the object of his research, which we
have already seen to be an inevitable condition for the

1 Ibid., p. 156. 2 The Philosophy of Physics, p. 80.

3 Where Is Science Going?, pp. 155-156.

HUMAN FREEDOM 435

application of the causal method in research. The nearer we
are to events in time the more difficult it is to trace their
causal structure." 1 This, in fact, is the explanation of the
use in science of such a thing as an "ideal spirit," or the
Laplacian omniscient being. "Scientific thought always re-
quires a certain distance and a clear separation as between
the thinking subject and the object of his thought, and this
distance is best guaranteed by the assumption of an ideal
spirit." 2

We are now ready for the application of this notion to the
problem of human freedom. It has already been shown that
human behavior is regulated by causal laws; hence there is
no reason for denying the fact of causation as applied to
human beings. But what may be said of the applicability of
the law? Here a genuine difficulty arises. "There is a point,
one single point in the immeasurable world of mind and
matter, where science and therefore every causal method of
research is inapplicable, not only on practical grounds but
also on logical grounds, and will always remain inapplicable.
This point is the individual ego." 3 What are these grounds,
practical and logical? The practical grounds are easy to
discern. In practice we can never discover the causal con-
nections in our own personal conduct, "because this would
mean that the observing subject would also be the object
of research. And that is impossible; for no eye can see itself.
But in so far as any man is not entirely today that which he
was years ago there is a relative degree to which he might
subject his own experiences to causal scrutiny." 4 Presum-
ably this limitation is due, then, merely to the limitations of
the human intelligence; were our understanding more com-
prehensive we should be able to make a complete analysis
of ourselves. This, however, is erroneous because of the
difficulties constituting the logical grounds. ' It would be a
complete mistake to attribute the impossibility of forecasting
the subject's actions on purely causal lines to a lack of knowl-

1 Ibid., p. 162. 3 Where Is Science Going?, p. 161.

2 Philosophy of Physics, p. 81. 4 Ibid., p. 163.

436 INTRODUCTION TO PHILOSOPHY OF SCIENCE

edge which might be overcome if the individual intelligence
were suitably increased." ! "Such an attempt is condemned
to failure in advance because every application of the law of
causality to the will of the individual and every information
gained in this way is itself a motive acting upon the will, so
that the result which is being looked for is continually being
changed." 2 Applying the general principle noted above,
"the nearer we are to the events of our own personal expe-
rience the more difficult it is for us to study ourselves in the
light of these happenings; for the activities of the observer
are here partly the object of research and, in so far as that
is so, the causal connection is practically impossible to
establish." 3 "We cannot possibly study ourselves at the
moment or within the environment of any given activity.
Here is the place where the freedom of the will comes in
and establishes itself, without usurping the right of any ri-
val." 4 "The impossibility of foretelling the subject's actions
on purely causal lines is not based on any lack of knowledge,
but on the simple fact that no method by whose application
the object is essentially altered can be suitable for the study
of this object." 5

If this be freedom, it is freedom of a different kind from
that demonstrated by Eddington and Compton. It is not a
freedom which is based upon the efficacy of a factor which
eludes physical analysis and which is itself not the result of
any physical processes. Nor is it a freedom which is self-
determination. It is rather a freedom which is equivalent to
unpredictability. The self is free because no one short of an
omniscient being could ascertain the complete complex of
causal factors effective in a given situation. Man acts,
therefore, not without cause, but without anticipated knowl-
edge as to how he is to act. He is under the control of a causal
law, but it is transcendental not empirical. At the level of
his understanding, therefore, he is free. But to assert this
means no more than that his actions are unpredictable, for,

1 Philosophy of Physics, p. 80. 2 Loc. cit. 3 Where Is Science Going?, p. 163.
4 Ihid.r p. 164. 5 Philosophy of Physics, p. 80.

HUMAN FREEDOM 437

apart from some direct consciousness of freedom, this is all
that can be meant by the term.

Criticisms of the foregoing positions on the question of
human freedom are not difficult to make, and the reader
will be able to supply them readily. As in the case of all
speculative problems, highly cogent arguments are not to
be found. The dependence of speculative considerations upon
the more critical questions is here more apparent, perhaps,
than anywhere else in the speculative field. Clearly the solu-
tion to the problem of human freedom is possible only on
the grounds of a more precise analysis of such terms as
"cause," "law," "determination," and the like, which are
common to the sciences, and such terms as "self," "voli-
tion," "mind," and the like, which are peculiar to the psycho-
logical sciences. It seems safe to say with reference to the
future that the problem of human freedom cannot be solved
until clarification is introduced into these more basic notions.

REFERENCES

A. S. Eddington, Nature of the Physical World (New York: Mac-
millan, 1929), Chaps. X, XIV.

New Pathways in Science (New York: Macmillan, 1935),

Chaps. IV, V, XIII.

A. H. Compton, The Freedom of Man (New Haven: Yale Uni-
versity, 1935).

Max Planck, Where Is Science Going? (New York: Norton, 1932).

Philosophy of Physics (New York: Norton, 1936).

C. J. Herrick, Fatalism or Freedom (New York: Norton, 1926).

Joseph Needham, Man a Machine (New York: Norton, 1928).

H. N. Russell, Fate and Freedom (Oxford: Oxford University, 1927).

H. Levy, Universe of Science (New York: Century, 1933).

CHAPTER XX
THE NATURE OF REALITY

The last of the speculative problems to be considered is,
in a sense, the most important of the three. At least it is
that which has been most debated by scientists and philoso-
phers. Much of the history of philosophy can be formulated
in terms of the controversies over the precise limits of the
realm of the given, and the justifiability of making inferences
beyond the obviously given to that which is required in
order to make it intelligible. All materialisms and idealisms,
subjectivisms and objectivisms, theisms and atheisms, mon-
isms and pluralisms, to mention only a few of the outstanding
metaphysical positions, are attempts to solve this problem
in one way or another. Hence so far as range of significance
is concerned, speculative problems in this field are important
among the problems in the philosophy of science.

This very fact makes a discussion of such problems diffi-
cult, for one hardly knows how to make a selection among
the possible candidates for consideration. To insist that only
those positions should be examined which are founded on
the facts of science is to employ a variable criterion, for prac-
tically every metaphysical position attempts to accommo-
date itself to science. Similarly, to include only those posi-
tions which proceed in the essential spirit and method of
science may be unduly severe, for, as was shown in Chap-
ter XVII, probably none of the speculative problems can
be solved by rigid adherence to the critical methods of
science. Yet to select on the grounds of personal bias, i.e.,
to include only those positions which seem to the writer to
be most adequate, is hardly fair.

The principle employed in the selection of the following
illustrations is very simple. It has resulted, perhaps, in an
unbalanced list. But since it is offered merely for purposes of

438

THE NATURE OF REALITY 439

example, there is no danger of misleading. The common
feature of all of the following positions is that they attempt
to draw conclusions as to a theory of reality upon the basis
not of the facts of science but of its methods. According to
all of them not what the scientist knows but the way in which
he knows is important for a more inclusive outlook. For
example, in three of the following cases there is specific
reference to the character of scientific symbols and the way
in which they presumably designate their referents; in the
fourth the data are to be found in the method of idealization,
which is, again, a fact about the knowing rather than that
which is known. The basing of speculative problems on the
techniques of knowing rather than on the actual conclusions
seems to give them a firmer foundation. For any fact of
science is more or less specific. But methods, in the very
nature of the case, are more general and permeate all of the
sciences to a certain extent. Furthermore, they are more
permanent, hence make the speculative superstructure less
precarious. It is probably true that each of the positions to
be considered makes an erroneous analysis of the specific
feature of method to which it refers, but this is of no impor-
tance when one's purpose is mere illustration. The actual
ways in which they make use of these methodological aspects
can be made clear only if there is a preliminary consideration
of the general problem.

GENERAL CHARACTER OF THE PRORLEM

The first feature to be emphasized is the fact that the
inference to a realm beyond that which is obviously given is,
in a certain sense, unavoidable. Though science — and even
philosophy — professes to be satisfied with a pure phenom-
enalism, it has not often remained long in this unstable posi-
tion. As Bacon long ago pointed out, the mind is prone to
soar into flights of the imagination, and can be restrained
only with difficulty; there is so little difference between the
disciplined imagination which is reasoning, and the undisci-
plined imagination which is speculation that the mind passes

440 INTRODUCTION TO PHILOSOPHY OF SCIENCE

almost imperceptibly from one to the other. But the insta-
bility of phenomenalism lies not merely in the character of
the mind; the given itself offers hints of something beyond.
No phenomenalism can fail to recognize the distinction be-
tween appearance and reality, yet the distinction, once ad-
mitted, compels one to abandon phenomenalism. Even
though reality is defined to be merely alternative appearances,
positivism must be forsaken; for the given then becomes not
that which is actually given, but that which is potentially
given as well, i.e., that which may be inferred to be given on
the basis of that which is given. To assert this, however, is
to abandon the phenomenalistic position and to admit the
legitimacy of the speculative problem. The views which
will be considered in this chapter are at one in their insistence
that the given is not to be identified with the obviously given;
the obviously given permits inference of greater or lesser co-
gency to a less obviously given. The fact that the inferred
realm is often spoken of as being "hidden," or as being "be-
hind" or "beneath" the more apparent world should not
lead to the impression that it is an unknowable world, or
that it is a product of the purely creative imagination. It is
always knowable at least inferentially (sometimes directly
as well as inferentially), and it cannot be purely imagi-
native for its character is determined by certain data; if
the data were different the inferred realm would have a
different character. Concern with the speculative problem
of the nature of reality is nothing more than the frank
recognition that the hints which events give as to the
existence of other events beyond themselves are to be
taken seriously, and are to be followed out to see where
they lead.

