What Science Really Means

TEXT FLY WITHIN
THE BOOK ONLY

8]<OU 166095 >m

^ CD :< co

OSMANIA UNIVERSrrV UBRARt

Call No. |3f DO * 3 Accession No, & 4 #"' ty

Author P9/^
Title
This book should be returned on or before the date last marked below.

WHAT SCIENCE REALLY MEANS

By the same Authors
SCIENCE AND THE SPIRIT OF MAN

A NEW ORDERING OF EXPERIENCE

Demy Svo. j2s. 6d. net

"The book is well written . . . concise rather
than diffuse, strong and vigorous in movement,
even with flashes of eloquence, and a constant
appeal to reality and experience which keeps one
fairly steadily 011 the ground, though mentally
some exhilarating flights are taken." Nature

THE UNLIMITED COMMUNITY

A STUDY OF THE POSSIBILITY OF SOCIAL SCIENCE

Demy 8vo. i$s. net

"The book contains interesting and stimulating
material, presented with real eagerness, and
should increase our understanding of the prob-
lems confronting society." Time and Tide

WHAT SCIENCE REALLY MEANS

AN EXPLANATION OF THE HISTORY

AND EMPIRICAL METHOD

OF GENERAL SCIENCE

BY

JULIUS W. FRIEND

AND

JAMES FEIBLEMAN

LONDON

GEORGE ALLEN & UNWIN LTD
MUSEUM STREET

FIRST PUBLf"ftED IN IQ37

All rights reserved

PRINTED IN GREAT BRITAIN BY
UNWIN BROTHERS LTD,, WOKING

CONTENTS

CHAPTER PAGE

I THE PROBLEM OF EMPIRICISM n

Undetermined Meaning of Science n

Conflicting Definitions of Empiricism 1 3

The Bias of Scientists 14

Idealism and Positivism 17

Rejection, of Both Theories . 1 8

Science and the Public 21

Purpose of the Book ' 23

II THE ORIGINS OF EMPIRICISM 26

Hellenic Empiricism 26

Hellenistic Empiricism 30

Byzantine-Moslem Empiricism 3 5

Christian-Mediaeval Empiricism 40

Renaissance Empiricism 46

III THE DEVELOPMENT OF EMPIRICISM 52

Seventeenth-Century Empiricism 52

Eighteenth-Century Empiricism 57

Nineteenth-Century Empiricism 61

Twlntieth-Century Empiricism 65

Empiricism Misunderstood . 69

IV MODERN MISCONCEPTIONS OF EMPIRICISM 75

From Hume to Cornte 75

Early Formulations of Positivism 77

Mach, Poincar, Pearson 79

The Mentalist View 83

The Logical Positivist View 85

The Operationalist View 91

The Realist View 96

8 WHAT SCIENCE REALLY MEANS

CHAPTER PAGE

V NATURE OF THE FIELD OF SCIENTIFIC

INVESTIGATION 101

With What is the Controversy Concerned ? 101

The Inquiry into Scientific Objects 106

Scientific Objects are Functions 1 1 1

Functions in the Various Sciences 116

Are Scientific Objects Empirical? 119

VI THE METHOD OF EMPIRICISM 122

The Brute Faith in the Given 122

Abstract Character of Common Experience 125

Procedure of Scientific Abstraction 128

The Principle of Economy 131

Relativity of Empiricism 134

All Sciences Experimental 137
The Experimental Sciences of Logic, Mathematics,

and Metaphysics 141

VII THE LOGIC OF SCIENCE 146

Induction and Deduction as Directions 146

The Logic of Scientific Method 149

Analysis and Synthesis 154

Mechanism and Purpose 158

Deduction versus Imagination 161

How Science Should Progress 164

VIII CAUSALITY AND PROBABILITY 168

Empiricism and Causality 168

Causality and Continuity 171

Causality is Non-Temporal 173

Probability Requires Causality 178

The Statistical Method and Causality 181

Probability and Logic 185

CONTENTS 9

IAPTER PAGE

IX THE FUTURE OF SCIENTIFIC EMPIRICISM 190

Summary of the Argument 190

Science Must Become Self- A ware 195

Relation Between Science and Society 198

Is Social Science Possible ? 202

The Future of Applied Science 205

The Future of Theoretical Science 207

INDEX 213

WHAT SCIENCE REALLY MEANS

CHAPTER I

THE PROBLEM OF EMPIRICISM

Ulysses has no use for Plato, and the bones of his
companions are strewn on many a reef and many
an isle.

A. N. WHITEHBAD
UNDETERMINED MEANING OF SCIENCE

THE modern world, which has lost faith in so many
causes, still accepts science nearly unchallenged. Science
to-day occupies the position held by the Roman Church
in the Middle Ages: as the single great authority in a
world divided on almost every object of loyalty. The
tremendous prestige which science enjoys is not unde-
served. Yet despite the extent of its reclame and the wide
reach of its practical effects, the genuine understanding of
its purpose and method remains obscure. The banker and
the barber share a conviction in the necessity for the con-
tinuance of scientific research, a conviction which far out-
runs their comprehension of what research consists of and
what it hopes to accomplish.

Still more extraordinary is the fact that most of its
practitioners, the scientists themselves, share this vague-
ness of what science is, or at best enlighten it with in-
tuitive insight. It may seem a strange assertion that those

12 WHAT SCIENCE REALLY MEANS

who lead a movement possess no clear idea of what they
are doing, no definite conception of where they may
expect it to lead. In short, there does not exist a single
abstract formulation of scientific method on which all
scientists agree.

Until the present, the successful procedure of science
has only in a very limited sense been a matter of planning,
and has often resulted from chance discovery and happy
following of the correct method. Curiously, the early
scientists who put physical science upon its right path
did not have to understand fully the philosophy of
science. Galileo, who led physics to its mathematical
basis, professed to believe in atomistic mechanism.
Newton, the great systcmatizer of physics, professed to
disbelieve in the importance of general theory. Thus far
this haphazard proceeding, with its cleavage between
theory and practice, has not prevented profitable dis-
coveries in the physical sciences, although it has led every
other would-be scientific endeavour astray. The social
studies have arrived nowhere as sciences because they
have followed the explicit creed of physical science.

The time is over when scientific method can be fol-
lowed without being explicitly understood. Not only
will such innocence prove crucial, as it has done in all
but the physical sciences, but it will also hinder and
perhaps destroy the progress of physical science itself.
The abstract understanding of a method may not be an
absolute necessity at the beginning, but after a certain
point it becomes indispensable for progress. Abstract
understanding not only serves as a guide for those who
have strayed from the true scientific method, but gives

THE PROBLEM OF EMPIRICISM 13

reassurance to those who have intuitively anticipated it.
Science, which has thus far blithely ignored definition,
to-day finds itself under the necessity of being accurately
defined.

CONFLICTING DEFINITIONS OF EMPIRICISM

All scientists agree that empiricism lies at the base of
science, and some would even make the terms synony-
mous. Empiricism is the rock on which the scientific
faith is built. Not only is this true of the physical sciences,
but it is also true of those who would ape their method,
and of those who wish to be 'scientific* in fields which
are not yet reduced to the condition of science. Yet the
very term which describes scientific labours is loosely
used and remains as to definition largely a matter of
disagreement.

What does empiricism mean? The following con-
flicting definitions, which have been drawn more or less
at random, offer little satisfaction on this score. Aristotle
employs the terms ' 'empirical" and "historical" as having
the same meaning. Sir William Hamilton states that "the
term empirical means simply what belongs to or is the
product of experience or observation." Whitehead offers
this illuminating definition of empiricism, "that eternal
objects tell no tales as to their ingressions." And Bridgman
states the matter as follows: "empiricism . . . recognizes
no a priori principles which determine or limit the possi-
bilities of new experience."

These definitions, mostly by philosophers, paint a
picture of confusion, and certainly do not define empiri-
cism as it is understood by the scientists. On the other

14 WHAT SCIENCE REALLY MEANS

hand, if there exists any single and unified definition of
empiricism upon which scientists in general do agree, we
have not been able to get them to tell us what it is.
Clearly no scientist accepts in practice any of the philo-
sophical definitions, since he is constantly dealing with
what to him are empirical entities, which are not derived
solely from sense experience. Metabolism, electro-
magnetic fields, ionization these are empirical scientific
entities, yet all are constructions of experience and none
is altogether presented by mere sensation.

Whatever else the scientists mean by empiricism, they
do not mean the limitation of all knowledge to sense
experience, which philosophical empiricism involves.
And the fact that they do not accept such a definition is
evinced by their practice. Nevertheless, this confusion
between philosophical and scientific empiricism may well
result in disaster unless it is dissipated.

THE BIAS OF SCIENTISTS

Why has there been no abstract understanding securing
full agreement concerning the aim and method of
empirical science? The answer must be sought in the
anti-metaphysical bias of the scientists themselves, a bias
which arose at the end of the Middle Ages and which
continues to colour the attitude of scientific men. The
emphasis away from theory and toward the accumulation
of indisputable facts of nature, to be learned by observa-
tion and experiment, precluded any possibility of specu-
lation concerning true definition. Just as the Middle Ages
appeared too metaphysical in their cloistered speculation,
so the ages that followed went to the opposite extreme

THE PROBLEM OF EMPIRICISM 15

and laid an implicit prohibition on all speculation.
Scientists in fighting shy of metaphysics supposed that
empiricism is not a philosophical affair at all. Their
premises, though based on a metaphysics, were not
understood as such, and since those premises were ade-
quate for the development of natural science up to the
end of the nineteenth century, the lack of interest in
philosophy seemed to be pragmatically justified.

But the old materialistic mechanism which tried to
present the world in purely tangible form, ruling out all
else as mental interpretation, was a crude formulation.
It had to postulate mysterious forces to work on tangible
matter; it had to conceive so-called secondary qualities,
such as colour, smell, etc., as unreal. Its very bedrock
was a belief in an indestructible substance, a world of
atoms each existing only by virtue of itself under various
combinations. As a consequence, such combinations were
not real in the same sense that the atoms were real, but
merely combinations of real atoms producing different
appearances. Nevertheless, such a belief was already
contradicted by many of the facts of the old science. For
instance, combinations of various atoms were tacitly
admitted to make different 'substances' in chemistry. No
chemist would have said that water and peroxide of
hydrogen are two 'appearances' of real hydrogen and
oxygen atoms. Thus tacitly it was accepted that dif-
ferences in combination and organization were at least
for purposes of manipulation realities. It is fair to con-
clude that even classical science dealt in non-sensuous
entities as empirical.

However, at the end of the nineteenth century science

16 WHAT SCIENCE REALLY MEANS

faced a crisis; it became questionable whether the
scientists had succeeded in dodging interpretation as
thoroughly as they believed they had. It seems strange
that they could have overlooked the fact that the doctrine
of exclusive reliance upon experiment is itself philo-
sophical no less philosophical for not being formulated
as such. As has been shown time and again, the theory of
empiricism is not itself empirically justifiable. Thus un-
consciously scientists have fastened on to a contradictory
theory: one that denies the validity of theory. Fortunately
for the development of science, however, the practice
has deviated from the theory. Had scientists been mere
accumulators of facts, science would never have become
the institutionalized search for truth that it is to-day.
Even such an assiduous experimenter as the late Pavlov
was, throughout his long career, advised young scientists
not to let themselves "become the archivists of facts." 1

The twentieth century brought about a new state of
affairs. With the acceptance of the theories of relativity
and quantum mechanics, the certitude resulting from the
anti-metaphysical bias of scientists was upset. It became
clear that the mechanical model of the universe which
followed the Newtonian conception was no longer
adequate to take account of all the fresh data. Physical
scientists were unable to describe their subject-matter in
picturable terms, and so were half led to accept the
public estimation of science as a mysterious affair. Still
reluctant to have recourse overtly to metaphysics, the
scientists began to talk about first principles in terms of
science, as though these were part of scientific findings.
1 Science, vol. 83 (1936), p. 369.

THE PROBLEM OF EMPIRICISM 17

And everyone concerned slowly had to admit that not
only was science returning to philosophy, but also that it
had never really abandoned it.

IDEALISM AND POSITIVISM

Now that science is driven back to search for its meaning
in philosophy, two schools arise which attempt to define
the first principles of science: idealism and positivism.
Popular exponents of the first are Eddington, Jeans, and
their followers. Their idealism, or perhaps as it is better
described, mentalism, sets forth in effect that the physical
world is a construction of the mind upon something
ultimately unknowable, or that ultimate physical reality
consists in mathematical thoughts in the mind of God, of
which human beings know only the appearances. Such
a subjectivism seems to cut the ground from under
empiricism, or at best to make that doctrine psycho-
logical. Plainly, here is a conclusion that scientists refuse
to accept. It has always been one of the tenets of scientific
faith that objective agreement is essential to the develop-
ment of science, and that such agreement must be kept
free from any psychological opinion. "Mind-spinning"
is just what the scientists have always been most suspicious
of. And here is a philosophy which seems to assert that
all scientific ideas are mind-spun.

The other school is that of positivism, which enjoys a
new vogue partly because of its antagonism to the
idealistic interpretation. This school, headed by Carnap,
Bridgman, and others, represents the old scientific re-
vulsion against metaphysics, though itself incurably
metaphysical. Positivists claim that the reality of scientific

1 8 WHAT SCIENCE REALLY MEANS

ideas rests solely upon their demonstrability in operation
or experiment. They deny causality and substitute in its
place the observation of the temporal sequence. Here is
an attempt to escape subjectivism. But since its objectivism
hangs entirely upon the sense experience and actions of
the experimenters, it falls back into a subjectivism which
makes scientific ideas mere shorthand summaries of
experience.

The general tendency of the last decade has been to
follow the positivistic rather than the idealistic interpre-
tation of science. Scientists lean toward positivism for fear
of wild and unrestrained theorizing. The attraction of
positivism for scientists is that it seems to be hard-headed
and practical, and to avoid metaphysical and mythological
elements. It seems to draw a very sharp dividing line
between what is scientific and what is not. This bias
should not surprise anyone familiar with the history of
science; nevertheless it is as wrong-headed as idealism.
That, in fact, positivism suffers from the same defect as
idealism will be shown later.

REJECTION OF BOTH THEORIES

There are many objections which will immediately appeal
to anyone who considers science according to the
doctrines of idealism or positivism. The exact con-
tentions will be examined in later chapters. At present
we may briefly group a few arguments to show how
dubious these positions are.

Is empirical science, which has always prided itself on
being objective, in that it allows no one man's opinion
merely by being an opinion to alter the facts, now going

THE PROBLEM OF EMPIRICISM 19

to assume that the only objective basis can be opinion?
Can science be what Bridgman calls it, "my private
science/' 2 and remain science? In other words, is science
to be reduced to a psychological matter of consciousness ?
Does anyone truly believe that the application of mathe-
matical laws to nature is mental ? In other words, do they
work because we know of them, or do we not rather
know of them because they work? Did iron assume
magnetic properties simultaneously with the discovery
of its magnetic properties ?

If we grant the idealist's contention that the photo-
electric cell and the Wilson cloud chamber are equally
mental, how can the differences between them be
accounted for ? Certainly this difference will have to be
explained in non-psychological terms. Therefore the
scientific problem from the idealist point of view remains
just what it was before. To place the observer within the
field of that which he observes is like making a camera
an essential part of every picture of Niagara Falls. The
idealist philosophy is plainly no answer to the much
sought-for philosophy of empirical science, and the
scientists are right in their intuitively arrived at decision
to refuse it.

The objections to positivism are equally cogent.
Whatever else empirical science may be, it is certainly
not positivistic. If it were, new empirical entities would
never come to light, since everything not already dis-
covered would remain a theoretical hypothesis. Thus
science could never have advanced. But ignoring this,
let us inquire in what way are electrons summaries of
2 The Nature of Physical Theory, p. 13.

20 WHAT SCIENCE REALLY MEANS

anybody's experience ? Are Kepler's laws of planetary
motion and Balmer's law for the position of lines in the
hydrogen spectrum altogether products of experience ?
The whole applicability of mathematical science would
be negated if scientific laws were merely summaries of
past happenings. Positivism overlooks the most obvious
ambition of science: the aim to reach exact predict-
ability.

The procedure of science toward the successful unifica-
tion of physical theory, as when gravitation and inertia
were enveloped by the theory of relativity, should indi-
cate that laws cannot be merely statistical summaries,
and that something more than a mental unification of
experiments is being reached. The grave objections to
positivism are enough to suggest that positivism is not
the required answer to the newly recovered need for a
philosophy of science. Positivism is more of a danger to
the future of science than idealism because the former
has secured more support from the scientists than its
rival, and indeed just now seems to be the choice wherever
scientific men feel the need for a philosophy. What the
positivists have done is to hold on to experimentation,
and thus as they see it to empiricism, at the cost of
denying reality to the scientific subject-matter itself.
They have saved the method only by sacrificing the
existence of that which the method studies.

In idealism and positivism there is no objective reality
to the entities of science. Neither idealism, which would
refer science to the psychology of consciousness, nor
positivism, which would refer it to the psychology of
behaviourism, is adequate to supply an understanding of

THE PROBLEM OF EMPIRICISM 21

what empirical science is. The first theory dissolves
empiricism; the second tries to hold on to it by dis-
solving everything else.

SCIENCE AND THE PUBLIC

The prestige of science is very great even outside
scientific circles. Thus far the public has not looked to
science altogether in vain. The tremendous hope invested
in science is amply justified at least by the physical
sciences, although to be sure this does not mean that
the public understands what science is or what it is try-
ing to do. Rather does the layman look to science to
announce what reality is. Thus it is not too much to say
that whichever way the interpretation of science turns
the popular understanding of reality will follow. Obvi-
ously, then, what has been said about the bias of the
scientists in favour of positivism applies with equal force
to the public. To the popular mind science is an
agglutinative compendium of facts largely unrelated.

The form which popular positivism assumes is that of
placing great faith in seemingly demonstrated facts and
of distrusting all theory. Its assumption that this procedure
is the scientific method is well shown by the constant
appeals in the popular Press, in advertisements, and in
innumerable arguments where the terms 'science' and
'scientific* are bandied about as conclusive and irre-
futable. The fact that the public accepts the contra-
dictory beliefs that science is altogether concerned with
final and utterly demonstrable matters of fact, and that
science is always in process of changing its mind, only
goes to reinforce the statement that the public knows

22 WHAT SCIENCE REALLY MEANS

no explicit formulation of science but implicitly accepts
positivism.

The question may be asked as to what difference it
makes whether the public understands science or not,
particularly in view of the fact that science has gone
forward without public understanding. It is true that
physical scientists have been able to proceed until now
unmolested, carrying through a rational programme
within a society which still tries to go on in the old
irrational manner. But it is already becoming obvious to
many thoughtful scientists that this condition cannot
continue indefinitely. We may say that the historical
career of physical science has so far been promoted by
good luck. Already, however, there are signs that the
rear-guard is deserting the scientific vanguard, and that
science is too far ahead of the main procession of humanity
and may soon be cut off from the service of supplies.
For this not to occur, it will be necessary for the public
to understand at least a little of the aim and methods of
science. In other words, the public must recognize the
value of theoretical science as well as the usefulness of
applied science.

If some such understanding of science does not reach
the public, it will no longer continue to have patience
with anything but immediately practical results. Need it
be urged that practical results do not come without a
theoretical background? Continued ignorance on the
part of the layman may have the social effect of abating
the development of theoretical science. Thus the clarifi-
cation of science and scientific method is much more
than a philosopher's idle speculation, or a theory spun

THE PROBLEM OF EMPIRICISM 23

to satisfy the desire of a few specialists to understand
what they are doing. The need for an understanding and
clarification of empirical science is not only a practical
necessity for science proper, but also one for the world
in general. Science and the public benefit together, or
neither benefits.

PURPOSE OF THE BOOK

We believe it can be shown that the subject-matter of
science has existence with or without its comprehension
by the mind, with or without the experiments by which
it is demonstrated. If empiricism can be shown to have
reference to an independent system which men can
discover and follow, but which they do not create either
by conceiving it or by performing certain operations,
then scientists need be in no doubt as to the objective
reality of their entities. In other words, a proper under-
standing of empiricism would exhibit that the so-called
'concepts' of science refer to entities which are not con-
cepts and not operations but independent facts. The
critical misunderstanding of reality as applying only to
tangible things is responsible for these two variants of
mentalism: idealism and positivism. The functions which
scientists analyse can hardly be called tangible or sensory,
though observable only in and through things and events
as processes. Empirical science needs further philosophical
exposition.

The main requirement, then, is the definition of the
aim and method of science, which in turn involves the
clarification of empiricism. The stubborn and intuitive
understanding that empiricism must at all costs be pre-

24 WHAT SCIENCE REALLY MEANS

served is a virtue of the physical scientists' practice. But
for this intuition to be rationally justified requires some-
thing more than mere faith. It deserves an explicit creed.
The utter exclusion from metaphysics in which science
thus far has tried to hold itself has been invaded, and
ostrich tactics will not avail.

In analysing empirical science as to its aim and method,
we do not claim the discovery of anything new. On the
contrary, we are trying to abstract and make clear what
that aim and method have always been, what they
should be, and what they must be. In so far as science
has succeeded during its historical career, it has followed
a certain method. Therefore we are not concerned with
the way in which it has proceeded historically, except in
so far as such an inquiry helps us to learn the way in
which it should proceed logically. The fact of the manner
in which scientists have stumbled upon or deliberately
reasoned their way to the truth must be distinguished
from the ideal toward which they have aspired only by
approximation. Whether a child learns arithmetic by
counting on his fingers or his toes has no effect upon the
cardinal number series with which he becomes familiar.
But obviously it is preferable to proceed logically, if only
because such procedure saves time and energy. The ideal
method of science is not of necessity the exact one
followed by any scientist.

What we are claiming, then, for the clarification of
the aim and method of empirical science is that whatever
procedure the scientist may take to arrive at new hypo-
theses and new facts, he will be able to understand far
better what he is doing; and in the long run this will

THE PROBLEM OF EMPIRICISM 25

unquestionably keep him from wandering too far afield,
as it will also set his inquiry into fruitful paths. In a word,
what he has been accomplishing mainly by intuition and
incomplete understanding should be available to him as
an abstract formulation.

CHAPTER II
THE ORIGINS OF EMPIRICISM

It is an unwarranted assumption that ancient
science differed in principle at any point from that
of to-day.

W. A. HEIDEL

IN order to understand the place which empiricism holds
in the esteem of scientists, as well as to expose the cause
of the antagonism of science to the speculative reason, it
will be necessary to give a short sketch of the history of
empirical science. Only history can show how scientists
could have made the error of absolutely dividing the
empirical from the logical. However, no attempt is made
here to sketch an adequate history of science; all we can
hope to accomplish in so short a space is to exhibit the
occasion for the rise of empiricism and to touch on the
significant points of its development.

HELLENIC EMPIRICISM

The history of empirical science is at least as old as re-
corded cultural history. In Egypt and Babylonia the
beginnings of the sciences of astronomy, medicine, and
mechanics were due to speculations upon problems of a
practical nature. It was necessary to make careful observa-
tions and to draw inferences from them. But of course
this early empiricism was neither formulated as a theory
nor segregated as a practice, but was resorted to along
with magic, astrology, and other pseudo-sciences.

THE ORIGINS OF EMPIRICISM 27

Early Greek empiricism was of this same sort, although
the Greek nature philosophers were more inclined to be
sceptical in regard to mythological and magical explana-
tions. Thales' belief that water is the prime substance was
an induction which went beyond the verifiable facts, yet
it was based on the empirical observation of the presence
of moisture in natural objects. Thales experimented in
other matters, as when he showed that amber rubbed
would attract light bodies.

The statement that the Greeks were not empiricists but
relied exclusively on reasoning is not true. Anaximander
observed that the heavens revolve around the pole star.
And although the name of Pythagoras is associated with
mystic sciences, such as numerology, he is said to have
accomplished one of the finest pieces of observation and
inductive reasoning, which he afterwards deductively
checked. Noting that the sound of two hammers on
an anvil were separated by an octave, he weighed the
hammers to find that the weight of the one was double
the weight of the other. This experiment was then re-
peated on the monochord, from which it was found that
the length of string was likewise proportional. The length
of string required to produce the concordant notes showed
the proportions 12 : 8 : 6.

Alcmaeon of Crotona, a younger contemporary of
Pythagoras, was likewise an experimenter. He dissected
animals; discovered the optic nerve; distinguished empty
veins from those carrying blood, etc. Xenophanes of
Colophon gave the correct interpretation of fossils.
Anaxagoras dissected the brain and recognized its lateral
ventricles; he discovered that fishes breathe through their

28 WHAT SCIENCE REALLY MEANS

gills. The Hippocratic Corpus is filled with all sorts of
examples of careful and minute observation. For instance,
embryology was studied by opening hen's eggs day by
day as incubation progressed. Euryphion of Cnidos,
among other experimental researches, discovered that
pleurisy is a lung affection. Eudoxus of Cnidos experi-
mented in astronomy, acoustics, mechanics. Philip of
Opus explained the rainbow as a phenomenon of re-
fraction. The observations of Aristotle in zoology are
famous; e.g. his description of the placental development
of the dogfish, and of the stomach of ruminants. Aristo-
xenus and Strato, both members of the Aristotelian
school, conducted rigorous empirical observations in the
physical field.

Enough has been said to show that the Greeks observed
as well as speculated. But if experimentation was as
plentiful as our random examples indicate, why was
Greek science not more fruitful? The reason for the
failure of Greek science is that observation by itself, like
speculation by itself, is not sufficient for science. The
Greeks, it is true, both experimented and speculated, but
theory and experiment were kept too far apart. Thus
their experimentation became positivistic and their
reasoning dogmatic. Aristotle exhibits both errors. At
times he is an empirical dogmatist (positivist), as when
he is certain that plants cannot feel "because they are
composed of earth." 1 and at other times he is a rational
dogmatist, as when he asserts that just as "the triangle is
implied by the quadrilateral," so "the nutritive faculty
[is implied] by the sensitive." 2

1 On the Soul, III, xiii. 2 Ibid., II, iii.

THE ORIGINS OF EMPIRICISM 29

It must be admitted that the general tendency of Greek
thought militated against the development of empiricism
as a creed. Unfortunately for the progress of empiricism,
Greek philosophy in its thorough grasp of the place of
reason, held experimentation back. There was a prejudice
in the Greek mind in favour of discovery by deduction
from principles held, instead of discovery by induction
from experiment. The world of actuality was derogated
in the Platonic version to a mere appearance of a divine
order of Ideas. And thus an intellectual demeaned him-
self somewhat by abandoning pure thought for vulgar
experimentation. " Science," said Aristotle, ' 'should con-
cern itself with eternal objects immutable and pure."
Socrates asserted that the subject-matter of physics is
'Vain, useless and perilous."

This whole attitude unquestionably held back science,
even though remarkable beginnings show the wide
interest of the Greeks in empiricism. "Theory and
practice do not always progress pari passu," 3 and the
Greeks understood at least the difference between how
science progresses and how it should progress. 4 Greek
theory and practice, however, broke away from each
other, and when Greek science was carried into Christian
Europe, it was the dogmatic categorization and reliance
on deductions from unproved assumptions which were
preserved; its empirical basis was forgotten. The bias of
this heritage should be carefully noted, because it was
the revulsion against the dogmatic aspect of Greek
science which led the early empiricists of Latindom to

8 W. A. Heidel, The Heroic Age of Science, p. 95.
4 Hippocrates, De Prisca Medidna, 12 (III, 596 f., L).

30 WHAT SCIENCE REALLY MEANS

rediscover empiricism, but with the difference of opposing
it to the speculative reason.

HELLENISTIC EMPIRICISM

Aristotle died in 322 B.C., and the Hellenistic Age of
Greek expansion which followed saw a greater develop-
ment of the practice of empiricism. Despite the weight
of Aristotle's authority this new age was to distinguish
itself principally in experimental science. Why was
empiricism more widely practised in the civilization
which centred around Alexandria than in the one which
centred around Athens ? While it is undeniable that the
new era had a respect approaching awe for the older
Greeks, it is also true that this very fact made the Hel-
lenistic Greeks commentators and analysers rather than
innovators. In literature this produced grammarians and
rhetoricians, but in the study of natural objects it brought
about the beginnings of a thoroughgoing science by
focusing attention on analysis, and a fortiori on experi-
ment. Moreover, Aristotle had excluded the mathe-
matical method from philosophy, and as a consequence
it went by default to science. This isolation of science
from philosophy proved pro tern, a good thing, though
in the end it corrupted both. Philosophy became more
concerned with the unearthly and the mystical, and
science became more positivistic.

But in the beginning of this period the return of
science from remote contemplation to practical research
proved fecund. Theophrastus of Lesbos wrote describing
minerals and plants, of which he certainly had experi-
mental knowledge. Dicaearchus of Messina noted the

THE ORIGINS OF EMPIRICISM 31

influence of the sun upon the tides. Herophilus and
Erasistratus rejected all references to the occult and in-
sisted upon natural causes. They practised dissection and,
it is said, vivisection, thus improving enormously the
knowledge of such organs and functions as liver, salivary
glands, brain, the relation of vascular to nervous systems,
and the relation of respiratory to arterial systems. Aris-
tarchus of Samos, who arrived at a heliocentric theory,
worked the results of his observations into geometrical
form. Note the difference between the use of mathe-
matics here and in Plato's astronomy: the first is based
on reasoning from observation of what is, the second on
reasoning from what (it seemed) ought to be. Era-
tosthenes' famous experiment in calculating the size of
the earth by actual observation of the latitudes and dis-
tances of Syene and Meroe failed only by fifty miles of
die true value of the diameter.

Archimedes was the greatest Hellenistic scientist and
one of the foremost experimental scientists of all times.
He had, moreover, a clear abstract understanding of
scientific method. He wrote:

Certain things first became clear to me by a mechanical
[i.e. experimental] method, although they had to be demon-
strated by geometry afterwards because their investigation by
the said method did not furnish an actual demonstration. 5

Accordingly, he weighed mechanical models of the
parabola and ellipse, demonstrating the result by the
geometrical method of limits, and finally generalizing
this method to an anticipation of the integral calculus.

5 Cited in Heidel, The Heroic Age of Science, p. 101.

32 WHAT SCIENCE REALLY MEANS

It is not true that Archimedes' procedure differed from
that employed by modern science. For example, in his
work on floating bodies, starting from the observation
that water has the geometric property of being fluid in
all its parts, he proceeded deductively to the conclusion
that a solid heavier than water will lose its weight in
water, a weight exactly equal to the weight of the water
displaced. This he verified experimentally, and thus
established the principle of specific gravity. Of course,
the train of reasoning might have been different. A
scientist of to-day might note through various experi-
ments the weight of the displacement of a body, and leap
to the induction that the weight of the body is equal to
the weight of the water displaced. He might then
formulate the principle mathematically. Both pro-
cedures, however, are equally empirical, equally deductive
and inductive.

Mystic neo-Pythagoreanism continued, but scientific
mathematics was also well under way by this time.
The name of Euclid needs no comment; but it is not so
well known that beside being a geometer he also worked
on optics, discovering the propagation of light in
straight lines, and the laws of reflection. Apollonius of
Perga was the same type of mathematical scientist. The
significance of his work was not so much the discovery
of the properties of the parabola, ellipse, and hyperbola,
but in generalizing these as sections of one cone, and thus
in beginning projective geometry.

The understanding of Hellenistic science as hopelessly
theoretical is without foundation. Indeed, we have been
attempting to show that its direction was the opposite,

THE ORIGINS OF EMPIRICISM 33

and that it too soon became 'practical' and positivistic.
Philo of Byzantium, though a mathematician, is chiefly
known as the author of an encyclopaedia of applied
mechanics, and for his work on pneumatic machines.
Likewise Hipparchus, though a mathematician, is mainly
notable as an inventor of astronomical instruments, and
for his rejection of the heliocentric system as too theo-
retical. The same practical turn is to be seen in Hero, who
was almost entirely concerned with the applications of
mathematics and mechanics, and who contrived many
machines, e.g. siphons, steam engines, and fire engines;
Hero's Pneumatics was almost a laboratory manual. 6

The growing interest in a positivistic point of view
and the narrow practicality of the late Hellenistic Age are
manifest in the next group of scientists we have to con-
sider. Strabo, Seneca, and Pliny the Elder wrote vast
compendia of knowledge. Vitruvius and Frontinus did,
it is true, make contributions of a scientific nature, but
these were chiefly practical devices which bore narrowly
on their own work. Frontinus wrote on hydrodynamics
in connection with the engineering of the aqueducts,
and Vitruvius contributed as an architect to acoustics,
and, as superintendent of military engines, to ballistics.
Celsus and Dioscorides were both medical encyclo-
paedists, notable recorders, but cautious theorists.

The Alexandrian period comes to an end with two
colossal figures, Galen and Ptolemy. With them the
positivistic progress of Hellenistic science reached its
culmination. Although Aretaeus, Galen's contemporary,
was a greater physician than Galen, it was the latter 's
6 Heidel, op. cit., p. 191.

34 WHAT SCIENCE REALLY MEANS

dogmatic and systematic summary which won him the
most acclaim.

His chief merit consists in having systematized and unified
Greek anatomical and medical knowledge and practice. 7

Although Galen did experimental work, e.g. on the
sensory and motor nerves, his chief historical importance
consists in the fact that he closed inquiry rather than
opened it.

Ptolemy played the same role in astronomy that
Galen did in medicine: he systematized the science on
positivistic lines. Note the common-sense empirical
argument of Ptolemy against the movement of the earth:
that if the earth were moving a bird on the wing would
soon be left behind. Herein is indicated the abandonment
of the attempt of Aristarchus to formulate astronomy in
theoretical terms which go beyond the appearances of
common sense. However, the Ptolemaic system was an
improvement in economy over the older and more
awkward crystalline spheres. The Ptolemaic system of
cycles and epicycles is a summary of observations, and
like all such summaries does not suggest any new con-
clusions, and was "primarily a bookkeeping device." 8
When such an ideal of science is adopted, it is the end
and not the beginning of speculation. This alone should
make the scientists beware of accepting the positivistic
version of empiricism.

The failure of late classical science to perpetuate itself
has a simple explanation. Its separation from abstract

7 George Sarton, Introduction to the History of Science, vol. i, p. 301 ff.

8 Benjamin Ginzburg, The Adventure of Science, p. 68.

THE ORIGINS OF EMPIRICISM 35

speculation rendered it cautious and down-to-earth, to
the extent of becoming more and more concerned with
special practical problems and summaries of past work,
until it died of positivism. Abstract speculation divorced
from science fled to philosophy, there to concern itself
altogether with ultimate problems of ontology. To
separate science and philosophy is hurtful to both. It
leaves philosophy without ground under its feet and
hence in the eerie realms of mysticism; it leaves science
flat on the ground, tied to the impotence of positivism.
This extreme is as harmful to science as is the wild
theorizing of a Plato, and curiously enough both result
in pesudo-empirical sciences like alchemy and astrology.
For, be it noted, the astrologists and the alchemists were
of all 'scientists' the most practical in ambition and the
most experimental in procedure however null the
result. In this nadir of scientific research the great flower-
ing of science was lost to the Hellenistic world to be
resumed elsewhere.

BYZANTINE-MOSLEM EMPIRICISM

It is generally believed that after Hellenistic science died
out, there was a period of perhaps four centuries when
the whole tradition of experimental science was dead,
and that it lay dead until Moslem culture resurrected it.
There is no foundation for this view. The truth is that
science shows a continuity from the ancient Greeks to
the modern scientists; and there was never a period when
science was abandoned altogether everywhere. After the
decline of the Hellenistic Age, empirical science was pre-
served in the Byzantine Empire. While it is true that

36 WHAT SCIENCE REALLY MEANS

there were no great Byzantine scientists, that the
Byzantine scientists added little to the tradition, still
they did serve the valuable function of keeping it
alive.

