The limitations of science

THE LIMITATIONS OF SCIENCE

THE LIMITATIONS
OF SCIENCE

BY

LOUIS TRENCHARD MORE, PH.D.

"i

Professor in the University of Cincinnati

NEW YORK.

HENRY HOLT AND COMPANY
1915

COPYRIGHT, 1915,

BY
LOUIS TRENCHARD MORE

Published April, 1915

THE QUINN A BODEN CO. PRESS
RAHWAT. N. J.

Hypotheses non fingo. Quicquid enim ex phae-
nomenis non deducitur, hypothesis vocanda est; et
hypotheses seu metaphysicae, seu physicae, seu qualita-
tum occultarum, seu mechanics, in philosophia experi-
mental! locum non habent. In hac philosophia proposi-
tiones deducuntur ex phsenomenis, et redduntur
generales per inductionem. — NEWTON.

PREFACE

THE separate chapters of this book have already
been published as essays in periodicals. The first, sec-
ond, third, and seventh appeared in The Hibbert Jour-
nal; the fourth, in The Philosophical Magazine and
in the University of Cincinnati Studies; the fifth, in
The Monist; and the sixth, in The Unpopular Review.
But they have been rewritten and enlarged so as to
form chapters for a connected discussion of the Limita-
tions of Science. This was not a difficult task since I
have had this purpose in mind from the beginning.

CINCINNATI,

December 2, 1914.

CONTENTS

PAGE
I

II THE METAPHYSICAL TENDENCIES OF MODERN

PHYSICS 32

III DESCARTES AND His INFLUENCE ON RECENT

SCIENCE 69

IV THE SCIENTIFIC METHOD . .. . . 107
V THE CLASSICAL AND THE NEW MECHANICS 142

VI SKEPTICISM AND IDOLATRY IN SCIENCE . . 187

VII SCIENCE AS THE ARBITER OF ETHICS . .212

INDEX 263

THE LIMITATIONS OF SCIENCE

CHAPTER I
SCIENCE AS A SYMBOL AND A LAW

Les theories contemporaines sont sur ce point d'accord avec
1'histoire ; elles consacrent la preponderance dans le domaine
scientifique, de 1'hypothese atomistique. — HANNEQUIN.

IT has grown to be an axiom in modern thought,
that the hope of discovering the laws of nature and
our relation to them by metaphysical reasoning is
impossible. The term metaphysical reasoning will be
used consistently to mean the method introduced by the
Greek philosophers who, however they might differ
in minor matters, were pretty well agreed in looking
upon what we call nature as something which could be
investigated subjectively ; that is, things are as we think
them to be. It is thus directly contrary to the physical
method, which maintains natural phenomena and laws
to be entirely objective and independent of our thought ;
according to this method no theory or fact can be
established unless it is completely verified by experi-
mental tests.

So little in the long years since Plato and Aristotle
has been done by the metaphysical philosophers to add

2 THE LIMITATIONS OF SCIENCE

to our positive knowledge, that they themselves are
abandoning their former methods for that of the
psychologist, who studies even the faculties and the
emotions of the mind objectively by means of the phys-
ical or experimental method. Many will frankly admit
that metaphysical studies are chiefly valuable now as
a history of the development of thought, and agree
with Renan that " Science, and science alone, can
give to humanity what it most craves, a symbol
and a law." If this be really the case, if the attain-
ment of our desire for an accurate and real knowledge
of our environment, its phenomena and the causes of
actions, rests with science alone, then it becomes neces-
sary to consider whether this hope also must prove to be
fallacious. Will the results of experiment made ob-
jectively, which must however be interpreted sub-
jectively, fail in their turn as criteria of truth?

Of the various sciences, physics offers probably the
best means of attacking this problem, for it lies be-
tween the concrete classifications of the natural sci-
ences, such as chemistry and biology, and the abstract
theories of pure mathematics. Physics, on the one
hand, is less disturbed by the multitude of details
which often, in the natural sciences, prevent the grasp-
ing of a central idea; while, on the other hand, it is
more circumscribed than mathematics by the necessity
of constant comparison with concrete phenomena, and
so avoids the danger of confounding speculation and

SCIENCE AS A SYMBOL AND A LAW 3

reality. Thus the methods of physics have, to a degree,
become the model which the other sciences seek to
follow, a logical mathematical theory based on, and
corrected by, experimental observation. Moreover,
this science presents a longer and more consecutive
history than most of the others.