The second feature to which attention should be called is
the possible ambiguity associated with the word "reality."
Unquestionably the word is essentially vague, and much
could be accomplished by following the suggestion of the
logical positivists and abolishing it entirely from the phil-
osophical vocabulary. What should be noted is merely the

THE NATURE OF REALITY 441

tendency in any explanatory act for the explaining entity
to assume greater importance than the explained entity.
Explaining is almost always assumed to be equivalent to
explaining away. When heat has been explained in terms of
molecular motion there seems to be no further occasion to
refer to heat since the molecules have taken its place; hence
heat is put into a subjective realm, or a realm of appearance,
and the molecules are located in the "real" world. That
which is logically more basic seems necessarily more funda-
mental in the structure of the world; consequently it tends
to displace that which is psychologically more primitive.
The most real aspect of the world then becomes not that
which is most obviously given, but that from which the given
can be derived by logical processes. The given then becomes
appearance, and the logically basic becomes reality. It is
only in this sense that the speculative problem may be said
to be a search for reality. In each case there is a search for
something beyond the obviously given in terms of which it
may be rendered intelligible. When this has been found,
and when it has been shown to explain the given, it takes on
a greater importance than the given and becomes thereby
more real. Nothing of a more metaphysical character should
be attributed to the word "real" than this.

The third feature of the speculative problem is the religious
tinge which is commonly given to it. The "reality " which is
found is frequently identified with the God of the religious
experience. The reasons for this identification are well
recognized, and probably, in ^ome sense, justify it. But
this close association of an emotional ideal with a more or
less rational hypothesis results in a certain amount of con-
fusion. It turns out, more often than not, that the essential
grounds for inference to a realm "behind" the given are
not the feature of science to which acknowledgment is made
but a much more subtle intuitive or mystic experience. As
a result the problem is not one of inferring to a realm of
reality but rather one of reconciling the facts of science
with the information disclosed by the emotional experience.

442 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Science does not prove God, though the religious experience
does; and the problem is to fit God into a scientific scheme
in which he is not obviously present. This makes the specu-
lative problem less an inference from the facts of science
and more an inference from the facts of religion or intuition.
There is probably something of this in all of the writers to
be examined. It does not necessarily invalidate their results,
but it makes their conclusions somewhat less directly depend-
ent on science.

In considering the various solutions to the problem of the
nature of reality it will be well to follow the outline suggested
in Chapter XVII. Accordingly, an attempt will be made in
each case to show (a) what the initial data are, (b) what the
character of the inference is, and (c) what the nature of the
inferred realm is.

SPIRITUAL IDEALISM

The data with which Eddington starts are such as con-
stitute the world-view of the sophisticated common sense
man, who proves to be really the scientist himself. For such
an individual the world consists of two kinds of objects,
with an important relation between them. On the one hand
there are the objects of everyday experience. Eddington
suggests that every conscious being is involved in a story,
which the perceiving part of his mind tells him of a world in
which he lives. This world contains familiar objects such as
colors, sounds, and scents, which are located in a boundless
space and in a stream of time.1 Consider, for example, such
a thing as a table. It would ordinarily be described as having
extension, as being comparatively permanent and colored,
and especially as being substantial.2 But there is another
world — the world of scientific objects. Physics contradicts
the story-teller. Science tells us that the table is not a sub-
stantial desk, not the continuous substance which it is sup-
posed to be according to the story. On the contrary it is a
mass of electrical charges in rapid motion. It is more like

1 New Pathways in Science, p. 1. 2 Nature of the Physical World, p. ix.

THE NATURE OF REALITY 443

a swarm of gnats than a substantial object.1 The specula-
tive problem begins, therefore, not with the fact of objects
but with the fact of duplicate objects. There is not only
heat but molecules, not only substantiality but disembodied
electric charges, not only colors but electro-magnetic waves.
What prove to be the real data upon which the speculative
problem builds, however, are certain facts pertaining to the
relation between these realms. The task of science is that of
constructing a world which is to be symbolic of the world of
commonplace experience.2 This must be a "world which
will imitate the actual behavior of the world of familiar
experience." 3 Using the word "infer" in a somewhat broad
sense science may be said to infer its description of the
external world from the facts of sense experience.4 This
determines an important relation between the realms. In
the vocabulary of the physicist one finds such words as
"length," "angle," "velocity," "force," "potential," "cur-
rent," etc., which are called "physical quantities." It is now
being asserted that these should be defined no longer in terms
of any metaphysical significance which may have been
attached to them but according to the way in which they
are actually identified when we are confronted with them.5
But how do we recognize them? By reading scales, dials,
clocks, and other measuring devices. In other words the en-
tities of science prove to be nothing but pointer readings
on recording instruments. Eddington's famous illustration
of the method of science in the problem concerning the ele-
phant sliding down the grassy hillside has already been
quoted.6 All of exact science consists of similar pointer
readings and other indications on instruments. The concep-
tions of objects which function in our common view of the
world do not enter into exact science. Science must replace
such conceptions by quantities representing the results of
physical measurement.7

1 New Pathways in Science, p. 1. B Nature of the Physical World, p. 254.

2 Nature of the Physical World, p. xiii. 6 Pp. 15-16.

3 Ibid., p. 249. 7 Ibid., p. 253.

4 New Pathways in Science, p. 9.

444 INTRODUCTION TO PHILOSOPHY OF SCIENCE

This fact has important implications for a theory of real-
ity, since it puts definite limitations on the scope of physical
knowledge. Our knowledge of the properties of a body con-
sists merely of the responses of various metrical indicators
to its presence. Beyond this knowledge cannot go. If one
could get the responses of an object to all sorts of devices —
scales, clocks, meter sticks, thermometers, etc., — he would
know it completely in relation to its environment. All that
he could not know would be its "inner un-get-at-able "
nature.1 Hence it turns out that the world of scientific ob-
jects becomes not only symbolic of the world of experience
but merely a 'shadow' world 2 without the substantiality
of the world of everyday objects. It is only such knowledge
of that world as we should have of a game of chess if we
knew merely the rules of the game and not the nature or
appearance of the chessmen,3 or such knowledge as we should
have if we knew only the structural form of the world and not
its content.4 Our conception of the physical world today is
essentially hollow. It is merely a system of symbols connected
by mathematical equations. Such a scheme, Eddington
maintains, is essentially a skeleton, and proclaims its own
hollowness.5 In fact, if anyone knew the method of the physi-
cist in advance he would be able to foretell the kind of world
which would be revealed through the use of this method.6

Such are the data of the speculative problem. What of
the inference? It appears that the nature of scientific sym-
bols hints at a reality which is non-metrical. The hollow
world "can be — nay it cries out to be — filled with something
that shall transform it from skeleton into substance, from
plan into execution, from symbols into an interpretation of
the symbols."7 A wave is an abstraction which may be filled
with a variety of contents; there may be waves of water,
waves of air, waves of ether, and waves of probability.
Physics shows only that the world is made up of waves, and

1 Ibid., p. 257. < Ibid., p. 200.

2 Ibid., p. xiv. 8 New Pathways in Science, p. 313.

3 Space, Time, Gravitation, p. 184. 6 Nature of the Physical World, p. 271.

7 New Pathways in Science, p. 314.

THE NATURE OF REALITY 445

leaves one to determine through some other avenue what
kind of waves these are.1 It is readily seen, therefore, that
the knowledge with which physics deals is inadequate to
the understanding of the human spirit in its broader aspects.
One could not live in the scientific world of pointer readings;
such a realm could be happily inhabited only by a symbol.2
But man is more than a symbol, and many of the aspects of
his life and activity take him beyond the outlook of physics.3

But where do we get a more specific indication as to the
character of this residue of reality ? Here we recognize for
the first time that the data upon which the solution to the
speculative problem is based are not to be found exclusively
in science. Scientific symbols would presumably permit us
to infer only a scientific world. But there seem to be two
important kinds of knowing which are outside of science.
One is the mystic experience. In it "we catch something of
the true relation of the world to ourselves — a relation not
hinted at in a purely scientific analysis of its content." 4
This intimate and personal knowledge will not permit itself
to be symbolized or codified; when we attempt such analysis
we find that the intimacy is lost.5 The mystic experience is
such as occurs to us under the starry heavens in the moments
just before daybreak, or when we pause for a minute on
Armistice Day to commemorate those who died in the war,
or when we are carried away by a great poem. Such expe-
riences give us an insight into something which is not science,
and which is incompatible with it if science is presumed to
give us a knowledge of the inner nature of things. Yet the
mystic experience reveals something which cannot be omitted
in a total picture of the world.