Oribasius, the last of the true Hellenistic scientists,
flourished about A.D. 370. He wrote a medical encyclo-
paedia in seventy books, and fought the growing super-
stition of the age. But there is no real break between him
and Proclus. Proclus may be termed one of the first of
the Byzantines. He worked in astronomy, describing the
method of measuring the apparent diameter of the sun
by means of Hero's water-clock. In mathematics he
worked particularly on the properties of certain higher
curves. Martin Capella, generally known as a Christian
theologian, set forth an explanation of the hemi-
heliocentric system, and discussed geometry and arith-
metic. Anthemius (fl. circa 510) was a practical mechanic
and mathematician. He was employed in the recon-
struction of the Cathedral of St. Sophia, but he also
wrote theoretical treatises on the parabola, and on the
properties of burning-glasses. His contemporary, Phili-
ponus, was a scientist in the best sense of the word. He
disproved Aristotle's law of falling bodies experimentally;
denied the Aristotelian theory of the impossibility of a
vacuum; and described astronomical instruments, especi-
ally the astrolabe. It is not difficult to see that there is
no qualitative difference between this kind of scientist
and those of the late Hellenistic Age. These names must
be considered a mere indication of the extent of experi-
mental science. For instance, Bishop Synesius of Ptole-
mais requested Hypatia to procure for him some

THE ORIGINS OF EMPIRICISM 3?

baryllium to make an hydrometer, proving that the
instrument was well known at the time.

Justinian, who closed the philosophical schools of
Athens, opened one of his own devoted to the study of
mathematics in 532. The seventh century contained
besides physicists many medical scientists. Alexander of
Tralles, Theophilus Protospatharius, Stephanus of Alex-
andria, Stephanus of Athens, Aaron of Alexandria, Paul
of Aegina, all were eminent doctors who wrote on the
theoretical side of medicine.

Although Byzantine science suffered a decline after the
seventh century it never entirely disappeared, and in the
ninth and tenth centuries underwent a renaissance. Leon
of Thessalonica was a notable figure in this period.
However, it was in the seventh century that Byzantine
science reached its height and began to influence the
countries further east, preserving the continuity between
Byzantium and Islam. Severus of Sebokht was a
Christian bishop who started a school of Greek learning
in Western Syria about 650. He added to the Greek
scientific tradition the use of Hindu numerals; without
them the high modern development of science would
have been impossible.

Towards the beginning of the Byzantine period (489)
Nestorian Christians emigrated to Edessa. They were dis-
persed further east by religious persecution and trans-
ferred to Ctesiphon, and in 762 they again transferred to
Baghdad. They were the principal agents by which
Greek science and learning were introduced to the
Moslem world. Therefore there is no hiatus between
Byzantine and Moslem science. It is notable that Baghdad

38 WHAT SCIENCE REALLY MEANS

became the great centre of Moslem culture after the
Nestorians had settled there.

The first Moslem scientists were mainly encyclo-
paedists and translators. Al-Fazari, who flourished late in
the eighth century, translated Sanscrit works and thereby
introduced Hindu numerals to the Moslem world. This
is the great advantage which Moslem science held over
Byzantine. Moslem science, however, had still to free
itself from pseudo-science, and in the works of Jabir
we can already see signs of chemistry emerging from
alchemy. Early in the following century Al-Quarizmi,
syncretizing Greek and Hindu science, developed mathe-
matics, particularly algebra, far beyond anything that
either Greek or Hindu alone had accomplished. Al-Kindi
and Al-Farghani made translations from the Greek, and
the latter as an astronomer following Ptolemaic theory
wrote on celestial motions. Ibn-Qurra illustrates again
the great reliance on Greek sources; he translated Apol-
lonius, Archimedes, Euclid, and Ptolemy into Arabic.

At the beginning of the tenth century Moslem science
had absorbed sufficient influences to become experimental
on its own account, and its learned men attempted to
treat of all fields of knowledge. Al-Razi was an important
physician who combined his knowledge of chemistry
with medical practice. He was much more than a mere
syncretizer of Greek and Hindu medical knowledge,
being an experimental chemist, physician, and physicist
(hydrostatics). Al-Battani was an astronomical scientist
who combined theory with observations; he discovered
the motion of the solar apsides, and in his trigonometry
employed sines instead of Greek chords. To correct the

THE ORIGINS OF EMPIRICISM 39

erroneous impression that Moslem science was confined
to mathematics and the natural science, we have only
to mention Al-Farabi, who wrote on psychology and
social science, e.g. a work entitled The Model City, in
which city planning is discussed. This same scientist also
dealt with the theory of music and the theory of science
in general. Al-Sufi was another observational astronomer,
who made the most complete map of the fixed stars. So
many are the Moslem scientists that the work in any one
branch would be astonishing. In mathematics alone it is
impossible even to give a list of all those who contributed.

The scientist Al-Hazen made most important contri-
butions to the study of optics, explaining atmospheric
refraction, the apparent increase in the size of the sun
when on the horizon (twilight phenomena), also the
theory of lenses. He was strictly an experimental scientist
who neither in method nor practice differs from the best
of any period.

Two great figures dominate the close of Arabic
scientific genius: Avicenna and Al-Biruni. Both were
systematizers and summarizers of all that went before.
Though experimenters, they are chiefly remembered for
encyclopaedias of existing knowledge, which, because of
their completeness, unfortunately helped to sterilize
Moslem science. Al-Biruni made geodetic measurements,
contributed to geology, surmised the rotation of the
earth on its axis. He was an experimental physicist, and
pointed out that the speed of light must be immense; he
was an observational botanist, who showed that the
petals of flowers are never seven or nine. He fought the
gathering forces of superstition, and objected that faith

40 WHAT SCIENCE REALLY MEANS

in the omniscience of Allah does not justify ignorance,
in effect stating that reference to a final cause is for
scientific purposes mere tautology.

Avicenna has well been called the Aristotle of the
Moslem world, for his systematization and encyclopaedic
summation of all knowledge. The Canon, his famous
medical encyclopaedia, consists of a million words, and
was held authoritative until the middle of the seventeenth
century. But he was a good deal more than a medical
writer, and is known to have experimented on specific
gravity and on the speed of light, which he declared was
finite. Also, like Aristotle, Avicenna's attitude was
philosophical and terminal. And by his very success he
discouraged original scientific advance.

After these large-scale figures there is a sharp decline in
Moslem science, marked by a new resurgence of mys-
ticism on the one hand and positivism on the other.
Despite the efforts of men like Al-Zarqali and Omar
Khayyam, science turned positivistic and toy-minded.

Instead of being concerned with ideas, they had but a
childish interest in automata and in mechanical toys and
contrivances. Without further theoretical studies, their pro-
gress in that direction was naturally very limited. 9

Positivism again proved the death of science. After the
twelfth century science turned toward the West.

CHRISTIAN-MEDIAEVAL EMPIRICISM

Although the full force of the continuous scientific tradi-
tion was not felt in Latin Europe until the infiltration of
9 George Sarton, Introduction to the History of Science , vol. ii, p. 22.

THE ORIGINS OF EMPIRICISM 41

Moslem learning, about the tenth century, there were
already signs of a turning toward the scientific temper.
Magic was the occasion for pre-Moslem European science,
as witness the magic doctor, Marcellus of Bordeaux,
who as early as 395 was already beginning to believe in
the efficacy of experience. Magic is indeed an old thing
in the world, having existed in the midst of the scientific
cultures we have discussed, but it had not in these cultures
reached the proportions which it attained in Latin
Europe. As Lynn Thorndike says, "magicians were the
first to 'experiment/ and . . . 'science,' originally specu-
lative, has gradually taken over the experimental method
from magic." 10

The early Christians had not abandoned Greek
science; they had been misled by such false theories as
those of the bodily humours and the four elements. Thus
we find at first popularized compendia of knowledge,
such as the Herbarium attributed to Apuleius and the
Cosmography of Aethicus. Between the years 510 and 845
there were the Consolation of Philosophy of Boethius,
the work of Cassiodorus, the Etymologies of Isidore of
Seville, the work on plants, animals, and minerals of St.
Aldhelm, the De Natura Rerum of Bede, the work of St.
Agobard, Walafrid Strabo, Macer, and Scotus Erigena.
In general, however, it must be admitted that this is a
period during which empiricism was at its lowest ebb.
Abstract thought was preoccupied with theological
matters, and what little interest remained for science
took at first the most pedestrian turn, as illustrated by
the reliance on early compendia, which degenerated into
10 A History of Magic and Experimental Science, vol. ii, p. 651 f.

42 WHAT SCIENCE REALLY MEANS

mere catalogues of reputed fact. Even in the study of the
quadrivium : music, arithmetic, geometry, and astronomy,
facts got mixed up with mystical meanings. "Music
included a half-mystical doctrine of numbers and the
rules of plainsong; geometry consisted of a selection of
the propositions of Euclid without the demonstrations;
while arithmetic and astronomy were cultivated chiefly
because they taught the means of finding Easter." 11

The continuous scientific tradition was brought to
Latin Europe in the conventional manner, namely, by a
host of translators and adapters of Arabic and Syrio-
Hellenic science. The school of Salerno, which is known
to have been a flourishing medical school as early as 946,
was one of the first to receive the Arabian heritage. We
know of at least two Salernitans, Petrocellus and Archi-
matthaeus, but even more illustrative of the course of
learning is Constantinus Africanus, who was born in
Tunis and went to Baghdad to learn Moslem science.
From Baghdad he went to Salerno, and later to the
monastery of Monte Cassino. Also typical is the case of
Gerbart of Aurillac, afterwards Pope, who lived in
Christian Spain but had contact with Moslem scientists.
He gave an account of Hindu numerals, without the
zero, and wrote on music, geometry, and the astrolabe.
These men were followed by a host of eleventh- and
twelfth-century translators. Among them were Walcher
Prior of Malvern, Plato of Tivoli, Robert of Chester,
Hermann of Dalmatia, Hugh of Santalla, Gerard of
Toledo, and Michael Scot.

11 W. C. Dampier-Whetham, "Science," Encyclopaedia Britannica,
fourteenth edition.

THE ORIGINS OF EMPIRICISM 43

It was in the first part of the twelfth century that
original science began to appear. William of Conches
confirmed the right of free speculation in natural science.
Adelard of Bath, the most outstanding scientist of this
period, travelled in the Moslem world and studied
Moslem science, yet was an original scientist on his own
account, far beyond the stage of Moslem science of the
time. Besides introducing Hindu numerals, translating
Al-Quarizmi's astronomical tables and Euclid's Elements,
in his Questiones Naturales he surveys the field of natural
science. Although many of his answers are incorrect, he
can be called the first Christian European scientist en-
dowed with the complete scientific mentality. He was
impatient of dogmatism and authority and relied on
reason backed by experimental verification. Without
denying final cause, he stressed the necessity of efficient
cause. Since nature "is not confused and without
system," 12 he held that "human science should be given
a hearing upon those points which it has covered." Reason
without authority and with evidence was his creed; he
was "not the sort of man that can be fed on a picture
of a beefsteak." He anticipated the conception that
science should be value free by saying that nothing in
nature is impure.

In the beginning of the thirteenth century there are
two major figures, Grosseteste and Nemorarius, and a
host of lesser men, e.g. Alexander Neckham, Alfred
Sarchel, Witelo, etc. Nemorarius made original contri-
butions to the study of mechanics, especially concerning

12 All quotations from Adelard cited in Lynn Thorndike, op. cit.,
vol. ii, pp. 28-30 (italics ours).

44 WHAT SCIENCE REALLY MEANS

trajectories and, more thoroughly, statics. He applied
the same mathematical technique to the subject as did
later and far more famous physicists. Grosseteste also
understood that reason and experience must co-operate
in science. He did original work on optics and astronomy,
saw the need of reforming the Julian calendar, and stressed
the use of magnifying-glasses in observation.

We have next to deal with three contemporaries of
the middle thirteenth century: Albertus Magnus, Thomas
Aquinas, and Roger Bacon. The first two, known better
as theologians, experimented also. Albertus wrote on all
subjects of natural science, and appealed to observation
and experience, even though his contributions are after
all meagre. Aquinas is known to have written treatises
on irrigation and mechanical engineering.

The third, Roger Bacon, did not, as is popularly sup-
posed, appear in the midst of an ignorant world hostile to
turn of mind. The prior and contemporary scientists
which we have mentioned illustrate this point. Indeed,
in most ways the times were propitious rather than other-
wise. The empirical attitude manifested itself on all sides.
Even in art, as Thorndike points out, the sculptors were
acute observers of natural objects and indeed went
further. They were "breeders in stone, Burbanks of the
pencil, Darwins with the chisel." 13 Roger Bacon, then,
was in no sense isolated.

But he stood alone in that he emphasized the need for

experimentation and mathematics to work together in

science, thus pointing science towards mathematics.

More especially, he saw the tremendous possibilities of

13 Op. cit., vol. ii, p. 537.

THE ORIGINS OF EMPIRICISM 45

applied science, and constantly stressed the utility of
scientific knowledge. He predicted the possibility of air-
planes, steamships, automobiles, the greater practicality
of explosives, and the Westward passage to India, which
indirectly influenced Columbus through the Imago
Mundi of Peter d'Ailly. His own experimental contribu-
tions were much poorer than his vision of what science
should be, and he was more of a herald of science than
a scientist, as his inadequate understanding of scientific
method proves.

The last half of the thirteenth century showed the
halting progress of scientific endeavour. An exception
must be made in the case of Peter the Stranger, whose
experimental work on magnetism and the compass
reveals a good grasp of experimental method. Peter of
Spain, who wrote on medicine and psychology, is chiefly
interesting because he became Pope John XXL From the
scientist Gerbart (Pope Sylvester II) to John XXI, to
say nothing of innumerable monks and friars who were
scientists, it is clearly erroneous to believe that the
Church was hostile to science during this period. At
the close of the century, William of St. Cloud was an
admirable observer in the astronomical field, who made
the first determination in Europe of the obliquity of the
ecliptic.

There is no doubt that there was much empirical
science during the period we have just discussed. Experi-
mentation is referred to again and again from the ninth
century onward. Nevertheless, little science resulted,
and we may well inquire why. The experimental science
of Roger Bacon and his kind turns out to be the con-

46 WHAT SCIENCE REALLY MEANS

ception of science as a directly practical affair. An em-
piricism of this sort finds it hard to distinguish between
natural science on the one hand, and astrology, alchemy,
and the black arts on the other. But Adelard of Bath
sometimes in practice and Roger Bacon often in theory
foreshadow true science, where experiment is not the
goal of research but a part of the method.

RENAISSANCE EMPIRICISM

There is no break between Christian-mediaeval and
Renaissance empiricism. However, it was in the period
between 1300 and 1600 that science was started on its
correct path. Unfortunately it was in this period that the
erroneous positivistic philosophy of science also got its
start. The revolt against authoritarian Aristotelianism
pure deduction from principles held without the em-
pirical sanction, the very revolt which was so fruitful
grew until it became bitterly opposed to abstract reason.
The rejection of one error seemed to be the signal for
the adoption of another. The early humanists made great
fun of the logic of Aristotle, which was afterwards
lumped with the science of Aristotle as outmoded and
ridiculous.

Despite the disrupted condition of Europe in the
century of wars and the Black Death, experimental
science was carried on as it had been in the thirteenth
century; with its random experimentation, uncontrolled
theorizing, and emphasis on practicality, and yet with
its groping toward true scientific method. There was
more interest in magic and the black arts than ever
before, and science reached as low a state as it had since

THE ORIGINS OF EMPIRICISM 47

the Greeks. Even the encyclopaedias, to which unin-
ventive periods always resorted, were degraded affairs.

Among such half-baked investigators of science as
William Merle, Andalo di Negro, Profatius, Dagomari,
Ferminius, John of Picardy, and John of Saxony, atten-
tion was paid to arid facts still confused with astrology.
Two men stand out from these: John de Murs and
Richard Swineshead (called the "Calculator"), who
flourished about 1350. The former insisted that facts
deduced from instruments can neither be denied nor
corrupted, and is said to have made a better astrolabe
than the one made for Tycho Brahe. "Calculator" wrote
a book in which there is abstract consideration of such
physical entities as density, velocity, rarefication, etc.
There was furthermore a tendency in the second half
of the fourteenth century to discountenance alchemy,
astrology, and magic in general. Petrarch, though no
scientist, used his great influence to derogate magic.
Nicholas Oresme devoted his life to writing books against
it, as did his follower, Henry of Hesse. And there were
others, such as Groot and Eymeric.

The next seventy years apparently wrought no change
in the development of science. Nevertheless, the ap-
pearance of such scientists as those of the second half of
the fifteenth century, starting with Cusa and ending with
da Vinci, shows the widening periphery of scientific
interests extending from flying machines to carto-
graphy. 14 Nicholas of Cusa worked on statics, antici-
pated Galileo by suggesting experiments to demonstrate

14 C/. Dana B. Durand, "The Earliest Modern Maps of Germany
and Central Europe/* in Isis, vol. xix (i933), P- 486 flf.

48 WHAT SCIENCE REALLY MEANS

the speed of falling bodies, and stressed the importance
of measure in physical science. He taught that everything
is in motion, the earth along with other planets. Regio-
montanus had an astronomical observatory and worked
on trigonometry; Toscanelli was an observer of cometary
motions, as was Peurbach, who corrected the Alphonsine
Tables. John de Fundis explained the process of erosion
and the gradualness of geologic change. The emphasis
on mathematics of the astronomers is notable, pointing
to the use of mathematics in natural science. Pacioli,
concerned with algebraic roots, worked with Leonardo
da Vinci, who also fully understood that science must be
expressed metrically. This he exemplified in optics,
astronomy, hydraulics, geology, architecture. Starting
always with an interest in particular practical problems,
he was led to understand that only by finding the general
principles involved could he hope to solve particular
problems.

The general interest of the period culminated in one of
the greatest of all scientists. Copernicus has direct his-
torical derivation. His teacher, Novara, of the University
of Bologna, was thoroughly imbued with the stress laid
upon the continuity of nature and the importance of
mathematics as taught by the Academy of Florence.
Also Copernicus derived encouragement for his helio-
centric theory from the classic writers who had favour-
ably mentioned that of Aristarchus of Samos. Nor
would his work have been possible without the previous
geocentric system of Ptolemy. Copernicus was mainly a
mathematical theorist, who observed, but who did not
really base his proofs on observation. The theory is non-

THE ORIGINS OF EMPIRICISM 49

empirical, in the positivistic sense of the term, since it
did not take into account common sense or the prevailing
data of physics. As Burtt points out, the chief merit of
liis theory over that of Ptolemy's was one of economy,
"saving the phenomena" by means of thirty-four epi-
cycles instead of eighty. "Contemporary empiricists [i.e.
positivists], had they lived in the sixteenth century, would
have been first to scoff out of court the new philosophy
of the universe." 15

Copernicus was a canon and addressed De Revolutionists
to Pope Paul III. At this time the Church's attitude
toward science was not strictly defined. The Church
opposed all heresy in general, in which both magic and
science were shortly to be included without any dis-
tinction between them. The confusion is illustrated in
Pico dela Mirandola, who though a good Churchman
believed in science, wrote against astrology, and yet
endorsed the Cabala. Later the Church took a much more
determined attitude against natural science, based on
the seemingly anti-theological import of Copernicus's
system.

Meanwhile the descriptive sciences showed signs of
development. Vesalius, in Belgium, in his De Humani
Corporis Fabrica, corrected false anatomical descriptions
of Galen and worked on exact anatomy. Eustachius,
Fallopius, and Fabricius in Italy continued this work.
Fabricius discovered the valves in the veins and was the
teacher of Harvey. In Spain Servetus contributed much
to anatomy. Palissy explained fossils correctly, and

15 E. A. Burtt, The Metaphysical Foundations of Modern Physical
Science, p. 25.

D

50 WHAT SCIENCE REALLY MEANS

Agricola, in Germany, wrote on stratographic geology.
Gesner, the Swiss, studied and classified plants and
animals; Bauhin systematized botanical classification.
Gilbert of England worked on static electricity and
magnetism from a purely empirical standpoint.

But the descriptive sciences showed no such remark-
able development as did the physical. Observation un-
aided is only half of science. It is true that Tycho Brahe,
by painstaking observation at Uraniborg and later in
Germany, where he made a giant quadrant, furnished
the empirical data for Kepler's theoretical formulations.
But Brahe alone would never have confirmed the
Copernican revolution. Kepler, the mathematician, dis-
covered the laws of planetary motion, showing that the
planets describe ellipses about the sun in one focus, and
that radius vectors from the sun sweep out equal areas in
equal times. Kepler is an arch example of the complete
scientist whose main preoccupation is with consistent
theory but who insists that it be based on empirical
observation. With Kepler's work, as with all great
scientific discoveries, the field was opened rather than
closed to new inquiry. The laws of planetary motion
discovered by Kepler did not check with the old physical
ideas, and so led to new physical questions and thus to
the development of modern physics in the seventeenth
century. All this was foreshadowed and proclaimed by
the martyr, Bruno, who predicted such discoveries as
the rotation of the sun, the enormous astronomical dis-
tances, unknown planets, and the conservation of
energy, etc.

In looking back over these three centuries, we note

THE ORIGINS OF EMPIRICISM 51

two kinds of empiricism. On the one side there were
those observers and experimenters who were seeking in
the facts for almost anything: the positivistic-minded
magicians, alchemists, and physicians. Almost as barren
was the descriptive science of this period. But on the
other side were those experimenting theorists who looked
for principles over and beyond the mere appearances
and who tested these against empirical fact. Alchemists
are 'practical* men; chemists are not. The paradox is
presented that science must abstract from practicality
in order to arrive at principles susceptible of being
practically applied.

However, despite the success of such pure theorists as
Copernicus and Kepler, the main opinion persisted even
among scientists that science is an affair of demonstration
only, opposed to abstract reason. The period under
review points the direction that modern science has
taken away from the occultists toward a further develop-
ment of this early science. But the conviction that ex-
perimentation is somehow opposed to abstract reason
continued to gather momentum and remains to influence
science to-day.

CHAPTER III
THE DEVELOPMENT OF EMPIRICISM

If you want to find out anything from the theoretical
physicists about the methods they use, I advise you
to stick closely to one principle; don't listen to
their words, fix your attention on their deeds.

EINSTEIN

SEVENTEENTH-CENTURY EMPIRICISM

THE opposition of science to reason in the beginning of
the seventeenth century does not at first show itself in
the revulsion against theory but only against the current
Aristotelianism, i.e. theory without experiment. 1 As a
matter of fact, the scientific theories of that age would
seem wild to a modern positivist. If Galileo and Newton
had revolted against all theory, science would never have
reached its great development. The chief source of the
development of science was an acceptance of mathe-
matical reasoning as applied to natural science. Mathe-
matics was encouraged and developed by such men as
Napier, the discoverer of logarithms, Descartes, the in-
ventor of co-ordinate geometry, Cavalieri, Fermat,
Desargues, Pascal, Wallace, etc., who covered the field
from the theory of invisibles to probability and analytic

1 "In the case of the vase emptied of air, Descartes asserted that
either some other material must enter the vase or else its sides would
fall into mutual contact; More was prepared stoutly to maintain that
the divine extension might fill the vase and hold its sides apart"
(Burtt, Metaphysical Foundations of Modern Physical Science, p. 138). It
occurred to neither to appeal to experiment!

THE DEVELOPMENT OF EMPIRICISM 53

geometry, leading up to the work of Leibnitz and Newton
on the calculus. But mathematics seemed to them to
have nothing to do with logic.

The rejection of the scholastic system alienated religion
and the universities from the new science. The Church
burned Bruno in 1600; shortly after this date science
began to organize its own academies: the Accademia dei
Lincei at Rome in 1603, followed by the Accademia del
Cimento at Florence in 1651, the Royal Society of
London in 1662, the Academic des Sciences at Paris in
1666, and the Berlin Academy in 1700. Stimulated by
the work of the academies the emphasis on observation
led to the invention and improvement of scientific
instruments: the thermometer, the barometer, the
microscope, the telescope, the air pump.

We may note two kinds of science in this century.
The mathematico-physical sciences were highly specu-
lative and developed rapidly. The descriptive-biological
sciences were equally empirical but less abstractive and
speculative, and developed very slowly. The period
shows that empiricism is the sine qua non of science, but
that it must not be held down to the entities of common
observation.

In physical science the century opens with Stevinus
who set forth the parallelogram of forces, the principle
of virtual displacement, and other work on statics.
Galileo's chief originality lay in the field of dynamics,
though, of course, he had hints from many predecessors.

Galileo was an important experimenter. Through the
telescope which he developed he observed sunspots,
mountains on the moon, the satellites of Jupiter, the

54 WHAT SCIENCE REALLY MEANS

phases of Venus, etc. His experiments, however, were
preceded by a study of the principles involved. 2 The
extent to which Galileo was preoccupied with abstract
principles and not primarily with mere exemplifications
is shown in the manner in which he generalized from
the inclined plane to the law of falling bodies, to inertia,
and thus to the generalized law of motion, incidentally
showing that his youthful discovery of the pendulum
principle was a special case of this general law. Galileo
understood that scientific method starts with the evidence
of common-sense experience but comes to theories,
experimentally verifiable, that do violence to common
sense.

Boyle is the first modern chemist. Basing his work on
that of such men as van Helmont and Jean Rey, in his
The Sceptical Chymist, 1661, chemistry is treated for the
first time as a science, and not as an empirical art for
working precious metals and useful medicaments. Boyle,
in fact, did for chemistry what Galileo did for physics.
Just as Galileo killed Aristotelian mechanics, so Boyle
destroyed the authority of the four elements, insisting
upon experimentation to find the true ones. Although
himself a patient experimenter and an opponent of wild
theories, he yet declared the principle that "experience
is but an assistant to reason/ '

Two main influences led to the great synoptic genius
of the century, Newton. First, the idea of die universe

2 By his own account, "the report by a noble Frenchman finally
determined me to give myself up first to inquire into the principle of
the telescope, and then to consider the means by which I might com-
pass the invention" (Dampier-Whetham, Cambridge Readings in the
Literature of Science, p. 17) (italics ours).

THE DEVELOPMENT OF EMPIRICISM 55

as a perfect mathematical scheme, via Kepler, Galileo,
and Barrow, his teacher. Second, the over-emphasis on
experimentation characteristic of the whole age, led him
to accept Galileo's atomistic mechanism with its objec-
tive atoms and the void and its subjerive interpretations.
It follows that these should have led to the brilliant
scientific scheme, and to the erroneous positivistic con-
clusions that the laws of nature are mere descriptions of
actuality. The scientific scheme was drawn from Kepler's
astronomy and Galileo's dynamics, generalized into the
laws of motion and gravitation. Thus astronomy and
physics became one science. The positivistic conclusions
consisted of a philosophy deduced from a method. The
method of treating phenomena in isolation had proved
successful with Galileo, Boyle, and in his own work. He
concluded that explanations of the whole were irrelevant,
and declared that he did not touch hypotheses. This
negative attitude is positivism, which derived terrific
prestige from the fact that it was endorsed by the very
man who gave mathematical physics its greatest impetus.

The influence of Newton confirmed the tendency of
the century toward a development of the mechanico-
mathematical interpretation of the universe, and its
investigation by experiment and mathematics. Huygens
proceeded to develop the theory of centrifugal force,
explaining the flattening of the earth at the poles, and
also his wave theory of light. The development of the
physical sciences was paralleled by an unfortunate
acceptance of positivism.

The biological and descriptive sciences in this century
could not avail themselves of mathematics. In spite of

56 WHAT SCIENCE REALLY MEANS

such spectacular achievements as that of Harvey's dis-
covery of the circulation of the blood, and Leeuwenhoek's
microscopic discovery of bacteria, more than a century
elapsed before biology reached maturity. Their work
is almost exclusively on the level of common-sense
observation, and mainly notable for the overthrow of
the old Greek biological ideas. Sydcnham insisted on a
material basis for disease, Borelli analysed the mechanics
of muscular action, Malpighi worked on embryology
and observed the flowing of the blood, and Hooke
examined living tissue under the microscope. Similar
fresh observations were made in other studies by men
freed from old preconceptions, such as Steno, the
Dane, who made investigations into the nature of the
earth's crust, and Lister, who drew the first geological
maps. This valuable spade-work must not be underrated,
but it does not represent the same advance as that made
by physics. The emphasis on description and classification
bolstered the positivistic account of what science is.

Positivism is as old as Hippocrates. 3 It has been easy
to show how the century which saw the origins of
modern science also saw the acceptance of the old
positivistic misunderstanding of science. The rejection
of final cause, together with the adoption of a mathe-
matical universe, required a mechanistic atomism. The
mistake arose when Galileo assumed that efficient and
final cause are not respectively equal to the actual and
the mathematical. This equates final cause with actuality,
i.e. a completely determined actual world of atoms.
Descartes exhibits this error in his 'physicalism* : all
3 Cf. Hippocrates, De Prisca Medicina, 1-2 (I, 570 ff., L.).

THE DEVELOPMENT OF EMPIRICISM 5?

reality is mathematical, but all reality is also extended.
Thus all mathematical sciences reduce to the science of
physics. This is positivism almost in its modern dress.

However, fortunately positivism was an induction
from science in the seventeenth century, and science was
not a deduction from positivism. If the latter had been
true there would be no science. And in so far as modern
science has taken this doctrine seriously, as in the
descriptive branches, it has been much hindered. Fortu-
nately and unfortunately, the early physical scientists got
hold of a method which they employed without under-
standing its philosophical meaning.

EIGHTEENTH-CENTURY EMPIRICISM

Accordingly, physical science proliferated tremendously
in the eighteenth century. Physics and astronomy had
already become largely systematized; in this century it
remained for chemistry to accomplish the quantitative
systematization.

Astronomy, however, was not without its develop-
ment, notably in the work of the Herschels, who dis-
covered Uranus, and traced the motion of the solar
system to a point in the constellation of Hercules, and
who identified over two thousand nebulae; and in the
work of Laplace, famous for the nebular hypothesis, and
for celestial mechanics. Other branches of physical
science which were developed included acoustics and the
theory of heat. One of the most prolific developments of
physical science in this century was the discovery of the
rudiments of electromagnetism. Grey and Wheeler at
the beginning of the century found that electricity could

58 WHAT SCIENCE REALLY MEANS

be transmitted through certain substances. Dufay dis-
covered that electrical charges were of two kinds, positive
and negative. Von Kleist, Musschenbrock, and William
Watson were responsible for the understanding of
electrical induction. Franklin showed that lightning was
an electrical manifestation. Coulomb demonstrated that
an electric charge has magnetic properties. But perhaps
the greatest impetus was given to the study by the dis-
coveries of Galvani and Volta at the end of the century,
that electricity is generated by chemicals as well as by
friction.

Meanwhile mathematics pure and applied continued
the splendid development of the previous century, in the
work of Maclaurin, who systematized the calculus;
Euler, who established analysis as a study independent of
geometry. Bernoulli, D'Alembert, and La Grange further
applied mathematics to mechanics and dynamics.

By far the most important scientific advance was that
made by chemistry. Moreover, it best illustrates the
manner in which a science should proceed. The interest
in chemistry was given a new impetus when the theory
of phlogiston was challenged by the experiment of Dr.
Joseph Black in 1756. By heating quicklime he showed
that there is a loss of weight exactly equal to the amount
of "fixed air" given off, and thus that fixed air (CO 2 )
is a constituent of the atmosphere. Bergmann soon
found that "fixed air" is not air, but the compound,
carbon dioxide. Cavendish in 1766 isolated "inflammable
air," which on burning condensed into water. The
significance of the combination of inflammable air
(hydrogen) with the oxygen of the atmosphere to form

THE DEVELOPMENT OF EMPIRICISM 59

water was not understood until Watt and Lavoisier re-
peated the experiment. Rutherford in 1772 discovered
that "inert air" was nitrogen.

Independently Scheele and Priestley discovered oxygen,
which the latter termed "dephlogisticated air/' He
found that it would support combustion and respiration
better than ordinary air. It should be noted here that
although superficially this chemical experimentation
appears as a trial-and-error random affair, it yet was
directed by certain pro tern, accepted hypotheses, with-
out which there could have been no revelatory experi-
mentation.

How the progress of science works is best shown by
the chemical labours of Lavoisier, who put together
Boyle's ideas of the elements with the discoveries of the
preceding eighteenth-century chemists, to form a quan-
titative system which gave a terrific spurt to further
quantitative research, leading to Dalton's atomic theory
and thus to the whole of modern chemistry. Convinced
that no ponderable matter disappears in chemical changes,
Lavoisier carefully interpreted quantitative results, and
in this way arrived at the conclusion that the different
"airs" of his predecessors were chemical elements.

Robert Boyle had "pleaded for a closer relation
between experimental facts and theoretical speculation." 4
But the unity of experiment and speculation need not be
simultaneous in time or contained in the same person.
Thus a hundred years elapsed between Boyle's definition
of chemical elements and Lavoisier's organization of the
table of chemical elements, in which the latter drew on
4 Douglas McKie, Antoine Lavoisier, p. 59.

60 WHAT SCIENCE REALLY MEANS

the interim experimental work. Thus without the defini-
tion, there would have been no experiments capable of
determining specific elements; but without the experi-
ments the definition might have remained an arid hypo-
thesis. With the two, though separated by a century,
there resulted a valid and progressive science of chemistry.
Had Lavoisier not systematized chemistry, he would
have accomplished little more than Priestley, Black, and
Scheele, and chemistry would still be an affair of piece-
meal and unrelated experimentation.

During the eighteenth century there was much work
done in the descriptive and biological sciences. It did not,
however, prove to be of the sort which leads to a valid
and fruitful system. There was some development in
physiology, comparative anatomy, embryology, and
'natural history.' Natural history included botany,
zoology, and geology. Physiology was connected with
medicine, but was not understood to be significantly
related to zoology. Buffon, in his Natural History,
described all known species of animals. Linnaeus classified
all known plants. Both were painstaking and accurate,
and the latter's classifications were worked out in great
detail. Nevertheless, description and classification do not
constitute the abstract systematization which is the aim
of science. They do not, because they remain on the
qualitative level, allowing of no mathematical applica-
tion. But as we have seen, science progresses in direct
ratio to its employment of the mathematical method.
Any elaborate qualitative system, such as Buffon and
Linnaeus set up, hinders rather than accelerates scientific
progress.

THE DEVELOPMENT OF EMPIRICISM 61

What eighteenth-century science demonstrates is that
there are different levels of empiricism. Certainly descrip-
tion and classification are as empirical as the experi-
mentation of Laplace and Lavoisier; but in the former,
observation remains at the common-sense level, or at
best systematization is accomplished by qualitative
categories. These two men worked with quantitative
relations, arcana to ordinary observation. For positivism,
if logically carried through, description would be the
most valid, classification next, and quantitative synthesis
last. But progress in scientific research has illustrated that
increasing validity lies in the other direction.

NINETEENTH-CENTURY EMPIRICISM

It was in the direction of increasing systematization that
the development of the nineteenth century lay, at least
in the physical sciences. But it took on a special phase.
Many new branches of the physical sciences were ex-
plored, and the systematization showed unification by
means of interconnection between these new branches.
In biological sciences there were brilliant discoveries, far
more brilliant than those of previous centuries, but little
unification was accomplished.