It is also noticeable that physics treats of problems
similar to those of metaphysics. During the sixteenth,
seventeenth, and eighteenth centuries philosophy and
physics were closely united, and were largely domi-
nated by the deductive method, which was introduced
by Descartes and which led to persistent attempts to
explain scientific laws by metaphysical causes. It was
then that the two great metaphysical ideas, of the con-
tinuity of matter with its identification with space, and
of matter as a form of indivisible and discrete atoms
different in kind from space, were adopted as scientific
postulates, and were expressed in mathematical form.:
The following century was distinguished by a separa-
tion of philosophy and physics, as that period is best
known by the extraordinary rise of the experimental
method and the classification of phenomena under
mathematical laws. With the mass of experimental
data now at our disposal, an imperative need is again
felt for theoretical laws which shall classify them, and
accompanying this correct scientific need there is a
disposition to re-introduce metaphysical systems, simi-
lar in aim to that of Descartes. The reason for this

4 THE LIMITATIONS OF SCIENCE

change in method in the nineteenth century is under-
stood if we consider the state of scientific knowledge
before that time.

Few of the properties of heat, light, sound, and
electricity were then known, but, on the other hand, the
laws of mechanics were well established, and a solid
foundation of experimental fact permitted a broad
and comprehensive application of pure mathematics to
that branch of physics. It is altogether natural that
mechanics should have developed first, for it is the only
part of the science which rests directly on the data of
experience. It considers only material bodies and their
sensible and common properties — such as the occupa-
tion of space and the resistance to motion. To measure
properties of matter other than spatial and dynamical
requires more elaborate apparatus, and it is more diffi-
cult to separate extraneous accidents from such at-
tributes as color, temperature, and tone. We cannot,
even in the present state of mathematical knowledge,
discuss the complex processes of nature as they are
presented to us ; for example, a mathematical law which
shall define all the changes of color, of electrical in-
tensity, etc., which occur when a body is heated, is
still beyond our powers. But it was possible, with the
knowledge then at hand, to abstract from matter all its
properties except that of a simple and uniform
space and force attribute, and to derive a theory of
mechanical action distinct and complete. And so the

SCIENCE AS A SYMBOL AND A LAW 5

philosophical scientists of the French revolutionary
period, with whom this mechanistic movement cul-
minated, had only mechanical problems to work on, in/
which their knowledge was practically as accurate as It
is to-day.

However we may regard the effect of the metaphys-
ical system of Descartes on science, there can be only
one opinion as to the value of his introduction of geom-
etry into physics. By it, he changed medieval natural
philosophy into modern physics. When he discovered
the method of locating the position of any point by
giving its distance from three rectangular straight
lines, he made it possible to represent the path of any
moving body by a geometrical line referred to the same
axes, which could then be fully defined by an algebraic
equation; he thus made it possible to classify all mo-
tions under a few general types, and so founded the
science of kinematics. For example, it became no
longer necessary to study projectiles individually, for
their behavior could be foretold from the general prop-
erties of parabolae. Shortly after this, Newton and
Leibnitz invented the calculus, which enables us to study
moving bodies during their transit. The solution of
problems of continuous motion in curved lines could
never be satisfactorily obtained by Euclidean geometry,
which could not overcome the break between rest and
motion, or between polygons and curves. But the
application of the infinitesimal calculus to Cartesian

6 THE LIMITATIONS OF SCIENCE

geometry gives us a solution of the problem, which,
while it may not be the true solution, approximates to
the truth as nearly as we please. This is accom-
plished by dividing the path of a moving body into sec-
tions so small that the ratio of any of these infinitesimal
distances to the time necessary to traverse it, or the
velocity, is constant and finite. Newton had discov-
ered and verified the law of universal gravitation, and
had also collected the data of the action of forces on
bodies, and embodied them in three laws which still
serve as the postulates for the science of dynamics;
and D'Alembert supplemented them by a general
dynamic law of the motion of a system of bodies
acted upon by forces which embraced all the hitherto
isolated problems of this character, and reduced them
to a special and simple case of statics.