The second sort of knowledge is the knowledge of our-
selves. An individual knows that he thinks with a certainty
far beyond that which he can attribute to any physical
knowledge. This fact of thinking must be investigated.
Suppose the physicist undertakes to solve the problem. He

1 Ibid., p. 320. 3 New Pathways in Science, p. 316.

2 Nature of the Physical World, p. 324. 4 Nature of the Physical World, p. 320.

6 Ibid., p. 322.

446 INTRODUCTION TO PHILOSOPHY OF SCIENCE

brings his instruments and begins to explore. What does he
find? Merely atoms, electrons, and fields of force, all ar-
ranged in a spatio-temporal system. His knowledge of think-
ing proves to be just like his knowledge of inorganic objects.
If he explores further he finds only such things as energy,
temperature, and entropy — none of which proves to be
thinking itself. What, then, is to be done with thought? Is
it to be waved aside as an illusion? There seems to be no
reason for this. For there is nothing in his knowledge of
atoms that makes it impossible for them to be at the same
time thinking objects. Science does not talk about the in-
trinsic natures of things. An atom is a schedule of pointer
readings. Presumably, however, it is not merely a schedule
of pointer readings. There must be some unknown back-
ground to which the symbol is attached. Now in the case of
introspective knowledge I know what this background is.
It is precisely that spiritual nature which I discover when I
examine thinking independently of science. Hence the two-
fold character of my knowledge of my own thinking permits
me to fill in the scheme of pointer readings with a definite
content. This content is something which may be called
"mind' or "consciousness." ! One might almost say that
modern science "had deliberately left room for the reality
of spirit and consciousness." 2

The character of the inference can now be clearly seen.
It is analogical. Both mind and nature are such as to be
describable through metrical symbols; but mind is also such
as to be describable in qualitative terms; hence nature is
susceptible of a similar description. Nature, therefore, may
be presumed to be like mind in its essential stuff. But our
knowledge of this realm is not merely analogical, since we
are immediately acquainted with it in the mystic experience.
Hence we know it both indirectly and directly.

The nature of the inferred realm is thereby determined.
The 'stuff' of the world is mind-stuff.3 Just what this

1 Ibid., pp. 258-259. 2 New Pathways in Science, p. 320.

3 Nature of the Physical World, p. 276.

THE NATURE OF REALITY 447

proves to be is somewhat vague. It is not to be identified
with consciousness,1 and is something more general than our
individual minds.2 However, it may be interpreted in terms
of personality,3 and is that with which one has contact
through the mystic experience. The mind-stuff is not spread
out in space and time, for the latter are metrical notions
associated with pointer readings. In fact the stuff of the
world proves to be just those features which elude metrical
methods — significance and values, beauty and melody, truth
and untruth. When the human heart, perplexed with the
mystery of existence, cries, "What is it all about?," the an-
swer cannot be given in terms of pointer readings. The
satisfying answer is in terms of "a spirit in which truth has
its shrine, with potentialities of self-fulfillment in its re-
sponse to beauty and right. Shall I not also add that even as
light and color and sound come into our minds at the prompt-
ing of a world beyond, so these other stirrings of consciousness
come from something which, whether we describe it as beyond
or deep within ourselves, is greater than our own personality. ' ' 4
It can be readily seen that this world of mind-stuff is not
really demonstrated on the grounds of science. Science does
not — in fact, science cannot — tell us of this world. Only intro-
spection and the mystic experience can do this. But science
permits such a world as this to exist by virtue of the character
of its symbols; scientific symbols are "hollow" and therefore
refer only in a highly abstract way to objects. But this resi-
due of objects, which is not represented in the symbols, must
be mind-stuff. Thus the conclusion from the nature of sym-
bols to the character of the real world is based upon the
inadequacy of symbolic representation. Because symbols
are unlike their referents, the real world cannot be like our
symbols of it; hence, since our symbols are mathematical,
the world itself cannot be mathematical. The nature of this
inference should be clearly seen, since it has an interesting
contrast in the position of Jeans, to be examined immediately.

1 Ibid., pp. 277-278. 3 Science and the Unseen World, p. 50.

- Ibid., p. 276. 4 New Pathways in Science, pp. 317-318.

448 INTRODUCTION TO PHILOSOPHY OF SCIENCE

MATHEMATICAL IDEALISM

Jeans begins, as does Eddington, with the general fact of
science as a system of symbols attempting to portray the
character of a world which is directly revealed. But the given
world proves to be one of shadows, not realities. In terms
of Plato's famous figure, man is imprisoned in a cave with
his back to the light, and he cannot observe reality but must
rest content with watching the shadows as they play on the
wall. The task of science is the task of the man in the cave,
viz., to classify and explain the shadows in the simplest pos-
sible way.1 Many historical attempts to explain the shad-
ows have failed. Primitive man tried anthropomorphic
concepts, and the science of the last century employed me-
chanical concepts. Both of these attempts proved unsuc-
cessful. But we have at last discovered an interpretation
which seems to be adequate. We find that every successful
picture of nature which we now draw is mathematical.2 This,
then, must be the magic key which unlocks reality, and our
only conclusion must be that nature itself is somehow more
congenial to the concepts of pure mathematics than to those
of biology or of engineering. This is not to deny that mathe-
matics may, in turn, be a man-made mold. But this sym-
bolic scheme "fits" nature in a way which surpasses those
already tried.3

It appears, then, that the shadow world is the world of
familiar objects. But science is not content with merely
accepting this realm as given; it attempts to explain. The
result of this attempt is the disclosure of a new realm which
might be called the realm of scientific objects, or symbols.
Here we find such things as differentials and integrals, space
which is curved and expanding, waves of probability and
entropy. An examination of these entities reveals their
mathematical character; in fact, it shows them to be
not merely mathematical but objects of pure mathematics.
As such they could not have been derived from our experience

1 The Mysterious Universe (New York: Macmillan, 1932), p. 151.

2 Ibid., p. 150. 3 Ibid., p. 158.

THE NATURE OF REALITY 449

of everyday objects, but must be pure creations. Examine
some of them — finite space, empty space, expanding space,
seven-dimensional space. What are these but structures of
pure thought? Or consider the notion of a sequence of events
following a probability rather than a causal sequence. What
can this be but a pure mathematical creation, "incapable of
realization in any sense which would properly be described as
material? " x Whatever is created out of pure thought must
be pure thought.

But, granting that this is the starting-point for Jeans's re-
flections, his conclusion is quite different from that of Edding-
ton. Both astronomers recognize, apparently, that scientific
knowledge is merely symbolic. But it is not clear from their
writings whether they are conscious of the nature of symbolic
reference. As has already been seen in Chapter III, every
symbol aims to represent its referent, and thus may be said
to be in some sense "like" its referent; but no symbol is able
to portray all of the features of the referent, hence is obliged
to omit one or more of them. Given any symbol, therefore,
one may infer the referent, since the symbol resembles it, but
not all of the referent, since the symbol is an abstraction.
Jeans accepts the former but forgets the latter; Eddington
accepts the latter but forgets the former. Hence for Jeans
the fact that scientific symbols are mathematical permits one
to infer that reality is mathematical, but for Eddington the
same fact argues for a non-mathematical residue.

Through this mode of inference Jeans arrives at the con-
clusion that reality is a world of pure thought. But it is not
the same type of thought which Eddington finds. The uni-
verse exhibits evidence of a designing power, which has much
in common with our individual minds. But it is not emotion,
morality, or esthetic enjoyment which we discover in nature.
Instead it is something which we find hard to describe, but
which we may characterize as "mathematical thinking." 2
The Great Architect of the Universe appears, when we ex-
amine his work, not as a personal being but as a pure mathe-

i Ibid., p. 166. 2 Ibid., pp. 186-187.

450 INTRODUCTION TO PHILOSOPHY OF SCIENCE

matician. l The conclusion is analogous to that of Berkeley,
who was led to suppose an Eternal Being as the locus of all
objects.2 Such a view does not reduce the world of science to
the status of hallucinations or dreams, for whereas the latter
are the creation of the individual mind the former is the
creation of the universal mind, of which "the uniformity of
nature proclaims the self-consistency." 3 Yet the view does
much to overcome the dualism between mind and matter.
The supposed hostility disappears "not through matter be-
coming in any way more shadowy or insubstantial than here-
tofore, or through mind becoming resolved into a function of
the working of matter, but through substantial matter re-
solving itself into a creation and manifestation of mind." 4
There is no longer any problem in understanding the way in
which mind can grasp nature, 'for it reduces merely to a
contact between mind and a creation of mind — like the
reading of a book, or listening to music." 5

The position of Jeans is somewhat less speculative in char-
acter than that of Eddington. Jeans does not bring in the
extraneous facts of introspection and the mystic experience,
and consequently his position may be said to follow more
directly from the facts of science. One can hardly deny the
effectiveness of mathematical symbols in the explanation of
the data of science. But that this argues for a mathematical
reality "behind" the world of everyday objects — which then
become shadows — is somewhat questionable. Certainly
Jeans places too much emphasis on the "pure" character of
these mathematical notions; though they are not such as can
be exemplified in the gross objects of experience, and hence
seem to be simply creations of the mind, nevertheless they
can easily be shown to be derivable from these gross objects
provided one admits the legitimacy of certain abstractive
operations. This makes the "Great Architect" much less
a creature of pure thought, remote from experience, and
much more a creature in and of the actual world. Other
criticisms of Jeans's position will occur readily to the reader.