The increasing specialization and unification are shown
in many fields. The relation between chemistry and
physics proceeded from Dalton's atomic theory to the
periodic law of the table of elements of Mendeleef. The
relation between electricity and other forms of energy
was first shown by Ampere and Ohm; the relation
between electricity and magnetism by Faraday and Max-
well. And all these were embraced by Hertz's discovery

62 WHAT SCIENCE REALLY MEANS

of the electromagnetic nature of radiant energy. In other
ways electricity, chemistry, and radiant energy were
shown to be interrelated, as with the discovery of
electrolysis by Arrhenius, the polarization of light by
Fresnel and Young, the X-ray by Roentgen, radio-
activity by Becquerel, and the properties of radium by
the Curies.

Even more generally, the interconnectivity between
forms of energy was exhibited by Avogadro, Sadi
Carnot, and Fourrier in their work on thermodynamics,
followed by that of Helmholtz, Joule, and Kelvin,
Clausius and Boltzmann on the conservation and degra-
dation of energy. To give but one example of the high
specialization which took place, we have but to mention
so elementary a science as geology, which was divided
into the sciences of stratigraphy, mineralogy, petro-
graphy, petrology, and palaeontology. On the other
hand, many more interconnections between sciences
were shown than those we have mentioned, such as
physiological chemistry, biochemistry, chemical biology,
etc. There were the sciences of spectroscopy, which
showed among other things the relation between radia-
tion and chemistry, and crystallography, which showed
the relation of geometry to chemistry. In chemistry,
geometric properties as well as arithmetic ratios were
demonstrated.

Mathematics in the nineteenth century went further
than it had in all its previous history. Not only was it
developed along with its application to physical sciences,
but also, as pure, it forged so far ahead of application
that even its adherents could conceive of no possible

THE DEVELOPMENT OF EMPIRICISM 63

field of application for the new systems. Legendre,
Jacobi, Cauchy, and Abel developed the theory of
elliptical functions, Cayley is responsible for the theory
of matrices, and, with Gauss and Sylvester, for the theory
of invariance. Gauss, one of the three masters of modern
analysis, also set forth the properties of imaginary
numbers, while Lobatchewsky and Riemann worked out
independent systems of non-euclidean geometry. Weier-
strass, Klein, and Poincare improved the theory of
functions. Sir William Hamilton developed quarter-
nions, and Cantor the theory of irrationals and of trans-
finite numbers.

During the nineteenth century 'natural history' was
divided into geology, botany, zoology, and physiology,
and these in turn were further subdivided. Two types of
investigation in the whole biological field predominated;
these we may call the microscopic and the macroscopic.
In the microscopic field von Baer in 1828 founded the
science of embryology, discovered the human ovum.
Ten years later Schleiden and Schwann developed the
cellular theory, which Claude Bernard organized into
the science of cytology. Virchow, following up this work,
recognized the part played by the leucocytes in pathology.
Pasteur made his famous discoveries of the functions of
micro-organisms in chemistry and the etiology of disease,
thus paving the way for a new type of surgical asepsis
and medical practice. Following the work of Pasteur,
rapid progress was made in segregating the micro-
organisms of typhoid, tuberculosis, diphtheria, bubonic
plague, etc. And the science of immunology made rapid
strides.

64 WHAT SCIENCE REALLY MEANS

The work on evolution accomplished in the nine-
teenth century started with the speculations of Lamarck,
on the origins and development of living organisms. The
Origin of Species, published in 1859, released a storm of
controversy. To be sure, in spite of the enthusiastic claims
of Darwin's followers, investigation at this level can
hardly be called exact science, though it pointed the way
toward scientific research into the laws of heredity,
which were worked out statistically by Mendel, and
studied at the empirical level by de Vries and Bateson.
These latter men created the science of genetics which
attempts to discover the mechanism of heredity and
variation in biologic elements.

In this century the social sciences may be said to have
first been studied with abstraction. They are mentioned here
for their ambition rather than for their accomplishment,
because it can hardly be said that any social science, with
the possible exception of economics, has begun to reach
the level of abstraction at which a study becomes a
science. Psychology in this period was first officially
introduced to the laboratory and began to assume the
status of an experimental science.

The nineteenth century also witnessed the culmination
of the materialistic conception of the universe, and the
triumph of the mechanical model, in keeping with the
Newtonian understanding. Accordingly, all actuality
was thought to be a strictly deterministic affair, and
thus cause-and-effect an historical chain which goes back
to the infinite past. In this scheme it was hard to place
the mental realm, since it appeared to be an intruder
into this tidy universe, and thus insusceptible to the

THE DEVELOPMENT OF EMPIRICISM 65

mathematical laws which otherwise rule. This inability
to place mentality was one of the causes of the confusion
regarding psychology and the social sciences. But the
greatest confusion obtained in regard to the meaning of
mathematics: since mathematics had been demonstrated
to be the best tool for the discovery of the laws of
nature, it must somehow be connected with the material
world. On the other hand, since it is a manifestation of
the human intellect, it is unmistakably mental. Pro-
vided mind and matter are categorically distinct, how
can mathematics as imbedded in the nature of things be
mental; or how, if it be mental, can it accord with the
nature of things ? This positivistic dilemma was largely
responsible for the misunderstanding as to what science
really means. Such was the status of scientific theory at
the opening of the twentieth century.

TWENTIETH-CENTURY EMPIRICISM

In this section we must abbreviate, for although the
period under consideration is only thirty-six years, so
great an acceleration in scientific activity of all kinds has
taken place that it would be quite impossible to give
more than a cursory account. The exposition must be
confined to the most significant developments rather
than to the many subsidiary contributions.

The branches of biology which have been developed
in the twentieth century are startlingly numerous. There
have been marked advances in old biological sciences,
and new sciences added to the list. For instance, the
science of genetics has gone forward under the leader-
ship of T. H. Morgan, through the discovery of muta-

66 WHAT SCIENCE REALLY MEANS

tions and genes. Bayliss and Starling since 1902 have
introduced the science of endocrinology, or the study of
hormones, which has had so many repercussions in the
practice of medicine. Hopkins, starting in 1912, dis-
covered the vitamins, which have been gradually sub-
divided into various types. Allergy and immunology
have been made into fruitful fields of inquiry.

Two difficulties present themselves to the science of
biology conceived as a general science. The first is the
random and seemingly unrelated nature of biological
investigation, and of discoveries so greatly multiplied
that the task of synthesis appears almost insuperable.
The second is that in too many fields investigation is still
held down by the nineteenth-century conceptions of
Darwin and Pasteur. Thus the favourite explanation for
the etiology of all disease is still the micro-organic one,
and the favourite explanation of all organic modification
is still the developmental one of mechanical evolutionism.
It is easy to say that the much needed synthesis of biology
will come in due time; but time alone is not enough,
for the right scientist is required, one who will take a
synoptic view which present biology is hardly calculated
to encourage.

The case of physical science in the twentieth century
has been far otherwise. Indeed, it accomplished the
greatest unification of its entire history. Curiously, this
unification was first suggested through difficulties en-
countered with the mechanical model of the universe.

The hypothetical ether was called on to carry different
kinds of waves, and thus a substance with properties
which could neither be discovered nor imagined. Ex-

THE DEVELOPMENT OF EMPIRICISM 67

periments on the ether led to the famous attempt of
Michelson and Morley to determine the ether drift. The
null result of this experiment, which was performed in
1887, called for a new explanation, which was first
attempted in terms of the old physics. Fitzgerald, Lorenz,
and others at the beginning of the century worked out
transformation equations which saved the appearances
but which called for a systematic deception on the part
of nature, incredible to the scientific world. The problem
was resolved by the subordination of the Newtonian
formulation of space and time. Einstein in 1905 an-
nounced his special theory of relativity, whereby space
and time are relative to a given frame, the speed of light
remaining the only constant. Minkowski, in 1908, em-
ploying non-euclidean geometry, showed that what the
special theory involved was a four-dimensional con-
tinuum. Einstein in 1916 with his general theory of
relativity worked out the mathematical formulation in
terms of the tensor calculus of Levi-Civita, a postula-
tional system giving the formulations for any frame. It
has no picturability.

Sub-atomic physics underwent a similar revolution,
starting from the discovery by Becquerel in 1896 of
radio-activity, whereby the atom was shown to be a
complex of still more fundamental particles. Five years
later Max Planck discovered that the interchange of
energy proceeds not gradually, as had been supposed,
but rather discontinuously, in atomic lumps of action
called quanta. Meanwhile attempts at a mechanical model
were made successively by Thomson, Rutherford, and
Bohr, comparing sub-atomic mechanics with celestial

68 WHAT SCIENCE REALLY MEANS

mechanics. It was discovered, however, that the inter-
change of energy within the atom in no way responded
to mechanical treatment, but that Planck's principle of
the quantum was involved. With Heisenberg, Dirac, and
Schrodinger employing the theory of matrices, non-
commutative algebra, and Hamiltonian functions, in the
period 1925-26, a new sub-atomic theory, sometimes
called the quantum theory, was devised entirely in non-
picturable terms one which contradicts practically every
tenet of classical mechanical physics.

Thus in both departments of physics, the mechanical
model definitely broke down and was supplanted by the
mathematical model. "Material points consist of, or are
nothing but, wave systems." 5 The change from the
mechanical model to the mathematical model involves
the change from categories of sense experience to cate-
gories of objective instruments. As Planck himself has
said, "It is much easier to establish exact physical laws
if the senses are ignored and attention is concentrated on
the events outside the senses. . . . The eye gave way to
the photographic film, the ear to the vibrating mem-
brane, and die skin to the thermometer." 6 Physics has
left the description of actuality for the systematic ex-
ploration of relations which are its invariables.

The most striking thing about abstract science is its
use of mathematics, and particularly significant is the
relatively high applicability of scientific principles which
were formerly considered pure, as in the use of matrices,

6 Schrodinger, cited in Dampier, A History of Science, p. 412.
6 Planck, The Philosophy of Physics t pp. 16-17 (George Allen &
Unwin Ltd.).

THE DEVELOPMENT OF EMPIRICISM 69

the tensor calculus, etc. The development implies a higher
and higher level of abstraction, which, as it rises in
abstractiveness, accelerates in its advance.

But in the abandonment of the conception of science
as a description of actuality, certain difficulties ensued.
Causality no longer appeared valid, and indeterminacy in
actual sub-atomic events refuted the locked temporal
chain of cause and effect. The implied moral, that science
deals with a mathematical realm, of which actuality is
only a probabilistic approximation, has been erroneously
read as though causality were ruled out of the physical
world, and as though all that could be known were laws
of probability. The disappearance of the mechanical
model and of the old interpretation of causality has been
responsible for two kinds of interpretation of what
science really means. On the one hand, there is the school
of objective mentalism of Eddington and Jeans. On the
other hand, there is an attempt by the conservatives to
save what can be saved of the old picturable model, 7
at the expense of the reality of natural law. This has taken
the form of the revival and emendation of positivism.

EMPIRICISM MISUNDERSTOOD

This rapid survey of the history of science has brought
out the fact that empirical science of a sort has had a
continuous history from early Greece to modern times.
The halting progress of science prior to the middle of
the sixteenth century apparently cannot be blamed on a

7 Cf. Bridgtnan's attempt to find the residue of the "physical models
of classical theory" in the text accompanying the equations of
mathematical models, in The Nature of Physical Theory.

70 WHAT SCIENCE REALLY MEANS

lack of experimentation but rather on the use to which
experiment was put and to the narrow practicality of
scientific ideals. Experimental science had to rise out of
magic and into the use of mathematics; whereas theo-
retical considerations had to come down out of
theology and submit themselves to empirical checking.
The meeting of both movements resulted in modern
science.

Experimentation seems to have gone hand in hand
with unsuccessful as well as with successful scientific
endeavour. Certainly there has been no valid science
without it, as is exemplified by Archimedes and the
Alexandrians as well as by Galileo and Faraday. But just
as certainly there has been much invalid science with it,
as is exemplified by the alchemists and astrologers of the
fourteenth century. We may conclude that experi-
mentation does not make the difference between science
and pseudo-science, although it is one of the necessary
elements of true science. What then is the difference
between the kind of experimentation which produces
science and the kind which fails ? A consideration of the
history of science should suggest an answer. Where
empiricism is understood as held down strictly to
common sensory observations, science can get no
further than description and classification, or so-called
empirical laws, i.e. inductions drawn at the qualitative
level of common sense. When, however, empiricism is
understood as the discovery of relations which sensory
observation leads to but which are not themselves
sensory, there emerge the beginnings of a quantitative
science with its abstract causal laws.

THE DEVELOPMENT OF EMPIRICISM 71

Had Galileo drawn only the induction that all falling
bodies drop at the same rate irrespective of weight, this
would have been a positivistic summary, a 'statistical
law,' which incidentally would only have been true
more or less, since it would not have taken into con-
sideration countervailing forces present in uncontrolled
conditions. So framed, it would certainly never have
suggested the law of inertia. It is because such scientists
as Galileo and Newton recognized the empirical nature
of entities like 'force,' 'space,' and 'mass,' which are not
completely equatable with anything actual, that they
were able to formulate laws of a generality great enough
to be applicable to varying conditions of actuality, and
thus practical in the largest sense of the word. The
reason the positivistic Greek physiologists did not dis-
cover the circulation of the blood, may be laid to their
prohibition against looking for anything which was not
immediately perceptible, the circulation of the blood being
not in itself a sensory fact but observable only in its
function. No such non-sensory empirical fact can be
arrived at without sought-for relations. This involves
theory as well as fact.

The guiding ideas and the procedure of the great
scientists illustrate that they have always been pre-
occupied with the discovery of relations and with the
necessity of weaving these into an abstract system.
They went to the sensory phenomena of nature only
for suggestion, allowance, or confirmation of theories of
underlying relations which could be formulated as ab-
stract causal laws. Convinced of the continuity of nature,
they have always been concerned to show the interrela-

72 WHAT SCIENCE REALLY MEANS

tions of these causal laws, thereby endeavouring to reveal
nature's system. This they have sought to accomplish in
two ways. First, they have aspired to consistency, order,
and unity within their sciences, by finding laws of a
generality which would show all laws of a lesser generality
as special cases. Secondly, they have worked toward
more specific relations. This direction of endeavour has
been misunderstood to mean the direction toward actual
sensory fact, but it is nothing of the sort. 'Tuberculosis'
is a more specific function than 'respiratory disease' or
'disease,' but none of them refers necessarily to actual
facts.

This attempt to find the abstract regularity in pheno-
mena cannot, however, be arrived at by pure speculation,
as Plato supposed. But neither can it be found by dumb
observation, as Francis Bacon supposed. It can be found
only through the judicious use of speculation carefully
held down by, and corrected according to, the observa-
tion of phenomena. Once tested, principles become in
turn empirical facts, and are employable as data for
further speculation and empirical demonstration.

Philosophical empiricism is therefore clearly not the
implicit philosophy of science, since it holds that the
only valid appeal to truth is limited to sense experience,
and that by consequence abstract reasoning is suspect.
This was the view of the British school of Locke and
Hume. Supposing that science was talking about pheno-
mena and not about abstract functions, Hume showed
that sensation presents no linkage of cause-and-effect
relation, but only the temporal succession of one event
after another. It would follow from this that causality

THE DEVELOPMENT OF EMPIRICISM 73

is a mental grouping of sense experiences, and thus
insusceptible of objective proof. This contention was
based on an entire misunderstanding of what science
really says. Science does not say with Hume that the
cause of the melting of wax is the heat which precedes
the melting. Rather it states the general principle that
heat accelerates the molecular velocity, and that at a
certain velocity the mass reaches the liquid state. It is
not the temporal succession of the demonstration which
is interesting to science, but the conditions necessary for
this transformation at any time or place. This function
is the linkage of cause and effect, which Hume stated to
be non-empirical. Such a function is not at the level of
common-sense experience, but it is empirical none the
less.

Although the empirical philosophy did not stop
scientific progress, the effect of it was toward rein-
forcing scientists in their erroneous belief that experiment
is the whole of method and that principles are sum-
maries of actual experiments. Plainly, this does not agree
with the procedure of science. With the employment of
abstract reason and the use of general principles, not to
mention mathematical analysis, scientific empiricism
will be recognized as essentially a rational and logical
procedure. Thus the distrust of abstract reason by the
scientists is misplaced; it should be directed against un-
bridled rationalism. Yet it is because of this anti-rational
orientation that modern science has come to look
askance at philosophy, and has preferred to take refuge
in the irrational doctrines of positivism. What science
objects to is bad philosophy; but it does not avoid bad

74 WHAT SCIENCE REALLY MEANS

philosophy by running from one bad philosophy to
another equally bad. The time has come when science
faces the necessity of discovering its true philosophy.
This can be accomplished only by a thorough-going
analysis of empiricism.

CHAPTER IV
MODERN MISCONCEPTIONS OF EMPIRICISM

Both romantic idealists and positivists banish
rigorous reason as a true integral part of the
natural world.

M. R. COHEN
FROM HUME TO COMTE

WE have shown that the philosophical understanding
of empiricism does not accord with the procedure of
science. Although such radical empiricism as Hume and
his followers set forth did not affect this procedure, it
did reinforce the scientists, already biased in its favour,
in their view that science is primarily empirical and that
empiricism is basically irrational. Philosophical thought
from Hume onward did not change this tendency but
rather emphasized it. In spite of the many reactions
against radical empiricism (positivism) in philosophical
circles, reactions which were regarded by the scientists
as flights of unscientific fancy and moony-eyed idealism,
the positivistic view became more and more widespread.
The eighteenth-century Enlightenment took for granted
the world-view of mechanistic materialism as a locked
system, but dwelt on the freedom of the human mind
to manufacture whatever conceptions it required and
thus to make over social life. Here was an absolute
hiatus between the brute facts of experience and the
reasoning powers of man. Diderot, Condillac, Condor cet,
and other 'rationalists' interpreted this dichotomy as

76 WHAT SCIENCE REALLY MEANS

favourable to the intellect; thus the title of the 'Age of
Reason' has been given to this period.

But to Rousseau and the romantic school, another
interpretation appeared just as satisfactory, namely, that
reason is a spurious and unreliable guide, and that man
should rely altogether on feeling and 'natural fact/
Disregarding the point that Rousseau was hardly a
thinker at all, and that Hume was a very exact thinker,
we may note that both arrived at the same conclusions
due to the premises they implicitly accepted: that sense
experience and not abstract reason gives the most indu-
bitable evidence on which to build permanent and
positive knowledge.

Without considering the tremendous import of Kant's
attempted resolution of the dilemma between reason and
phenomena, it may be said that in its effect the philosophy
of Kant was more influential on the side of radical
empiricism than on that of rationalism. Kant maintained
that we cannot have knowledge of the supersensory,
and that metaphysics which attempts it is pseudo-science.
Kant himself modified his position on the impossibility
of metaphysics, yet the notion that metaphysics is
'mind-spinning' prevailed in scientific-philosophical
circles. Thus, more and more, scientists and the edu-
cated public in general were led to the belief that science
is altogether concerned with the sensible world of
phenomena, and that philosophy is engaged in talking
about mere concepts of the mind. That such a belief
should assume the proportions of an explicit system was
to be expected. This was accomplished by the posi-
tivistic school of Saint-Simon, Comte, Littre, in France,

MODERN MISCONCEPTIONS OF EMPIRICISM 77

and the utilitarian school of Bentham and the Mills in
England.

EARLY FORMULATIONS OF POSITIVISM

The primary purpose of Comte's positivism was the
rational reform of society by scientific method, thus
instituting the idea of sociology, or the science of society.
In so doing, of course, he had first to define science and
scientific method. Science according to Comte is that
stage of positive knowledge which is reached after
traversing the theological and metaphysical stages. The
third stage, the positive or scientific, abandons the
attempt to find absolute causes and contents itself with
invariant relations between facts established by the
method of observation. This knowledge is sufficient for
practical purposes, and the attempt to reduce everything
to unity is a mere subjective tendency of the mind.
Experience proves it impossible. Comte was not a
scientist and had no knowledge of scientific experi-
mentation. So he concluded that invariant relations could
be found by the mere observation of phenomena at the
ordinary level of sense experience. If he had known
more about science he might have realized that the
objects of observation of experimental science do not
stop with empirical entities overt to untutored eyes.
But through lack of this understanding, he was led to
the false assumption that the laws of science are mere
summaries of past observation.

John Stuart Mill arrived independently at a position
very close to that of Comte; but, as he himself asserted,
he was for a time a disciple of Comte, though he de-

78 WHAT SCIENCE REALLY MEANS

veloped another side of positivism. He went much
further than Comte into the methodology of science,
particularly into the inductive method. It was the
emphasis on the inductive side of scientific reasoning
which led Mill to undcr-emphasize the part of deduction
and to see induction too narrowly as derived from sense
experience. Thus an induction was for him a generaliza-
tion of uniformities in phenomena, and this uniformity
among phenomena he called the laws of nature. A law
to Mill was a name for observable uniformities and not
in itself a part of nature. Looked at in the historical
order, cause and effect became the inevitable temporal
relation of antecedent to consequent. Thus he did not
understand causality non-temporally, as it is presented in
such a science as chemistry, i.e. as the involvement of
one function with another, capable of being presented
as the succession of actual experiments which exemplify
it. Mill's failure to isolate causality from the temporal
order was occasioned by his acceptance of the associa-
tionist psychology of Hartley which defines ideas as the
mere succession of images in the mind. Thus scientific
functions were not disconnected from the perception of
them, and logical factors were confused with their con-
ception by the mind, i.e. logic was made a branch of
psychology.

The net effect of Mill on those scientists who read him
at all was toward increasing their conviction that the
whole of science is the observation of phenomena, and
that the concepts of science are mere mental summaries
of experience. So-called latter-day English empiricism
turns out to be positivism. From it flow modern posi-

MODERN MISCONCEPTIONS OF EMPIRICISM 79

tivism on the one hand and mentalism on the other.
Neither Comte nor Mill understood the whole of
scientific procedure. Many of the principles of science
derive their authority from the manner in which they
embrace and generalize other principles already found,
and often it is not until later that they are experimentally
'proved/ Comte and Mill fell back into almost com-
plete subjectivism in the very act of seeking a firm
empirical objective basis for science. Psychological
certitude has nothing to do with objective truth (as far
as science is concerned).

The certainty which science aims to bring about is not a
psychologic feeling about a given proposition but a logical
ground on which its claim to be truth can be founded. 1

The unfortunate introduction of the observing subject
into the observed field has led the understanding of
empiricism astray.

MACH, POINCARE, PEARSON

The positivistic bent of scientific theory was carried
forward into the later nineteenth century principally by
three men: Mach, Poincare, and Karl Pearson. It is
interesting to note that these three men were scientists,
and that their work had a wide currency among other
scientists, thus showing the greater and greater acceptance
of positivism by scientists themselves.

Ernst Mach, a physicist, attempted to interpret physics
entirely in terms of psychology. That is to say, he held
that science ought to be "confined to the compendious
1 Cohen, Reason and Nature, p. 84.

80 WHAT SCIENCE REALLY MEANS

representation of the actual/' 2 Mach meant that sensa-
tions make up the stuff of reality, whether experienced or
not, but ideas which connect them are mental fictions.
Two things are evident in this scheme: first, that science
is pure description of sensations, and secondly, that no
natural laws exist, laws being but summatory fictions.
On this view, scientific entities, such as atoms, are
fictions, but sensations (which never appear atomisti-
cally!) are real atoms. In this extreme attempt to hold
science down to the vividity of actuality and disallow
real mathematical relations, we get no picture of any-
thing which resembles the world of science, for science
is concerned not with sensuous imagery but with abstract
relations. Mach escaped complete subjectivism only by
using the term 'sensation' as though it were non-
psychological. We can already see how close to posi-
tivism is subjectivism, though the ambition of the former
is to escape 'mind-spinning' and to concentrate on the
objective and undeniable.

In the case of Poincare the same tendency is evident.
Poincare was a positivist, yet scattered throughout his
writings there was the attempt to get outside of the
charmed subjective circle. Instead of trying to make
psychological sensations the stuff of the world, as did
Mach, he took the social mind, particularly as it under-
stands mathematical relations, and made it the objective
world.

Does the harmony the human intelligence thinks it dis-
covers in nature exist outside this intelligence? No, beyond

2 Mach, The Analysis of Sensations, preface to the fourth edition
(Eng. trans. Chicago, 1914, Open Court), p. xii.

MODERN MISCONCEPTIONS OF EMPIRICISM 81

doubt a reality completely independent of the mind which
conceives it, sees it or feels it, is an impossibility. A world
as exterior as that, even if it existed, would for us be forever
inaccessible. But what we call objective reality is, in the last
analysis, what is common to many thinking beings, and
could be common to all; this common part, we shall see,
can only be the harmony expressed by mathematical laws. 3

But despite this effort to set up a quasi-objective realm
of pure mathematics for science, Poincare is thrown back
upon subjective feeling in defining objective fact.

When it is said that we 'localize' such and such an object
at such and such a point of space, what does it mean ?

It simply means that we represent to ourselves the movements
it would be necessary to make to reach that object. 4 '

Of course this is nothing more than pure operationalism
of the later Bridgman variety. And that it reduces to
subjectivism of the Machian brand Poincare himself
could not avoid.

None of our sensations, isolated, could have conducted us to the
idea of space; we are led to it only by studying the laws, according
to which these sensations succeed each other?

What Poincare is constantly confusing is the way in
which ideas are conveyed to the mind and the meaning
of those ideas. In discussing mathematics this leads him
to confuse mathematical relations with the symbols used
to express them. Certainly it may be admitted that
mathematical symbols are a convention, without thereby

3 Poincar, The Foundations of Science, p. 209.

4 Ibid., p. 70. 5 Ibid., p. 71.

F

82 WHAT SCIENCE REALLY MEANS

admitting that the relations they express are also con-
ventional, arbitrary, or mental.

Karl Pearson agrees with Mach and Poincare in seeing
scientific laws mainly as summaries of experience,
psychological or historical. Scientific laws

simply describe, they never explain the routine of our per-
ceptions. The sense impressions we project into an 'outside'
world. 6 It [scientific law] is a brief description in mental
shorthand of as wide a range as possible of the sequences of
our sense-impressions. 7

This is the familiar error of assuming that because all
which the eye sees is seen by the eye, all must be of
the nature of eye. Thus Pearson too confuses scientific
laws with the sense-impressions whereby scientists have
been able to discover them. The confusion is between
the psychological fact of knowing and the logical con-
ditions of knowledge. Quite naturally Pearson as a
positivist denies any connection between sequences of
events other than the mental "routine of perceptions,"
and thus with Hume makes causality a non-empirical
fact.

We are neither able to explain why sense-impressions have
a definite sequence, nor to assert that there is really an element
of necessity in the phenomenon. 8

All positivists make the mistake of confusing causality
with the temporal sequence of experience, the latter being
only a special and therefore often misleading exemplifica-
tion of the former.

6 Karl Pearson, The Grammar of Science (London, 1892, Scott), p. 99.

7 Ibid., p. 135. 8 Ibid., p. 140.

MODERN MISCONCEPTIONS OF EMPIRICISM 83

"The compendious representation of the actual" of
Mach, the "sensations [which] succeed each other"
of Poincar, and the "routine of our perceptions" of
Pearson, are all the same. A like confusion prevails in
all three: that of identifying the succession of experience
with that which is experienced, the first being a psycho-
logical, the second a logical, fact. If with these men
we wish to confine science to descriptions of actual
happenings, we get away from the succession of
psychological experiences only to fall into the temporal
succession of history. There is an objectivity to the latter
which has recommended it to scientists.

THE MENTALIST VIEW

The "compendious representation of the actual" might
have passed muster as a description of science in Mach's
day, when the mechanical model of the universe domi-
nated physical science. But with the introduction of
relativity and quantum physics, the mechanical model
broke down. Whatever the explanation, it was recog-
nized that the representation of physico-mathematical
equations could no longer be anything picturable. Thus
no description of actuality answers to the new physics.
This fact left scientists in a quandary as to how to explain
what scientific 'concepts' meant. A whole new flood of
scientific-philosophical explanations was poured forth.
In general these were divided into two classes: the
mentalistic interpretations and the operational interpre-
tations.

The mentalist view has been made popular through
the work of Eddington and Jeans. According to them,

84 WHAT SCIENCE REALLY MEANS

science is concerned with the mental constructions on an
objective reality which is entirely unpicturable and, in
fact, unknowable in esse, but which is represented best
by mathematical symbols. Their eventual conclusion as
to the substratum of physical reality is that it is "mind
stuff." This, as Eddington says, 9 is not exactly mind and
not exactly stuff, since it is not identifiable with individual
consciousness nor spread out in space and time.

Jeans, taking mathematics as the nearest human formu-
lation of reality, decides that the stuff of the world is
mathematical thought, but again not thought in any
individual's mind, but rather in the mind of God.
Clearly both men believe that science is concerned with
finding not the what of reality but the how, and that this
can be represented mathematically in terms of symbols,
which to Eddington are "pointer readings" and to Jeans
pure mathematical symbols. The merit of these theories
is that they point to the extreme abstractive character
of the scientific subject-matter. They have incidentally
shown that the scientific 'picture* cannot ever be com-
prehended in terms of common-sense actuality.

Despite this merit, however, the total effect of denying
the objectivity of the scientific subject-matter has brought
the investigator back into the objective scientific field.
'Mind-stuff/ as set forth by Eddington and Jeans, turns
out in the end not to be dependent on the mind. If it
serves any purpose to call this 'mind-stuff/ when it is
neither mind nor stuff, well and good, but interpreted
in the light of other passages in Eddington's books, it
must be insisted that he does seem to mean both mind
9 The Nature of the Physical World, p. 276.

MODERN MISCONCEPTIONS OF EMPIRICISM 85

and stuff. Thus the mental is confused with the physical,
with the added assumption that the mind never really
knows the physical. From this hash of subjective and
objective idealism, it is small wonder that scientists
should rebel, confirmed in their old opinion that
philosophy is time wasted over words, and that the life
of science consists in doing things. The mentalist inter-
pretation plays havoc with empiricism, since according
to it observed phenomena are only the mental interpre-
tations of an unknowable reality underlying the pheno-
mena. This seems to leave no basis for agreement other
than private opinion; and from the scientific point of
view is its greatest source of repugnance.

The most cogent argument against the mentalist view
is to show that it resolves nothing. The determination to
call all things stuff of the mind is to put them all on a
parity. But science is known for the distinctions it makes
and not for the names which it can apply equally to all
phenomena. Mind-stuff, like any term which can be
equally applied to all things, leaves the theory of science
exactly where it was.

THE LOGICAL POSITIVIST VIEW

From out this maze of metaphysical theory, the scientists
have sought to save themselves by the discovery and
embrasure of that philosophy of science which seems to
contain the least metaphysics and to permit scientists to
confine their speculations and efforts to the empirical.
Often called operationalism by scientists, this theory is
known more generally as logical positivism.
The position has been put forward and systematically

86 WHAT SCIENCE REALLY MEANS

formulated by the logical positivists of the Vienna
Circle: Wittgenstein, Schlick, Reichenbach, Waismann,
Neurath, and Carnap. These men are by profession
philosophers whose chief interest is science, but they are
all violently anti-metaphysical. They trace their trend of
thought back to Comte and Mach, but assume a much
more radical position. Logical positivism asserts that all
metaphysical questions are meaningless, e.g. the question
of whether the nature of the physical world is mind-
stuff or matter or subjective interpretation. All problems
which cannot be verified in experience come under this
category.

Most propositions and questions, that have been written
about philosophical matters, are not false, but senseless. We
cannot, therefore, answer questionsof this kind at all but only
state their senselessness. 10

And Carnap presents exactly the same point of view. 11
His explanation is as follows :

But this question [the reality of the physical world] has no
sense, because the reality of anything is nothing else than a
possibility of its being placed in a certain system . . , and
such a question only if it concerns elements or parts, not if it
concerns the system itself. 12

Every science must express itself in the language of
physics, the "protocol language."

In our discussions in the Vienna Circle we have arrived at

I Wittgenstein, Tractatus Logico-Philosophicus, 4.003 .

II Carnap, The Unity of Science (London, 1934, Kegan Paul), p. 21.
12 Carnap, Philosophy and Logical Syntax (London, 1935, Kegan

Paul), p. 20.

MODERN MISCONCEPTIONS OF EMPIRICISM 87

the opinion that this physical language is the basic language
of all science, that it is a universal language comprehending
the contents of all other scientific languages. . . . Dr.
Neurath, who has greatly stimulated the considerations which
led to this thesis, has proposed to call it the thesis of
physicalism. 1 *

For example, psychology would reduce to behaviour-
istic psychology; biology to descriptions and terms which
reduce to something perceptible and not to non-empirical
entities; and so on.

This school accepts logic without question and uses it
to reinforce its positivism. The logical positivists say that
logical analysis is the only real problem of philosophy.

The function of logical analysis is to analyse all knowledge,
all assertions of science and of everyday life, in order to make
clear the sense of each assertion and the connections between
them. One of the principal tasks of the logical analysis of a
given proposition is to find out the method of verification for
that proposition. 14

For example, this school would say that the logical
analysis of the concept, metabolism, shows that it does
not refer to a mysterious non-empirical entity but to an
observable process which must be specified in terms of
physical measurement. Thus to discuss what metabolism
is in itself is meaningless. The Vienna Circle's reliance
on logic and the doctrine of physicalism or the "protocol
language" which is applicable to all science, inevitably
led to the doctrine of the unity of science.

13 Carnap, Philosophy and Logical Syntax, p. 89.

14 Ibid., pp. 9-10 (italics ours).

88 WHAT SCIENCE REALLY MEANS

Because the physical language is thus the basic language
of Science the whole of Science becomes Physics. 15

If we have a single language for the whole of science the
cleavage between different departments disappears. Hence the
thesis of Physicalism leads to the thesis of the unity of Science. 1 *

There is a tendency on the part of some members of
the Vienna Circle to emphasize the logical side of logical
positivism. It is possible to endorse at least some of the
utterances of Moritz Schlick, which, in so far as they are
valid, seem to us to depart from the position of positivism.
Schlick says, for instance, that

the question of meaning has nothing to do with the psycho-
logical question as to the mental processes of which an act
of thought may consist. 17

This denial of the primacy of sense-experience is not in
keeping with the radical empiricistic view of most of
the logical positivists. But Schlick ventures even farther
than this in his defence of logic.

It must be emphasized that when we speak of verifiability
we mean logical possibility of verification, and nothing but
this. 18

The truth simply is that such an assertion contradicts the
postulates of the modern logical positivistic school, and
is much more conformable with the realistic view, which
will be examined on page 96.

Logical positivism may be summarized under two
headings, the logical and the empirical.

15 Catnap, The Unity of Science, p. 97. 16 Ibid., p. 96.

17 The Philosophical Review, vol. xlv (1936), p. 355.

18 Ibid., p. 349.

MODERN MISCONCEPTIONS OF EMPIRICISM 89

The logical position states the valuable truism that
logical analysis involves the relations of parts of a system
to the whole system, and has nothing to say about the
system as a whole or about anything beyond that
system. The analysis of the building bricks, which may
happen to be part of a house, into their chemical con-
stituents has nothing to say about brick or about house.
And to bring such questions into the logical analysis is
irrelevant, or, in terms of the positivist in this connection,
"meaningless." But the statement that such questions are
irrelevant at this level of analysis certainly does not
imply that they are altogether irrelevant to the whole
of knowledge, or that they are meaningless. Meaning-
lessness in one connection does not imply meaningless-
ness in another. Neither is the question of the reality or
unreality of the physical world meaningless, even though
it is irrelevant to physics qua physics. The positivists have
done a service and a disservice: a service by calling
attention to what should be a platitude, and a disservice
by holding down speculation to analysis.