On the theoretic side, Kant, Lagrange, and others
had discussed the general axioms of mechanics, and
had established the three fundamental units — length,
mass, and time; and it is generally conceded that the
solution of any problem of mechanics into the simplest
combination of these three quantities is incapable of
further reduction.

But one thing remained before an imposing structure
could be raised which should withstand criticism, and
that was a general law to include and solve problems
relating to a system of bodies in equilibrium and at
rest. And Lagrange accomplished this.

SCIENCE AS A SYMBOL AND A LAW 7

Such was the state of science when Laplace, in his
Systeme du Monde, and Lagrange in the Mecanique
Analytique, attempted to construct a theory and his-
tory of the universe by means only of the general and
accepted laws of the two mechanics: celestial, which
concerns the heavenly bodies, and terrestrial, those on
the earth. Their problem has been stated in many
ways, but this may serve : — Given the positions, masses,
and forces of a system of bodies at any time, to find
the configuration of the system at any other time, previ-
ous or afterward.

By the aid of the principle of centers of inertia, each
celestial body could be replaced by a mathematical
point, at which the whole mass was concentrated, and
endowed with a force of attraction according to New-
ton's law of universal gravitation. In a similar way
each terrestrial body was divided into a great number
of small elastic particles, or atoms. These were con-
sidered to be invariable and indivisible, and they were
arbitrarily endowed with the same force of universal
gravitation, acting through their centers of inertia.
This force could be assigned to these imponderable
masses, separated by insensible distances, with some
probability of truth, although it could not be scien-
tifically verified by experiment, because it was known
to be a property of ponderable bodies separated by
sensible distances. This conception of matter was
generally accepted, as the original atomic theory of

8 THE LIMITATIONS OF SCIENCE

Democritus had been extended and adapted to mathe-
matical analysis by Gassendi, Huygens, and Boscovich,
Thus all bodies and systems of bodies became ab-
stractly alike in character, a collection of mass points
acted upon by an attractive force common to all; and
if the state of the universe were given at any time, it
became merely a problem in mechanics, whose laws are
fully known, to find its history from the beginning
to the end. As Laplace proudly and naively answered :
" In this system there is no need of a god." Evidently
this statement was a climax of materialism, and prob-
ably can never again be uttered with such assurance.

So solidly was this theoretical universe built, that it
defied criticism for a century, and finally, as it seemed,
established science on a mechanical basis. The other
branches of physics, which advanced rapidly during the
nineteenth century, fell promptly under the influence of
this mechanistic idea. The names employed show this
clearly. We have the wave theories of light and
sound, the dynamic theory of heat, and the mechanical
theories of electricity and magnetism. In all these
theories, attributes of matter, such as color, tempera-
ture, musical pitch, electrical charge, etc., are ex-
pressed by the mechanical motions and forces of
atoms, and are measured solely in terms of the
mechanical units of length, mass, and time. The
method absolutely eliminates our senses, not only as
instruments capable of measuring the quantity of an

SCIENCE AS A SYMBOL AND A LAW 9

action, but even denies them the power of deciding
qualitatively between phenomena; for the light which
affects the eye, the sound heard by the ear, and the heat
perceived by temperature are essentially the same thing,
mere variations of a universal force of gravitation.
These different attributes of matter are scientifically
identical if the forces involved are equal; for as force,
however manifested, was held to be a mechanical at-
traction between atoms, all these quantities can be
weighed in a chemical balance and have no essential
difference. While there may have been great diver-
sity amongst the physicists of the last century as to de-
tails, there was but this one explanation of nature:
The universe was a complicated machine, whose visible
parts were connected together by a system of intangible
links called atoms, whose complex motions, while they
might defy our analytical skill, were yet completely
expressible by general mechanical laws.