» Ibid., p. 165. 2 Ibid., p. 170. 3 Ibid., p. 175. 4 Ibid., p. 186. 6 Ibid., p. 178.

THE NATURE OF REALITY 451

It is in sharp contrast with another position, to be examined
immediately, viz., that of Bergson.

CREATIVE EVOLUTION 1

In both method and content, the position of Bergson bears
closer kinship to that of Eddington than to that of Jeans. All
three would agree that the character of the scientific method
determines the character of the world which is disclosed there-
by; but whereas Jeans insists that the world thus revealed
is reality, Eddington and Bergson insist that it cannot be.
Science, according to the latter, gives only a partial, and to
that extent erroneous, view of reality. Hence whereas Jeans
concludes as to the nature of reality from the adequacy of
symbols, Eddington and Bergson both conclude as to its
character from the inadequacy of symbols.

The primary data for Bergson are concepts and the con-
ceptual method, which constitute, respectively, the tools and
techniques of science. Now the characteristic method of
science is analysis.2 "Analysis ... is the operation which
reduces the object to elements already known, that is, to
elements common both to it and other objects." 3 "The
different concepts that we form of the properties of a thing
inscribe round it so many circles, each much too large and
none of them fitting it exactly."4 "Simple concepts have
. . . the inconvenience of dividing the concrete unity of the
object into so many symbolical expressions." 5 "These con-
cepts, laid side by side, never actually give us more than an
artificial reconstruction of the object, of which they can only
symbolize certain general, and, in a way, impersonal aspects;
it is therefore useless to believe that with them we can seize
a reality of which they present to us the shadow alone." 6

The real difficulty with the method of analysis is that it
substitutes for 'the real and internal organization of the
thing" something which is merely 'an external and sche-

1 The position of Bergson has already been considered briefly in another context.
See above, pp. 18-20.

2 Introduction to Metaphysics, p. 8.

3 Ibid., p. 7. * Ibid., p. 19. 5 Ibid., p. 21. c Ibid., pp. 18-19.

452 INTRODUCTION TO PHILOSOPHY OF SCIENCE

matic representation." 1 Analysis gives not parts of a whole
but merely notes of a total impression. For this reason, by no
act of reconstruction can one regain the whole upon which an
analysis has been performed; thought may proceed from
objects to symbols but it cannot retrace the route from
symbols to objects. Hence scientific knowledge is always
partial and relative, and to this extent erroneous. It sup-
poses that since an object has a number of aspects it is there-
fore itself a plurality; it endeavors to construct an object by
multiplying to infinity the abstract symbols in terms of
which it is portrayed; it attempts by representations which
are outside the object to get inside it.

One of the best illustrations of the inadequacy of the con-
ceptual approach to reality can be seen in the scientific
attempt to explain motion. Motion is analyzed into briefer
and briefer durations terminating in mere positions, which
represent the points through which the moving body passes.
Motion is then defined as a series of such positions. But from
a mere series of positions, argues Bergson, we cannot get
motion. The positions "are not parts of the movement, they
are so many snap-shots of it. . . . The moving body is
never really in any of the points ; the most we can say is that
it passes through them. But passage, which is movement, has
nothing in common with stoppage, which is immobility."
The points "are not, properly speaking, positions, but 'sup-
positions,' aspects or points of view of the mind." 2 Thus by
means of a characteristically scientific approach to reality
we find that we have lost that very reality; science is in-
capable of revealing the true nature of things.

It soon becomes clear that Bergson's theory of reality is
based not merely upon the inadequacy of scientific symbols.
As in the case of Eddington, Bergson finds the scientific
approach to be unsatisfactory because there is another
approach which seems to be more satisfactory. It seems
impossible to conclude that science fails to disclose reality
unless there is some other method which does disclose real-

1 Ibid., p. 27. 2 Ibid., p. 49.

THE NATURE OF REALITY 453

ity. This, for Bergson, is the method of intuition. "By in-
tuition is meant the kind of intellectual sympathy by which
one places oneself within an object in order to coincide with
what is unique in it and consequently inexpressible." 1 The
intuitive method is 'truly itself when it goes beyond the
concept, or at least when it frees itself from the rigid and
ready-made concepts in order to create a kind very different
from those which we habitually use; I mean supple, mobile,
and almost fluid representations, always ready to mould
themselves on the fleeting forms of intuition." 2 Intuition
gives us that which is essential and unique in the object; it
is that mode of knowing in which we are not merely ac-
quainted with the object, but united with it in that intimate
way which enables us to grasp its differentiating features.
Whereas concepts draw circles around objects, intuition re-
veals their individualities; whereas conceptual knowledge is
external, representing so many points of view, intuitive
awareness discloses the inner nature of things; whereas
symbolic knowledge is relative and indirect, intuitive knowl-
edge is absolute and direct.

When we recognize the complete range of data upon which
the solution to the speculative problem is based, there is
reason to doubt whether Bergson has really made an infer-
ence from the character of scientific symbols to the character
of reality. It is not scientific symbols which reveal the char-
acter of reality in a negative way, but the intuitive method
which reveals it in a positive way. There is probably an
analogical inference of somewhat the same kind as is found
in the case of Eddington, though it is not so clearly defined.
For Eddington inference may be made from the spiritual
character of mind, to the spiritual character of inorganic
nature; for Bergson the obvious inadequacy of static scien-
tific symbols in our attempt to understand the character of
certain types of object such as the self, motion, and growth,
argues for a similar though less obvious inadequacy in the
attempt to understand things in general; hence science may

1 Ibid., p. 7. 2 Ibid., p. 21.

454 INTRODUCTION TO PHILOSOPHY OF SCIENCE

be presumed, by virtue of the nature of its method, to lose
the significant features of things. In a word, because science
fails to reveal mobility in a realm where it is known to be
present, this method cannot be expected to reveal mobility
in a realm where it is not known to be present; hence reality
as a whole may be presumed to exhibit mobility.

The inferred realm is thus defined essentially in terms of
mobility and evolution. " Not things made, but things in the
making, not seK-maintaining states, but only changing states,
exist. Rest is never more than apparent, or, rather, relative.
The consciousness we have of our own self in its continual
flux introduces us to the interior of a reality, on the model of
which we must represent other realities. All reality, there-
fore, is tendency, if we agree to mean by tendency an incipient
change of direction." x Reality is duration, but duration which
is lived and not symbolized. "We can, no doubt, by an effort
of imagination, solidify duration once it has elapsed, divide
it into juxtaposed portions and count all these portions, yet
this operation is accomplished on the frozen memory of the
duration, on the stationary trace which the mobility of dura-
tion leaves behind it, and not on the duration itself." 2 This
reveals duration only as a multiplicity. "On the contrary,
when I replace myself in duration by an effort of intuition, I
immediately perceive how it is unity, multiplicity, and many
other things besides." 3 "Inner duration is the continuous
life of a memory which prolongs the past into the present.
. . . Without this survival of the past into the present there
would be no duration, but only instantaneity." 4 Reality is
thus a growing and evolving entity, characterized essentially
by motion, change, and emergence. Time is its most signif-
icant property. Its present is to be understood only in terms
of the past out of which it is passing, and the future into
which it is merging. It is not being, but becoming.

The essential similarity between the position of Rergson
and that of Eddington is obvious. Roth argue that symbols
are incompetent to portray the significant aspects of the

1 Ibid., p. 65. - Ibid., p. 22. 3 Ibid., p. 23. 4 Ibid., pp. 44-45.

THE NATURE OF REALITY 455

world — aspects which must be revealed, therefore, by some
method other than the symbolic one. For Eddington this
method is that of introspection and the mystic experience;
for Bergson it is intuition. Hence reality for Eddington is
essentially spirit and consciousness, while for Bergson it is
mainly growth, motion, and tendency. In both cases the
important datum offered by science is not a fact about the
world, but a fact about method; it is because science has an
improper method that it fails to grasp reality. For Jeans, on
the other hand, science has at last found the proper method,
hence is able to grasp reality. The fourth position to be
examined, that of the mathematician, Keyser, is established
upon slightly different grounds. Though it is a fact of method
which argues for the existence of a superrational realm, it is
a relatively specific kind of method rather than a general
feature of the symbolic approach as a whole.