The empirical position of logical positivism asserts that
whatever cannot be verified in experience is meaningless.
Stated in this manner, the proposition is a truism but one
which has given rise to a vicious notion, namely, that
what has not been done cannot be done. Unfortunately,
the positivists mean by 'cannot/ 'has not/ And this
entitles them to throw out as meaningless all speculations
which concern unsettled problems. The erection of a
failure into a principle serves only to insure the con-
tinuance of the failure. The history of science is full of
examples of the verification of that which was at one

90 WHAT SCIENCE REALLY MEANS

time thought to be permanently unverifiable. 19 In
ancient times the distances of the stars from the earth
was deemed unverifiable. But if on the positivist principle
the problem had been thrown out as meaningless, no
verification would ever have been made. Indeed the whole
advance of science has been that of verifying what was
once pure speculation. The problem of the nature of
beauty, for instance, would be considered by the logical
positivists a meaningless question. Perhaps it is. But
certainly no one has ever been able to demonstrate con-
clusively its meaninglessness. If we should proceed on
this assumption, the problem would come to an end and
be dropped from speculation. If, however, we should
proceed on the opposite assumption that it might have

19 To make the positivistic assertion that this or that cannot be
done is contradictory to positivism, since it represents reasoning which
has gone far beyond the empirical facts. Quite an imposing list could
be drawn of accomplishments which had been formerly proved to
be 'impossible of accomplishment.' For instance, Aristotle said that
"one may be satisfied that there are no senses apart from the five"
(On the Soul, book iii, i) yet modem physiological psychology has
discovered others. "Legendre said of a certain proposition in the theory
of numbers that, while it appeared to be true, it was most likely
beyond the powers of the human mind to prove it ; yet the next
writer on the subject gave six independent demonstrations of the
theorem. Auguste Comte said that it was clearly impossible for
men ever to learn anything of the chemical constitution of the fixed
stars, but before his book had reached its readers the discovery which
he announced as impossible had been made" (C. S. Peirce, Collected
Papers, 6.556). "We [wrote J. Muller] shall probably never attain the
power of measuring the velocity of nervous action, for we have not
the opportunity of comparing its propagation through immense space,
as we have in the case of light" (J. C. Fliigel, A Hundred Years of
Psychology, p. 89). But a few years later, as Fliigel points out, the task
was accomplished by Helmholtz, who had been one of Miiller's pupils.

MODERN MISCONCEPTIONS OF EMPIRICISM 91

meaning, some verifiable knowledge might be discovered
which the positivist would then accept as meaningful.
We can therefore allow the statement that whatever
cannot be verified is meaningless, but it will not make
any difference to the procedure of science except as a
caution against unbridled speculation.

Logical positivism helps to clear up certain logical
misunderstandings about science, but it does not con-
stitute a programme for scientific activity. And its
physicalistic understanding of empiricism is an insufficient
formulation. For science to accept entire the philosophy
of the Vienna Circle would be equivalent to signing its
own death-warrant. Empiricism is something broader
than the caution to hold science down to the sensory.

THE OPERATIONALIST VIEW

The second group of modern positivists whose views on
empiricism we have to consider is not composed of pro-
fessional philosophers but of physical scientists, who have
in a sense stepped out of their role as physicists to con-
sider the theoretical nature of the scientific subject-
matter. Prominent among them are Lenzen 20 and
Bridgman, 21 Heisenberg and Dirac. In general, the
position of Heisenberg and Dirac is expressed by that of
Lenzen.

In agreement with the empiricistic point of view my
theory of science assumes a subjectivistic criterion of reality.
A physical body is a class of aspects which are or can be
given to some mind. In general one may say that the criterion

20 The Nature of Physical Theory.

21 The Logic of Modern Physics.

92 WHAT SCIENCE REALLY MEANS

of the reality of aspects is that they be possibilities of experi-
ence. . . . The objectivity of the physical order is grounded
in correlations between aspects given to different minds. 22

The derivation from Mach, which Lenzen freely admits,
is obvious in the above passage. "Aspects" are the same
as Mach's "sensations," and they both turn out to include
more than sensations, namely, "possibilities of experience."
This is the same question-begging device employed by
Mach. 23

But let us read a little further.

All entities of physical science can be characterized in terms
of experienceable aspects. 24

How we are to distinguish between what is "experience-
able" in advance ot experience and what is not, is not
suggested. Thus Lenzen concludes by accepting positivism
and seeing that it implies all that subjectivism implies.

... the positivistic criticism is that a subjectivistic criterion
should be employed. 25

Let us see which way his theory, that all the entities
of physical science can be characterized in terms of
"experienceable aspects," leads. It led with Mach and
Ostwald to the rejection of molecules and atoms as
fictions because these had not yet been experimentally
observed. It leads with Lenzen to the acceptance of
microscopic entities not as fictions but as realities, because
their existence is now inferable from observation. Thus
the same premises accepted by Mach and Lenzen lead

22 Lenzen, op. cit., p. 6. 23 See above, p. 80.

24 Lenzen, op. cit., p. 8. 25 Ibid., p. 10.

MODERN MISCONCEPTIONS OF EMPIRICISM 93

them to contradictory conclusions. This confusion well
illustrates that much can exist which is not at any given
time experienced, and it also exhibits the question-
begging device of "experiences We" which offered no
help to Mach. As a matter of fact, none of the entities
of physical science are aspects of experience per se, though
aU are inferred from experience.

That Heisenberg and Dirac agree with positivism,
Lenzen has noted. For instance, he quotes Dirac,

A fraction of a photon is never observed, so that we may
safely assume that it cannot exist. 26

Whether a fraction of a photon can exist or not we do
not know, but certainly we can say that the fact that it
has never been observed is no proof of its non-existence
any more than the fact that the planet Pluto had not
been observed in 1900 proved its non-existence. Did the
heavy isotope of hydrogen come into being in 1935?
This kind of nonsense is just the sort of thing which kills
off speculation as fast as it is attempted, since science has
always gone on the assumption that there must be
entities and processes to be discovered which nobody has
yet experienced.

Let us now turn to the work of P. W. Bridgman,
another scientist whose theory of science has had much
influence in America. Bridgman admits that his work is
derived largely from Clifford, Stallo, Mach, and
Poincare, and he brings their theory to bear on the new
concepts of physics. Particularly noticeable is the deriva-
tion from Poincare. 27 He has taken the quasi-objective

28 Lenzen, op. cit., p. 10. 27 See above, p. 81.

94 WHAT SCIENCE REALLY MEANS

side of positivism which makes physical concepts not the
summaries of sensations but the performances of ex-
periments. This is "operationalism."

In general, we mean by any concept nothing more than a
set of operations: the concept is synonymous with the corre-
sponding set of operations , 28

Bridgman does not admit any validity to concepts other
than as summaries of operations. This insistence on
operations seems to satisfy the demand of science to be
empirical, and seems, moreover, to hold science down to
the laboratory and to do away with all metaphysical
speculation. But it really cuts the ground from under
empiricism and is incurably subjective, since it ends by
telling science that its concepts do not refer to entities
but to the perception of scientists.

That the subjectivity of the observer must on this view
enter into the operations observed, to an indeterminable
degree, is admitted by Bridgman when he says that

it is evident that the nature of our thinking mechanism
essentially colours any picture that we can form of
nature. . . , 29

Thus Bridgman not only denies the objectivity of the
entities of science but he confounds the issue by insisting
upon a subjective criterion while admitting the existence
of a dualism whereby the mind contributes part and the
operations contribute part. This leads to an utter distrust
of rationality, even to the denial of the validity of logic.
Bridgman tells us that

28 Bridgman, The Logic of Modern Physics, p. 5.

29 Ibid., p. xi.

MODERN MISCONCEPTIONS OF EMPIRICISM 95

our conviction that nature is understandable and subject to
law arose from the narrowness of our horizons, and ... if
we sufficiently extend our range we shall find that nature is
intrinsically and in its elements neither understandable nor
subject to law. . . . 30

If nature is not subject to law, then the whole of science
is a fruitless proceeding. What, then, are the discoveries
of science, and why do contemporary scientists whose
horizons have recently been broadened continue to look
for uniformities in nature? The mere fact that physics
has so far discovered no way to study the occurrences
within the atom except in statistical computations of
results is used as an argument to show that causality does
not apply to the sub-microscopic world, and indeed that
it does not apply at all, i.e. causality is not in any way a
principle of nature. Surely to erect a failure into so
general a principle with which to contradict all prior
assumptions of science is a ridiculous attempt.

The same criticism which applies to all positivists
applies to Bridgman. There is exhibited the failure to
distinguish between the fact of perception and that which
is perceived; between the operations or experiments
which reveal laws and the laws thus revealed; between
the observed and the existence which is covered by the
term * observable/ In attempting to make empiricism the

80 "The New Vision of Science" in Harper's for March 1929. In a
later work this is contradicted by Bridgman : "Chance has no meaning
except in a setting of order/' The Nature of Physical Theory, p. 123.
In the latter work, in which Bridgman brings his position up to date,
there is so much confusion and contradiction that further refutation
is unnecessary.

96 WHAT SCIENCE REALLY MEANS

whole of scientific method, the very idea of empiricism
is rendered incomprehensible by the positivists, who must
eventually refer it to the subjective category mental
classification. The end accomplished by the positivists is
exactly the opposite of their aim, which is to keep science
empirical and clear of metaphysics. The result is deadening
to all scientific advance.

THE REALIST VIEW

Mentalism was unsatisfactory to the scientists because,
although it allowed objective reality to the objects of
scientific investigation, it denied reality to phenomena
and thus seemed to negate the validity of empiricism.
Positivism was unsatisfactory to the scientists for the
opposite reason, namely, because although it allowed
reality to the phenomena observed, and thus to empiri-
cism, it denied reality to the objective physical world,
and thus seemed to negate the scientific search for the real,
making its discoveries at last a subjective affair.

Among modern scientists there is a group whose
theory of science is neither mentalist nor positivist but
who believes, on the contrary, that the concepts of science
refer to real conditions, that causality holds in the uni-
verse, and that therefore there is such a thing as law
independent of our mental generalizations. The present
gaps in detecting causality in sub-microscopic regions are
attributed by them to ignorance of the factors involved
and not to a basic indeterminism. Neither do they make
the attempt of Eddington and Heisenberg to generalize
from the sub-microscopic level to the macroscopic level,
e.g. to prove or disprove free will. To quote Einstein,

MODERN MISCONCEPTIONS OF EMPIRICISM 9?

The belief in an external world independent of the per-
ceiving subject is the basis of all natural science. 31

But for Einstein this reality is not for ever hidden from
view but can be known to the human mind, which grasps
it through mathematical concepts.

In a certain sense, therefore, I hold it true that pure thought
can grasp reality, as the ancients dreamed. 32

Max Planck, the discoverer of the quantum, agrees
with Einstein in rejecting positivism and holding fast to
the validity of the principle of causality as based upon
an independent and real physical world. Even such an
extreme example as Heisenberg's Principle of Inde-
terminacy, which has been used by philosophers of
science to prove the non-existence of causality, is seen
by Planck to be fundamentally causalistic. Regarding
this principle, he says,

Here the causal principle is not applicable. That is to say,
we cannot estimate simultaneously both the velocity and
position in space-time of a particle and say where it will be
a moment hence. But this does not mean that the causal
sequence is not actually verified objectively. It means that we
cannot detect its operation. . . , 33

And in regard to the positivist position, Planck is very
strenuous in his denial; pointing out that science is con-
cerned neither with the accidental, the contingent, nor
the observable, i.e. not with sensations but with the
reality which can be found by their help.

31 The World as I See It (New York, 1934, Covici-Friede), p. 60.
82 Ibid., p. 37-

38 Planck, Where Is Science Going? p. 33 (George Allen & Unwin
Ltd.).

G

98 WHAT SCIENCE REALLY MEANS

That we do not construct the external world to suit our
own ends in the pursuit of science, but that v ice versa the
external world forces itself upon our recognition with its own
elemental power, is a point which ought to be categorically
asserted again and again in these positivistic times. From the
fact that in studying the happenings of nature we strive to
eliminate the contingent and accidental and to come finally
to what is essential and necessary, it is clear that we always
look for the basic thing behind the dependent thing, for what
is absolute behind what is relative, for the reality behind the
appearance and for what abides behind what is transitory. In
my opinion, this is characteristic not only of physical science
but of all science. 34

Not only is this understanding of science recognized
by a few physicists, but at least one biological scientist
states the same position unequivocally.

From the things encountered in the material world, whether
atoms or stars, rocks or clouds, steel or water, certain qualities,
such as weight and spatial dimensions, have been abstracted.
These abstractions, and not the concrete facts, are the matter
of scientific reasoning. The observation of objects constitutes
only a lower form of science, the descriptive form. Descriptive
science classifies phenomena. But the unchanging relations
between variable quantities that is, the natural laws, only
appear when science becomes more abstract. 35

This version ot empiricism in science is not shared at
present by many scientists. Most scientists prefer the
positivistic point of view, which we have been criticizing.
But even with Planck, Einstein, and Carrel the rejection

34 Planck, Where is Science Going? p. 198.

35 Alexis Carrel, Man the Unknown, pp. i and 2.

MODERN MISCONCEPTIONS OF EMPIRICISM 99

of positivism and the assertion of the reality of the
entities of science is based upon happy intuitions and is
more of a hope and a faith than a demonstrable belief.
There is therefore some force to the point made by
Eddington 36 that the present stage of physical science leads
neither to an acceptance nor to a rejection of causality,
and that therefore it is held by these men as a pure theory
and cannot employ present-day physics as a basis for its
proof.

'Happy intuitions' are not enough. The theory of
science must be understood by the scientists abstractly
and theoretically, in a form as universally acceptable as
the findings of science itself.

We have already pointed out that the theory of science
must he outside the scientific field proper, and that one
cannot make use of scientific findings to prove the theory
by which such findings can be connected up with the
rest of existence. The reality of the physical world and
the existence of causality are thus not questions which
can be resolved by the mere appeal to physics or to any
other special science. Recourse must be had to philosophy.
The history of science reveals that the practice of science
has not been at one with the theory. The fact that reason
and experiment have both been employed wherever
valid science has taken root may be contrasted with the
fact that throughout the history of modern science
scientists have unfortunately believed these two prin-
ciples to be opposed. They have clung to empiricism for
fear of going off into metaphysical quiddities. The re-
futation of positivism is easy, but the true definition of

36 See Eddington, New Pathways in Science, especially p. 297 fF.

ioo WHAT SCIENCE REALLY MEANS

the place of empiricism in science requires more. It
requires an analysis of logic and empiricism as practised
in science, to demonstrate their essential reconcilability,
and thus give rational justification to what is now only
a hope and a faith. In the next chapters we shall turn to
the fulfilment of this task.

CHAPTER V

NATURE OF THE FIELD OF SCIENTIFIC
INVESTIGATION

For modern scientists, as for Plato, IDEAS are
the sole reality.

A. CARREL

WE have come to the end of our brief survey of the
history of empiricism, in practice and theory. It has
been seen that the controversy over the question of
empiricism centres around a single comprehensive
issue. We shall now have to separate this issue from the
various historical figures who have taken sides with
regard to it. This will entail leaving history and con-
centrating upon the abstract problem.

WITH WHAT IS THE CONTROVERSY CONCERNED?

The various schools and traditions whose doctrines we
have exhibited are in effect so many answers to one
question, namely, what is the true subject-matter of
science ? Science itself can restrict its abstract interest to
the problem of method, whether this be logical or ex-
perimental. But philosophies of science must be con-
cerned with something more than method. They must
be concerned with subject-matter. Even those abstract
speculators who suppose that their preoccupation is only
with method are mistaken. For what is a method, if not a
step toward something else, a means of achieving an
end? Thus science is more than method, even though

102 WHAT SCIENCE REALLY MEANS

strict scientific analysis may not have to take this fact
into consideration.

Thus the three schools which we have examined, the
positivists, the mentalists, and the realists, all primarily
direct their attention to the nature of the field of scientific
inquiry. The positivists believe that they can make the
method of science itself into the subject-matter of
science. But even this is an attempt to define the subject-
matter. The mentalists find the nature of the scientific
subject-matter 1 in mysterious noumena, an unknowable
something lying behind the field of sensory phenomena.
The realists find the nature of the scientific field in a
directly knowable set of relations, which phenomena
only exemplify. Let us take some familiar entity of
science and show how each school would regard it.

The physical law of action and reaction is a scientific
entity. The question then is : what is the status of its
reality ? To this question the answer of each of three
schools is different. For the positivists, the reality of this
law resides only in the actual or observed phenomena.
As to the reality of the law itself, they would deny its
existence as an independent entity and claim for it the
status of a mental concept. For the mentalists, the reality
of this law resides in its existence as a mental concept
derived from real but unknowable objective conditions
of nature. For the realists, the reality of this law resides
in real and knowable objective conditions of nature.
The law is thus a reality independent of both subject
and object, independent of the subject since existing

1 The mentalists seem to have confined their remarks to the science
of physics and the nature of the physical world.

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 103

without its knowledge, and independent of the pheno-
mena because existing without such exemplification.
Thus the understanding of such a law* or scientific entity
as the law of action and reaction differs in all three cases.

One clear fact must be admitted at this point. This is
that physicists, though they hold different philosophical
views concerning the reality of the physical subject-
matter, seem to function equally well as physicists. For
instance, Heisenberg, Eddington, and Planck seem to
have no disagreements over each other's work as
physicists. Their disagreement comes only with the
interpretation of their work. Does this mean, then, that
the question of the reality of the scientific subject-matter
is meaningless? Certainly it does not seem to have
affected the procedure of the science of physics. It is just
this point which makes the scientists so professionally
disdainful of metaphysics.

To this question of what difference does it make there
are many answers. First of all, procedure does follow from
philosophy. When the physicists hold one philosophy
and practise the procedure that would follow from
another philosophy, this merely means that they are not
holding the philosophy they think they are holding.
Newton could not possibly have leaped from terrestrial
to celestial mechanics without the belief in the uni-
versality of natural law, which certainly is not to be
found in any analysis of the motions of bodies. From a
purely analytic point of view, there is no warrant for
such a theory. Again, without a belief in the continuity
of natural phenomena, no one would ever have tried to
find the proper equations for the cicatrization of wounds.

104 WHAT SCIENCE REALLY MEANS

In other words, analysis is not the whole of scientific
procedure, although nothing unanalysed can be called
scientific.

Plainly any science must start by seeking isolatable
systems to be analysed, and these systems cannot be
found by analysis. Granting it to be true that the analysis
is not affected by the interpretation put upon the meaning
of the isolated system, it is still true that without some
meaning for the total system, no new system could be
found. Certainly the anatomical analysis of the spleen is
unaffected by the function of the spleen in the animal
constitution; but until the relation of the spleen to the
whole organism is better understood, this analysis will
not only be largely meaningless but also undirected.
Thus what does not affect analysis directly does affect
the understanding of that analysis and, indirectly, the
analysis itself. An example may be taken from common
experience. A chair could be analysed without the
analyst knowing its use or purpose. But certainly such
analysis would be entirely without value and without
interpretation. What purpose would be served by
specifying the weight-bearing properties of the legs
unless in the light of the use of the whole chair ?

If physicists came to the conclusion that analysis of
systems now known is the whole of physical science, there
would be no more systems to analyse. In other words,
with the wrong philosophy, science cannot keep on
developing, but must stagnate. In so far as physical science
has followed the wrong philosophy, it probably has,
despite its brilliant success in the past, been somewhat
retarded. It will certainly be brought to a halt in the

NATURE OF FIELD OF SCIENTIHC INVESTIGATION 105

future unless its first principles are straightened out. About
other sciences we can speak with more confidence. The
far less successful biological sciences owe their partial
failure and retardation to a timidity of theory which
lays the injunction upon scientists only to analyse. The
positivistic or 'empirical' creed of the social sciences has
strangled them in gestation. So vicious has been the effect
of the wrong philosophy in the social sciences that, at
least in some quarters, even the possibility of exact social
science is denied.

Besides the crippling of science itself, there is the large
and unavoidable question of the place of science in the
scheme of things. For instance, what of science with
regard to society ? Surely on the answer to this question
the future of science will largely depend. And unless
science can answer the question as to what it is concerned
with, it may be challenged by society and prove unable
to defend itself. Finally, the scientists themselves are
something more than scientists: they are human beings
who require some answer to the question of what they
are spending their lives doing. In the course of every
laboratory day, the question is bound to occur to the
scientist of the meaning of his activity, even though he
dismiss such considerations as irrelevant to the imme-
diate business at hand. But the question cannot be dis-
missed for ever and is bound to recur to every human
being, until he answer it at least to his own satisfaction.
If the answer be that there is no answer, i.e. that it is a
meaningless business, he could not go on in a whole-
hearted way. It is at least arguable that the great advance
in physical science in the past three hundred years has

io6 WHAT SCIENCE REALLY MEANS

been activated by the belief that this is the best way to
find out the nature of reality.

We may conclude by saying that scientific method
depends upon the philosophy of science. The future of
science depends upon the philosophy it adopts. Therefore
the sooner the scientists become aware of this condition,
the better it will be for the welfare and development of
science.

THE INQUIRY INTO SCIENTIFIC OBJECTS

We have seen that the philosophical problem of the
nature of science cannot be dodged by science. This
problem is the nature of the objects with which scientific
analysis works. Let us attempt to determine what their
nature is by examining them under their various names.
In attacking this problem no mystical or complex meta-
physical theory or discussion need be introduced. The
nature of scientific objects must be, like the nature of
anything else, defined by what is implied by them. The
technique of philosophical analysis does not differ essen-
tially from that of scientific analysis, though it operate
from a different level.

Scientific objects are known variously, and sometimes
interchangeably, as entities (e.g. a molecule), concepts
(e.g. entropy), processes (e.g. radio-active disintegration),
events (e.g. an electromagnetic force field), and laws
(e.g. Avogadro's Law). These may all be described as
scientific objects. It is at once obvious that some of the
terms are interchangeable. In order to examine their
nature let us start by finding out and discarding what
they are not. Are scientific objects mental ? No, since by

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 107

mental is meant something which depends for its
existence exclusively upon the mind. All our scientific
objects give every evidence of existing, and exerting
influence, indifferently as to whether they are perceived
or thought about or not. Thus it would be idle to call
them mental. The conditions which are described as
entropy continue whether there is consciousness of them
or not, and indeed we are assured by the astronomers
that entropy will go on long after animal life has become
impossible on a rapidly cooling planet.

The same independence of knowledge holds for
Avogadro's Law: under the same temperature and
pressure, equal volumes of gases continue to have equal
numbers of molecules, regardless of whether we know
about this fact or not; and this condition will continue
to prevail even if in the future it is forgotten. Perhaps the
notion that scientific objects are mental has arisen from
the recognition of the fact that in so far as these conditions
are known they are known. But why confine this to
scientific objects when the same is true of an elephant
in the zoo ? We have already shown that when scientific
objects are dubbed mental, the implication is that they
depend for their existence upon the mind, which is
simply not true. 2 Thus the concept of entropy is mental

2 If the old subjective argument be invoked that we cannot know
anything about anything when we are not knowing it, and that there-
fore we cannot assume the existence of anything when we are not
knowing it, the answer is that it is irrefutable but also undemonstrable.
It is, moreover, incredible and fruitless. Whoever chooses to believe
that radio-active disintegration ceases when it is not in any human
consciousness, will have to take the same position with regard to the
elephant.

io8 WHAT SCIENCE REALLY MEANS

in so far as it is a concept, but entropy in so far as it
refers to conditions which are not mental. Similarly
with the concept, elephant.

Mentalism, however, is generally put forth as a sort of
objective mind-stuff theory. The 'stuff' of physics is said
to consist of mind, perhaps thoughts, in the mind of
God. But does this theory help any more than the other
to explain what scientific objects are? Let us accept it
and see where it leads. The mind-stuff called sulphuric
acid analyses into the mind-stuffs called hydrogen,
oxygen, and sulphur, which in turn analyse into mind-
stuffs called electrons, protons, etc. It is evident from
this analysis that the term mind-stuff is being carried for
nothing, and since it appears on both sides of each equa-
tion, can be cancelled out with no loss to the knowledge
of what is involved. 3 Our knowledge of sulphuric acid
is neither helped nor retarded by the term mind-stuff.
An explanation which makes no difference is not an
explanation but a restatement, more or loss clumsy, of
the original problem. Unless differentiae can be shown
to arise from the distinctions made, they are not worth
making. Thus to say that the nature of the physical
world is mental in either the subjective or objective
sense of the term, is to use 'mental' to describe every-
thing, and therefore to rob it of any sense it may have.
It is also to leave the problem of the nature of scientific
objects just where it was.

3 Let mG = the mind of God. Then

mG H 2 SO 4 -> mG SO 3 + mG H 2 O

It is obvious that dividing through by mG will give an equation which
yields the same result.

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 109

It has been shown that scientific objects are not, in the
usual sense of the term, mental; and if called mental
in the unusual sense of mind-stuff, the proposition is
nugatory. We have now to consider whether scientific
objects are actual. By 'actual' is meant phenomena which
are experienced, with all their affects and values. In
other words, are the objects of science to be wholly
identified with the common-sense objects of our daily
observation, such as red apples, sunsets, parades, water,
turtles ? Plainly, science is not primarily concerned with
such common-sense objects, and does not rest content
with them. Science always abstracts certain qualities
when it experiments with common-sense objects. Thus
it was not the apple but the apple's fall which interested
Newton; and it is not the wetness of water or its
potability which interests the chemist.

But the inquiry of science goes beyond even the
abstractions of qualities from particular objects. For
instance, it is not even the apple's fall which is ultimately
interesting to the scientist who works with mechanics,
but the relations of mass, distance, and time, which the
fall of the apple exemplifies. It is not the particular
length of a bar of metal which concerns the physicist,
but relative dimensions. The same is true of biology,
though not so obviously. The zoologist who examines
the relation of the temperature of turtle blood to turtle
heart-beat is not the least concerned with the awkward-
ness of the turtle or the edibility of turtle meat or the
decorative value of the shell. In other words, the par-
ticular common-sense turtle means nothing to the
zoologist, who is employing certain abstractions from a

no WHAT SCIENCE REALLY MEANS

particular turtle only because he believes on sufficient
evidence that he has got hold of a fair sample of heart-
beat and temperature of the species, turtle. Thus again
science proceeds from the common-sense phenomena to
the abstractions of certain qualities from such phenomena,
to generalizations about the relations of such abstract
qualities, or to what are called laws.

Those qualities which science abstracts tend to become
those which are commensurable. This is the ideal of
every science, but at early stages qualitative differentiation
is abstracted. In general, we may say that scientific
abstractions proceed from qualities to quantities.

At this stage we reach entities or laws or processes or
concepts which can hardly be said to be phenomena,
though they be reached in and through phenomena
or by abstraction from phenomena abstractions many
times abstracted. This is why mere description or classi-
fication is the most rudimentary form of exact study; it
stops at the first stage of abstraction. We arrive at the
conclusion that scientific objects are not actual, even
when they are exemplified in actuality. The scientific
molecule is not identical with the actual molecule, even
admitting that such an exemplification could be demon-
strated. Entropy is not understood by science as the
actual disbursement of energy; degradation goes on at
any moment, but is only an exemplification of entropy.
Radio-active disintegration may be observed to take place
over a period in radium, uranium, etc., but the process is
not confined to detectable occurrences. Electromagnetic
fields are studied independently of actual fields set up,
e.g. mathematically. And Avogadro's Law is merely

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION in

exemplified by any gas under pressure, and is a state-
ment of conditions which do not become dissipated with
the dissipation of the gas. These arc the objects of science,
and as such are hidden from common observation as
they occur. They are empirical because they are detectable
in and through actuality by trained observers; they are
non-sensory and have no dependence upon phenomena,
i.e. phenomena depend upon them. It is for this reason
that experiment is used in science to prove or disprove
theories or laws.

SCIENTIFIC OBJECTS ARE FUNCTIONS

We have seen that scientific objects are essentially
neither mental nor actual, and that the end of scientific
investigation concerns the finding of abstract relations.
It proceeds from phenomena to abstractions from
phenomena, to abstractions concerning relations between
abstractions. The relations between abstractions can be
best understood as representing constant functions, the
invariant relations between variable quantities. Functions
are therefore the objects of scientific inquiry. They are
the scientific objects. And this is seen as soon as we dis-
card the pictorial or mythological tags by which they
are ordinarily represented. How can we best understand
without reference to the formulations of science what a
function is ? Function is defined 4 as "that power of acting
in a specific way which appertains to a thing by virtue
of its special constitution." The function of anything,
then, is its necessary relation to something else. It is what
is essentially true about a thing so long as it is a thing.

4 The Century Dictionary.

ii2 WHAT SCIENCE REALLY MEANS

If, for example, we say that the function of a lead-pencil
is to write in a certain way on paper, we are saying two
things: (i) that it must be composed of something
capable of performing this function; and (2) that it is
potentially capable of acting in a certain way. Thus
however variable may be the constitution of a lead-pencil,
and however variable its use, the function between the
constitution and the use is constant and necessary.

The functions of a right-angled triangle are studied in
trigonometry. They are the necessary conditions to which
any right-angled triangle must conform to be a right-
angled triangle.

Hypotenuse

is a statement of an invariant relation between variable
quantities, which lays no restrictions upon the size of the
triangle nor the degree (within limits) of the angle A. It
is to be noted that this is not an accounting of anything
actual but an abstract condition to which any actual
triangle must answer. In other words, it is the special
constitution of a triangle by which it can be operated in
a certain way.

The definition of scientific objects as functions must be
noted to include the various names given to scientific
objects: entities, concepts, processes, events, laws. Now,
an entity or a thing is defined by its function, as we saw
above. A match, a street car, copper sulphate, velocity,
all these are defined by their function, i.e. by the way
they can act. And we have seen that this is the determining

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 113

fact in their constitution. Thus we always mean by an
entity (in science or out) a function.

It may not be so clear that a concept is a function, but
such is the case. A concept is the mental recognition of a
function which is not mental. Thus the concept, table,
refers not to a particular table but to any table, i.e. to the
function, table. Similarly, democracy refers to a possible
condition or function and not to anything actual. The
mental image by which the mind grasps ideas or functions
is not itself the concept. Thus the word, beefsteak, may
bring up in many minds different images, visual, auditory,
olfactory, or gustatory or many of these; but that to
which the image refers, i.e. the concept, beefsteak, is the
same. When a concept is spoken of in science, it is
obviously not the mental aspect of it which is meant,
but rather that to which the mental refers. And this is
identical with the scientific entity.

That a process is also a function becomes evident from
an examination of process. A process is a course of events
which is separable from the sum-total of happenings. It
Is only separable on the basis of its special manner of
procedure. Thus what defines any certain process is not
events so much as the certain form they take. But this
form is a function in operation. The 'processing' of wood
pulp into rayon is obviously a function, since it is defined
primarily by the end in view, and secondarily by the
particular events which are means to that end. In other
words, processes are defined by the end toward which
they are directed. And this determines the events which
lead up to that end. The process of electrolysis is like-
wise a function, inasmuch as it is defined by the breaking

H4 WHAT SCIENCE REALLY MEANS

down of water into oxygen and hydrogen, and second-
arily, by the electro-chemical events which bring this
about.

It is apparent, however, that when a process is referred
to, reference is not made to any particular actual process
but rather to certain possibility of actual process, so that
the process is not confined to place or date. In this light
it will be seen that a process is a function. It is also to be
noted that there is no logical distinction between a pro-
cess and an entity; one is merely viewing a function as a
possibility of action (entity), and the other is viewing a
function as in action (process). 'Entity' is function as
potential; 'process' is function as kinetic. The distinction
between these can be more clearly understood when we
note that processes arc constantly spoken of as entities.
The term, hypostatization, or reification, means the
viewing of a process as an entity. But this is no figure
of speech, since whenever we talk of an entity we also
mean a process, and v ice versa. For instance, a mouse
and a mountain are entities; but they are equally pro-
cesses, since that which makes their functions what they
are is in a constant state of change and motion. Mice
grow and die; mountains constantly erode. And the parts
which make up these entities are always in flux: cells,
molecules, atoms, etc. All actual things are in process,
and it is the process itself which shows enough uni-
formity to be isolated and spoken of as persistent.
When this is done, we have hypostatized the process
into an entity.

Obviously, an event is a function since it answers to
the same definition as a process. No event can be called

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 115

an event without defining its purpose or end or direction.
Thus whatever we have said about process applies
equally to event.

Of our group of scientific objects, it remains now only
to show that a law is a function. A law is a necessary
uniformity to which relevant processes and events must
conform. It may therefore be called a general function
which conditions particular functions, just as Ohm's Law
is a general function conditioning the particular function

V
of a given electrical current in a given wire. = R,

where V is the potential (volts), and I the current
(amperes) and R the resistance (ohms). A law, then, is
the notation for a general function which governs par-
ticular functions inexorably, and is therefore a statement
of fact, which is just as objective as a mouse or a
mountain or electrolysis or entropy. It is observable in
the same way, namely, in and through experience, and
it is conceivable in the same way, namely by means of
words, symbols, or images. It is equally with them not
actual, being the governing function for actuality, i.e. it
can be actualized or even exemplified in actuality. Thus
a law can be called a scientific object: an entity, a con-
cept, a process or a series of events.

We have seen that the best and most embracing term
to cover all of these terms is that of function, which
may be taken to mean what it means in ordinary dis-
course: possibility of certain action or a special constitu-
tion by which it enjoys a certain possibility of action;
or which may be taken to mean what it means in mathe-
matics : an invariant relation between variables. Thus the

n6 WHAT SCIENCE REALLY MEANS

scientific objects the subject matter of science consist
in a world of real relations, expressible by functions. 5

FUNCTIONS IN THE VARIOUS SCIENCES

Let us take examples from each of the various sciences
in order to show that their subject-matter is always that
of abstract relations or functions and never that of any-
thing actual. This is obvious in the more abstractive
sciences, but perhaps it should be illustrated.

In analytic geometry, x* + y 2 = r 2 (for rectangular
co-ordinates, x and y) is the equation of the circle. But
obviously this equation does not represent any given
circle or any actual circle, but rather the conditions which
any actual circle must satisfy.

In physics 'density' is the mass per unit volume of a
substance, i.e. it is the relation between mass, expressed
in units, and volume, expressed in units, and is not to
be understood as an actual 'quality' of any actual thing
in the sense of being actually separable from it.

In astronomy, 'planet' does not refer to a certain
actual body of matter in all its sensible effects. It refers
to the function of any body, except a comet or meteor-
oid, that revolves about the sun. The actual bodies
named Venus, Mars, Saturn, etc., perform this function;
and in so far as they do they are planets. Should these
bodies, from some cause or other, cease to so revolve,
they might continue to be actual bodies but they would

5 Since mathematical symbols are the most abstract (i.e. non-actual)
expressions which can be found to represent relations, it follows that
mathematical formulations of functions become the true goal of all
science.

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 117

certainly not be planets. The term planet refers to the
function and not to the actualization of it. Similarly, if
new bodies are discovered to revolve about the sun, they
would be rightly termed planets in so far as they fulfil
this function.

In chemistry, Valence' is defined as the ability of an
element to combine with another element. This does
not refer to any given actual quality of an element, in
the sense of a property which can be actually separated.
It is a function of the combination or relation between
elements. It is true that it could be determined by the
number of free electrons on the outer layer, but this does
not affect the logical fact that valence is to be defined
only in terms of relations between elements.