To find the weak spot in this mechanistic theory,
based on the hypothesis of the atom, is not only a dif-
ficult task, but is one which ran so counter to the
accepted teachings of science and to the natural preju-
dices of the mind, that it is not strange if most men
of science now reason as though the atom were a
matter of experimental proof rather than of metaphys-
ical speculation. Such a mechanistic theory of natural
law as Lagrange and Laplace evolved, and as scientific
thought of the last century extended, must necessarily

io THE LIMITATIONS OF SCIENCE

depend on some similar atomistic hypothesis. Complex
material bodies must be divided up into elementary
masses so small that any conceivable variation in them,
except mere inertia, must be forever beyond our meas-
urement or even conception. Because, if the atom
were divisible or variable, which its very name denies,
then the actions of its component parts and their varia-
tions might be productive of such an attribute as
temperature or color, and thus introduce into the atom
properties other than those purely mechanical.

From experience we know of only one way a tangible
body may make another move, and that is by a direct
push. Either atoms must be granted a mysterious
power of attraction through empty space, or else the
part of the universe unoccupied by ponderable matter
must be filled with a medium or ether, to act as the
mechanical link between atom and atom. Now this
ether is either continuous or discontinuous. If con-
tinuous, it would serve as a link ; but how is matter to
move through it or even to exist in it unless two bodies
may occupy the same space at the same time, or unless
ponderable matter is but an attribute of this ethereal
matter, of some such nature as a whirlpool on the
surface of water? Such a variation maintains its
identity of form as it moves, but not of the matter
composing it ; this is to replace concrete matter by the
abstract idea of form or motion, which, in the end, is
always repugnant to our sense of reality, and arouses

SCIENCE AS A SYMBOL AND A LAW 11

the impression of an existence in a world of dreams.
On the other hand, if the ether be discontinuous, it
must be porous, and what becomes of our link between
atoms? We are driven to the creation of a second
more tenuous medium to fill the spaces between the
grosser one, and so on to the reductio ad absurdum
pointed out by Clifford.

This discussion may be readily summarized in two
metaphysical hypotheses which are frequently ac-
cepted as the axioms of the atomic theory.

First. — Given the masses and the configuration of
the centers of inertia of all the atoms, with the law of
their mutual attraction, then all the attributes of mat-
ter are determined and the problem of the universe is
solved.

Second. — As a visible link is required between mov-
ing parts of a machine, so invisible links, called ethers,
multiplied indefinitely, must exist between atoms.

While most scientists were endeavoring to extend
and to perfect this mechanical theory, there were a
few inclined to question the validity of the axioms
on which it rested. Among the latter, Rankine de-
serves the first place. In a memoir read before the
Philosophical Society of Glasgow in 1855, he discusses
scientific methods in general, points out the defects and
advantages in the prevailing theories, and outlines a
new method which he calls the science of energetics.
His criticism is of the highest importance; with sub-

12 THE LIMITATIONS OF SCIENCE

tile irony he exposes the absurdity of a materialistic
theory derived from mechanics which itself inevitably
rests on a purely metaphysical basis.

According to Rankine, a true physical theory is the
most simple system of principles from which the formal
laws of phenomena, experimentally discovered, may be
deduced. Such a theory resembles a science like
geometry in that it originates with definitions and
axioms for first principles, and derives their con-
sequences logically, by propositions. But, in general,
a physical theory differs because these fundamental
definitions and axioms discovered first are numerous
and complex, since they are deduced from the mass of
facts presented to us immediately by nature; whereas
the first principles and axioms of geometry are few
in number and simple in character, — such as a mathe-
matical line has length only, — and are the results
deduced from bodies not necessarily real. In other
words, the method pursued in the physical theory is
inductive, and is consequently more tentative and
laborious than the deductive method of geometry, as
the acceptance or rejection of the principles derived
must depend upon their agreement with facts dis-
covered gradually by observations, and not upon gen-
eral properties agreed upon once for all. The proposi-
tions of geometry are final, if the axioms and defini-
tions are granted; a theory of physics is more or less
conjectural, as its first principles are always subject

SCIENCE AS A SYMBOL AND A LAW 13

to revision because of the discovery of new phe-
nomena.

Two methods of framing a physical theory may be
distinguished. They may be termed the abstractive and
the hypothetical methods.

According to the abstractive method, a class of ob-
jects or phenomena is described and a name or symbol
assigned to that assemblage of properties common to
all the objects or phenomena composing the class, as
perceived by the senses, and without introducing any-
thing hypothetical.