LOGICAL REALISM

C. J. Keyser, too, feels that the importance of science lies
not so much in what it says as in what it suggests. Specula-
tion about the sciences is therefore a legitimate enterprise.
His main emphasis is upon a feature of the scientific method
— "Idealization regarded in the light of what mathemati-
cians call the method or the process of Limits. The central
thesis is that this process in the domain of reason or of ra-
tional thought indicates the reality and, in part, the nature
of a domain beyond, a realm superrational, and that this
realm is the ultimate and permanent ground and source of
the religious emotions." x

The data of the speculative problem are, for Keyser, of
two kinds. Though these are primarily features of method,
they are features of subject matter as well. On the one
hand, there is the fact of idealization. "The countless phe-
nomena in the world of sense form and present to us there
innumerable series or sequences having for their limits ideal
things that belong only to the world of reason: the realm of

1 Science and Religion (New Haven: Yale University, 1914), preface.

456 INTRODUCTION TO PHILOSOPHY OF SCIENCE

things perceived has for its border the realm of things con-
ceived." For example, "perfect solids, like perfect gases, are
nothing but limits, sheer ideals without existence in the
world of sense, pure concepts in the domain of reason."
These forms "are never actually realized in the subrational
world of sense: they are there but indicated as limits be-
yond." 1

On the other hand there is the method of limits, applied
within the realm of the rational. If there be inscribed in a
circle an equilateral triangle, then a regular hexagon, then a
polygon of a dozen sides, and so on, forever, there is created a
series of a certain type. ' In respect of size, these approach
nearer and nearer, as close as we please, to the size of the
circle's area, yet they remain inferior to it forever. And we say,
in technical language, that the circle's area is the sequence's
limit. It is important to note that the sequence's limit is not
a term in the sequence, for all these terms are polygonal
areas — shapes bounded by polygons — but that of the circle
is not, for the circle is not a polygon." 2 If the series of poly-
gons be called the Domain of Polygonal Areas, one may say
that the circle does not lie in this realm but upon its border.
"Here, then, we have a clear presentation, within a given
domain, of something that is not within: we have a clear
presentation, by the law of an inner sequence, of a limit on
the rim — of an ideal, if you please, which, so long as we
operate within the domain, may be aspired unto, approached
and pursued forever, but can never be attained." 3

These, then, are the data : two types of serial order exhibit-
ing limits. In the one case the limit is outside of the realm in
which the series itself resides; in the other the limit is within
the realm though outside of the series itself. What is com-
mon to the two cases is the fact that a serial principle of a
certain kind apparently affords a basis for an inference be-
yond the series itself to an entity which is demanded by the
series yet exhibits properties essentially different from the
members. Keyser's next step is to generalize this principle

1 Ibid., pp. 61-63. 2 Ibid., p. 55. 3 Ibid., p. 56.

THE NATURE OF REALITY 457

to similar series in which the limit is not given. Hence his
inference is essentially analogical in character: Since series
in which the limit is not given are like the series in which the
limit is given, a limit may be presumed to exist also in the
former. This limit proves to be the realm of the super-
rational.

The application of this principle, however, demands that
the author "produce in the world of logical thought rational
sequences that, by the law of their formation and progress,
approach and betray as a border-domain a region of reality
from which the dominion of logic is forever barred." x He
finds no difficulty in locating such instances. One has simply
to arrange all classes into a series upon the basis of compre-
hensiveness; such a series would have for a limit the class of
all things. But such a class would be a very peculiar thing,
for it would have to contain itself — something which cannot
occur without contradiction in the world of familiar logic.
Hence the fact that there are things demands that there be
a universe which includes everything, yet this universe must
be significantly different from the things which it contains.
Another example can be found in the arrangement of proposi-
tions into a series, each proposition being the joint affirma-
tion of the proposition immediately preceding it and some
other proposition, until the limit is reached which would be
the joint affirmation of all propositions. This, again, is itself
a very peculiar proposition, for it must make an affirma-
tion about itself — a fact which is forbidden in the realm of
the rational. Hence the fact that there are propositions
demands that there be a proposition of a type which is
significantly different from the elements which required its
existence.

Situations of these types are characteristic of the rational.
" In every category where the laws of reason reign we find
that the great process of Idealization points aloft to some
form above the laws: we find that — like the Class of all
Classes, like the Joint Affirmation of all Propositions, like the

1 Ibid., p. 64.

458 INTRODUCTION TO PHILOSOPHY OF SCIENCE

Logical Sum of all Relations, like Omniscience, like Beauty
Absolute — so, too, Eternity or Fate, Unconditioned Free-
dom or Self-determination, Perfect Justice, Universal Har-
mony, the Goodness of God, Felicity Divine, and many other
supreme ideals and supreme perfections of rational experi-
ence and thought, are all of them forms of Being absolute,
constituting an Overwork!, a realm Superrational." *

Unfortunately Keyser has not told us any of the details of
this Overworld. To debate its existence is vain. It is not
only demanded by the rational, but required also by our
aspirations. "In some sense, whatsoever quickens, lures
and sustains, exists." 2 As to its nature, we are left more
or less completely in the dark. Since it is superrational we
are not entitled to ask that it be described. All that we can
know is that it differs from the rational in the same way that
a perfect lever differs from actual levers, and a circle differs
from the series of polygons. But there seems to be no princi-
ple according to which the nature of this difference can be
ascertained. Hence we cannot conclude, for example, from
the nature of human knowledge to the nature of Omniscience.
But we can argue that Omniscience need not be the same as
finite knowledge, hence the fact that human knowledge im-
plies a realm of the unknown within which it operates is in
no way incompatible with true Omniscience. Beyond this we
cannot go in the penetration of the Overworld. For the
rest we must remain satisfied with the fact that it sheds
"a mystic radiance like the 'obscure clarity that falls from
the stars.'" 3

The most interesting feature of Keyser's position is the
way in which he endeavors to follow out the hints which the
realm of obvious data offers of something beyond itself.
Phenomenalism insists that the given should be limited
strictly to that which is clearly given. But what is one to do
with hints? Is the fact that a datum suggests something be-
yond itself part of that datum? The way in which a series of
elements suggests its own limit is quite compelling. But

i Ibid., p. 73. 2 Ibid., p. 75. 3 Ibid., p. 74.

THE NATURE OF REALITY 459

should this limit be included within the realm of data by
virtue of having been suggested in this forceful way? An ex-
treme phenomenalism would say, no; a moderate phenome-
nalism would be in doubt; a realism would say, yes. Keyser
deserves credit for having attempted to make as precise as
possible the character of the suggestion. Certainly a more
critical analysis of the notions of series and limits would
help to throw the problem in its proper light. But this is not
the place to make that analysis. Keyser's formulation at
least outlines the problem, and suggests the direction for
further consideration.

What may be said, in conclusion, as to the general charac-
ter of these solutions to the problem of reality? They are
hardly such as to impress a critical mind, and one might
easily condemn them to oblivion on these grounds. But in
taking this attitude one should note two facts with reference
to them. The first is that they are commonly put forward
merely as speculative conclusions, having a greater rather
than a lesser degree of probability; they are not final solu-
tions but merely somewhat plausible suggestions. They
must, accordingly, be estimated from this point of view.
The second fact is that they do suggest further problems of a
more critical nature. It seems quite clear that the conclu-
sions considered in the foregoing pages can be either more
firmly established or greatly weakened by a more careful
analysis of the scientific knowing techniques in general, and
of symbols in particular. Hence recognition should be made
of the fact that the problem of the nature of reality, as the
other speculative problems, rests upon the more critical
problems of the philosophy of science. It seems likely, there-
fore, that the problems of the immediate future are the criti-
cal rather than the speculative ones. Fortunately, the atten-
tion of investigators has been increasingly directed in recent
years to problems of formal logic and the general theory of
symbols; to problems of actual scientific methodology; and
to problems of the foundations and interrelations of the
sciences. These offer great promise for the future.

460 INTRODUCTION TO PHILOSOPHY OF SCIENCE

REFERENCES

A. S. Eddington, Space, Time, Gravitation (Cambridge: Cambridge

University, 1920).
Science and the Unseen World (London: Allen and Unwin,

1930).

—Nature of the Physical World (New York: Macmillan, 1929).
-New Pathways in Science (New York: Macmillan, 1935).

James Jeans, The Mysterious Universe (New York: Macmillan,

1932).

New Background of Science (New York: Macmillan, 1933).

H. Bergson, Introduction to Metaphysics (New York: Putnam,

1912).
C. J. Keyser, Science and Religion (New Haven: Yale University,

1914).
Herman Weyl, Mind and Nature (Philadelphia: University of

Pennsylvania, 1934).

The Open World (New Haven: Yale University, 1932).

Hugh Elliot, Modern Science and Materialism (London: Longmans,

Green, 1919).

INDEX

A- M- B- P - 0 analysis of percep-
tion, 89-102; diagrams of, 92, 94.

Abstraction, 74-5, 250, 251, 256, 270,
275, 297, 301, 302, 321, 356; ex-
tensive, 299, 300; level of, 246-8;
and classification, 184; see Gen-
eralization.

Abstractive method, 190; distin-
guished from hypothetical, 183-4;
as method of construction, 184-5.

Act of discovery, see Scientific dis-
covery.

Ad hoc explanation, 186.

Aliotta, A., 77.

Ampere, A. M., 180.

Analogy, 188-9.

Analysis, 188, 193-4, 250; vs. intui-
tion, 18-20.

Analysis of scientific concepts, see
Scientific concepts.