In zoology, 'marsupial' is defined as a mammal having
a pouch in which the young are carried. Plainly this does
not describe any actual opossum or kangaroo except in
so far as they exemplify this function. A female kangaroo
born without a pouch would be a kangaroo but not a
marsupial.

In botany, 'chloroplast' is defined as a plastid containing
chlorophyll, developed only in cells exposed to the light.
Obviously we have in chloroplast a function between
certain plastids and light, which is only exemplified in
actuality when this function is satisfied. Thus it cannot
properly be identified with any actual plant which may
or may not exhibit it.

In economics, 'economic man' is defined as that man
whose activities are entirely concerned with the economic
level. Certainly no such actual man exists, since although
every man is sometimes and somewhat concerned with

n8 WHAT SCIENCE REALLY MEANS

economic activity, no man is altogether so concerned. But
the fact that the economic man is non-actual does not
make the abstraction, the 'economic man/ an unreality.
Its reality lies in its functional nature which actual men
may or may not share in more or less degree. Thus once
again 'economic man' refers to abstract relation or
function. Similarly the 'bourgeois class* does not refer
to any actual member of this economic class who may
at the same time be or become in other ways members
of the proletarian or capitalist class. It therefore refers to
a certain function in society, which varying members
to some extent fulfil at different times.

In sociology, 'criminality* is defined in terms of the
breaking of certain established laws of society. Thus it is
not properly applicable as a fixed attribute of any actual
person. There is no criminal type per se but only persons
who participate more or less in such anti-social behaviour,
i.e. in the particular social (or rather anti-social) function.

In politics, 'parliamentarianism' is defined as that form
of government in which the State confers upon the
legislature (elected by popular vote) the complete control
of the administration of law. Probably no actual State
has ever been entirely governed in this way, yet parlia-
mentarianism applies to some states in so far as they
partially fulfil this function.

We have seen that the subject-matter of every science
is a set of functions which are strictly non-actual, being
exemplified more or less in actuality, but never identifi-
able altogether with it. They arc the forms or relations
which actuality must follow and by which actuality is
understandable. When these functions or abstractions are

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 119

known, they are properly called concepts; but they are
not created by the mind nor do they depend upon it
for their functions to be fulfilled, in the sense of having
no existence when not cognized. The subject-matter of
science is therefore strictly abstract and non-picturable,
and whenever pictured is a convenience which finally gets
in the way by being misleading. Thus the symbols of
mathematics are the best scientific representation.

ARE SCIENTIFIC OBJECTS EMPIRICAL?

From the above exposition of the nature of scientific
objects, we can perhaps see why the mentalistic and the
operational interpretations arose and how they went
astray. The mentalists correctly comprehended the fact
that scientific objects are not to be strictly identified
with actuals, and that scientific functions are most easily
manipulated in their mathematical formulations. They
understood very well that the world picture of science
could be put without distortion only into mathematical
terms. But once having decided that scientific objects are
not actual, this school declared them mental, presumably
because they are conceivable by the mind.

On the other hand, the operationalists, striving to save
the reality of scientific objects, tried to hold on to
actuality. They went half-way in the understanding of
the fact that scientific objects are functions, i.e. that
scientific functions are actually operable. But the existence
of functions as such when not in process or operation
was denied. Thus scientific functions when not in
dynamic relation, were supposed to be only summaries of
real dynamic relations, and thus concepts in the mind.

120 WHAT SCIENCE REALLY MEANS

We may conclude by pointing out that both mentalists
and operationalists are partly right and mostly wrong in
their understanding of the nature of scientific objects.
They are non-actual, they are operated in actuality, they
are conceivable; but they are also real, abstract, and
non-mental.

Where, then, has our inquiry into the nature of
scientific objects led in regard to the main thesis of this
work: the nature of empiricism ? In other words, what
is the relation between empiricism and the objects of
science as defined, namely, as functions? On the one
hand, can we assert that the actual objects of ordinary
observation are not empirical? Certainly we cannot.
Apples, horses, dances, and storms are empirical; they
are also actual. But on the other hand, can we throw
out of the category of the empirical those abstract
scientific entities which we have been discussing, such
as valence, density, radio-active disintegration, etc. ?
Obviously to do so would be to destroy the claim of
every science to be empirical. This is tantamount to
destroying the idea of science itself. Assuredly empiricism
has some close connection with actuality but is not to
be understood as being identical with it.

Ultimately empiricism docs rest upon the observation
of actuality. But the understanding of observation as the
mere run of experience tells us nothing. At the lowest
level of observation, patterns are discovered within
actuality which are not strictly sensory. For example,
that a chair or a table has the function that it does is
not revealed by sensory analysis or observation unin-
tegrated. Thus observation is shot through with inferences

NATURE OF FIELD OF SCIENTIFIC INVESTIGATION 121

of function, which finally become so familiarly accepted
that functions are thought to be,, sensed. For instance, the
average city dweller 'sees' the black instrument on his
table as a telephone, but to one ignorant of the use and
purpose of the telephone it would only be a black object
of a certain shape to which he could assign no meaning.
But that the function of an ordinary object is not sensory
per se surely does not mean that it is not empirical, since
its function is demonstrable in experience. If this is the
case, the term, empirical, can and must be applied to any
function which is either observable in operation or which
can be inferred by observable processes in nature.

Empirical entities do not stop here, since the inferences
from agreed on hypotheses may be verified by reference
to the body of agreement. Thus that which was not
empirical can become empirical, e.g. molecules which
were once only hypothetical, are now empirical. They
are empirical even though they are not yet visible through
the microscope. The empirical field is not a fixed affair
but is made comprehensive according to the body of
agreement. The law of action and reaction always
existed and always will, but became through scientific
recognition an empirical fact. In other words, we have
discovered that empiricism is not a quality of the ob-
jective world but a function of scientific inquiry.

In this chapter we have examined the nature of
scientific objects. In the next chapter we shall make an
analysis of scientific method or the method of empiricism
in science.

C H AFTER VI
THE METHOD OF EMPIRICISM

/ hope I shall not shock the experimental physicists
too much if I add that it is also a good rule not to
put over-much confidence in the observational
results that are put forward until they have been
confirmed by theory.

A. S. EDDINGTON
THE BRUTE FAITH IN THE GIVEN

WE have arrived at the conclusion that the entities of
science are not per se either empirical or non-empirical.
Empiricism concerns the status of scientific knowledge.
We must now make an analysis of the empirical method
as employed in science, and in order to accomplish this
task we must examine empiricism at the level where it is
not exclusively scientific, even below the common-sense
level, at the barest giveness of sense experience.

There is an element in all experience which is insus-
ceptible of further analysis. This element cannot be
rationalized any further than to state that it is for sense
experience. Such brute facts are those which thrust
themselves upon us without any explanation. Nothing so
sophisticated as a lump of sugar or a book or a carnation
is meant. We mean the sight of redness, the smell of
honeysuckle, the touch of a stone, the sound of a bell,
the taste of salt. For all these cases, the sources which
convey the sensations must be dropped. The bruteness
concerns the sensation itself, and not any judgment about
its source or cause, or even position of occurrence in

THE METHOD OF EMPIRICISM 123

time and space. It must also be noted that the existence
of these brute facts cannot be proved or explained in
any final way. In other words, these presentations are
accepted on faith, agreed upon roughly by convention,
and regarded as merely 'given/ As such they are the
irreducible building blocks on which all experience is
mounted, and therefore the basis on which science and
even logic ultimately rest. On the identity of these
presentations and their differences, all rationality relies.
Such facts constitute the final court of appeal for both
logic and empiricism. Nevertheless, the rational structure
has to do with differences and relations between such
things which in themselves tell us nothing about their
intrinsicness.

The pure bruteness of experience, as we have set it forth,
has never been entertained by anyone. There is no con-
tent without form in anything experienced; no sensation
has ever taken place without some kind of minimal
judgment. We cannot see red without the idea of redness
or the understanding of something red. A sound or an
odour is at least given spatial location, however vague,
simultaneous with the sensation itself. These brute facts,
together with judgments about them, constitute indi-
vidual experience and the world of social agreement.
Inasmuch as there is no purely brute experience, per-
ception is made possible by an understanding of the
relations between brute facts. Thus the cubeness of a
cube is not a fact which can be experienced as such,
since what is seen or felt is always a surface. A cube is,
then, an inference from the relations of sensations of
brute facts. But certainly a cube is part of the social

124 WHAT SCIENCE REALLY MEANS

world, and as such, an empirical fact. The sciences largely
concern this social world. However, this statement must
be modified in two important respects. The science of
psychology, for example, may take as its field of study
the private order of experience dreams, phantasms, and
images. And all the developed physical sciences, though
they start with the world of social agreement, suppose
the existence of a natural world of which social agreement
covers only a small part.

We have seen that brute facts underlie empiricism, but
that no empirical facts, even at the common-sense level,
are purely sensory. We might also infer from the above
that the data which constitute empirical subject-matter
for one science would not be empirical for another. For
instance, the pink rats seen in delirium tremens are not
empirical from the point of view of zoology. But the
same bit of evidence is accepted as empirical by abnormal
psychology. So far it would appear that the test of
empirical subject-matter is a function of agreement
among those qualified to judge. But this is not enough.
Social agreement is still undercut by the brute facts of
sense experience, which are 'agreed' upon, without
choice and of necessity. Science does often contradict the
judgments of common sense which rest upon experience,
but it cannot ultimately contradict the senses themselves.
The abstractions of science leave sense experience so far
behind that they do not seem ever to have started from
it. Nevertheless, the structure has been built ad seriatim
from brute facts upward, and must be demonstrably
non-contradictory to them. Science, therefore, does start
from sense experience.

THE METHOD OF EMPIRICISM 125

ABSTRACT CHARACTER OF COMMON EXPERIENCE

It is not ordinarily recognized how much beside sense
experience enters into the world of common agreement.
We have only to mention such non-sensory facts as
time, space, causality, and chance, to show that without
such categories sense experience does not make 'sense/
It need hardly be urged that we do not directly experience
time, space, causality, or chance. These are constructions
of brute facts, yet they are facts just as hard and fast as
the evidences of sense experience themselves. And unless
one assumes the philosophy of radical empiricism, they
are accepted as such.

This necessity of categorization, with its universal and
implicit acceptance, is well illustrated by the existence
of what is called history. History understood as a succes-
sion of actual events which have happened is nothing
anyone would consider to be history. Particular events
must be shown to have some kind of direction or meaning
before history is admitted. The direction and meaning of
events arc notoriously judgments. But even if we admit
that the mere succession of actual events is history, such
a chronicle akeady presupposes a fixed time-order, which
is surely never sensed. And as we have shown, even the
observation of these events as they occur cannot be made
without non-sensory inference. The movements of
horses and men is already an inference from brute
sensations. But the movements of horses and men can
only be called a 'battle* by inference. However, no
history stops with even such judgments, but goes on to
infer results and causes and .to link these up with such

126 WHAT SCIENCE REALLY MEANS

abstract facts as 'revolution/ 'increasing nationalization/
the 'decline of the West/ etc. Despite the fact that
historians will largely disagree on the speculative truth
of such broad movements, speculation is always de-
manded, and all historians are in agreement concerning
what they call the 'facts/ i.e. rudimentary constructions
(less daring inferences).

From recorded history of the more remote past, we
may turn to the daily affairs of common experience.
Here we can see also that abstractions play the part of
accepted fact in the understanding of brute experience.
For instance, no one doubts that there is a political
'sphere* or an economic 'scene/ Indeed, most of our
discussions about 'what is going on in the world' take
place in terms of non-sensory abstractions. Will the
United States Government become more or less cen-
tralized ? Will the stock market recover ? Is agriculture
to become industrialized? Is communism in Russia
moving to the right ? Every one of these questions is
framed almost altogether in abstract terms, terms many
times removed from the sensory. Yet they have the
validity and reality of stubborn hard fact. No one doubts,
for instance, that agriculture is a real thing though no one
can sense agriculture. The operations of the stock market
are to many persons the most real of all realities; yet who
has ever sensed a stock market operation ? The best that
can be seen are brokers walking to and fro and writing on
slips of paper, or ticker tape, or chalk marks; but certainly
these are not equivalent to the fact of the stock market.
We have seen that the empirical world we live in is
shot through with, and indeed mostly composed of,

THE METHOD OF EMPIRICISM 127

non-sensory and abstractive facts. To understand this
world to some extent is the test of sanity. The insane
man is not the man who lacks his five senses (indeed,
many sane persons lack one or more senses, e.g. no one
would call Helen Keller insane). What the insane man
lacks is the ability to make abstractions from his sense
experience in a way which agrees with the abstractions
of his fellows. Hence it is upon the quality of abstractions
and not upon the quality of sense experience that sanity
depends. The insane are said to live in an unreal world,
e.g. they cannot understand social realities, and social
realities are abstractions. Nobody acts as though he truly
doubted that social facts are real and that abstractions are
empirical.

Having seen how the actuality of common experience
is compounded of abstractions far in excess of the
sensory, let us now turn to science to see how the process
of abstraction is carried further. Just as common experi-
ence infers from pure sensation, science starts from the
facts of common experience and makes inferences from
these to arrive at its peculiar abstractions. True science
does not start until abstractions are made from actuality.
Science begins by abstracting from actuality, past and
present, and thus from place and date. It therefore follows
that science does not deal with unique particulars;
indeed, it gets away from sense experience altogether,
even though the terms which it uses to express its mean-
ing have perforce a certain sensible aspect. These ab-
stractions from actuality are the first empirical entities of
science, non-sensory. Thereafter science deals with these
abstractions as though they were given, and no further

128 WHAT SCIENCE REALLY MEANS

with the sensory facts on which they ultimately rest.
Indeed, for purposes of procedure, these abstractions are
the 'given' of science.

PROCEDURE OF SCIENTIFIC ABSTRACTION

The subject-matter of science is removed from actuality,
to which it returns only to make sure that its entities
are still empirical, i.e. that they check with sensory fact.
We have seen in the last chapter that the subject-matter
of all the sciences is functions. We have seen in the last
section how these functions are arrived at by abstracting
from actuality. Thus the realm of science is the real but
non-actual realm of functions, and each science deals
with a set of functions abstracted by means of some
canon or level of analysis. For instance, physics deals
with the space-time functions of actuality abstracted
from actuality, and biology deals with organizational
functions of the living physical organism abstracted from
those actual living organisms, etc. In this realm of
functions the categories of actuality have no application.
Functions do not change, since they are the unchanging
expressions of change between actuals. Thus functions
are timeless. Again, the category of space has no applica-
tion to functions, since the relation between things in
space has no location. Functions have no affective value;
not only are they non-picturable and non-sensory, but
neither do they have the value connotations of good,
bad, ugly or beautiful, worthy or unworthy. Science for
the purposes of science is wertfreiheit. 1

1 This term, coined by Max Weber, is translated by Brock as the
"necessity of abstaining from valuations in science." See Werner
Brock, An Introduction to Contemporary German Philosophy, p. 27.

THE METHOD OF EMPIRICISM 129

When science reaches its abstractions from actuality, it
does not stop with them, nor does it simply accumulate
a set of these abstractions, largely unrelated. It rather
endeavours to build a system of such functions by (a) find-
ing through analysis the implication of those functions,
and (b) abstracting from those functions and arriving by
induction at functions of greater generality which include
the lesser as special cases but do not replace them.

An example of (a), the finding through analysis of the
implications of functions, may be taken from the fact that
Priestley's discovery of oxygen is a specific implication
of the more general function of chemical element.
Specificity in the finding of less general subsidiary func-
tions is as essential for scientific knowledge as is the dis-
covery of the more general. But specificity in this sense
is not to be confused, as it so often is, with unique
individuality. 'Oxygen/ as a scientific entity, is no more
actual than is 'chemical element/ but it is more specific.
Both have to deal with possibilities.

An example of (6), the process of abstracting from
abstractions, may be taken from medical science. The
first abstraction in regard to immunity was made from
actual cases of special diseases, e.g. immunity from
diphtheria, from smallpox, and then abstracted as the
principle of immunization, regardles of any particular
disease. Another example of the process of abstracting
from abstractions may be taken from the differential
calculus. Rate of change is certainly an abstraction; but
we can abstract from it to the second rate of change (the
rate of acceleration). This second derivative is the rate of
a rate, and thus a further level of abstraction.

130 WHAT SCIENCE REALLY MEANS

As the empirical test of the first abstractions of science
is actuality or demonstration, just so the empirical test of
the higher abstractions arrived at by induction are the
first scientific abstractions akeady tested. It is true that
in most cases the second level of abstractions can be
tested directly against actuality, i.e. experimentally. But
this is not the prime test. The prime test is against the
first level of abstraction. Nor does science necessarily stop
here, but can go on indefinitely; and in each case the
empirical test can be either against the last level of
abstraction or against any level or against actuality itself.

A system erected in this way ultimately rests, as it
must, on brute sensory fact. But the dependence is neither
apparent in the higher levels nor necessarily remembered
in the empirical check. The roof of a house does not
seem to rest on the ground; nor does a builder fashion a
roof with this thought in his mind, but rather to conform
to the structure of die whole. Nevertheless, the roof rests
on the joists, the joists on the uprights, the uprights on
the foundation, and the foundation on the ground. The
roof must, of course, rest finally on the ground, but it
must also form with the rest of the house a self-consistent
structure.

It is sometimes supposed that non-Euclidean geometry
has no necessary connection with experience but is a
purely formal science. Non-Euclidean geometry has its
origin in the denial of the parallel postulate and the ac-
ceptance of certain others. But, of course, Euclidean
geometry is an abstraction from the observed motions of
rigid bodies, and therefore plainly empirical. Since non-
Euclidean geometry is only once removed from the

THE METHOD OF EMPIRICISM 131

empirical basis, it too is empirical in the same sense that
all the abstractions of so-called applied mathematics are
empirical. If Tom stands on John's shoulders and John
stands on the ground, can it be said that because Tom
no longer has any direct contact with the ground that
he is independent of it ? All sciences are empirical inasmuch
as they directly or indirectly depend upon sensory fact,
and all sciences are empirical in so far as they form self-
consistent systems.

THE PRINCIPLE OF ECONOMY

However necessary the connection between empiricism
and the sensory, more is needed for the empirical proof
in science than demonstration by observed fact. Contra-
dictory theories can be shown to agree with observation.
A notorious case is the Ptolemaic and the Copernican
systems which take into consideration sensory fact, on
the basis of which they would still be valid. Nevertheless,
the Ptolemaic system is no longer held to be an empirical
fact of science, since it no longer agrees with the other
inferences built up in modern astrophysics, with its
telescopic and spectroscopic inferences. It must be noted
that these newer theories are also based on observances
and thus we have two theories in agreement with
sensory fact yet mutually contradictory. The preference
for the Copernican does not depend at all upon sensa-
tions, but upon its ability to embrace and form one
system with new inferences and old laws.

Thus the first and main empirical test in science is that
of self-consistency within the given system, i.e. the body
of accepted theory. If a new theory meets this test, it then

132 WHAT SCIENCE REALLY MEANS

rests directly upon older and accepted theories, and so
ad seriatim, until it rests upon theories which fit the
observed facts. Thus the consistency of a theory with a
given system means ipso Jacto that it is dependent upon
sensory fact. But something more is involved. One part
of empiricism is the principle of economy, the admonition
that no more explanation than is absolutely required be
introduced. This is a variant of Occam's Razor, which
states that entities must not be multiplied beyond neces-
sity. Thus one theory which covers two separate groups
of fact and theory is always preferable to two theories.
And a theory which is addressed only to an isolated
group of facts and has no relation to other theories is
immediately suspect and never altogether accepted as
empirical. This is what the scientists denounce and reject
as ad hoc theory.

Einstein's general theory of relativity, so completely
endorsed that it is already the empirical basis for further
investigation, was largely accepted by physicists because
it was able to embrace and agree with both the Newtonian
theory of gravitation and inertia, and the new facts dis-
covered since Newton, e.g. the failure to detect the ether
drift. 2 The theory of relativity has supposedly been
proved by three experimental tests: (i) the precession of

2 Lorenz and Fitzgerald explained the null result of the Michelson-
Morley experiment by supposing that motion through the ether
altered the linear dimensions of bodies in a way which could be ex-
pressed mathematically. Here was an ad hoc theory which was sup-
planted by relativity, and the alleged 'conspiracy' to prevent the
measurement of absolute motion was reformulated as a uniformity of
nature in the principle of relativity, in a way to make absolute motion
supererogatory.

THE METHOD OF EMPIRICISM 133

the perihelion of Mercury, (2) eclipse photographs, and
(3) the shift toward the red end of the spectrum in the
companion of Sirius. All these experiments bore out
Einstein's law to closer approximations than Newton's.
However, the theory of relativity does not rest on these
experiments but was proved before them, and has only
been confirmed by them. The theory of relativity
eventually is acceptable because of its consistency with the
prevailing body of physical theory. For obviously many
theories might be constructed to explain the results of
these three experiments. But unless they agreed with
the main body of physical theory, no physicist would
give them an instant's consideration.

We have been exhibiting empiricism as the principle of
economy. As such it is a cautionary measure and not
strictly a method, not the leading principle of science,
since by itself it does not constitute science, forming
nothing new but holding down the new to conformity
with the old and accepted. Without it, scientific specula-
tion would be too wild and unintegrated. Thus it is a
warning that too many steps in the development of
science cannot be skipped. This is not a matter of time
since development can be slow or rapid; but it must
always integrate itself with what has gone before. With
this principle in mind, science is justified in holding in
abeyance, or in throwing out, all theories which, though
they check with sensory fact, make no connection with
the given stage of knowledge. We are reminded of
the anecdote of the Pope who rebuked Galileo by saying
that the earth could move around the sun or the sun
around the earth. Here was an anticipation of relativity

134 WHAT SCIENCE REALLY MEANS

which could have no scientific standing since it was
highly disconnected from the stage of scientific inquiry
of that day. Again, the alchemists' theory of the transmu-
tation of the elements has been shown to be possible;
nevertheless, alchemy has no scientific standing, since it
failed to show how the transmutation was to take place.
The occult sciences of our day astrology, theosophy,
and spiritualism may entertain theories which are true,
and certainly they have unearthed facts for which some
accounting will have to be made, but they are rejected
by the body of science to-day for the simple reason that
so far they have not been confirmed by scientific theory,
i.e. no explanation in terms of accepted scientific facts
has as yet been given. Thus in spite of their sensory data,
which is empirical, these sciences are not empirical. All
this is another way of saying that sensory facts by them-
selves are not enough for scientific empiricism but must
be supported by theory which economically embraces
all of them and shows them consistent with older
accepted theories.

RELATIVITY OF EMPIRICISM

Empiricism is a relative term. It is relative to the pre-
vailing acceptance of what is real. This broad statement
must not be read to mean that what can be considered
empirical is an arbitrary affair. It is, on the contrary, a
fixed affair, as we have shown, always inevitably de-
pendent upon the stage of knowledge at any time. But
no more is it a matter of the subjective will. Neither the
impulse nor the reasoning of the individual can make
empirical what is not empirical, nor make what is non-

THE METHOD OF EMPIRICISM 135

empirical empirical. To explain what is meant by
saying that empiricism is a relative term, we may give
three examples of its relativity.

First, what is empirical for one science is not necessarily
empirical for another. The atom of physics is an empirical
entity for physics. The atom of chemistry is an em-
pirical entity for chemistry. But the atom of chemistry,
with its many combining qualities, is not empirical to
the science of physics, the only empirical property for
the latter science being its mass. In biochemistry the
biological functions of growth, self-repair, and repro-
duction are not empirical; whereas in botany and
animal biology these qualities are the most empirical.
For the etiology of disease, capitalism is not an em-
pirical fact, whereas for political economy it most
certainly is. In other words, for any special science the
empirical can only apply to what is relevant. And the
relativity of empiricism is seen to mean the relevance. It
does not necessarily follow, however, that all these
examples are reversible. On the contrary, as we shall
show, 3 the series of relevance is non-reversible.

Secondly, what is empirical for any science is not
necessarily empirical for common sense. This should be
obvious. The symbiosis of biology, the dipole orientation
of electromagnetics, the spinors of mathematical physics,
the joint cost of economics, the pyritohedrals of crystallo-
graphy, are none of them observable to common sense,
that is to say, they are not empirical to common sense,
but require special knowledge to be observed.

Thirdly, what was once non-empirical can become
8 Cf. p. 148.

136 WHAT SCIENCE REALLY MEANS

empirical and vice versa. The former assertion will be
readily acceptable. We have only to mention electrons,
protons, quanta, vitamins, planets, etc. The latter asser-
tion is not so readily acceptable, but true nevertheless.
Phlogiston, caloric, epicycles, the bodily humours, these
were once empirical entities, empirical by every test that
science could devise. They were manifest in sense ex-
perience and they agreed with the existing body of
knowledge. But these entities which were empirical are
no longer empirical because they no longer answer the
second requisite, i.e. they no longer agree with the
accepted systems of knowledge, or at best they are not
necessary and therefore they are thrown out on econo-
mical grounds. For instance, forces are not required to
explain anything; they are therefore dropped. Entities
which are found to have no necessity are destroyed rather
than allowed to multiply, in the interest of empiricism.
Three kinds of entities appear in science, the empirical :
the heuristic, and the mythologic. An empirical entity is
any entity whether actual or non-actual which has been
tested against actuality and found to be allowed. An
heuristic entity is one which is set up but which has
neither been accepted nor rejected. A mythologic entity
is a purposive entity employed as efficiently causative. 4
It is clear from the foregoing that empiricism is a con-
stant function which has to do with self-consistency
within a given system, granted the understanding that
any such system indirectly and finally rests on unde-
niable brute facts. Into and out of this constant function,

4 No derogation of the reality of purposive entities is intended, but
only of their illicit use in science.

THE METHOD OF EMPIRICISM 137

items pass, so that while the empirical colours are fading
on some entities, others are being freshly painted with
them. But the fact that entities once deemed empirical
are no longer so considered means only that such entities
have been redefined and given new terms; and that new
entities constantly enter the empirical field means simply
that knowledge of the world is increasing with the pro-
gress of science. Too much has been said about the
'fictions of science.' In truth there are no fictions in
science in so far as there is science. The fictional aspect
of scientific entities, such as forces, phlogiston, etc., is
the illegitimate attribution of actuality to the name of a
function. When the names of these functions are changed,
the fiction of the old disappears, but the truth about the
function remains. Scientifically, the 'fiction' never was a
fiction.

There are, then, no limits to what may become em-
pirical. What may become empirical is limited only by
its ability to continue to have relations with existing
knowledge in an orderly, economic, and necessary
manner. In short, there are no limits to what can become
empirical, but there are absolute limits to empiricism. It
must be noted that the degree of abstractness of an
entity has nothing whatever to do with whether it is
empirical or not.

ALL SCIENCES EXPERIMENTAL

Every science has its empirical aspect. There are no non-
empirical sciences. But the experimental field of each
science is different, depending upon the portion of the
totality of existence selected for study. Every science, in

138 WHAT SCIENCE REALLY MEANS

other words, abstracts from a portion of actuality and
omits everything else as irrelevant. The portion of
actuality abstracted by physics is not that abstracted
by sociology, and vice versa. Thus the sciences can be
arranged in a hierarchy, according to the level of actuality
from which they take their start. This is the hierarchy
of the sciences arranged according to their organization
of actuality.

Taking our start from physics as the lowest known
science in the organization series, we can readily see
that the biological is an organization of the physical, and
that the sociological is an organization of the biological,
and that each of these sciences has, appropriate for study,
functions of organization not included in lower sciences.
But the abstractiveness of each science is independent
of the hierarchy of organization. Each proceeds from
brute facts through partly logical actuality to logical
abstractions and then on to still more abstractive levels,
and finally to still higher abstractive levels where mathe-
matical formulation is possible. It is, of course, true that
at earlier stages of abstraction, mathematical formulation
is possible; but if a science becomes mathematical before
it is sufficiently abstractive (i.e. before it is sufficiently
logical) its mathematical formulations will have little
validity.

No matter how abstractive a science becomes, it is not
carried to the next organizational level. The abstractive
level goes out, not up ; and the organizational level goes
up, not out. Quantum mechanics does not help in the
understanding of heredity, any more than did Newtonian
mechanics. The appropriate field for experimental

THE METHOD OF EMPIRICISM 139

METAPHYSICS

W

H
U

<
fc

w

H
D

Pi

PQ

ULTRA^CIOLOGICAL

(when found)

CO

o

SOCIOLOGICAL o
*"* ri >-

+1

<
O

-H

H

v

PSYCHOLOGICAL H

iJ -*

<

s

\^

BIOLOGICAL cd

^ r 4 n

-a
w

u

w

^

PHYSICAL W
O < CQ

PC

o

H
<

^

INFRA^^PHYSICAL (if

any)

S

^

Direction of ^ Direction of

Abstraction Empirical Proof

DIAGRAM I

THE FIELD OF THE SCIENCES

The diagram is not intended to be an exhaustive list of the sciences.
We have given the main divisions which, broadly speaking, may be
taken as including the others. For instance, physics includes mechanics,
thermodynamics, chemistry, crystallography, astronomy, physiology,
medical science, etc.; sociology includes economics, anthropology,
politics, philology, criminology, etc., and each in turn may have its
subdivisions, ad seriatim. We have included, however, at separate
levels the infra-physical, if there be any science dealing with organiza-
tion at a lower level than the physical, and ultra-sociological, when
that science is discovered.

HO WHAT SCIENCE REALLY MEANS

demonstration is the total ground covered between brute
facts and the point arrived at in abstraction. The em-
pirical proof works back to the less abstract, and not up
in the organizational series. We cannot demonstrate the
validity of bimetallism by reference to the atomic table
of the elements. We cannot disprove the teleology of
living organisms by reference to biochemistry. We
cannot demonstrate free will at the sociological level by
reference to indeterminacy at the sub-atomic level.

When we state that the appropriate field for experi-
mental demonstration is the total ground covered between
brute facts and the point arrived at in abstraction, we
mean exactly what was stated above, 5 where it was said
that the first empirical test in science is that of self-
consistency within the given system, that self-consistency
within the given system is ipso facto dependent upon
sensory (i.e. brute facts) but involves something more.
In the empirical proof it is always possible to return to
the level of sensory brute facts, but it is seldom necessary.
Empirical proof usually consists of going backward one
step to the immediately preceding stage of abstraction.
The new and more abstract generalization is empirically
proved when the immediately preceding abstract general-
izations are shown to be more special instances of the
one under consideration. This holds for every branch of
science; and to the extent to which every study generalizes
in this way it is equally empirical.

5 See this chapter, section on "The Principle of Economy.'*

THE METHOD OF EMPIRICISM 141

THE EXPERIMENTAL SCIENCES OF LOGIC, MATHEMATICS,
METAPHYSICS

The classical sciences, e.g. physics, biology, etc., are
recognized to be empirical sciences. But logic, mathe-
matics, and metaphysics are not so recognized, chiefly
perhaps because they do not fit into the hierarchy of
sciences arranged according to levels of actuality. As
our diagram suggests, logic and mathematics can be
abstracted from any and all sciences or from brute facts
directly, whereas metaphysics is the widest generalization
from all knowledge, including logic and mathematics as
well as brute facts and the sciences. But, as we have
shown, the empirical status of science has nothing to do
with the organizational series. The series only delimits
what are the empirical fields for those sciences. We shall
show that logic, mathematics, and metaphysics them-
selves can be and indeed must be empirical.

Logic is an empirical science. When abstracted and
presented as an independent system, logic is inde-
pendent of actuality. But it rests on the most empirical
facts in experience, namely, the distinctions and dif-
ferences between brute facts, without which there would
be no such facts. The three postulates of Aristotle:
identity, non-contradiction, and the excluded middle,
are the basis on which all logic rests. But they them-
selves are not susceptible of logical proof; they are
indeed the basis of our sensory knowledge of brute facts.
Thus they are empirical in the most radical sense. Our
experience starts with the separation of a brute fact from
its surroundings, and the recognition of it (a) as an

142 WHAT SCIENCE REALLY MEANS

identical fact, (6) as being not its environment, and (c) as
having no zone common to it and its environment.

All the formulations of logic, then, start with the brute
fact of identity, without which nothing would be ex-
perienced. But once abstracting identity and its implica-
tions, logic treats the purely formal and abstract system
so derived as itself a series of given facts, and proceeds to
draw further inferences from them. Thus the major and
minor premises of every syllogism are brute givens,
corresponding to the accepted theories of the physical
sciences, which hi turn rest on brute difference, just as
the theories of science eventually rest on brute sensory
fact. The ideal science of logic corresponds exactly to
those sciences which have abstracted from actuality. All
the propositions of logic are stated conditionally: if A
then J3, just as all the abstractive laws of a science are so
stated, e.g. if action then reaction. Thus both logic and
natural science are free from actuality in their formula-
tions but applicable to actuality conditionally.

If logic is an empirical science, then so is mathematics.
Mathematics is merely one kind of abstract extension of
logic, rigidly depending upon the laws of logic, and thus
finally resting upon basic difference. A large part of
mathematics, however, depends upon assigning exact
measurements to difference, Mathematicians try to arrive
at the most general and abstract formulation of what
appears experimentally as special mathematical formula-
tion. The instantaneous speed of a moving object and
the tangent of a curve are both generalized under the

dy
same formula, -, where y is indifferently the distance

THE METHOD OF EMPIRICISM 143

or the ordinate, and x indifferently the time or the
abscissa. The fact that the generalization covers the special
cases can only be proved experimentally. Thus all opera-
tions in mathematics are experimental, even when they
do not appear so. But in certain instances the method is
more obviously experimental. The method of finding
invariance under successive transformations in affme and
projective geometry, and in the theory of groups, is that
of performing operation after operation to find empiri-
cally what properties of the system remain identical. 6
Thus the theory of invariance is arrived at experimentally.
To quote Felix Klein, the problem is

Given a manifold and a group of transformations of the
same, to develop a theory of invariants relating to that
group. 7

The fact that the operations of mathematics are so far
removed from sense experience does not make mathe-
matics one whit less empirical than chemistry.

The statement that metaphysics is also properly an
empirical science is apparently hard to accept. In fact the
quarrel with metaphysics is just that it deals with absolutes
which arc beyond demonstration. But when we take into
consideration that metaphysics is a certain kind of

6 But this is only what is done in every science: the accidental is
discarded and the necessary retained. However, what is accidental for
one department of science may be necessary for another. Black spots
before the eyes are accidental for bacteriological analysis but necessary
for medical diagnosis. Similarly, what is not invariant (i.e. changing)
under a group of transformations also may be studied for change as
itself an invariant.

7 Cited by E. T. Bell, The Queen of the Sciences, p. 69.

144 WHAT SCIENCE REALLY MEANS

generalization and abstraction from actuality and brute
fact, we shall more clearly see what its experimental field
is. It is obvious that a metaphysical system which fails
to check with the accepted theories of science and the
facts of common experience is a bad one, and will never
gain any lasting acceptance. The task of philosophy is
made difficult by the very fact that its generalizations
must embrace so much, and thus its conclusions are more
tentative than those of the special sciences, since meta-
physics must stand the test of all knowledge. But this
fact does not mean that it is thereby rendered exempt
from its proper empirical test. Agreement in philosophy
is thus far a great deal harder to attain than in science.
But random vagaries and vague mysticism .are no more
philosophical for philosophy than they would be
scientific for science. Moreover, every metaphysical
system must be self-consistent, since this is everywhere
the empirical test. And like science, new generalizations
which are found to agree with the old are not sum-
maries merely but throw light on new facts. Thus
ontology, like the self-consistent systems of science, is a
fact-finding instrument and not simply a systematic
accounting and arrangement.