There is only one example of a complete physical
theory formed exclusively from the data of experience
by the abstractive method, — the principles of the sci-
ence of mechanics. The objects discussed in mechanics
are material and real bodies, all of which possess the
sensible properties of occupying space and resisting
change of motion. The phenomena dealt with are
confined to those attributes of matter distinguished by
the words force and motion, which we have found to
be common to all bodies of which we have any knowl-
edge. And the laws deduced follow from axioms and
definitions which express this universal experience.

According to the hypothetical method, the existence
of a class of fictitious objects or phenomena, which can-
not be perceived by the senses, is assumed. And prop-
erties are assigned to them, similar to those known to
be true of a class of real objects or phenomena, which

14 THE LIMITATIONS OF SCIENCE

can be perceived by the senses. If the consequences
of such a hypothesis are afterwards found to be in
agreement with the results of observation and experi-
ment, then the laws, known to be true for the class of
real objects or phenomena, may be applied to the hypo-
thetical class. The objects or phenomena considered
by this method are thus merely matters of conjecture,
and their nature may be modified at any time so as to
make the propositions derived from them conform to an
expression of experimental fact. Such, for example, has
been the method followed in the wave theory of light.
To explain the observed action of light, the existence
of hypothetical bodies, called atoms, and the luminifer-
ous ether, is assumed, and properties are assigned to
them similar to those of sensible matter. As new
phenomena are discovered the attributes of the atom
and the ether are modified to fit the requirements.
This theory can be considered only as a convenient
means of expressing natural laws, and is always sub-
ject to change, as it does not depend on the objective
realities fundamental to an abstractive method.

Just because the theory of the mechanical motions
and motive forces of sensible bodies is the only com-
plete physical theory, and because it does not require
the use of a hypothetical method in its development,
we have been led to give the hypotheses, advanced as
theories in the other branches of physics, a mechanical
form. The classes of phenomena considered in all

SCIENCE AS A SYMBOL AND A LAW 15

these theories are defined conjecturally as being due
to some kind of mechanical motion and motive force,
as when heat is defined as consisting in molecular mo-
tions, or the rigidity of solids in molecular attractions
and repulsions.

The motions and forces involved in these theories
can no longer be ascribed to sensible matter, but either
hypothetical bodies, such as the luminiferous ether, or
hypothetical parts of real bodies, such as molecules,
atoms, ethereal vortices, or other imaginary elements
of matter must be created. And to them are assigned
properties and laws resembling as closely as may be
those of sensible bodies. In explaining new facts, as
they are discovered, the attributes of the hypothetical
matter are modified, or such new ones assumed as may
best fit the case. Such mechanical hypotheses, not be-
ing based on experimental evidence, are held to fulfill
their purpose when these conjectural attributes explain
in the simplest and most plausible way the largest
body of known phenomena and when they anticipate
phenomena afterwards observed. The importance and
weight of these hypotheses increase with the number of
phenomena whose laws they express.

Certain hypothetical theories, such as the wave
theory of light, have been undoubtedly useful, since
they have reduced complicated actions to a few simple
laws. And also they tend to combine all branches of
physics into one system in which the axioms of

16 THE LIMITATIONS OF SCIENCE

mechanics are the first principles of the whole science.
But they must be employed with great caution and
judgment. Their free use tends to confuse the essen-
tial differences between hypothesis and fact, between
metaphysics and physics, and this confusion does now
exist in the minds of the public generally and even in
those of many men of science. A desire is, conse-
quently, often shown to explain away, or set aside,
facts inconsistent with a preconceived hypothesis.

Such is briefly Rankine's criticism of the prevailing
mechanical and materialistic theories of physics. His
conclusions are worthy of thoughtful consideration.
It has always been the boast of science that by its
methods we may avoid the pitfalls in which meta-
physical reasoning inevitably ends. Now, if our most
elaborate and complete scientific theory is really meta-
physical, we must renounce all our proud claims and
consider atomic and mechanical theories solely on the
grounds of their utility and simplicity.

A metaphysical hypothesis, valuable solely for its
utility, is always dangerous, for by constant use we
tend inevitably to give an objective reality to things
which in the beginning we knew to exist only in our
own minds. And this tendency is especially deplor-
able in science, which does little for education if it does
not recognize clearly the limits of our knowledge and
distinguish accurately between reality and speculation.