Approximation, 357-8.

Archimedes, 176.

Aristotle, 5, 409, 433.

Awareness, 50, 52-3, 90-102; as
transforming, 53, 98, 99-100, 105-
6; error in, 97; inferential, 94-101;
see Knowledge.

Bacon, F., 57, 59, 127, 224, 371, 409,

439.
Barry, F., 230.
Bavink, B., 14 and n., 20, 115 and

n., 148, 150, 167-70, 172, 183, 184,

203, 346, 369 n.
Beethoven, 433.
Benjamin, A. C, 38, 60, 77, 146, 195,

213, 247, 417.
Bergson, H., 18, 19, 20, 147, 394, 397,

451-5, 460.
Berkeley, 339.
Bernard, C, 244.
Betweenness, 255.

Bliss, G. A., 368 n.

Bliss, H. E., 400 n., 401 n., 403 n.,

406, 408 n., 409, 410, 412-5, 416,

417.
Bridgman, P.W., 148, 150, 154-8, 171,

333 n.
Broad, C. D., 33 and n., 34, 36, 38,

237, 248, 252, 311, 318, 324 n., 325,

336, 345, 396.
Buchanan, S., 77.
Burtt, E. A., 126, 230, 420 n.

Campbell, N., 112 n., 133, 200, 213,
233, 383.

Carmichael, R. D., 177 and n., 194,
213.

Carnap, R., 11-2, 20, 148, 150, 164-7,
172, 219.

Cassirer, E., 183 and n.

Cause, Chap. XVI; as concomitant
variation, 370-2; Hume on, 351-2
not required at scientific level, 369
74; present state of in science, 374
Whitehead on, 352-3; and indeter-
minism, 376-83; and law, 348, 351
and temporal asymmetry, 372-4.

Cause and effect inference, 193, 250.

Chapman, F. M., 146, 213.

Classification, 121-2; diagnostic, 136;
in descriptive science, 133-7; and
abstraction, 184.

Classification of the sciences, 388, 391,
395, Chap. XVIII; Bliss's illustra-
tion of, 414-5; definition of, 400;
difficulties of, 403-8; empirical
nature of, 404-5; general character
of, 399-403; historical illustration
of, 408-9; logical form of, 402;
motive for, 400-1; orders of sciences
in, 406-7; Peirce's illustration of,
411; terminological difficulties of,
498-9.

461

462

INDEX

Clusters of experience, 89-90.

Cohen, M. R., 37 and n., 38, 112 n.,
126.

Collective properties, 262.

Compton, A. H., 379 and n., 380 n.,
393, 397, 418, 419, 428-32, 436,
437.

Comte, A., 8, 9 n., 409, 411, 412.

Concepts; analysis of, Chap. XII;
list of theories of, 148; relation of
to data and knowing, 148-9;
theories of, Chap. VIII; and con-
structionalism, 158-60; and con-
ventionalism, 160-3; and logical
positivism, 164-7; and measure-
ment, 114-5; and operationalism,
154-8; and scientific realism, 167-
70; and strict empiricism, 151-4;
see Symbols.

Concretive techniques, 190-1.

Confirmation, 222, 223-30; and per-
ception, 224-5; and probability,
361.

Connexity, 258.

Construction; method of, 185, 215,
297; techniques of, 187, 188, 189-
92; and explanation, 186.

Constructionalism, 148, 158-60, 170.

Content of symbols, 237; difficulties
in ascertaining, 245-50.

Continuum, 260.

Conventionalism, 148, 150, 160-3,
170.

Correlation, 123-4, 184, 297, 300-1;
in descriptive science, 138-9; see
Law; Functional correlation.

Creative evolution, 451-5.

Creighton, J. A., 126, 230.

D'Abro, A., 306 n., 307 n., 309 n.,
311.

D'Alembert, J. L., 249.

Dante, 433.

Dantzig, T., 278.

Data, 80-1, 101-2; difficulty of
getting, 125-6; variably given, 131-
4, 243-4; see Descriptive tech-
niques; Given.

Definition; function of, 1; in explan-
atory science, 210; nature of, 248;
need for, 68; on empirical level, 244.

Dense series, 259-60.

Descartes, 180.

Description; definition of, 120; and
explanation, 197-200; vs. explana-
tion, 8-11; see Symbolism of data;
Descriptive techniques.

Descriptive science, Chap. VII; def-
inition of, 134; difficulty of deter-
mining, 131-2; existence of, 128-9,
145-6; extensional features of,
130-9; intensional features of, 139-
45; method of, 134-5; more or less
descriptive, 131-4; non-explana-
tory, 144-5; order of elements in,
139-41; propositions of, 141-2;
sensitive to new discoveries, 143-4;
structure of, 139-40; symbolic
nature of, 130-1; and science, 144;
and scientific law, 138-9.

Descriptive techniques, Chap. VI;
classification of, 104; function of,
103-4; see Data; End-object; Phys-
ical medium; Sense organs; State
of mind.

Determinism, 376-8, 380, 381-2;
see Human freedom; Indetermin-
ism.

Dewey, J., 60, 146.

Dingle, H., 183, 184 n., 185.

Discovery, 107; experiments of, 107,
225; see Logic of discovery; Psy-
chology of discovery; Scientific
discovery.

Discrete series, 259.

Distributive properties, 262.

Dotterer, R. H., 146.

Ducasse, C. J., 384.

Eaton, R. M., 60, 68 and n., 77,
248 n.

Eckart, Carl, 286 n., 379 n.

Eddington, A. S., 15, 16 n., 28, 85
and n., 87, 97, 100, 101, 102, 110,
117, 192, 241, 247, 288, 296, 306 n.,
310 n., 373 and n., 379 and n.,

INDEX

463

384, 388, 393, 394, 396, 397, 398,
425-8, 436, 437, 442-8, 449, 450,
451, 452, 453, 454, 455, 460.

Einstein, A., 28, 183, 206 and n.,
309 n., 379, 382.

Elliot, H., 460.

Empirical foundation of symbols,
237, 240; difficulties in ascertain-
ing, 243-5.

Empirical necessity, 354-5.

Empirical space, 289-96; anisotropy
of, 295-6; discreteness of, 291— 3|;
finitude of, 293-4; non-homoge-
neity of, 294-5; plurality of, 291;
relativity of, 289-90; transforma-
tion into scientific space, 296-303.

Empirical time, 289-96; anisotropy
of, 295-6; discreteness of, 291-3;
finitude of, 293-4; non-homoge-
neity of, 294-5; plurality of, 291;
relativity of, 289-90; transforma-
tion into scientific time, 296-303.

End-object, 90-102; change of loca-
tion of, 107-9; changes in, 105-7,
109-10; control of, 104-9; known
only potentially, 106-7; see Phys-
ical medium.

Enriques, F., 195.

Entropy, 373, 374.

Euclidean space, 24-5, 281-9, 317;
continuity of, 282-4; derivation
from empirical space, 296-303;
homogeneity of, 285-6; infinity of,
284-5; isotropy of, 286-9; objec-
tivity of, 281-2; singleness of, 282.

Event, 50.

Experimentation, 107, 225-7, 229.

Explanation, 186; as implication, 200;
as greater familiarity, 200-2; as
purely verbal, 202-4; in descrip-
tive science, 144-5; nature of, 197-
205; types of, 204-5; and descrip-
tion, 197-200; and realism, 203-4;
and verification, 198; vs. descrip-
tion, 8-11.

Explanatory science, Chap. X; also
descriptive, 205-7; constituents of,
205-6; distinguished from descrip-

tive science, 198-200; examples of,
196; explanation in, 212-3; exten-
sional features of, 204-8; high
integration of, 208-10; intensional
features of, 208-13; and symbolism
of obscurely given, 207-8.
Extension; of classes, 122; of symbols,
66-7; and descriptive science, 130-
9; and explanatory science, 205-8;
and intension, in descriptive
science, 142-3; and intension, in
explanatory science, 210-1.

Faraday, M., 73, 175, 176 n.

Fictionalism, 148, 158-67.

Fine, H. B., 267 n.

Flint, R., 38, 408 n., 417.

Force, 323-7; as quantitative, 327
difficulties in discussion of, 323-4
empirical foundation of, 324-7
measurement of, 333-6; opera-
tional definition of, 331-7; psycho-
logical or objective, 325; relation
to events and motion, 325-7;
scientific content of, 327-31; and
Newton's laws of motion, 328-31.

Frequencies, statistical, 362-3.

Function, 368.

Functional correlations, 368-74.

Gauss, K. F., 176.

Generalization, 268, 356-7; see Ab-
straction.

Given, the, 53, 56-7; as variable, 131-
4, 243; controversies about, 438-9;
-necessity of inference from, 439-
40; see Data.

Gladstone, J. H., 176 n.

Goethe, 433.

Gore, G., 176 n., 194.

Gutenberg, 180.

Haldane, J. B. S., 389.

Hamilton, W., 176.

Hegel, 504.

Heisenberg, W., 28; principle of inde-
terminacy, 106, 378-9, 382, 419,
421, 432, 433, 434.

464

INDEX

Helmholtz, H., 177 and n.