To generalize from our investigation of empiricism in
the various fields, the essential nature of empiricism is
the limiting conditions of the speculative reason. Thus
what appears as speculative from the immediately pre-
ceding lower level of abstraction appears as empirical
from the immediately following higher level. What is
involved is a matter of direction and not one of intrinsic

THE METHOD OF EMPIRICISM 145

dissimilarity. The distinction between the empirical and
the logical has been too severely drawn. All that em-
piricism states is that nothing can be constructed except
in and through lower levels of accepted fact, which,
abstractive as they may be, finally rest upon the mere
faith in the bruteness of given sensory experience. From
the brute given upward indefinitely, all that matters is
self-consistency and economy. Empiricism finally reduces
to the question of relevance.

CHAPTER VII
THE LOGIC OF SCIENCE

Nature syllogizes from one grand major
premiss. . . .

CHARLES S. PEIRCB
INDUCTION AND DEDUCTION AS DIRECTIONS

The close relationship between empiricism and logic
has been indicated. It must now be further explored. To
do so we must first examine inductive and deductive
logic, and then show what these mean in terms of
scientific method. Some scientists make the mistake of
supposing that scientific method is exclusively a matter
of induction, whereas others suppose, just as mistakenly,
that scientific method is exclusively a matter of deduc-
tion. A plague should be cried on both these houses.
Scientific method requires both, and the validity of the
one certainly requires no rejection of the other. The two
methods are complementary and not antithetical. From
the point of view of logical experiment, deduction is the
process of drawing necessary conclusions from premises.
Induction is the choosing of premises.

What is induction? It is a process which starts with
certain givens and moves to a generalization which will
subsume them so that they appear as related parts of one
system. The movement of induction is always in the
direction of greater generality, from the less general to
the more general. Irrespective of what mental aspect an
induction is, it appears logically as a partial sublation of

THE LOGIC OF SCIENCE 147

otherwise unsublated data, and therefore as an explana-
tion, since the explanation of anything consists in its
being assigned a place in a system.

What is deduction ? It is a process which starts with a
given generalization or system and moves to find the
parts of that system included as implications. The move-
ment of deduction is always in the direction of lesser
generality, from the more general to the less general.
The explication of any system is all the deductions which
can be drawn from it.

We can see that the possibility of induction or deduction
takes for granted the existence of both. Without data no
induction could be made to a system; without a system
no deduction could be made to implications. The move-
ment in the first case is up from the parts to the whole;
the movement in the second case is down from the
whole to the parts. The main and important distinction,
logically speaking, between induction and deduction is
one of direction.

We are trying to present a system of relations which
is discovered by two methods : induction and deduction.
The start can be made from any given system, and that
system analysed into subsidiary systems, or synthesized
with other systems into a more inclusive system. There
are thus series or layers of systems, arranged in a hierarchy
by order of inclusiveness, which the mind ranges over
by running up inductively or running down deductively.
Inductions always have a deductive background, whether
this is recognized or not. 1 And what is induced to is

1 "Practical inventions do not really come as 'bolts from the blue*
to those who have never thought of or studied a given topic. . . .

148 WHAT SCIENCE REALLY MEANS

always another deductive level, whether this is recognized
or not.

The relevance, then, of any item to any other item can
only be by reference to place within a system, and cannot
refer to anything outside that system. This makes possible
the investigation of a system in isolation, otherwise im-
possible. If everything in the universe had to be taken
into account in order to explain an item, explanation
would be impossible. But explanation is made possible
by confining attention to a given system. This fact
defines relevance and irrelevance. We have already
demonstrated relevance. Irrelevance consists in referring
to something outside a given system as an explanation of
something inside the system. For instance, the analysis of
a dining-room table into legs, top, drawers, etc., does
not involve the system of which the dining-room table
is a part, e.g. other furniture in the room, or the room,
or the economy of the household, etc. Therefore to bring
in these wider systems in the analysis of the table is
irrelevant. On the other hand, synthesis is impossible
merely in terms of elements of analysis, since no number
of items of a system can by themselves yield the whole
system. For instance, the freedom of the will cannot be

Even the celebrated case of James Watt inventing the steam engine
after observing his mother's teakettle, breaks down when one dis-
covers that other steam engines were already in use and that Watt
studied the problem for years before he invented anything. One of
the most spectacular strokes of genius in the nineteenth century,
Hamilton's discovery of quarternions (which, as he has told us, came
to him in a few seconds), is known to have been based upon twenty
years of study of the very problem which he suddenly solved"
(Gardner Murphy, A Briefer General Psychology, p. 358).

THE LOGIC OF SCIENCE 149

inferred from the Principle of Indeterminacy at the
sub-atomic level. Nor can biological phenomena be
entirely explained in physico-chemical terms.

Induction and deduction constitute the movements of
logic. But logic per se has nothing to do with anything
moving. It deals with the conditions of possibility.
Actuality we take to be the succession of sensory facts
which can be experienced. The logical order of possi-
bility is not a temporal succession at aU, but a set of
unchanging conditions mutually implicative. All logical
propositions are thus formal and have nothing to say
about any actual thing or event. To apply logic, there-
fore, in natural science, other factors than the purely
logical must be considered, since science is concerned
with determining the extent to which actuality is formal.

THE LOGIC OF SCIENTIFIC METHOD

Since science is concerned with actuality to the extent to
which it is formal, scientific method must be a particular
application of logic. 2 The very feasibility of the applica-
tion of formal logic to actuality in scientific method pre-
supposes the continuity, or what John Stuart Mill called
the uniformity of nature. It takes for granted that nature
is objectively a consistent system, continuous and uni-

2 Since experimentation seems to deal with sensible qualities, and
logic with formal qualities, the conception of the logic of science often
appears to the experimenter to be a contradiction. But in successive
experiments the sensible qualities change, whereas the formal qualities
remain the same, and it is the latter which enable an experiment to
be called scientific. The presence of the sensible qualities blind the
experimenter to the fact that from his point of view the formal are
prior.

I 5 o WHAT SCIENCE REALLY MEANS

form, which can be known. We have shown that logic
deals only with possibility and not with actuality, and
that scientific method deals with the verifiable possi-
bilities of actuality. For instance, that all unicorns are
horses having a single horn, is a proposition which has
no application to zoology since no actual unicorns have
ever been observed. In other words, both the major
and the minor premises of a logical proposition are always
ideal and conditional, i.e. possible.

If unicorns arc hdrses having single horns,
And if this horse has a single horn,
Then this horse is a unicorn.

But scientific method differs from formal logic in
having as the minor premise an actual fact, i.e. in
determining that the condition applies. And this is what
experiment or demonstration is.

If unicorns are horses having single horns,
And since this horse is observed to have no horn,
This horse is not a unicorn.

The first syllogism is purely logical; the second corre-
sponds to the procedure of scientific experiment. It must
be noted that in both syllogisms the major premise is
conditional and ideal. As far as deduction is concerned,
the major premise is treated as given, and has empirical
standing, having itself once been the minor premise of
some other syllogistic movement. In science, inductions
from observed facts, when mathematically formulable,
have been employed to yield new results deductively.
But the inductions from which this train of reasoning

THE LOGIC OF SCIENCE 151

started have often themselves later been shown to be
deductions from some apparently unrelated deduction.
For instance, Balmer's Law for the position of lines in
the hydrogen spectrum was a mathematical induction
from certain observed measurements. Since this time
the law has been deduced from wider systems : atomic
theory and quantum mechanics, which have been shown
to include Balmer's Law as a special case. 3

Scientific method, in contradistinction to logic, in-
volves two procedures: it goes down to be tested
against actuality; it goes out to be tested against a
given system for logical consistency. Thus again it is the
logic of actuality. On p. 132 above we showed that
Einstein's general theory of relativity was demonstrated
in two ways: by testing against actuality in the three
experiments noted; and by logical consistency, showing
that it agreed with the previous body of physical
knowledge. The test by actuality or experimental
demonstration is not a proof of the validity of the
scientific hypothesis involved; it is merely an allowance;
whereas the failure of the empirical allowance of an
hypothesis does constitute an absolute disproof. 4 It
should be noted that the appeal to prediction is one form
of the appeal to actuality. The test by consistency with
logical possibility is proof. For proof means the ability

3 We owe this illustration to Morris R. Cohen, Reason and Nature,
p. 120 f.

4 On page 150 we gave an example of the syllogism of disproof.
We may also give here an example of the syllogism of allowance.

Perhaps all frogs hop,

Certainly some (all observed) frogs hop,

Therefore it has not been disproved that all frogs hop.

152 WHAT SCIENCE REALLY MEANS

to place a given item, in a system where it will form part
of a larger system without disturbing its consistency.
Thus empirical proof is allowance; logical proof is proof. 5
Chantecler's theory that he crowed up the sun was not
proved by the many times that the coincidence happened,
but was absolutely disproved by the one time that it
didn't. As Jeffreys says, 6 "one of the chief functions of
exceptions is to improve the rule."

The two procedures can be validly conducted without
reference to actuality solely on the level of possibility.
This is what happens in the science of mathematics,
where the proof of logical consistency and the test by
experimental demonstration turn out to be identical.
The only possible tests in mathematics are to verify the
consistency of a given mathematical hypothesis by
reference to sub-systems, or to wider systems. That is
what experiment means in mathematics. 7

But the two procedures cannot be validly conducted
solely on the level of actuality and without reference to
possibility. Here the two movements are not the same.
For to transport the two procedures to actuality means
that the major premise of the syllogism which cor-
responds to experimental demonstration must also be an
actual. When this is done, the procedure down to
experimental demonstration is retained, but its logical
consistency is omitted, and what results are so-called

5 Cf. the instance of Balmer's Law, p. 151, where induction is
eventually shown to be a special case of deduction from a more in-
clusive induction.

6 Harold Jeffreys, Scientific Inference, p. 5.

7 For a good illustration of this, see H. Levy, The Universe of Science,
p. ii6f.

THE LOGIC OF SCIENCE 153

empirical laws, generalizations from observed phenomena
which may or may not hold as laws.

England was prosperous under Elizabeth, Anne, and

Victoria,

England is always prosperous under queens,
Therefore England will be prosperous under the next

queen.

Or, formulated deductively,

Prosperity under Elizabeth, Anne, and Victoria means

prosperity under all queens,
Queen X is a future queen of England,
Therefore England will be prosperous under Queen X.

This is an empirical law which, like all other empirical
laws, holds only with exceptions. It is therefore not a
scientific law. The next queen may disprove it. The
difficulty lies in the lack of logical consistency, there
having been no necessity shown between the sex of the
monarch and the prosperity of the realm. If such necessity
could be shown, it would take the form of a logical
proposition and not of an actual fact. No exception can
prove a rule; but on the contrary any exception can
disprove it.

It is therefore true that all scientific laws must occupy
the status of ideality, of possibility, and cannot be mere
generalizations of actual facts.

Experiment is a variety of deductive logic, that variety
where the determination of implications involves refer-
ence to the observation of actuality. But logical analysis
equally involves experiment, though here the experi-

154 WHAT SCIENCE REALLY MEANS

ments performed do not candidly present themselves as
such. For instance, the analysis of the term 'queens' or
the term 'prosperity' cannot be made without reference
to a typical case. Such reference constitutes a logical
operation. Experiment is involved in logical analysis,
and logical analysis is involved in experiment. The proof
by deduction and the proof by experiment turn out to
be the exploration of what is involved in a system (i.e.
its implications) so that all the parts of the system are
seen as consistent parts of a larger system.

Those who say that analysis or deduction is the whole
of scientific method have been misled by too narrowly
considering scientific procedure, which always analyses
to establish an hypothesis. They have neglected to per-
ceive that no analysis can be effected except in terms of
an embracing system, and that such systems are not
merely given to ordinary observation, but require in-
sight and valid induction.

ANALYSIS AND SYNTHESIS

We have shown the two movements of logic in scientific
method and the absurdity of trying to confine scientific
method to either movement. The difference between
induction and deduction is a difference of direction, so
that what is an induction from one level is a deduction
from a higher. The same thing applies mutatis mutandis
to the question of reason and empiricism, where reason
alone or empiricism alone is championed to the exclusion
of the other. It has been shown that any theory arrived
at by speculation may become an empirical fact, and is
ipso facto an empirical fact when deduced from a higher

THE LOGIC OF SCIENCE 155

level. Thus what is speculative from one level is em-
pirical from another, and again what is involved is a
matter of direction. The further problem of the dif-
ference between pure and applied sciences is resolved in
the same manner, by showing that there is no absolute
distinction but only a relative one.

The exclusive reliance on rationalism or empiricism
produces a pair of dogmatisms. Rational dogmatism con-
sists in the assumption that it is possible to reason to the
facts without the aid of experimental demonstration.
Plato's dogmatic rationalization that the universe being
harmonious, there must be harmonic intervals between
the planets, was overthrown by the empirical observations
of Tycho Brahe. The mistake lay in supposing not that
there was a regularity, but that the particular regularity
could be found by deducing from the larger system.
Empirical dogmatism, on the other hand, consists in the
assumption that it is possible to discover laws without
the help of the speculative reason. The social scientists
working from this position have been accumulating ex-
perimentally determined facts for decades, without
having been able to produce a single valid law (from the
very fear of being too speculative).

Rational dogmatism and empirical dogmatism are
each half-truths and half-errors. The truth of rational
dogmatism consists in the fact that reason is required as
pointing the way down towards discovery, without
which there could be no discovery. The truth of empirical
dogmatism consists in the fact that without experiment
the nature of the constituents of a system can never be
known (no number of theories being able to prove an

156 WHAT SCIENCE REALLY MEANS

actual). The error in rational dogmatism consists in the
truth of empirical dogmatism, and vice versa. Rational
dogmatism is uncontrolled speculative generalization;
empirical dogmatism is positivism. One never touches
the ground; the other never leaves it. Scientific method
cannot be confined to either but must employ the truth
that is involved in both, in a complementary manner.
Where empiricism and speculation are seen as two
directions, it becomes clear what the limits of each are.
Since the explanation of anything lies in showing its con-
sistency within a larger system, speculation about that
larger system is the first requisite. But the placing of the
parts of the smaller system within that smaller system is
irrelevant to the larger system. And thus the second
cannot be deduced from the first.

Equally, it is impossible to find a system which explains
the parts of analysis of the parts, since this is looking in
a lower system for an explanation of the higher. The
attempt to jump from the constituents of one system to
another system either higher or lower is misleading and
fallacious.

We now come to the relative distinction between pure
and applied science. Sciences cannot be divided into those
which are pure and those which are applied. Some
sciences appear to be merely applied sciences; their
theories are not in evidence because they are overlooked
or have not been formulated. Agriculture is an example.
Other sciences appear to be pure or merely formal because
little or no application has been found for them. For
example, many branches of mathematics have remained
notoriously pure, i.e. no use has as yet been found for

THE LOGIC OF SCIENCE 157

them. But scientific progress has moved two ways:
toward the abstract formulation of applied techniques,
and toward the application of pure formulations. The
practice of medicine which was altogether and is still
somewhat an e^Trcipia is daily becoming more of a
rex^, as is also cookery, business management, etc.
On the other hand, conic sections, non-commutative
algebra, and the tensor calculus were once branches of
purely formal science, for which applications were later
found.

Within any given science, every abstractive level
appears as formal to the level below it, and as applied to
the level above. Physics appears as 'formal 5 to technology,
and mathematics appears as 'formal* to physics. Con-
versely, technology appears as 'application' to physics,
and physics appears as 'application' to mathematics.
Thus so apparently useful a discipline as technology is a
formal study from the point of view of its application
to industry. And so apparently abstract a study as higher
mathematics is an applied affair from the point of view
of logic.

We have in this section been exhibiting a single point
which appears under several guises, namely, that there
are levels of investigation which require two directions
to be fully understood. Only one direction can be em-
ployed at a time, but both must finally be employed in
each instance of scientific method. We have seen this point
illustrated in the question of induction and deduction,
rationalism and empiricism, pure and applied science. But
in science, this quasi-opposition is more familiarly known
as the problem of mechanism versus teleology or purpose.

158 WHAT SCIENCE REALLY MEANS

MECHANISM AND PURPOSE

Mechanism and purpose in science are merely the general
doctrines covering the questions of analysis and synthesis,
the employment of empiricism, and the speculative
reason. Mechanism in science states that the explanation
of die phenomena of nature requires only an analysis
of given items into constituent parts, and that such
an explanation exhausts the phenomena without the
introduction of purpose. Purpose, it further states, is an
unnecessary and thus an illicit conception, and efficient
causation is alone scientific. Those who oppose this
doctrine maintain that many of the phenomena of
nature cannot be explained without introducing the
category of purpose, and final causation. Purpose in
science is the statement that any given item contains
more than the sum of its parts.

Mechanism is known as atomism, materialism, "physi-
calism," etc. Atomism is the variant which may be
defined as the belief that all things are the results of un-
changing particles in motion; materialism, that matter
alone is real, and all else configurations of it; and physi-
calism, that all the sciences are reducible to the science of
physics. Purpose is known as vitalism, creative evolution,
entelechy, etc. Vitalism is the variant which may be
defined as the belief that a mysterious binding quality,
called life, is involved in living organisms beside their
material parts; creative evolution, that there is a force,
e.g. the elan vital, which is the 'drive' working within
things toward some mysterious end; and entelechy, that
there is a mysterious determining principle germinating
within things to guide them toward an end.

THE LOGIC OF SCIENCE 159

Both these doctrines fail to be completely explanatory
of scientific method or of the data with which the
sciences deal. Mechanism accounts for analysis well
enough, but fails to account for wholes which defeat
every effort to build them up with elements of analysis
alone. Purpose accounts for organizations well enough,
but begs the question of constituent parts which cannot
be accounted for by purpose. It is quite understandable
why most scientists should consider that purpose is not
properly part of the procedure of science, since it does
not appear under this guise. Purpose appears in scientific
analysis not as purpose but as empirical fact, and it is
only recognizable as purpose in regard to systems above
it. For instance, in the analysis of blood, blood appears
as an empirical fact, a brute item for analysis, and it is
only with reference to the function of blood that one can
recognize this empirical fact to be also a purposive affair
in regard to the nourishment of tissues, etc. In isolating
an item for analysis, it is forgotten that the only canon
of isolation in the first place was its purpose. Function is
purpose, and function defines an item.

The inception of any single application of scientific
method presupposes an hypothesis or an induction (pur-
pose) at once predicated and left behind. The scientist is
mainly concerned with exploring the deductive implica-
tions of an hypothesis, and thus he tends to forget the
original leap to the predicated purpose. It is not easy to
see a scientist leap to an hypothesis in the bathtub, but
anyone can actually observe him working in the
laboratory exploring deductive implications. The fact that
mechanism is indefinable without purpose is well shown

i<5o WHAT SCIENCE REALLY MEANS

when we consider the definition of a machine. A machine
is a purposive organization of parts and not a mere
agglomeration.

On the other hand, die presence of purpose in scientific
method does not mean that the vitalistic theories are
valid. Purpose is not a mysterious something added to
empirical entities to give them 'meaning.' It is the relation
which the parts bear to a whole. Necessarily such
organization is abandoned in analysis. But this does not
mean that it does not continue to exist. Water is not
composed of oxygen, hydrogen, and wetness, but of
oxygen and hydrogen in certain proportion and organi-
zation, which is water and, as such, wet. Since purpose
is, then, the organization of parts, it is not to be found
in the parts alone; it is the whole of a system and not
any part. Thus the attempt to find a life principle, an
entelechy, etc., in analysis is an absurdity.

Both mechanism and vitalism are each partly true,
though each in itself is false if taken as being the whole
truth involved. Both mechanism and vitalism, as false,
point the same moral as the exclusive claim of analysis
and synthesis, namely, that of trying to account for the
whole of scientific method by one direction instead of
by two. Mechanism and purpose yield the same caution:
it is impossible to move from the parts of one system
outside that system. Mechanism as an exclusive theory
wrongly supposes that the sub-systems of parts can yield
the system which includes those parts. Purpose as an
exclusive theory wrongly supposes that a system which
embraces given systems as parts can be brought in to ex-
plain the parts of the embraced systems. An example of

THE LOGIC OF SCIENCE 161

the first error is the proposition that life is a property of
the carbon atom. An example of the second error is the
proposition that the elan vital works on the carbon atom
to produce living tissue.

In conclusion it should be pointed out that mechanism
as a method in science is the essential element, since every
purpose is explained only in terms of elements of analysis
in relation to a system, i.e. for science purpose is die
explication of the how. But the positivistic reading of
mechanism as a scientific philosophy would exclude pur-
pose, and therefore if followed logically, exclude also
induction and hypothesis. It would thereby prevent all
advance. Mechanism is just as vicious as purpose when
erected into a scientific philosophy. In science what
appears as purpose is rightly considered in its empirical
aspects, i.e. analysed down, and when so analysed kept
clear of higher systems. This is the empirical method.

DEDUCTION VERSUS IMAGINATION

With the understanding that deduction alone is insuffi-
cient in science, and that purpose is implicitly involved
in the start of analysis, we shall attempt to show that the
direction of the development of science involves a greater
and greater use of deduction and a lesser reference to
purposive entities.

With the development of a given science inductively
the consistent logical system becomes by definition wider.
This means that higher levels of abstraction are being
attained, and that the appeal to actuality for allowance
or disproof becomes less and less necessary. When a

162 WHAT SCIENCE REALLY MEANS

science is in this advanced stage of development, it has
resort largely to mathematical formulation; its deductions
yield brilliant results, often more brilliant than those
attained through induction. Induction is not abandoned
when a science advances to the mathematical stage, but
it becomes less apparent, and requires less imaginative
flight, approaching closer and closer to the process of
deduction.

We have shown that in mathematics the empirical
proof can be either deductive or inductive, and that both
are experimental. The place of brilliant insight in the
advance of science has perhaps been over-emphasized,
particularly in the more developed sciences. Brilliant
results do not necessarily mean brilliant insight. Emile
Meyerson points out that many of the discoveries which
have been arrived at by deduction could never have
been the results ot imaginative insight, since they are too
fantastic ever to have appealed to any scientist. The
superhuman vision obtainable with the photo-electric cell,
is the application of a deduction from sub-atomic physics,
and is certainly one which could never have been
imagined. The same is true of television. None of these
is as remarkable a feat of scientific imagination as the
public assumes. They are clever adaptations of deductions
from known principles.

Admitting, however, that great scientific discoveries
have been made inductively, through psychological in-
sight, does not logic play a large part here as well ? Are
not scientific discoveries as much a function of the given
stage of a science's development as of the imaginative
capacity of the individual scientists ? Certainly successful

THE LOGIC OF SCIENCE 163

scientific leaps in the dark' are not made by those
ignorant of the background of the scientific system. They
are not made by poets and prophets but often by scientists
otherwise prosaic and unimaginative. Scientists who make
brilliant guesses do so because of their knowledge of the
consistent system which presents itself as a series of de-
ductions. The logical status of a science is important in
the understanding of scientific discovery and advance.
The rapid advance of physics as contrasted with social
science is certainly not to be explained by supposing that
all the genuises have become physicists and that social
science has in its service only mediocre intelligences.

The development of a science to the level of abstraction
which is fit for mathematical formulation accomplishes
something else of value. It reduces to a minimum mytho-
logic entities, which are the cryptic introduction of pur-
pose into scientific analysis. For instance, medical science
which has not reached the stage of physics or chemistry
is cluttered up with such mythologic and crypto-
purposive entities as immunity, resistance, defence, anti-
body, agglutinin, lysin, etc. The scientific problem con-
cerns the analysis of these entities into their mechanisms.
They are useful, but only in the intermediate stages of
science. In a mathematical-deductive science, like physics,
purpose appears as the geometric properties of an arith-
metic system.

Thus induction and purpose do not disappear in the
development of a science, but begin to become one with
deduction and mechanism. In the ideal science all prin-
ciples appear arranged ad seriatim as deductions from a
single grand major premise. And purpose is seen as the

164 WHAT SCIENCE REALLY MEANS

hierarchy of the organizational series of systems in one
system.

HOW SCIENCE SHOULD PROGRESS

We have been presenting the logic of science as direction
of movement in scientific discovery. Induction, synthesis,
purpose, hypothesis, arc all indicated as the directions up
toward the more embracing, or that which embraces.
Deduction, analysis, mechanism, empirical proof, are all
indicated as the direction down toward the less embracing,
or that which is embraced. These movements of dis-
covery imply an order of existence to be discovered. This
order of existence considered by itself cannot properly be
called a direction or movement, since it does not change.
It is a completely independent system, a hierarchy of
embracing and more embracing functions, which are
therefore independent of any method of discovery. It will
be recognized that this must be the case, since we have
shown that what is an induction from a given set of
data is a deduction from another seemingly unrelated
induction. Thus induction and deduction are seen as
different approaches to the discovery of the same set of
conditions.

This independent set of conditions or, as we have
previously termed it, this hierarchy of functions, may be
compared with a spider web, in which the concentric
threads form a dense manifold. Each thread embraces
all threads below it as themselves less embracing. The
investigator is the spider, not as the spinner of the web
but as the one who can move over it, but only in one
direction at a time. Obviously, when the spider is in a

THE LOGIC OF SCIENCE 165

shorter orbit, all outer orbits are to the spider more
embracing or 'up' in the series; but when the spider
moves to an outside orbit the shorter orbits are less
embracing or 'down' in the series; yet they remain
unchanged by the spider's position. The logical order of
existence is independent of the method of its discovery.
But obviously the method of discovery must conform
to the logic of that which is to be discovered.

In the conception of scientific method which we have
been setting forth, given a dense hierarchy of functions,
empiricism is the proof by logical consistency downward,
a checking over of included systems to show that the
more inclusive system from which the investigation
starts is logically a system of those systems. We have
further shown that whether this proof takes the form of
experimentation candidly, or of deduction abstractly,
the method is the same, requiring both logical con-
sistency and experimental verification. In some cases
these are identical.

The way that science has progressed is not the ideal of
science. The ideal method which should obtain and which
begins to obtain whenever a science approaches a certain
stage of development, is quite something else. When
large inclusive systems are reached in a science, every
other system must be shown to be a deduction from it,
and lesser systems deductions from those, ad seriatim,
until the whole system is seen as a pattern which inter-
laces, and thus no item appears as disconnected from the
rest. Granting that such an ideal could be approached,
the need for allowance or disproof by reference to
actuality must become less and less requisite, and proof

166 WHAT SCIENCE REALLY MEANS

by logical consistency serve the task of both proofs.
The more that is known of a system, the less investigation
is required to determine whether a newly discovered item
is or is not a part of that system. Just as a nearly com-
pleted picture puzzle is easier to complete the more
nearly it is completed, because the remaining pieces are
readily found to fit, so it is easier to determine where a
new piece of knowledge will fit in the scheme of modern
mathematical physics. And the reverse is true of the
effort to determine the place of any item of knowledge
in such an unorganized science as political economy. By
the same token, it follows that the imaginative genius
required to initiate a science is far greater than that re-
quired to help it to progress after it has reached a certain
stage.

The ideal science presupposes the completion of the
discovery of an already existing system. Obviously,
there is as yet no such science, and it is of little practical
help in producing one to refer only to what one ought
to be when completed. Yet for the perfection of working
method it is necessary to know what the ideal is. The
ideal working method of science is the subjection of every
hypothesis, after empirical proof, to subsumption by a
more inclusive hypothesis which shows it as a special case
of the more inclusive, i.e. as a deduction from it. The
movement is, therefore, in widening concentric circles,
so that the older and lesser hypotheses arc shown to be
more restricted than was formerly supposed, but per-
fectly valid within limits.Thus no scientific theory is ever
truly abandoned, as it would seem to those ignorant of
scientific method. The advance of science does not stagger

THE LOGIC OF SCIENCE 167

from extreme to extreme, abandoning one direction in
favour of another, like the practice of politics, but rather
resembles the concentric waves in a pond which widen
out after a stone has been dropped. Human ignorance
restricts at any given time what the last and most in-
clusive circle shall be; and it is not until contradictions
appear to universal claims that men are led to seek for
more inclusive circles which will reconcile it and give it
proper limitations. This is the best that any human
endeavour can expect to accomplish.

CHAPTER VIII

CAUSALITY AND PROBABILITY

In point of fact statistical laws are dependent upon
the assumption of a strict law of causality functioning
in each particular case.

MAX PLANCK
EMPIRICISM AND CAUSALITY

More is involved in the logical nature of empiricism
than the strict question of induction and deduction. The
problem of causality arises. That the idea of causality is
involved in empiricism is well shown by the fact that
all radical empiricists or philosophical positivists deny
that causality is an objective fact of nature. Just as the
idea of causality is denied by those who see science as a
"compendious representation of the actual," so the
understanding of science as a purely abstract domain
requires causality.

Throughout this book we have been gradually demon-
strating the existence of a logical series of functions,
independent of observation and mutually implicative. If
the radical empiricists are correct in their contention that
causality has no objective status, then such a realm of
functions as we predicate is challenged and held to be a
merely mental construction which has no necessary cor-
respondence to nature. This would make nature an
irregular and irrational affair, and would leave as an
insoluble puzzle the question of how it could be investi-
gated by the minds of men. Nevertheless, P. W.

CAUSALITY AND PROBABILITY 169

Bridgman for one does not hesitate to make the bold
assertion that the universe is just this kind of unintelligible
affair. He says,

The world is not a world of reason, understandable by the
intellect of man, but as we penetrate ever deeper, the very
law of cause and effect, which we had thought to be a formula
to which we could force God Himself to subscribe, ceases to
have a meaning. 1

In refutation of this position, there is little more to add
to what has already been said in Chapter in. Let us only
repeat that if the world is as irrational as Bridgman pre-
dicates, then his predication has no standing as true or
false. But even if we accept his argument, then the very
universality of irregularity implies a kind of dependability
upon regularity. Thus irregularity for the totality of the
universe is a contradiction.

Aside from such extreme statements as Bridgman's,
however, there is a general tendency on the part of
physicists and, by consequence, other scientists, to doubt
the existence of causal laws in nature. Eddington, for
example, asserts that causal laws are truisms, but that
statistical laws are real laws which in high averages have
given the appearance of causal laws. This rejection of
causality implies a rejection of ideal entities, since causal
laws must all be framed in terms of such entities. If
causal laws are mere appearances, ideal entities have only
a fictional value. Lenzen makes the statement that
classical physics deals with ideal entities, like "ideal

1 P. W. Bridgman, "The New Vision of Science," in Harper's for
March 1929.

170 WHAT SCIENCE REALLY MEANS

particles, ideal rigid bodies, ideal fluids," 2 whereas
modern physics is purely mathematical. The term
'ideal' has unfortunate connotations; it is supposed to
mean subjective, imaginative, unreal. But what it denotes
is a set of conditions abstracted or isolated from actuality
and only approximated to in actuality. The mathe-
matical symbols, co,X, 8,A, are just as ideal as chemically
pure iron, absolute rigidity, etc. An ideal proposition is
one to which no actual has been assigned. The whole
present misconception that science has abandoned ideal
formulations and, as a consequence, causality, rests on
the inability to see that mathematical symbols are merely
better substitutes for the older ideal entities. We have
shown that the nature of such ideal entities was merely
mathematical, and that the pictorial representation of
them was unnecessary and misleading. But to state that
science has taken an entirely new tack because of the
elimination of such pictorial representations is evidence
of a lack of understanding of science itself.

The idea of causality only seems to have been dropped
by modern science. There is no categorical distinction
between classical physics and modern physics. There has
certainly been an advance, but in the direction of greater
generality and emphatically not in basically logical pro-
cedure. What appeared in classical physics as causality
appears in modern physics as function. And it is only
because the nature of causality was misunderstood in
classical physics, and has since been given a new name,
that it seems to have been abandoned. The question of
probability versus causality is one of the argumentative
2 V. F. Leiizen, The Nature of Physical Theory, pp. 44-5.

CAUSALITY AND PROBABILITY 171

by-products of the misunderstanding of the integral
history of science. Its occasion, however, is irrelevant to
the logical question of causality, as we shall later show.
Causality properly understood by whatever name is
implicit in modern as well as in classical physics.

CAUSALITY AND CONTINUITY

Let us leave the subject of causality for a moment and
discuss the manifold of natural phenomena as it is as-
sumed everywhere in science. The "uniformity of nature"
means a series such that between any two items in the
series a third can always be found, and such that in any
definition of an item of the series the beginning and end
of the item are the end and beginning of adjoining items
in the series. Continuity "is the absence of ultimate parts
in that which is divisible." 3 It is "nothing but perfect
generality of a law of relationship." 4

In terms of science this means, first, that there are no
ultimate constituents of the universe, but that every
quasi-element of analysis is subject to further analysis in
an unending series, whether such analysis has yet been
accomplished or not. Secondly, it means that there is
always a system more inclusive than any given system,
whether such a system has been found or not. In short,
the doctrine denies that nature is discontinuous, and that
finitude has any limits. There are no final irrational ele-
tional elements, no brute givens, even though there will
always at any time be what appear as brute facts. Such a
doctrine is radically insusceptible of proof, yet its ac-

8 Charles S. Peirce, Collected Papers, 6.173,
4 Ibid., 6.172.

172 WHAT SCIENCE REALLY MEANS

ceptancc is tacit in scientific procedure. Thus the mole-
cule was superseded by the atom, and the atom, that
supposedly indivisible entity, was superseded by the
quasi-ultimate particles, electron, proton, neutron, etc.
We take it that science in general will not accept the
indivisibility of these entities any more than it did that
of the old 'atom/

Similarly, no system, however inclusive, has persisted
as the final system for very long, but one more inclusive
has always been found to take its place. Newton's
cosmology was supplanted by the relativity cosmology;
and we take it as axiomatic that science will not accept
as final even the relativity cosmology. Thus science
accepts nothing as brute and final except pro tern, and of
necessity.

The definition of continuity as the perfect generality
of a law of relationship means in science that the ac-
ceptance of law is equivalent to the rejection of the
possibility of exception. As a practical matter, this indi-
cates that what will apply to a given number of instances
will apply to all instances, if the abstraction of instances
has been fairly made. It indicates also that a given
principle remains the same though it appears conditioned
in various ways. When Galileo generalized the law of
falling bodies, the principle of the inclined plane, and the
principle of the pendulum, all into one principle: the
law of inertia (to use Newton's later terminology), he
was presupposing the continuity of nature. That the as-
sumption was not unfounded, need not be argued. In
fact, it may be said that without the assumption of this
principle the whole of science would be at best a

CAUSALITY AND PROBABILITY 173

description of how certain particular experiments re-
sulted. Science would be a partial history and not a basis
for prediction.

What do all these definitions of continuity mean in
terms of causality ? We have shown that continuity in
science means the rejection of anything ultimately un-
analysable or ultimate. Science finally refuses to believe
that any finite tiling is just a brute fact without reason,
or that any event is uncaused. To put this in the ter-
minology of cause-and-effect, it means that the minutest
elements of analysis at any stage are the result of still
more minute elements and, conversely, that the largest
system which has been discovered at any stage is the
effect of more inclusive systems. Moreover, the ac-
ceptance of a principle as operative without exception
throughout its sphere of applicability is tantamount to
the declaration of inexorability, which is to say, strict
causality or causal law. In fact, there is no difference
between the acceptance of the principle of continuity or
the uniformity of nature, and of strict causality. He who
accepts one is perforce driven to the other. The scientists
accept causality by accepting the continuity and uni-
formity of nature. And the fact that they do so im-
plicitly, without awareness of the multiple implications
in which they are involved thereby, does not change the
situation. Thus every scientist in so far as he is a scientist,
and despite his protestations, accepts causality.

CAUSALITY IS NON-TEMPORAL

Why, then, do the scientists suppose that causality has
been abandoned in science ? The answer is that the idea

174 WHAT SCIENCE REALLY MEANS

of causality has been persistently misunderstood as
meaning the determinism of history, a locked sequence
of actual happenings. Hume, for instance, denied that
there was any continuity, or that there was anything more
than a sequence of events which by itself manifests no
causal nexus. John Stuart Mill, however, formulated
even more succinctly the point of view of the strict
mechanistic scientist of the Newtonian era. He defined
causality as the aggregate of all the circumstances under
which an event occurs. 5 It is this understanding of causality
as temporal which modern science has rendered un-
tenable, and which therefore seems to indicate to the
scientists that causality has been overthrown.

The most notorious instance of the failure to predict
actual occurrences is the behaviour of an actual sub-
atomic particle. But if causality had been properly
understood in the days of classical physics, it could have
been demonstrated that the inability to predict any actual
occurrence with absolute exactitude was due to ignorance
of some of the factors involved. When an experiment is
performed to demonstrate a law, the attempt is made to
isolate a system for analysis. Perfect isolation, however,
is never accomplished, because 'controlled conditions'
cannot be absolutely controlled. Thus every actual ex-
periment will bear out a law only approximately, though
often with very minute variations.

The application of general principles to actuality must
always admit of modifications, which modifications do
not serve to nullify the invariability of the principle but
rather serve to modify the actual effects produced

6 John Stuart Mill, System of Logic, book iii, chapter 5.

CAUSALITY AND PROBABILITY 175

thereby. Indeed, it is in terms of an unchanging principle
that the modifications themselves must be understood.
Strict causality cannot be demonstrated because it does
not occur pure in demonstration. But this is no proof of
its non-existence as pure. Indeed, the fact that its work-
ings can be approximated to in an experiment under
properly (i.e. the most perfectly) controlled conditions
is an argument for the existence of causality, and not the
reverse.

Let us see if 'the aggregate of all the circumstances
under which an event occurs' can properly be called
causal. Suppose that the chairman of a meeting strikes
the desk with his gavel, causing ripples in a glass of
water on the desk. The desk had just been painted brown;
the weight of the gavel was seven ounces; at the time
the event occurred the room was full of people; the
initial velocity of the blow was one foot per second; the
room temperature was 85 degrees Fahrenheit; the dis-
tance from the glass to the place where the gavel struck
was sixteen inches; the day was Tuesday in the month
of March; the place, Wichita, Kansas. Note that the
effect is the rippling of the water in the glass. We have
mentioned only a few of the vast aggregate of all the
circumstances under which the event occurred. How
many of these circumstances bear on the effect as its
cause ? Causally are they all of equal importance, merely
by virtue of their participation in the aggregate ? Obvi-
ously, the initial velocity of the gavel was of more
importance than the temperature of the room. Certain
conditions, such as the day of the week, can plainly be
ruled out as causes. Without labouring the point, it is

iy6 WHAT SCIENCE REALLY MEANS

clear that the cause of an event cannot be the aggregate
of all the circumstances under which that event occurs,
but must be certain of the circumstances.

What, then, is the canon of selection whereby certain
circumstances can be called causal and others not ? The
canon is one of relevance, and the relevance of a physical
event can only be to a physical system. Thus velocity,
mass, and temperature may be relevant, but date, location,
colour, and social surroundings can have no relevance.
But once admitting only physical factors as causal for a
physical event, the main cause, of which the others are
merely modifying causes, still remains to be isolated.
And this can be found only through a general principle
known or discovered by experiment. Experimentation
in this connection is seen to consist in the reproduction
of the event with certain factors omitted and certain
kept. When the paring down of circumstances reaches
the point where the omission of any more prevents the
event from happening, then cause has probably been
found. The true cause of the trembling of the water
must be laid to the mechanical principle of action and
reaction. A cause will always reduce to a matter of abstract
function.

Going back to the actual event, can it be said that any
factor was the cause of the rippling of the water before
the event took place ? Suppose we take as an hypothetical
cause die momentum of the gavel at any time before it
struck the table. Then the hypothetical cause was still not
absolutely certain, since many chance factors could have
intervened to prevent the gavel hitting. The hypothetical
cause was only a probability, growing stronger and

CAUSALITY AND PROBABILITY 177

stronger as the time interval was cut down. When that
time-interval reached zero, the probability of the event
happening reached absolute certainty. When event A
approaches event B as a limit, probability reaches cer-
tainty as a limit. But when event A and event B have the
intervening time element eliminated, they are not two
events but one, AB, in which the distinction between
A and B has been made not on a temporal but on a
logical basis. Thus cause and effect are seen as a logical
nexus and not as a temporal sequence. Causality asserts,
if A then B. In this particular case, if action, then re-
action. This means that two functions are involved in
one function, i.e. that two functions have been analysed
as parts of a single function.

Here causality shows its true nature as the deduction
from premises. Causality rightly understood means that
every function is included or is the deductive consequence
from a more inclusive function, i.e. is the effect. In other
words, it means that the more inclusive function is the
cause. When cause and effect are considered in actual
happenings, it is the more inclusive function which
determines the lesser, and which is segregated as the cause.
Causality in actuality exhibits the logical order running
through the temporal order. To the extent to which one
is able to segregate out the logical element in any situa-
tion, that situation will be understood and subjected to
control. In a comparatively well-developed science, the
employment of mathematics means the widening of the
knowledge of the logical order at that level of investiga-
tion. Cause and effect appear explicitly as functions. Thus
in advanced science, causality seems to be left out. But

178 WHAT SCIENCE REALLY MEANS

what is left out is only the old error of formulating
causality as a temporal affair.

PROBABILITY REQUIRES CAUSALITY

The occasion for the apparent abandonment of causality
as a principle in modern physics (and a fortiori in all other
sciences) is the vogue of statistical laws. Modern phy-
sicists, assuming that causal laws are coercive, and
demonstrating that invariance does not exist in actuality,
wish to substitute the idea of probability for that of
causality. Causal laws, they inform us, are too rigid,
whereas statistical averages merely yield a formulation of
what is likely to happen, and thus the concept of proba-
bility instead of strict causality reigns.

Can probability be accepted as supplanting causality?
In order to answer this question it will be necessary to
make an analysis of probability. Abstractly understood,
what is it? Probability is the asymptotic approach to
certainty. Certainty is the predication of absolute in-
variance. Probability, then, is that which approaches but
never reaches absolute invariance. In the example given
above, of the gavel approaching the table, it was shown
that as the time-interval decreased to zero, the proba-
bility of the gavel striking the table grew greater and
greater, until as the time-interval reached zero, proba-
bility reached i, which is the symbol of certainty.
Thus certainty cannot be predicted since the time-
interval must be zero. Invariance, as we have shown, is a
logical affair which applied to any actual occurrence is
applied conditionally, i.e. if A then JB. Thus we can
speak of the future only in terms of probability, and

CAUSALITY AND PROBABILITY 179

this probability increases as the future becomes less
remote.

If, then, probability is the asymptotic approach to
certainty, certainty is involved in probability. It is pre-
dicated as the goal, or else probability would have no
definition. Who would attempt to predict the proba-
bility of what John Smith is going to think about next
Tuesday morning at ten o'clock from the knowledge of
what he has thought about on past Tuesdays at ten,
unless there were some logical connection between that
hour on Tuesdays and John Smith's thoughts ? Without
the assumption of some logical connection, known or
unknown, no one would make a prediction of proba-
bility. When the average period of gestation of a human
being is said to be 279 days, this means that any baby
probably will be born at the end of this period, though
there is no absolute certainty and indeed wide variation.
Surely such a probability takes for granted that there is
some invariant connection between the gestation in-
terval and birth, which is modified by many incidental
factors in any given case. The statement that it will
probably rain some time next month would make no
sense if rainfall were purely a random affair. What gives
it meaning is the fact that certain complex factors com-
bine to yield the event wherever undisturbed by still
others which are just as causal. Thus causality is always
implied in any meaningful predication of probability.

The history of scientific inquiry reveals the fact that
causal laws were discovered through the finding of
certain behaviouristic patterns where it was probable
that certain events could continue to manifest invariance.

i8o WHAT SCIENCE REALLY MEANS

Any of the discovered laws of causality might have been
formulated by means of probability, i.e. statistically. And
so they would have remained, unless science had gone
deeper to isolate necessary cause. If, ignoring such
questions as air resistance, the law of falling bodies had
been formulated statistically, i.e. from a compilation of
many actual instances of various kinds of falling bodies,
it would have taken this form: it is probable that any
object falls at the rate of thirty-two feet per second per
second. But instead of this, Galileo made but few ex-
periments not enough for a law of probability and
leaped to the conclusion that this acceleration was in-
volved in every instance of every falling body, thus
showing special cases to be modifications of die principle,
because of calculable interfering factors.

The rash overthrow of causality, where laws of proba-
bility take their place, is based on the assumption that
no causality is involved in probability. This we have
shown to be an utterly indefensible assumption wherever
statistics are expected to have any relevance to the future.
Inasmuch as the laws of probability are relied upon by
modern physicists, they are being used as quasi-causal
laws, relied upon for their dependability and not for
their undependability. They involve causality, whether
that causality be known or unknown. And where it is
unknown, they are interim laws, which will be discarded
as soon as and if causal laws are found. Thus the attempt
to predicate statistical laws as final is the same treason
to the progress of science as the refusal to admit as
possibly existent anything not already demonstrated.
Both refusals are involved in the platform of positivism.

CAUSALITY AND PROBABILITY 181

THE STATISTICAL METHOD AND CAUSALITY

Having shown that probability requires causality, we
must now more specifically show that the statistical laws
are another way of presenting causal laws. It will be
remembered that causal laws are so framed as possibilities
that when put into application they must always be
modified by all the incidental factors which are not ex-
cluded. A controlled experiment is an attempt to exclude
as far as possible all such incidental factors. This cause
corresponds to dominating function, modified in actuality
by incidental factors. Causal laws merely state the domi-
nating factors and purposely omit the questions of
incidental factors.

In the statistical method no attempt is made to state
a priori what the cause or dominating function is. A
function is chosen, and incidental factors slowly elimi-
nated in favour of it. Given a certain function to examine
in its actual operation, experiments are conducted which
will give results tabulated in reference to this function.
The function is understood throughout not as an abstract
legal affair but as a prevailing tendency, which the
experiment is supposed to reveal by averages. In such a
situation, where it is impossible to eliminate many of the
incidental factors, it is clear that the dominating function
will be modified in a number of ways, varying according
to the presence and interplay of the incidental factors.
But it is also clear that the dominating function will,
given a sufficient iteration, show itself, whatever it be
called, cause or probability. What is being done when an
average is struck of these iterations is the ruling out of

1 82 WHAT SCIENCE REALLY MEANS

incidental factors. In this case they are being ruled out
not by abstraction deliberately planned, but by showing
that in the long run of instances they do not really count.
Thus cause or dominating function is obtained by experi-
mental selective abstraction. A cause is shown to be at
work.

We are not denying that the statistical method has
great usefulness. Its usefulness is apparent from what we
have said above : in any situation where through ignorance
or pure difficulty of manipulation it is impossible to
isolate cause, the statistical method is helpful. This is the
case of thermodynamics and quantum mechanics. It has
been found practical in thermodynamics because it is
impossible to follow the path of the individual molecule.
It has been found practical in quantum mechanics, the
study of sub-atomic entities, because not only is it im-
possible to study the path of these entities, but even their
continued identity is questionable.

In practical affairs, for instance in the life insurance
business, the statistical method has been useful, because
it is impossible for a life insurance company to calculate
the tremendously complicated and fantastically modified
causes of death. If all the factors affecting the life of every
individual could be known and traced at any given
moment, the exact risk would be ascertainable. But as
it is, the life insurance company can group all these
causes into a gross probability. And in so doing they
depend upon the uniformity of natural occurrences, and
risk only the possibility that these causes will be greatly
modified. Thus they depend upon causality for their
solvency, and go bankrupt in so far as they depend upon

CAUSALITY AND PROBABILITY 183

the random element in nature. All planned human actions
depend upon the regularity of occurrences and not upon
accidents.

It must be noted that the dominating function exposed
by the statistical method approaches but never reaches
certainty, only a high probability. Put in another way,
it requires an infinite repetition to reach certainty. This
is to say that to exhaust all the modifying factors of the
actual environment absolutely, an infinite iteration of
the experiment would be required. No actual element is
ever absolutely isolated from the environment, which is
another way of saying that no causal principle can ever
be exactly fulfilled in any event. But an infinite number
of such events must prove equivalent to the absolute
causal principle.

Perhaps an example will make this question of infinity
clear. In the throwing of a pair of dice we know that
ideally 12 will come up once in every thirty-six throws,
since there are thirty-six combinations of all numbers
and one combination of 12. This is figuring the situation
abstractly. What happens if it is tried out experimentally ?
In a limited number of throws, say two hundred, this
situation will most probably not be borne out. But given
a very high number of throws, say io 6 , the ideal relation
will be very closely approached. Increase this number of
throws indefinitely, and the results will bear out closer
and closer to the ideal. But only an infinite number of
throws can be expected absolutely to correspond to the
ideal of ^g-. We need no experiment in this case to
discover what the dominating function is, since die
relation of one combination to all combinations can

1 84 WHAT SCIENCE REALLY MEANS

be calculated in a minute by means of arithmetic.
But in the case of many occurrences this is not always
possible.

What, then, does such an ideal statement mean that
when a pair of dice is thrown, 12 will come up once in
thirty-six times? It means that the dominating function
or cause in the situation is this arithmetical relation.
When put into application, it means that an incalculable
number of incidental factors are influential but that none
is invariant.

Causal laws are independent of actuality. But when
applied the dominating function or cause is always
operative in an actual situation as its invariant. But this
function or cause does not show itself as invariant
because the situation is modified by all the incidental
factors, which, if completely taken into account, would
finally have to exhaust the universe. Thus according to
the uniformity of nature, strict causality reigns, but does
not candidly so appear since we do not know in any
actual situation what all the causes of the so-called
incidental factors are. Thus the best that can be done is
to find the necessary element, and to consider all others
as unnecessary or 'chance.' To demonstrate the complete
causality of every actual thing, we should have to under-
stand the infinite interrelations of the entire universe. In
statistical probability we reach an approximation to the
cause of any situation, but cannot reach it absolutely
without infinite repetition. In either case we see that in
actuality no absolute prediction could be made without
having on the one hand infinite knowledge, and on the
other infinite time. The remote ideal of the causalistic

CAUSALITY AND PROBABILITY 185

method requires infinite knowledge; at any time the
remote ideal of the statistical method requires infinite
time. The results which the statistical method reaches
by mathematical probability are just as causal and
abstract as the results reached by the causal method.
Both depend upon the logical invariance of functions;
neither can be applied exactly to actual prediction,
though both approximate it more or less closely.

The whole attempt on the part of recent scientists and
positivists of science to declare that causality is not a
principle of nature, while admitting that probability is,
constitutes a contradiction. It comes about through
ignorance of two facts: (i) that causal laws never did
attempt to predict actual occurrences absolutely, and
(2) that probability requires for its very meaning the
goal of certainty, or it has no definition.

PROBABILITY AND LOGIC

We have shown that causal laws are logical conditions,
and are better understood as the more inclusive functions
of less inclusive functions. With this understanding of the
uniformity of nature as an unchanging hierarchy of
functions, probability and the statistical method can be
reduced to the logical up and down movements of an
operator. In Chapter v we defined function as an in-
variant relation between variables, which is an adequate
definition so long as function is being viewed as present
in actuality. But in the hierarchy of functions as we
present it, the abstraction from actuality has been en-
tirely accomplished, and function is then seen as having

1 86 WHAT SCIENCE REALLY MEANS

nothing to do with variables, but as being better definable
as an invariant relation between invariant relations. Thus
a function may be illustrated as one of the rungs in the
ladder of the logical series, or perhaps better as one of
the concentric circles.

Any actual event, experiment, or demonstration must
take place in terms of abstract functions. Any action is a
particular consequence of the logical conditions, and may
be viewed as a deduction from logical premises. Actions
are implications of conditions. The freezing of water by
an experimental method is an action; and as such it is
compelled to conform to the uniformity of the nature
of water, which freezes at zero Centigrade, under ordinary
pressures. What, then, defines the freezing point of water
is not the method by which it is frozen, but rather the
law of its freezing, which determines whatever method
is employed. This fact is the reverse of that assumed
by Bridgman and the operationalists. A thing is not a
thing because of the way in which it acts; rather it acts
in a certain way because of its logical nature. A tiling is
as it acts, not because it acts, but because it is. The neces-
sity is a one-way affair from being to action and not
from action to being. Action, which takes place in the
temporal order, illustrates and does not constitute the
conditions of action. Thus again we see that causality,
which is reducible to function, is not a temporal affair,
but is constantly being illustrated and exemplified
mediately in time.

Given this understanding of action and of the con-
ditions from which action springs, we may illustrate the
syllogistic nature of the statistical method.

CAUSALITY AND PROBABILITY 187

Perhaps the relation of i surface to 6 surfaces of a die is

constant;
Certainly these throws (a goodly number) are observed to

approach constancy,
Therefore it has not been disproved that constancy exists in

this relation.

Something like this is what is done in the experiments
by which the statistical method is carried on. It will be
noted that the result is a probable conclusion which
occupies the same status as the conclusion from the
syllogism on p. 150, illustrative of the experimental
method from a causal hypothesis.

In n experiments an average of -^ Jz was f un( i,
Therefore it may be concluded that the abstract function
involved in all instances is ^.

This is a 'law of probability,' inductively discovered in
the same manner as a causal law. There is no difference
between them, inasmuch as causal laws do not claim
absolute invariance in actual demonstration, whereas laws
of probability seek in actual demonstration to approach
as closely as possible to absolute invariance. Hypothesis,
experiment, allowance, or disproof of hypothesis,
abandonment, or correction of hypothesis this is the
frank and classical method of discovering laws of
causality.

It is difficult to see where the statistical method of
probability differs from this. Both conclude with
abstract functions formulated as rigidly as possible.
The fact that the statistical method ends with a

1 88 WHAT SCIENCE REALLY MEANS

mathematical formulation of function docs not dis-
tinguish its results from those of causality. We have
shown that cause properly understood is function, and
that probability properly understood is cause, and there-
fore also function. The statistical method is only a
roundabout, but perfectly valid, way of following the
causal method.

Here, however, we reach an important caution.
Statistical results must not be viewed as the final aim of
a science. If they are so viewed, the progress of science
is hindered and finally stopped. To consider laws of
probability as the best that science can accomplish, is the
same positivism which asserts that deduction is scientific
but induction not, that science is empirical but not
rational, that mechanism does not imply purpose and,
finally, that the aim of science is directed toward appli-
cation and practicality rather than toward abstract truth
for its own sake.

We have been demonstrating throughout that em-
piricism is the direction down in the effort of discovering
to what extent actuality is logical. There is no such thing
as an empirical fact in itself, but a fact is empirical only
in relation to a higher system. Such a higher system is
itself an empirical fact from the point of view of a still
higher system. In the light of this conception, causality
and probability appear as one and the same, and the
statistical method as both empirical and logical: em-
pirical to the extent to which it refuses to leap to un-
proved conclusions, logical to the extent to which it
seeks to find abstract and invariant conditions of
which actuality is only a set of illustrations often

CAUSALITY AND PROBABILITY 189

modified. Both causality and probability aid science
in its mission of discovering the abstract hierarchy
of logical functions, which is the condition of all
natural existence in so far as reason is able to understand
and control it.

CHAPTER IX
THE FUTURE OF SCIENTIFIC EMPIRICISM

/ am come that they might have life: and that they
might have it more abundantly.

THE GOSPEL ACCORDING TO ST. JOHN

SUMMARY OF THE ARGUMENT

The revolution in physics has been the occasion for the
return to philosophical speculation on the nature of
science. This philosophical speculation has become
divided into two positions: mentalism and positivism.
Of the two, positivism, revamped and refined, threatens
to become the orthodox philosophy of science. This
preference for the positivistic philosophy is understand-
able in view of the fact that it seems to fly the banner of
empiricism itself. And empiricism is the indispensable
bedrock of science, which it would be suicide to abandon.
What has happened is that science, through its develop-
ment, has unwillingly been forced toward a philosophical
reconsideration of its own nature. In this reluctant
effort, the charm of positivism has been that it seemed
to necessitate the least amount of metaphysics and to
possess the greatest appeal to hard stubborn facts.

Undoubtedly scientists have been right in holding on
to empiricism as the essential of scientific method. But
empiricism does not involve positivism. Positivism denies
the validity of the speculative reason. Empiricism rightly
understood does not deny the speculative reason but
rather requires it. Positivism is purely analytical, whereas

THE FUTURE OF SCIENTIFIC EMPIRICISM 191

empiricism requires both analysis and synthesis. Positivism
is application, whereas empiricism requires both theory
and application. Positivism would stop the advance of
science, whereas empiricism requires continual advance.
The proper understanding, then, of what science is
depends upon the proper understanding of empiricism.
Empiricism is a logical affair, and can be reduced to its
syllogistic form.

That empiricism, and a fortiori science, should have ever
been considered an anti-rational affair, is only to be ex-
plained in terms of its historical development. Experi-
mentation was the watchword of those men who broke
away from cloistered speculation and unexamined
premises. In throwing over sacrosanct premises they
believed that they were throwing over the whole of
logic in favour of brute facts. Consequently the Renais-
sance, which witnessed the birth of modern science,
came to suppose that the empirical observation of fact
and the speculative reason were opposed. The develop-
ment of science necessarily drew these two threads to-
gether in scientific procedure, but did not resolve the
anti-intellectual bias of the scientists. Thus the procedure
and the philosophy of science were, and still are, at
variance.

The preoccupation of scientists with experimentation
led them to conclude that science is a description of
actuality, and thus that actuality is an absolutely deter-
mined affair. But the development of science, in the late
nineteenth and twentieth centuries, toward more and
more abstract and mathematical formulations, has made
scientists realize that there was here no picturable cor-

192 WHAT SCIENCE REALLY MEANS

respondcnce between their formulations and the world
of actuality. In short, the realm of physics represented
nothing actual except mathematical symbols on paper.
Such a realization has appealed to some interpreters as
meaning that scientific formulations are inherently
mental, having been formed in the mind and indicating
the existence of a mind-stuff, of which actuality is but
the appearance. As a check on this wild metaphysical
'explanation,' the positivists have reformulated the older
view into what is called operationalism and its similar
theories, such as that of logical positivism, which asserts
the concepts of science to be merely names for operations
performed or performable. This denies objective reality
to the objects of science, but does not evade subjectivism,
as it attempts to do. It only states subjectivism bchaviour-
istically, that is, it makes scientific concepts dependent
upon the mind, and thus unintentionally destroys the
basis of empiricism while endeavouring to save it.

Science is neither "the compendious representation of
the actual" (die history of actual occurrences) nor
thoughts in the minds of scientists or of the race in
general. The subject-matter of science turns out to be
functions independent of consciousness and therefore
non-mental; independent of actuality, and thus non-
actual. Functions are the inexorable conditions of
knowledge and actuality. The analysis of the scientific
subject-matter shows it to be not the content of actuality
but conditions abstracted from actuality, conditions
which are purely formal. And thus science reaches and
strives to make manifest an unchanging hierarchy of
functions which is through and through logical. The

THE FUTURE OF SCIENTIFIC EMPIRICISM 193

whole success and direction of science illustrate that it is
dealing with such a formal world, best represented by
the least connotative symbols, i.e. those of mathematics.
Science is the entire effort of man to acquire knowledge
of this abstract world of independent real functions,
which are the invariant conditions of existence.

Given this independent subject-matter the abstract
world of independent real functions induction and
deduction may be seen as procedures ascending or de-
scending, in short, as two directions of reasoning.
Demonstration, as employed in scientific method, tests an
induction by checking its deductive consequences against
actuality. The test by consistency is the derivation of
that induction from a more inclusive induction as a
deductive conclusion. The first is merely allowance; the
second is proof. It is to be noted that what is empirical
is always the deductive direction down; and the status
of items varies in accordance with the direction selected,
so that what is empirical from one point of view is
theoretical from another.

The whole empirical proof may be understood,
regardless of experiment or deduction, as the finding
of what is involved in a system. Thus rationalistic and
empirical fallacies may be seen as prohibitions against
irrelevance, or the jumping from one system to another.
When a higher system is dragged in to explain the con-
stituents of a lower (the rationalistic fallacy), the results
are contrary to economy or empiricism: that the simplest
explanation must suffice. On the other hand, when the
constituent parts of a system are employed by themselves
as explanations of die system (the empirical fallacy),

194 WHAT SCIENCE REALLY MEANS

the result is too rigid an attempt at economy. Thus the
fact that science works mechanistically (down) must not
be construed to mean that there is no purpose (up), but
only that science is concerned with analysing purpose
into its mechanism.

The vastly greater part of scientific attention is devoted
to analysis. Induction may take five seconds; deduction
twenty years. Induction is a flash, but deductive analysis
and checking is a deliberate and often painstaking and
long-drawn-out affair. Thus scientists are nearly always
directed down, but can only be so because of a prior
leap up. The method of science is down; the leading
principle of science is up.

In the light of the abstractive nature of scientific subject-
matter, causality is seen not as a determinism of actuality,
but as the principle of continuity, whereby the same
function is present in different instances of actuality
modified by accidental factors. Causality states the in-
variance of a principle and not the invariance of its
practice. Thus in application a causal principle can only
be more or less unmodified, i.e. its absoluteness is more
or less probable. The formulation of laws of probability
does not deny causality but restates it in application.
The statistical method examined shows itself to be a
roundabout method of abstraction, ending in laws
of causality abstract invariance stated mathematically.
What are not invariant are their applications. Thus
statistical probability does not in this regard differ from
strict causal law.

We have stressed scientific empiricism as the correct
method and equated it with deduction, mechanism, and

THE FUTURE OF SCIENTIFIC EMPIRICISM 195

application. But these presuppose a logically prior
direction: higher systems to analyse, theories to be made
empirical, probabilities to be rendered invariant, pure
science to be some day applied. All this may be sum-
marized in the statement that science accepts no datum
or system as final except pro tern., which means that the
first postulate of science is the rationality of nature.
Empiricism does not dispense with but requires the
speculative reason.

SCIENCE MUST BECOME SELF-AWARE

The assumption is held in most scientific quarters that so
long as science proceeds with the right method, it does
not make any difference to the welfare of science whether
scientists abstractly understand what their method is or
not. Of course it must be admitted that physics has in
the main kept to the correct scientific method. But the
fact that it has done so is no warrant that it necessarily
always will. How can it be expected to carry on for ever
with a method which it does not abstractly understand ?
Historically, the physical sciences stumbled upon the
right procedure, misinterpreting causality as a locked
determinism of actuality. This conception did well
enough until further discovery showed it to be true
only within narrow limits. Thus to-day the old presup-
positions of a mechanistic world have proved inadequate,
and science is left without a whole-hearted belief in the
reality of its subject-matter.

This eventuality has driven it to two errors : unbridled
speculation and over-rigid empiricism. The first is repre-
sented by wild and meaningless theorizing, the second

196 WHAT SCIENCE REALLY MEANS

by an over-emphasis on experimentation alone. But it is
the latter direction in which the scientists arc tending.
Either would kill the advance of physical science; the
first by abandoning empiricism, the second by giving
empiricism nothing to operate on. In the latter case, the
presupposition that speculation is unscientific, and that
the laws of science are nothing more than names for
operations, may eventually destroy the very method of
empiricism. The absurdity of considering every operation
a disparate, unique and particular occurrence would
render science nugatory by destroying all its attempts at
unification. There would be nothing left but a catalogue
of isolated experiments, a history of disconnected events.
The positivism which poses as the true philosophy of
science would hinder the future of physical science. But
it has already prevented other studies from becoming
sciences. Psychology, economics, sociology, and anthro-
pology have all suffered. There being no correct abstract
formulation of what scientific presuppositions and
methods are, these social studies have endeavoured to
follow what they conceived science to be, as exhibited
by the physical sciences. The result is that they have
swallowed positivism and ignored the implicit but
correct method of physical science. In other words, they
have already fallen into the same sterile procedure as
we predict might happen to physics if it continue on a
positivistic basis. The accumulation of uncorrelated data
in social studies is already enormous, and indeed perhaps
outweighs the data of the physical sciences. But this
enormous accumulation has not been synthesized, and in
fact now stands in the way of synthesis.

THE FUTURE OF SCIENTIFIC EMPIRICISM 197

Social studies have never reached the deductive stage,
and indeed distrust deduction. This lack alone should
indicate that here is no following of physics. The social
studies are inductive, but they are inductive mainly at
the level of common-sense observation, and thus have
never attained any high abstractive level from which
deductions could validly be made. The reason that they
fight shy of such speculation is their false understanding
of empiricism as precluding anything not observable at
the level of common sense. Their kind of procedure
might go on for ever, piling up generalized observations,
without leading to one significant generalization which
could throw light on new and unsuspected facts, and
thus open up a fruitful field of inquiry. The most
developed of the social studies are economics and psy-
chology, which have to some extent looked for invariant
and abstractive conditions. But even they have been
hopelessly confused, and have failed to obtain anything
solid enough for agreement, by their failure to understand
the nature of scientific empiricism, which they per-
sistently misread as a prohibition against the drawing of
conclusions.

The failure to understand explicitly what science is has
not yet proved crucial to the physical sciences. But it
may, and certainly will, if this condition is allowed to
continue and science persists in its positivistic misinter-
pretation. What is a danger to the physical sciences is
already a disaster to the social sciences. The need for
the abstract formulation of science is of the utmost
importance to all science.

198 WHAT SCIENCE REALLY MEANS

RELATION BETWEEN SCIENCE AND SOCIETY

So much for the correct understanding of science as it
affects science itself. Science as an active institution, how-
ever, is not an isolated affair. It is an integral part of
society. Science is one social institution among many, and
it demonstrably affects and is affected by all others. It
cannot thus go on for ever in Olympian isolation, but
requires integration with society as a whole. Therefore
it can readily be seen that the correct understanding of
science by society is of the utmost importance for science
and for society.

What does science require of society? Science requires
that society support it and at the same time leave it
free to develop as it sees best. What does society require
of science? Society requires that science produce miracles
in the shape of tangible results having practical applica-
tion. So long as science furnishes these, it will be supported
and lauded and left free. But if it should fail to rain
benefits immediately understandable as such, there is
always the danger that the public will become impatient
of mere theory and withdraw its support. There is a
paradox in all this, that if science deliberately sets about
to produce practical results, it will not continue to pro-
duce them. Practical results do not follow from previous
practical results but are the by-products of development
in speculative theory. Thus science is being most practical
for society when it is considering practicality the least.

The danger of the positivistic understanding of science
on the part of non-scientists can be readily seen. Society
will not wait patiently upon science but insists upon

THE FUTURE OF SCIENTIFIC EMPIRICISM 199

directing its course toward practical application. It does
not want theory, it wants results; and will not give
money for the benefit of abstract speculators, although it
will give millions for laboratories. But of course without
theory practicality is an impossibility. Unquestionably,
if the pressure of popular positivism is exerted on the
scientists, the results must be disastrous regardless of
whether scientists themselves concur in such a philosophy.

But if, on the contrary, society could form some
understanding of what science is, of what it is engaged in
doing, and of what it hopes to do, it would be realized
that the greatest practicality to society lies in pure
science. Society would cease its importunings for quick
results. It would then be content to support science and
leave it free to follow its own development.

The relation between science and society involves far
more than the question of whether science will be
allowed to develop unimpeded. It involves the question
of whether society will itself be allowed to develop. No
one will dispute the great social benefits which are
attributable to science. The whole stage of development
of modern civilization can be laid directly or indirectly
to the physical scientists. It is a platitude to assert that the
modern standard of living depends upon technological
proficiency; and modern technology, of course, is a by-
product of the physical sciences. Its tremendous accelera-
tion has paralleled the acceleration of physical science.
There are also great benefits which have accrued from
the biological sciences. The technology of medical prac-
tice: hygiene, immunization, etc., are by-products of
the biological sciences. It is not too much to assert that

200 WHAT SCIENCE REALLY MEANS

the whole superiority of the present day over the
eighteenth century is almost entirely due to the progress
of the physical and biological sciences.

But meanwhile what has happened in the field of
social relations? Have we any such improvement over
the eighteenth century, or is there perhaps a retrogres-
sion? It is rather the latter. The contradiction has
developed in the last few decades that the greater the
advance in technology, the greater the disaster in social
life. Every time a labour-saving device is invented, and
greater efficiency achieved, it means that more labourers
starve, and thus a decrease in consumption follows an
increase in productivity. 1 As another example of what
happens when the sciences do not advance together and
one science runs wild, we have technology producing
equally 'beautiful work' in medicine and chemical war-
fare. Without social science to guide technological
chemistry, its applications may often cancel each other.
Without social science to decide, we have only the
vague normative judgment of good or bad, which is
neither sufficient nor authoritative.

This chaos in social relations has not been alleviated
by the social sciences, in spite of their pretensions. In
other words, social science has shown no such advance
in understanding as has physical science. Now we must
note that physical science was the occasion for the dis-
location of social relations, as well as for the advance of
technology. In fact, the advance in technology has occa-

1 This is definitely true of capitalist society, but, logically speaking,
need not be true of communist society, where a technological advance
should result in an advance along the whole front of society.

THE FUTURE OF SCIENTIFIC EMPIRICISM 201

sioned the dislocation of social relations, in the absence
of any exact knowledge or ability properly to organize
them in accordance with technological advance. If this
dislocation be permitted to go much further, the advance
in physical science will destroy the organization of society
which makes science possible. Thus by its very merit,
physical science may cut its own throat.

The question reduces to this. There is a race in progress
between science and society. Will society understand
science soon enough to allow science to develop a science
of society by which both science and society can be
saved ?

The conclusion which develops from a consideration of
the interrelation of science and society is that the de-
velopment of every science is dependent upon the
development of every other science. The rapid advance
of any given science therefore forces the necessity for the
rapid advance of every other science. Otherwise one
science developing too rapidly will end by destroying
society, and therefore put an end to its own development
as well. It is one thing to have a leader, but quite another
to have that leader so far ahead of the main body that
he cannot any longer be followed. As a result, the army
fails to hold the advance it had already made, and falls
into chaos, whereas the leader is cut off from his support
and perishes.

Physical science has now forced the necessity for the
development of social science, and this is imperative lest
all science perish from contemporary society. If it be
suspected that we are making wild and abstract pre-
dictions based on pure speculation, and that there is no

2oa WHAT SCIENCE REALLY MEANS

observable immediate danger of any such eventuality,
we have only to call attention to what is happening to-
day in Germany, where an anti-liberal and reactionary
social order gives no support and has no tolerance for
anything not immediately useful to its narrow purposes.
German society has failed to keep up with the standard
set by German science, and has therefore discontinued
German science. There is a deadly logic involved between
the given stage of a social order and the given stage of
science. Though some small leeway may be allowed,
their ability to separate is definitely confined within
certain limits. Therefore the understanding of science on
the part of a society is requisite for both science and
society.

IS SOCIAL SCIENCE POSSIBLE?