Henle, P., 146, 213.

Herrick, C. J., 437.

Hilbert, D., 253.

Hobbes, 409.

Hobson, E. W., 38, 74, 148, 150, 158-
60, 162, 163, 164, 165, 167, 171,
252, 278, 311, 384.

Holt, E. B., 102.

Human freedom, problem of, 392-3,
Chap. XIX; ambiguity of, 418-9;
Compton on, 428-32; deterministic
solution of, 423-4; Eddington on,
425-8; general character of, 422-5;
Planck on, 432-7; relation of to
science, 419-22; requirements for
positive solution to, 424-5 ; urgency
of, 418.

Humboldt, F. H. A., 412.

Hume, 351, 354, 355, 370, 384.

Huntington, E. V., 258 and n., 259,
278.

Huxley, J., 389.

Hypothesis, 70; discovery of, 173-5;
four stages of, 214-8; modification
of, 227-8; prediction from, 221-2;
relation of to data, 181-2; and
verification, 214.; see Theory; Ver-
ification.

Hypothesis-formation, techniques of,
187-9, 192-4; see Verification.

Hypothetical method, 183-4, 185-6;
see Hypothesis-formation, tech-
niques of.

Icons, 72.

Idealization, 83, 357, 439, 455-9.

Images, 72.

Imagination, 175-6, 192-4.

Indeterminism, 376-83; argument of,
379-80; and Heisenberg principle,
378; see Heisenberg; Human free-
dom, problem of; Determinism.

Index symbol, 76.

Induction; problem of, 358-66; and
nomic necessity, 364-5; and prob-
ability, 359-63; and statistical law,
362-3; see Correlation.

Infirmation, 222; consequences of,
227-30; and probability, 361; and
verification, 223-30.

Innate ideas, 236.

Instant of time, 299-300.

Integration, of descriptive science,
139-44; of explanatory science,
208-12.

Intension; of classes, 122; of symbols,
66-7; and descriptive science, 139-
45; and explanatory science, 208-
13; and extension, in descriptive
science, 142-3; and extension, in
explanatory science, 210-1.

Interpolation, 83, 192, 357.

Interpretation of facts, 57-9.

Intuition, 18-20, 453-5.

Irreflexiveness, 258.

Irreversible processes, 287-9.

Isolation, 45, 69-70, 83, 110-2, 118.

James, W., 178.

Jeans, J. H., 28, 373 n., 388, 394, 447,

448-51, 455, 460.
Jevons, W. S., 57 n., 112 n., 127, 129,

136 and n., 138 n., 146, 230, 261.
Johnson, W. E., 271 n.

Kelvin, Lord, 73 and n.

Keplar, J., 180.

Keynes, J. M., 359, 360, 361, 362,
363, 384.

Keyser, C. J., 146, 213, 394, 455-9,
460.

KirchhofT, G., 8, 152.

Knower, the, 47, 48 n., 82; see Scien-
tist.

Knowing, the, 47, 56-60; see Descrip-
tive techniques; Perception; Scien-
tific discovery; Verification.

Knowledge, the, 47, 50-5, 61, 82; by
acquaintance and by description,
51-5; see Awareness; Descriptive
science; Explanatory science; Sym-
bolic schemes.

Known, the, 67, 48-50; see Data;
Given.

Koenigsberger, L., 177 n.

INDEX

465

Laplace, 377, 423, 434, 435.

Law, Chap. XVI; empirical founda-
tion of, 348-55; empirical neces-
sity of, 354-5; of coexistence and
of succession, 350-1, 368-9; opera-
tional definition of, 355-66; quali-
tative, 366-7; relation of to other
scientific concepts, 347-8; scien-
tific, 375-6; scientific content of,
366-76; statistical, 362-3; and em-
pirical correlations, 350-4; and
functional correlations, 367-76; and
indeterminism, 376-83; and nomic
necessity, 364-5; and probability,
359-63; and problem of induction,
358-68; see Correlation.

Lenzen, V. F., 70 n., 334, 335 n., 336,
341, 345, 383.

Leonardo, 433.

Levy, H., 45 n., 106 n., Ill n., 114 n.,
127, 437.

Lindsay, A. D., 269 n., 280 n., 286 n.,
288 n., 289, 322 n., 329 n., 335, 345,
367 n., 370 n., 373 n., 380 n., 383.

Lobachewski, N., 24, 25.

Locke, 224, 339, 409.

Lodge, O., 73 and n.

Logic of discovery, 181-9; existence
of, 181-2, 189; two problems of,
187.

Logic of science, 34, part I; see Log-
ical structure of science.

Logical positivists, 11-3, 148, 164-7,
170, 398, 440.

Logical realism, 455-9.

Logical structure of science, Chap.
Ill; clarity of, 45-6; importance
of knowing, 41-3; possibility of,
43-6; and scientists, 41-2; see
Science.

Lotka, A. J., 244.

Mach, E., 8, 74, 84-5, 102, 148, 164,

167, 171, 335, 351.
Magnitude, 271.

Margenau, H.; see Lindsay, A. D.
Mass, 331, 333-6, 343.
Mathematical idealism, 448-51.

Mathematical operation, 264-5, 266,
268, 270.

Mathematics, 24, 206, 246, 253, 267,
268, 270.

Matter, 337-45 ; empirical content of,
337-41; operational derivation of,
343-5 ; relation of to measurement,
343-4; scientific content of, 341-3;
summary of discussion of, 345;
variety of meanings of, 337-8.

Maxwell, C, 73, 219.

McClure, M. T., 127.

Meaning, 67-9.

Measurement, 112-4; conditions for,
113-4; importance of in science,
356; in descriptive science, 137-8;
in explanatory science, 209; and
basic concepts, 246-8; and force,
332-3; and law, 349-50, 356, 365,
366-7; and matter, 343-4; and
motion, 317-8; and quantity, 274-
6; and space-time, 305-6, 308.

Mental elements in perception, 90-
101.

Metaphysics of science, 34-5 ; part II.

Method of limits, 455-9.

Meyerson, E., 133, 148, 172.

Michelson-Morley experiment, 304,
308, 322.

Mill, J. S., 127, 148, 171, 226, 230,
339, 351, 359, 371.

Millikan, R. A., 396.

Mill's methods, 226, 371.

Mind, 224.

Modified positivism, 148, 149, 150,

- 158-67, 170.

Montague, W. P., 102.

Montmasson, J. M., 180, 195.

Motion, 312-23; absolute or relative,
318-9, 322-3; empirical definition
of, 313; empirical foundation of,
313-6; operational definition of,
321-3; relation of to measurement,
317-8; relation of to particle, 317;
scientific content of, 317-21; sum-
mary of discussion of, 323; and
change, 315-6; and relativity, 313-
4; and quantity, 316.

466

INDEX

Nagel, E., 112 n.

Nature, 103, 144-5.

Nature of reality, problem of, 480-1,
Chap. XX; ambiguity of, 440-1;
general character of, 439-42; in-
evitability of, 439-40; religious
aspect of, 441-2; and more critical
problems, 459.

Necessity in scientific law, 359, 363-5.

Needham, J., 437.

Neuman, C, 319.

Newton, Isaac, 5, 176, 180, 183, 219,
281, 282 n., 319, 322, 323, 324, 328
and n., 329, 334, 428.

Newtonian time, 281-9, 317; con-
tinuity of, 282-4; derivation from
empirical time, 296-303; homo-
geneity of, 285-6 ; infinity of, 284-5 ;
isotropy of, 286-9; objectivity of,
281-2; singleness of, 282.

Newton's laws of motion, 528-
31.

Nicod, J., 222 n., 351, 360, 361, 362,
363, 384.

Nomic necessity of law, 364-5.

Non-Euclidean geometry, 24.

Normal observation, 98-100, 116-8.

Number, 253, 260-71; dual reference
of, 260-1; empirical foundation of,
260-6; operational derivation of,
266-7; postulate system for, 269;
scientific content of, 267-71.

Objects, 89, 104, 106, 110; see End-
object.

Observation, 56-7, 225-6, 229-30;
see Perception.

Ogden, C. K., 62 n., 63, 67 n., 77.

Operationalism, 148, 154-8, 170.

Operators, 92-101; normal, 98-
100.

Order, 253, 254-60; empirical founda-
tion of, 254-6 ; Huntington's postu-
lates for, 258-60; operational deri-
vation of, 256-7; requirements for,
254-6; scientific content of, 257-
60; see Ordering of events.

Ordering of events, 122-3, 184; in

descriptive science, 137-8; in ex-
planatory science, 189-90, 208.
Ostwald, W., 74.

Parker, D. H., 291 n., 311.

Particle, 317, 328, 342-3, 344.

Pasteur, L., 180.

Patrick, G. T. W., 14 and n., 20.

Paulsen, F., 20.

Pearson, K., 8, 132 n., 148, 150, 151-
4, 157, 158, 163, 165, 167, 171, 252,
329 n., 351, 384.

Peirce, B., 253.

Peirce, C. S., 72 and n., 77, 384, 399,
405, 409, 410-2, 415, 416, 417.