We have pointed the extreme snd urgent need for social
science. Two objections will be made to this. The first
will state that social science is already in process of
development, and that it must be given enough time
to become an adult science. The second will state that
social studies can never become sciences on which to
base predictions sufficient to guide society. Let us answer
these objections. To the first we may reply that, as
already indicated, a continuation of the present methods
in social science will never yield an exact science because
abstract and independent laws are not being sought,
and will never be sought so long as social scientists mis-
understand scientific empiricism. Social science is not a
young science, but has been before the public as an
organized affair nearly as long as chemistry. Moreover,

THE FUTURE OF SCIENTIFIC EMPIRICISM 203

during the time it has been promoted as a science, it has
shown no signs of development. The development of a
science is not a function of time but of the understanding
of method.

The second objection will require more consideration.
There is a widespread conviction that a sharp break
exists between the physical and the social sciences, and
that the same method cannot prevail in both branches.
This conviction has been given categorical authority in
German philosophy, which distinguishes between natur-
ivisscnschaften and geistesivissenschaften the mathematical
natural sciences and the normative social sciences. What
is implied, of course, is that exact mathematical measure-
ment applicable to physical subject-matter has of neces-
sity no applicability to social subject-matter. If this were
true it would have to be granted that social relations could
never be made the basis for an exact science, and therefore
never broadly applicable to the guidance of society.

The division between the subject-matter of physical
science and the subject-matter of social science, naming
the former empirical and the latter normative, assumes a
fallacy which we have exposed above. 2 No subject-
matter considered by itself can properly be labelled em-
pirical or normative. It has been shown that the same
subject-matter which is normative from one level is
empirical from another, just as purpose analyses into
mechanism and mechanism synthesizes into purpose.
There is no a priori principle which forbids the treatment
of values in social relations from being the subject-
matter for empirical analysis, and from being analysed

2 See p. 158 ff. for mechanism, and purpose.

204 WHAT SCIENCE REALLY MEANS

into their mechanisms, exactly as is done with the
physical subject-matter.

Value-judgments do not have to be regarded as un-
analysable and as merely normative. For instance,
biology might have taken the arbitrary position that the
quality of livingncss is a value primitive and irreducible,
and as such not subject to analysis or measurement.
Certainly it is a value, but this docs not prevent biology
from analysing this value into its mechanisms, without
the need of introducing the value as an element in its
analysis. Similarly, the analysis of the values involved in
social relations must be for the uses of science wertfreiheit.
Thus the fact that social relations are themselves values
does not mean that as values they cannot be scientifically
treated. They can be subjected to isolation, on which
induction, deduction, and experimental verification are
brought into play, until a sufficient deductive system is
formulated which allows of mathematical treatment.

We are unimpressed by the argument that social
science is for ever precluded from the same procedure
and therefore from the same measure of success that
physical science enjoys. The proponents of this theory
offer no argument in defence of their position. They
seem to have taken the failure of social science and made
it causal: because there has been no social science, there
can be no social science. To erect a failure into a necessity
is orthodox positivism. The door to science must be left
open. That anything is more than likely to be discovered,
is the true scientific attitude. Social science is a definite
possibility.

THE FUTURE OF SCIENTIFIC EMPIRICISM 205
THE FUTURE OF APPLIED SCIENCE

Science, like all rational endeavour, is directed toward the
future. What has already been accomplished in its short
past may be taken as the merest hint of what is to follow.
Theoretical scientific formulations will be utilized for
practical purposes in the future to a much greater extent
than they are at present, even though such practicality is
not at the moment envisaged.

The future of applied science is not to be conceived
merely in terms of great improvements along lines
already laid down by present inventions. It does not
mean only faster airplanes, better air-conditioning,
lighter metals of greater tensile strength, etc. Nor must
the advance of applied science be conceived narrowly in
terms of mechanical technology and the saving of factory
labour, although this is one of its services. The application
of science must be understood more comprehensively in
terms of the annihilation of the limitations of time and
space, which is only another way of saying the saving of
energy. What has formerly been conceived to be the
'natural' and hence inevitable way of achieving material
ends is shown by science to be a wasteful and often
roundabout method. Many years ago no one would
have dreamed that the production of agricultural pro-
ducts could have been indefinitely improved and ac-
celerated. They rather depended on 'nature.' But now,
by the greater understanding of nature, its processes have
been speeded up and made more efficient. For instance,
the 'ageing* of spirituous liquors may be accomplished
speedily. 'Napoleon' brandy, being a function of the

206 WHAT SCIENCE REALLY MEANS

action of enzymes and not of Napoleon, will be made
overnight. It is not too much to predict that advance in
biology will make the sowing of vast acres for a small
yield unnecessary, and the same yield will be obtainable
on a small patch controlled and not subjected to the
accidents of weather.

Since time immemorial, men have kept animals for
their milk, meat, hides, and hair, and this has necessitated
the slavery that goes with a parasitic existence. For the
nomad practically lives like a parasite on cattle, and must
therefore follow the cattle's way of life. But applied
science, no less than theoretical science, abstracts to
dominant functions. Technology poses the question of
how much can be left out in the solution of any given
practical problem. If we want only meat, hair, hides, and
milk from cattle, why go to all the trouble of having
to take care of herds? If we expect the action of
enzymes, why wait on 'time' ? Why not merely manu-
facture items where it is more economical ? Mr. George
W. Gray points out 3 that given the wholesale manu-
facture of the Lindbergh perfusion pump and, given the
technique of keeping organs alive outside the organism
in vitro perfected by Dr. Carrel, it requires no great
imagination to suggest the picture of bovine mammary
glands kept to perform their function udders without
cows and such products as insulin produced by merely
keeping part of the pancreatic gland rather than whole
sheep to be butchered.

But this is a timid and half-way presentation. Science
abstracts from abstractions. And applied science will
3 Harper's Magazine for February 1936.

THE FUTURE OF SCIENTIFIC EMPIRICISM 207

finally abstract from even the secretion of glands to the
manufacture of the essential substances. Certainly milk
and insulin will be synthesized in the laboratory without
the useless cultivation of waste by-products. Moreover,
technology need not copy the so-called natural product;
it can make better milk and better insulin than the glands.
What the practical results of a true social science would
be staggers the imagination. If the world has wasted time
and energy on material problems because of its ignorance
of natural science, what was and still is its plight in
wasted time and energy in social endeavour? Wars,
revolutions, and social conflicts generally would be
resolved by a proper social science. The hit-or-miss
political blundering which goes on unaltered from
ancient times would at last change into something
rational and planned. This does not mean, of course, that
at any stage of advance an effortless Utopia or a heaven-
on-earth can be achieved. It does mean the resolution
of those importunate problems which have held down
human energy by demanding the most of it. This energy
would be released not for a silly leisure of amusement
and boredom but for the attacking of problems at a
higher level. To paraphrase Plato, the purpose of applied
science is not to create mere material riches (though these
have their place) and the furtherance of life for its own
sake, but to set men free for the pursuit of the good life.

THE FUTURE OF THEORETICAL SCIENCE

The marvels of applied science are not, however, the
whole story of science nor even its leading purpose.
Unfortunately, the public has no comprehension of

208 WHAT SCIENCE REALLY MEANS

science other than in its practical capacity. Thus, as H. G.
Wells says, to most persons science is alchemy. The
applications are the merest by-products of the great
domain of science, which is once and for all concerned
with the truth, and which must hew to that line and let
the chips fall where they may. In this domain of science
there are many yeomen who only stand and apply the
technique, but the real advance of science is due to a few
leaders who arc entirely occupied with carrying forward
the theoretical aspects of science.

The advance of science has been directed in the past
toward greater specialization within sciences. Chemistry
has split up, for instance, into physico- and bio-chemistry,
biology into a score of special branches, each of which
goes as a separate science. But the advanced science of
physics begins to manifest another direction besides this
one. The second movement is toward unification of
branches previously considered disconnected. For in-
stance, astronomy and physics have become one science,
and the attempt is being made to discover a unified field
theory which will subsume relativity and the quantum.
The advance of science should move in these two
directions: toward greater and greater analysis, and thus
specialization, and toward greater and greater synthesis,
and thus generalization.

But the movement toward synthesis in the separate
sciences is not enough. What is required is a synthesis
which will be capable of embracing all the sciences
already known and those to be known under one grand
science. Such a general science of sciences would have to
show each science as a special case of its universal laws,

THE FUTURE OF SCIENTIFIC EMPIRICISM 209

and thus exhibited the continuity between chemistry
and biology, biology and psychology, psychology and
sociology, etc. Its laws would have to be of a generality
such that the laws of all separate sciences could be deduced
as special cases, and yet not be superseded by the more
general.

With the development of science, a greater and greater
rationality is required. But this does not mean a greater
and greater mentality. In other words, men will not have
to be born with greater cerebral capacity, either quanti-
tative or qualitative. The advance of the race depends
upon the discovery of ideas and not upon an advance in
innate psychological capacity. A fairly stupid man, by
using trigonometric tables, can accomplish what a great
intellect would be unable to accomplish without them.
We have shown that as a science advances it relies less
and less upon flashes of genius and more and more upon
a solid deductive background. Were it not for this fact,
we might indeed look with dismay at the future of
science, and a fortiori at the future of the human race.
But with this understanding it may be seen that if all
sciences advance together, their acceleration may increase
indefinitely and this without a corresponding increase
in innate mental capacity. The fact that each stage of
scientific advance can start from the accumulated body
of knowledge, and does not have to start from scratch,
takes science out of the mentalistic psychological category,
and even in the last analysis out of its reliance upon
genius.

We have already enunciated and subscribed to the
principle of wertfreiheit, according to which science is

210 WHAT SCIENCE REALLY MEANS

free from values. But this does not mean that it does not
start from values and emerge with them. It resolves
values into rational equivalents, whereby newer values
are allowed to be actualized. It is by virtue of the fact
that science proceeds rationally and not affectively, that
it is able to obtain new values. The achievement of values
is not obtained through the envisagement of values but
through scientific rationality which is value-free.

The whole advance of reasoning may be said to have
been this very reduction of that which was first normative
to that which later became empirical. And thereby more
and higher normative problems are perceived. The
savage who sees the whole environment as normative
friendly or unfriendly is not able to manipulate it,
i.e. to increase its 'friendliness'; and thus he is precluded
from envisaging higher values. To-day when we look
to the good intentions of rulers rather than to scientific
systems of government, and indignantly punish crimi-
nality, we are in the plight of the savage: we have not
reduced these normatives to empiricals.

A similar reduction in the affective has taken place in
some sciences: 'spirits' to 'properties' and 'properties' to
pictorial entities, and finally pictorial entities to mathe-
matical symbols. From the affective to the mathematical
is the true direction of science. This is only another way
of stating that the direction of all reasoning is from the
normative to the empirical.

The hope of the human race rests upon the develop-
ment of science, which will discover for it values
immediately useful and practical, and intrinsic values,
to be appreciated far beyond anything that may have

THE FUTURE OF SCIENTIFIC EMPIRICISM 211

already been indicated. But hope and longing, and
the attainment of immediate application, will not by
themselves accomplish anything. All depends upon the
understanding and allowed procedure of strict scientific
empiricism.

INDEX

Aaron of Alexandria, 37

Abel, F. A., 63

Abstract functions, and actuality,

186
Abstractive levels, as formal and

applied, 157
Abstract systems, as resting on

facts, 130

Actual prediction, failure of, 174
Adelard of Bath, 46 ; importance

of, 43

Aethicus, 41

Agricola, 50

Al-Battani, 38

Albertus Magnus, 44

Al-Biruni, as culmination of
Moslem science, 39

Alchemists, compared with chem-
ists, 51

Alcmaeon of Crotona, 27

d'Alembert, 58

Alexander of Tralles, 37

Al-Farabi, 39

Al-Farghani, 38

Al-Fazari, 38

Al-Hazan, 39

Al-Kindi, 38

Alphonsine Tables, 48

Al-Quarizmi, 43

Al-Razi, 38

Al-Sufi, 39

Al-Zarquali, 40

Ampere, 61

Analysis and synthesis, as direc-
tions, 1 54 f.

Analysis, not whole of science,
103 f.

Anaxagoras, 27
Anaximander, 27
Andalo di Negro, 47
Anthemius, 36
Apollonius of Perga, 32, 38
Applied science, as application of

pure, 156; future of, 205
Apuleius, 41
Aquinas, Thomas, 44
Archimatthaeus, 42
Archimedes, 38, 70; and principle

of specific gravity, 32; quoted,

31

Aretaeus, 33

Argument, summary of, 190 f.
Aristarchus of Samos, 34, 48
Aristotle, 28, 30, 36, 40, 46, 141;

quoted, 29, 90
Aristoxenus, 28
Arrhenius, 62

Astronomy, development of, 57
Atomism, 158
Avicenna, 40; as culmination of

Moslem science, 39
Avogadro, 62; Law, as scientific

object, 107

Babylonian science, 26

Bacon, Francis, 72

Bacon, Roger, 45, 46; importance

of, 44

von Baer, 63
Balmer, 20; Law, 151
Barrow, I., 55
Bateson, W., 64
Bauhin, C., 50
Bayliss, 66

214

WHAT SCIENCE REALLY MEANS

Becquerel, 62, 67

Bcde, 41

Bell, E. T., quoted, 143

Bentham, 77

Bergmann, E. von, 58

Bernard, Claude, 63

Bernoulli, 58

Biology, failure to use mathe-
matics, 56

Biological development, difficul-
ties of, 66

Biological sciences, development
of, 60

Black Death, 46

Black, Joseph, 60; phlogiston ex-
periment of, 58

Boethius, 41

Bohr, N., 67

Boltzmann, L., 62

Borelli, G. A., 56

Boyle, R., 54; and development
of chemistry, 59

Brahe, Tycho, 47, 50, 155

Bridgman, P. W., 13, 17, 19, 81,
1 86; quoted, 69, 91, 93 ff.,
169

Brilliant insight, place of, 162

Brock, Werner, quoted, 128

Bruno, Giordano, 50, 53

Buffon, G. L. L., 60

Burtt, E. A., quoted, 49, 52

Byzantine, and Moslem science,
continuity of, 37; empire, 35;
science, renaissance of, 37;
scientists, kept science alive, 36

'Can not' confused with 'has

not,' 89 f
Cantor, 63
Capella, Martin, 36

Carnap, R., 17; quoted, 86 fF.

Carnot, Sadi, 62

Carrel, Alexis, 206; quoted, 98,
101

Cassiodorus, 41

Cauchy, A., 63

Causal laws, and dominant func-
tions, 184; in nature, 169

Causality, as deduction from
premises, 177; a principle of
nature, 185; and invariance,
194; confused with temporal
sequence, 82; defended, 97;
freedom from time of, 173 f;
problem of, 168; retained in
modern science, 170; wrongly
defined, 174

Cause and effect, as function, 73 ;
confused with history, 64

Cavalieri, B., 52

Cavendish, H., 58

Cayley, A., 63

Celsus, 33

Chemistry, and quantitative
method, 58; development of,
58

Chloroplast, as function, 117

Christian and renaissance empiri-
cism, continuity of, 46

Church, attitude towards science,

49

Circle, as function, 116
City planning, first work on, 39
Clausius, R., 62
Clifford, W. K., 93
Cohen, M. R., quoted, 75, 79, 151
Comte, Auguste, 76 ff., 79, 86,

90; influence of, 77
Concepts, as functions, 113
Condillac, 75

INDEX

215

Condorcet, 75
Constantinus Africanus, 42
Continuity, and cause and effect,

173; and causal laws, 71 f.;

defined, 171
Copernicus, 51; importance of,

48 f.

Coulomb, 58

Criminality, as function, 118
Curie, Pierre, 62

Dagomari, 47

Dalton, J., 59, 61

Dampier-Whetham, 68; quoted,
42, 54

Darwin, Charles, 66; influence
of, 64

Deduction, and induction as com-
plementary, 146; analysis of,
147; in scientific method, 161;
importance of, 163

Definitions of science, confusion
of, 13

Demonstration, as empirical test
of abstractions, 130

Density, as function, 116

Derivatives of abstractions, 129

Desargues, 52

Descartes, Renee, 52, 56

Descriptive sciences, development

of, 49

Dicaearchus of Messina, 30
Diderot, 75
Dioscorides, 33
Dirac, P. A. M., 68, 91, 93
Dufay, G., 58
Durand, D. B., 47

Early Christian compendia, 41
Economic man, as function, 117

Economy, as check on wild
speculation, 132

Eddington, A. S., 17, 69, 83, 96,
169; quoted, 84, 99, 103, 122

Edessa, 37

Egyptian science, 26

Einstein, Albert, 67, 98, 132;
quoted, 52, 97

Empirical, compared with norma-
tive, 203 ; dogmatism analysed,
156, dogmatism defined, 155;
entities, 14, 136, entities, differ
in various sciences, 135, enti-
ties, pass in and out of science,
136, entities, recognition of
true, 71; facts, as non-sensory,
124; laws, 152 f, laws, in-
validity of, 153; objects, as
functions, 120; philosophy,
bad effect on scientists of, 73 ;
proof, direction of, 140, proof,
involves system, 193; relation
to logical, 145 ; science, failure

of, 45

Empiricism, absence of limits of,
137; definitions of, 13; in-
volves theory and fact, 71;
levels of, 6 1 ; misunderstanding
of, 69 f. ; not philosophical,
14; and observation of actual-
ity, 120; as principle of
economy, 13 if; and the
speculative reason, 144; as
relative, I34f; as true scien-
tific method, 190; two kinds
of, 51

Energy forms, interconnectivity
of, 62

English empiricism, as positivism,

216

WHAT SCIENCE REALLY MEANS

Entities, 106; of science, 136

Entity, and process compared, 1 14

Erasistratus, 31

Euclid, 32, 38, 42 f.

Eudoxus of Cnidos, 28

Euler, L., 58

Euryphion of Cnidos, 28

Eustachius, 49

Events, as functions, 1 14 f.

Exception, rejections of, 172

Experience, analysis of, 122; as
abstract, 125 f., and the given,
123; and social agreement,
124; bruteness of, 123 ; divorced
from reason, 75

'Experienceable* analysed, 92

Experiment, as deduction, 153 f.

Experimentation, as preoccupa-
tion of scientists, 191 f.; no
guide to true empiricism, 70

Eymeric, 47

Fabricius, 49

Fact and reason, occasion for
divorce of, 191

Fallopius, 49

Faraday, M., 61, 70

Fermat, 52

Ferminius, 47

Fictions of science, as non-
existent, 137

Fitzgerald, 67, 132

FlugelJ. C, 90

Fourrier, J. B., 62

Franklin, B., 58

Fresnel, A., 62

Frontinus, 33

Function, as cause, 188; defined,
in; as independent of vari-
ables, 185 f.

Functions, and the statistical
method, 181; as abstractions
from abstractions, 129; scien-
tific implications of, 129

de Fundis, John, 48

Galen, 33 f., 49

Galileo, 12, 47, 50, 52 ff., 55 f.,

70 f., 133, 172, 180
Galvani, L., 58
Gauss, C. F., 63
Genetic biology, development of,

6 5 f.

Gerard of Toledo, 42

Gerbart of Aurillac, 42

Gesner, J. M., 50

Ginzburg, B., quoted, 34

Gray, George W., quoted, 206

Greek, empiricism, early, 27;
philosophy, stopped experi-
mentation, 29; science, failure
of, 28

Greeks, interest in empiricism, 29

Grey and Wheeler, 57

Groot, 47

Grosseteste, 43 f.

Hamilton, Sir William, 13, 63,

148

Haphazard progress, danger of, 12
Harvey, W., 49, 56
Heidel, W. A., quoted, 26, 29
Heisenberg, W., 68, 91, 93, 96,

103
Hellenistic science, too 'practical,'

32; turned positivistic, 50
von Helmholtz, H. L. F., 62, 90

van Helmont, 54
Henry of Hesse, 47
Hermann of Dalmatia, 42

INDEX

217

Hero, 33
Herophilus, 31
Herschel, J. and W., 57
Hertz, 61

Heuristic entities, 136
Hipparchus, 33
Hippocrates, 56
Hippocratic Corpus, 28
History, examined, 125
Hooke, R., 56
Hopkins, 66
Hugh of Santalla, 42
Hume, David, 73 f., 75 f., 82, 174
Huygens, 55
Hypatia, 36

Hypothesis, in scientific method,
159

Ibn-Qurra, 38

Ideal science of logic, as abstrac-
tion from actuality, 142

Idealism, defined, 17; objections
to, 19

Ideas, confused with thoughts, 81

Impossibilities, later accomplished,
90

Indeterminacy, principle of, 97

Induction, analysis of, 146; and
deduction as complementary,
146

Irrelevance, meaning of, 148

Isadore of Seville, 41

Isolatable systems, the start of
science, 104

Jabir, 38

Jacobi, 63

Jeans, Sir J., 17, 69, 83 f.

Jeffreys, Harold, quoted, 152

John of Picardy, 47

John of Saxony, 47
Joule, J. P., 62
Justinian, 37

Kant, influence of, 76
Keller, Helen, 127
Kelvin, Lord, 62
Kepler, 20, 5 of., 55
Klein, Felix, 63 ; quoted, 143
von Kleist, 58

La Grange, 58

Lamarck, 64

Laplace, 57, 61

Lavoisier, organizer of chemistry,

59 ff-

Law of action and reaction, 102;
positivist view of, 102; men-
talist view of, 102; realist view
of, 102

'Law of probability,' 187

Laws, 106; as functions, 115

Leeuwenhoek, 56

Legendre, A. M., 63, 90

Leibnitz, 53

Lenzen, V. F., 169; quoted, 91 fF.,
170

Leon of Thessalonica, 37

Levi-Civita, 67

Levy, H., quoted, 152

Lindbergh, Charles A., 206

Linnaeus, 60

Lister, Win., 56

Littre, 76

Lobatchewsky, 63

Locke, 72

Logic, as empirical science, 141;
becomes branch of psycho-
logy, 78 ; utter reliance on, 87

218

WHAT SCIENCE REALLY MEANS

Logical positivism, 86 fF., as em-
pirical, 89; as incorrect pro-
gramme, 91; as logical, 89

Lorenz, H. A., 67, 132

Macer, 41

Mach, Ernst, 86, 92 f. ; father of
positivism, 80; influence of,
79; quoted, 79 f., 83

Maclaurin, 58

Magic in Middle Ages, 41

Malpighi, 56

Marcellus of Bordeaux, 41

Marsupial, as function, 117

Materialistic mechanism, diffi-
culties of, 15; upset by rela-
tivity, 17

Mathematical model, substituted
for mechanical, 68

Mathematical science, method of,

H3

Mathematics, as empirical science,
142; development of, 58, 62

Maxwell, C., 61

McKie, Douglas, quoted, 59

Mechanical model, breakdown
of, 83

Mechanism, analysed, 158; and
purpose, as mutually impli-
cative, 160; and purpose, in
scientific method, 161; and
scientific method, 159

Mendel, 64

Mendeleef, 61

Mcntalism, rejection of, 109

Mentalist view, proponents of, 83 f.

Merle, Wm., 47

Meroe, 31

Metaphysics, as empirical science,
143 ; rejection of, 86

Meyerson, Emile, 162

Michelson, 67, 132

Michelson-Morley experiment,67

Microscopic physics, 67

Mill, John Stuart, 77 ff. , 1 49 ; and in-
ductive science, 78 ; quoted, 174

Mind of God, as mathematical, 84

Mind-stuff, 84; analysed, 108

Minkowski, H., 67

Modern chemistry, rise of, 54

Modern physics, interpretive
difficulties of, 69

Morgan, T. H., 65

Morley, 67, 132

Moslem encyclopaedists and
translators, 38

Moslem science, becomes experi-
mental, 38; decline of, 40

Muller, J., quoted, 90

Murphy, Gardner, quoted, 148

de Murs, John, 47

Musschenbrock, 58

Mythologic entities, 136, 163

Napier, J., 52

Natural history, division into

sciences of, 63
Natural science, falsely divorced

from social, 203
Neckham, Alexander, 43
Ncmorarius, 43
Neo-pythagoreanism, 32
Nestorian Christians, 37; in

Ctesiphon and Baghdad, 37
Neurath, 86

New sciences, rise of, 62
Newton, Sir Isaac, 12, 52 f., 71,

103, I32f; and mathematical

interpretation, 5 5 ; work of, 54 f.
Nicholas of Cusa, 47

INDEX

219

Non-empirical, as becoming em-
pirical, 136

Non-euclidean geometry, as ex-
ample of high abstraction, 1 3 o f.

Normative compared with em-
pirical, 203

Novara, 48

Occam's Razor, 132

Occult sciences, difficulties of, 132

Ohm, 61

Omar Khayyam, 40

Operationalism, defined, 94;

reputation of, 95
Operationalist view, 91 f.
Operationalists, and scientific

functions, 119
Oresme, Nicholas, 47
Organizational levels, direction

of, 138

Organizational series, 138
Onbasius, 36
Origin of Species, 64
Original science, beginnings of, 43
Ostwald, W., 92
Oxygen, discovery of, 59

Pacioli, 48
Palissy, 49 f.
Parliamentarianism, as function,

118

Pascal, B., 52

Pasteur, Louis, 66 ; influence of, 63
Paul of Aegina, 37
Pavlov, 1 6
Pearson, Karl, 79; positivistic

influence of, 82; quoted, 82
Peirce, Charles Sanders, quoted,

90, 146, 171
Peter of Spain, 45
Peter the Stranger, 45

Petrarch, 47

Petrocellus, 42

Peurbach, 48

Philip of Opus, 28

Philiponus, 36

Philo of Byzantium, 33

Philosophical empiricism, not

philosophy of science, 72
Philosophy, empirical test of, 144
Physical sciences, development

of, 50

Physicalism, 87; Cartesian, 56
Physics, increasing objectivity of,

68

Pico della Mirandola, 49
Picturable model, abandonment

of, 69
Planck, Max, 67 f, 103; quoted,

68, 97 f, 168
Planet, as function, 116
Plato, 31, 35, 72, 107
Plato of Tivoli, 42
Pliny the Elder, 33
Poincare, Henri, 63, 79, 93; as

positivist, 80 f. ; quoted, 80 f.
Poor investigators of science, 47
Pope John XXI, 45
Pope Paul III, 49
Pope Sylvester II, 45
Positivism, as danger to future of
science, 196; as logical and
empirical, 88 ; danger of, 190 f. ;
defined, 18; denies reason,
190 f. ; induced from science,
57; objections to, 19; the
preference of scientists, 18;
spread of, 77
Positivist view, proponents of,

85 ff.
Priestley, Joseph, 59 f., 129

220

WHAT SCIENCE REALLY MEANS

Principles, application of, 174

Probability, a principle of nature,
185; as false substitute for
causality, 178; defined, 178;
examples of, 179, 183; in-
volves causality, 180; involves
certainty, 179

Procedure and philosophy, danger
of divergence of, 103

Process and entity compared,
114

Processes, 106; as functions, 113

Proclus, 36

Profarius, 47

Properties, 210

'Protocol language,' 86 f.

Ptolemaic system, 34

Ptolemy, 33 f, 38, 48

Pure science, as unapplied, 156

Purpose, 158; analysed, 160; and
mechanism, as mutually im-
plicative, 160

Pythagoras, and experiment on
monochord, 27

Quantum theory, 67 f.

Rational dogmatism, analysed,
156; defined, 155

Rationality, independent of men-
tality, 209; of scientific world,
169

Realist view, 96 rT.

Reason, abandonment of, 76

Regiomontanus, 48

Reichenbach, H., 86

Relativity, as example of true
scientific method, 132 f.;
general theory of, 67; special
theory of, 67

Relevance, as canon of causality,

176; meaning of, 148
Revolution in physics, as occasion

for speculation, 190
Reyjean, 54
Riemann, 63
Right-angled triangles, functions

of, 112

Robert of Chester, 42
Roentgen, 62
Roman Church, 12
Rousseau, 76
Rutherford, Lord, 59, 67

St. Agobard, 41

St. Aldhelm, 41

St. John, quoted, 190

St. Simon, 76

Sarchel, Alfred, 43

Sarton, G., quoted, 34, 40

Scheele, 59 f.

Schleiden, 63

Schlick, M., 86; quoted, 88

Schrodinger, E., quoted, 68

Schwann, 63

Science, abtsract nature of, 98; as
necessity of interpretation, 16;
as abstraction from experience,
127; as abstraction of func-
tions, 129; aim of, 1 88 f.; and
increasing use of mathematics,
68; and instinctive method,
danger of, 195; and the
modern world, 1 1 ; and philo-
sophy, fatal separation of, 34;
and the public, 23 ; and society,
race between, 201; as know-
ledge of external world, 98;
as deductive system, 163; as
hierarchy of functions, 164;

INDEX

221

as hope of human race, 210 ;
as observation of phenomena,
78 ; as system of relations, 71 ;
as wertfreiheit, 128 ; begins and
ends with values, 210; directed
toward application by society,
198 f. ; directed toward future,
205 ; distinguished from
pseudo-science, 70; hierarchy
of, I37f.; how it abstracts,
128; ideal progress of, 164;
ideal method of, i65f.; in
twentieth century, rapid de-
velopment of, 65; low state
of, 46 ; not isolated affair, 198 ;
necessity for public under-
standing of, 22; nineteenth-
century systematization of, 61 ;
misunderstanding of, 207 f. ;
more than method, 101;
opposed to reason in seven-
teenth century, 52; popular
opinions of, 21; public faith
in, 21 ; regarded by scientists
as irrational, 75; requires
metaphysics, 23; relation to
society, 105; single grand, of
future, 208 f. ; social require-
ments of, 198; subject-matter
of, 101 ; wrong understanding
of, 192 f.

Sciences, field of, 139; one way
direction of, 140

Scientific, academies, rise of, 53;
advance, directions of, 208;
developments, interdepen-
dence of, 201; distinctions,
undisturbed by similarities,
108; endeavour, progress of,
45; entities, not phenomena,

no; empiricism, distinguished
from common-sense empiri-
cism, 135; inquiry, field of,
102; laws, not mental sum-
maries, 20; method, analysis
of, 151, as application of logic,
149; correct, 193, dependent
on philosophy, 106, in mathe-
matics, 152; objects, abstract
nature of, 109 , as empirical,
119, as functions, in, defined
by functions, H2f., nature
of, io6f, not actual, 109;
progress, haphazard, 12;
theory, as not affecting science,
103; tradition, no break in, 35

Scientists, anti-metaphysical bias
of, 14; vague about science, n

Scot, Michael, 42

Scotus, Erigena, 41

Self-consistency, as scientific re-
quirement, 131

Seneca, 33

Servetus, 49

Severus of Sebokht, 37

Social relations, progress of, forced
by science, 200

Social science, argument for,
202 f. ; confused with psy-
chology, 65; failure of, 200;
false divorced from natural,
203 ; forced by physical, 201 f. ;
possibility of, 204

Social sciences, rise of, 64

Social studies, predicament of,
197

Society, development of, depends
on science, 199

Socrates, 29

Specialization, increase of, 61

222

WHAT SCIENCE REALLY MEANS

Specific, distinguished from actual,

72

Speculation, judicious use of, 72
Speculative vs. descriptive science,

S3

Spirits, 210

Stallo, 93

Starling, 66

Statistical method, and certainty,
183; syllogism of, 187; use-
fulness of, 182

Steno the Dane, 56

Stephanus of Alexandria, 37

Stephanus of Athens, 37

Strabo, Walafrid, 33, 41

Strato, 28

Sydenham, 56

Syene, 31

Syllogism, logical, 150; of demon-
stration, 150; of empirical
laws, 153

Sylvester, 63

Synesius, Bishop of Ptolemais, 36

Systems, hierarchy of, 147; in-
clusiveness of, 171; infinality
of, 172

Swineshead, Richard, 47

Technology, future development
of, 206 f. ; ideal future of, 207

Tensor calculus, 67

Thales, 27

Theophilus Protospatharius, 37

Theophrastus of Lesbos, 30

Theory and practice, thought
opposed, 99

Theory of science, as outside
science, 99

Thomson, 67

Thorndike, L., quoted 41, 43 f.

nor-

Toscanelli, 48
Transformation equation, 67

Unification, increase of, 61
Uniformity of nature, 1 171
Universe, materialistic conception
of, 64 f.

Valence, as function, 117
Value-judgments, as merely

mative, 204
Vesalius, 49
Vienna Circle, 86
da Vinci, Leonardo, 48
Virchow, 63
Vitalism, 158
Vitruvius, 33
Volta, 58

Waismann, 86

Walcher Prior of Malvern, 42
Wallace, A. R., 52
Watson, William, 58
Watt, James, 59, 148
Weber, Max, 128
Wells, H. G., 208
Weierstrass, 63
Wertfreiheit, 204, 209
Wheeler and Grey, 57
Whitehead, A. N., 13 ; quoted, n
William of Conches, 43
William of St. Cloud, 45
Wilson, 19
Witelo, 43

Wittgenstein, L., quoted, 86
Wrong philosophy retards science,
104

Xenophanes of Colophon, 27
Young, 62

particulars of publications

of similar interest

issued by

GEORGE ALLEN & UNWIN LTD

LONDON: 40 MUSEUM STREET, W C.I

LEIPZIG: (F. VOLCKMAR) HOSPITALS! R 10

CAPE TOWN: 73 ST. GEORGE'S STREET

TORONTO: 91 WELLINGTON STREET, WEST

BOMBAY: 15 GRAHAM ROAD, BALLARD ESTATE

WELLINGTON, N.Z.: 8 KINGS CRESCENT, LOWER HUTT

SYDNEY, N.S.W. : AUSTRALIA HOUSE, WYNYARD SQUARE

Science for the Citizen

A SELF-EDUCATOR BASED ON THE SOCIAL BACK-
GROUND OF SCIENTIFIC DISCOVERY

by LANCELOT HOGBEN

Author of Mathematics for the Million
Royal 8vo. Illustrated by J. F. Horrabin 12$. 6d. net

"Such philosophy as shall not vanish in the fume of subtile, sublime
or delectable speculation but shall be operative to the endowment and
betterment of Man's life." FRANCIS BACON

Mathematics for the Million became a best-seller because it took the
mystery out of mathematics and expounded the Language of Science
as a means of organizing social experience for an age of plenty. In
Science for the Citizen Professor Hogben does the same service for
science itself. The reader is made familiar with the potent instruments
by which man has conquered the problems of time reckoning and
earth survey, materials and power, hunger, disease, and behaviour.
Clarity of exposition and breadth of learning combine to make a
text-book of astonishing power. Yet this is more than a text-book.
Science is presented as a tool that shapes society and that society in its
turn sharpens to a keener edge. The tangled web of thought and action,
from the early calendar civilizations to the tasks and opportunities of
to-day, is brilliantly portrayed.

The book is written primarily for "the intelligent layman," but
the science teacher will find it indispensable. It will influence the
teaching of science at all stages for many years to come.

Heredity and Politics

by J. B. S. HALDANE

La. Crown 8vo. js. 6d. net

Are men born equal? Are there superior races? Should the unfit be
sterilized ? Is race-crossing harmful ? Is the nation degenerating because
the poor breed quicker than the rich ? These are vital questions in the
twentieth century. They arc still being answered, both by would-be
reformers and by conservatives, in terms of nineteenth-century science.
Yet during this century we have learned more about heredity than in
the whole preceding eternity. Some of these questions can be answered.
Others turn out to be as meaningless as "Why does the sun go round
the earth?" Others again cannot be answered until we know more.

Such are some of the topics dealt with in this highly provocative
book by Professor Haldanc, one of the most outstanding and challeng-
ing personalities in science and politics to-day.

LONDON: GEORGE ALLEN & UNWIN LTD.