Perception, Chap. \;A-M-B-P-0
analysis of, 89-102; definition of,
81, 88, 101-2; in verification, 224-
5; positivistic theory of, 84-6, 87;
representative theory of, 81-3,
86-8; subjectivistic theory of, 85,
87, 102; and scientific realism, 88-
102; see Awareness; Knowing; Ob-
servation.

Perceptual act, see Perception.

Philosophers and science, 36-7.

Philosophy, Chap. I; as clarification
of ideas, 11-3; as critique of
science, 23-4, 26-7, 31-2, 33; as
description of values, 13-5; as
explanation, 8-11; as intuition,
18-20; as qualitative, 15-8; nar-
rowing of, 6.

Philosophy and science, Chap. I;
antagonism of, 6-8; reconciliation
of, 21-3; separation of, 4-6; supple-
mentary character of, 8, 10-1.

Philosophy of science, Chap. II; as
logic of science, 34; as metaphysics
of science, 34-5; as speculation
about science, 33-4; contributors
to, 28; controversies in, 170-1;
courses in, 28; emergence of, 21-8;
general character of, 35-8; method
of, 37-8; problems of, 28-9, 31-2,
33-5.

Physical medium, 90-101; control of,
109-15; see Measurement.

INDEX

467

Planck, M., 28, 81 n., 132, 148, 175 n.,
378, 379 and n., 382, 393, 418, 419,
432-7.

Plato, 5, 224, 405, 408, 448.

Poincare, H., 28, 74, 148, 150, 160-3,
164, 171, 176, 284 n., 286, 311, 335,
346.

Poinsot, L., 244.

Pointing, method of, 244-5, 249-50.

Positivism, 8-9, 10, 86-7, 148, 149-
50, 170, 351; as theory of percep-
tion, 84-5; see Descriptive science;
Logical positivism; Modified pos-
itivism; Operationalism ; Strict em-
piricism.

Pragmatism, 44.

Prediction, 218-23.

Price, H. H., 102.

Primitive concepts, 248-9.

Probability, 359-63.

Progression, 259, 267.

Propositions; analytic and synthetic,
142-3, 210-1; in descriptive science,
141-2; integrating, 141, 209-10;
underived and derived, 140, 209.

Psychology of discovery, 178-81.

Quality, distinguished from quantity,
15-8.

Quantity, 253, 271-8; empirical foun-
dation of, 271-4; operational deri-
vation of, 274-6; relativity of, 271-
3; scientific content of, 276-8; and
measurement, 274-6; and order,
273-4; and quality, 15-8, 271; see
Measurement.

Rationalism, 149, 170.
Realism, see Scientific realism.
Reality, see Nature of reality.
Relativity of motion, 313-4.
Relativity theory, 25-6, 303-11.
Retrospective inference, 106.
Reversible processes, 288-9.
Ribot, T., 249 n., 252.
Richards, I. A., 62 n., 63, 67 n., 77.
Richardson, E. C, 408 n., 417.
Riemann, G. F. B., 24, 25.

Rignano, E., 195.

Ritchie, A. D., 38, 60, 112 n., 230,
384.

Rueff, J., 213.

Russell, Bertrand, 20, 51 and n., 52,
54, 60, 70 n., 102, 148, 170, 184,
238, 243, 248, 252, 253, 255 n., 261,
263 and n., 264 n., 271 n., 278, 299
and n., 300, 311, 315, 316 n., 320 n.,
321 n., 323, 341 n., 345, 388.

Russell, H. N., 437.

Rutherford, E., 169

Saunders, F. H., 334 n.

Schlick, M., 11, 148.

Science, Chap. I; as analysis, 18-9;
as descriptive, 8-11; as factual,
13-5; as factual description, 11-3;
as never purely descriptive, 104-5;
as quantitative, 15-8; as resting
upon data, 80-1; as reducible to
quantity, 312-3; as selective of
events, 78-9; basic entity of, 50;
broadest definition of, 128; con-
tradiction in, 24-6; empirical study
of, 43-6; limiting of, 49-50; prag-
matic explanation of, 44-5, 78-
80; self-criticism of, 23; social
aspects of, 27; specialization of,
29-30; subject matter of, 50; task
of, 78; and sensitivity of organ-
isms, 79; see Descriptive science;
Explanatory science.

Sciences, classification of, see Classi-
fication of the sciences.

Scientific cognition, 47, 48; see
Kno wer ; Knowing ; Knowledge ;
Known.

Scientific concepts, analysis of, 30-1,
Chap. XII; definition of, 235-7;
difficulties of, 233-4; general char-
acter of, 234-43; task of, 237; and
empirical foundation, 243-5; and
operational derivation, 250-2; and
scientific content, 245-50.

Scientific discovery, Chap. IX; act
of, 175-8; mystery of, 173; spon-
taneity of, 176-8; twofold char-

468

INDEX

acter of, 182-9; see Discovery;
Logic of discovery; Psychology of
discovery.

Scientific method, 56; see Knowing.

Scientific realism; as theory of per-
ception, 88-102; as theory of con-
cepts, 167-71; and explanation,
203-4.

Scientist, 46; uncritical attitude of,
30-1, 35-6; and imagination, 175-
6; and philosophy, 36; and specu-
lative problems, 394-5; see Know-
er; State of mind.

Sense organs, control of, 115-7.

Serial arrangements, 254; see Order;
Ordering of events.

Serial operations, 192; see Ordering
of events.

Shakespeare, 433.

Sheen, F. J., 20.

Sign situations, 62-3.

Silverstein, L., 285 n., 384.

Space, Chap. XIV; complexity of
problem of, 279; empirical, 288-96;
Euclidean, 281-8; operational deri-
vation of, 296-303; see Empirical
space; Euclidean space; Space-
time.

Space-time, 303-11; continuity and
infinity of, 306-9; four-dimensional
character of, 307-8; homogeneity
of, 309; isotropy of, 309-11;
plurality of, 305-6; relativity of,
304-5.

Spaier, A., 271 n.

Speculative problems, 33-4, part III,
Chap. XVII; characteristic fea-
tures of, 394-8; chief examples of,
388-94; difficulties in classifica-
tion of, 287-8; general character
of, 388-91.

Spencer, H., 411, 412.

Spiritual idealism, 442-8.

State of mind, control of, 117-26.

Statistical laws, 362-3.

Stefansson, V., 365.

Strict empiricism, 148, 151-4, 170.

Subjectivism, 85-7, 100-1.

Symbolic knowledge, 54-5; see Sym-
bolic schemes; Symbols.

Symbolic schemes, 58-9, 61; ab-
stractness of, 69-70; adequacy of,
69-71; kinds of, 72-6; variations
in, 69-71.

Symbolism of data, 118-25; as dis-
tinct from direct awareness, 119;
as present in all awareness, 119;
form of, 121; and obvious features
of events, 120-1.

Symbols, 58, 100-1, Chap. IV; anal-
ysis of, 63-9 ; as events, 64 ; content
of, 237, 240-1, 245-50; emotive
and cognitive, 63; empirical foun-
dation of, 237, 240, 243-5; iconic
and characterizing, 73-6; kinds
of, 72-6; operational derivation of,
241-2* 250-2; referential property
of, 64-6; subjective aspect of, 67-8;
and creative evolution, 451-5; and
mathematical idealism, 448-51;
and spiritual idealism, 442-8; see
Concepts; Extension; Intension;
Symbolic schemes.

Synthesis, 188, 193-4, 250.

Taube, M., 353 n.

Taylor, A. E., 10 n.

Tennant, F. R., 58, 417.

Theory, 80; development of, 214-8;
see Hypothesis.

Thomson, J. A., 38, 60, 417.

Time, Chap. XIV; complexity of
problem of, 279; empirical, 288-96;
Newtonian, 281-8; operational der-
ivation of, 296-303; see Empirical
time; Newtonian time; Space-
time.

Time's arrow, 287, 296, 373.

Transitivity, 122-3, 258.

Truth, 69-71, 142-3, 210-1, 236-7.

Tyndall, J., 176 and n., 182, 195.

Uniformity of nature, 189, 359.

Vaihinger, H., 148, 167, 172.
Values, 13-6,

INDEX

469

Variability; of the given, 49-50, 131-
3; of levels of abstraction, 245-8.

Venn, J., 112 n.

Verification, 107, Chap. XI; as pre-
diction, 218-23; compared with
discovery, 107, 218, 225; confirma-
tory-infirmatory movement of,
223-30; experiments of, 107, 225;
Mill's methods of, 226-7; nature of,
218; observational and experi-
mental, 225-6; see Hypothesis.

Vienna circle, see Logical positivists.

Wallas, G., 178, 194.
Watt, J., 176.

Weyl, H., 460.

Whitehead, A. N., 28, 60, 61 and
n., 70 n., 132, 148, 172, 278,
299, 311, 346, 351, 352, 353, 354.

Wittgenstein, L., 11, 12, 73, 77, 148,
172, 253.

Wolf, A., 213, 230.

Wolff, C, 5.

Woodworth, R. S., 179, 194.

Words, 67, 72.

Young, J. W., 213, 265 n., 269 nM
278, 363 n.

Zeno, 321.