Now the belief in the objective reality of molecules,

SCIENCE AS A SYMBOL AND A LAW 17

atoms, ethers, and ethereal vortices has grown so
steadily that little objection has been made to the
recent creation of a whole new class of such hypothet-
ical objects, called indifferently ions, corpuscles, elec-
trons, or particles, which are assumed to be the con-
stituent elements of the hypothetical atom. Of the
three classes of objects it is, at the present time, the
existence of the sensible bodies which is in danger
of repudiation. This is the case not only in the minds
of the thoughtless but in those of the leading men
of science. For example, Sir J. J. Thomson, in the
preface to his Conduction of Electricity Through
Gases, says : " The possession of a charge by the ions
increases so much the ease with which they can be
traced and their properties studied that, as the reader
will see, we know far more about the ion than we do
about the uncharged molecule." Such a statement is
on a parallel with the remark made to me by another
distinguished physicist, that we know far more about
the ether and the atom than we do about sensible
matter. This is true, and in the same way as a
Frankenstein might say of a mechanical man which
he had conceived and constructed, — I know more about
him than I do about a real man.

Such confusion of thought is directly traceable to
the fact that many men of science have forgotten the
distinction between the creations of nature and the
creations of their imaginations. We can never say

i8 THE LIMITATIONS OF SCIENCE

more of molecules, ions, and the ether, than that they
may exist; but ponderable matter, as perceived by the
senses, has an objective existence, or else there is no
place for science. Since Kant's time the existence or
the non-existence of those insensible links in the uni-
versal machine is known to be equally demonstrable;
we have no criterion of proof. It is curious that we
still refuse to acknowledge this. If we look askant
at Kant, the metaphysician, we have only to turn to
Lagrange, whose scientific claims cannot be ignored,
and find he has proved by rigid mathematical analysis
that any phenomenon, which obeys the law of conser-
vation of energy, is capable of an explanation by a
mechanical theory ; but, and here is the important point,
as there is always one adequate theory, so there are
also an indefinite number of other mechanical theories
which will, so far as our minds are concerned, satisfy
all the requirements of the case. We have no criterion
in mechanics by which we may determine what is the
actual process of nature. There is no experimentum
crucis, and we choose the explanation which for the
moment seems to be the simplest.

Our inability to decide unequivocally for one me-
chanical hypothesis instead of another is shown also
by the actual history of physical science. Since the
time of Huygens and Newton we have attempted to
settle the question whether light is due to a wave
motion in an ether or to small particles emitted from

SCIENCE AS A SYMBOL AND A LAW 19

luminous bodies. Many times it has been announced
that the question has been decided experimentally ; for
instance, when Foucault found that the velocity of
light decreased when passing through transparent
bodies, instead of increasing as Newton's hypothesis
had predicted. But, on the other hand, the aberration
of light discovered by Bradley is a stumbling-block
to Huygens' theory and is a simple consequence of
Newton's. Neither of these experiments caused the
abandonment of a theory. A Newton could have
altered the properties of the corpuscle and a Huygens
is sure to arise who can alter the character of ethereal
waves so as to explain aberration; in fact, it has been
done with considerable success by Sir Joseph Larmor.
We may then take it as established, both on theoretical
and on historical grounds, that no experiment has
been, or will be, devised to decide finally between the
claims of the two hypotheses, yet the corpuscular
theory was abandoned. The reason was not that either
was impossible, but that the corpuscle, with the accre-
tions added to it as new facts were discovered, became
too unmanageable. Huygens' mechanical wave theory
having outgrown its usefulness has suffered the same
fate. He ascribed light to a series of mechanical
waves propagated through an elastic ether, but the at-
tributes necessary to the medium became so contra-
dictory that a new theory, advanced by Maxwell, was
accepted as a great relief. In this theory, the ethereal

20 THE LIMITATIONS OF SCIENCE

waves are not mechanical but electro-magnetic, similar
to those we now use in wireless telegraphy. But the
difficulties are still pursuing us. We may assume that
such waves can pass through space, but we cannot con-
struct a mechanical model of an atom or ether which
will produce or maintain these vibrations, nor have we
any evidence that electro-magnetic disturbances can
affect the optic nerve and produce the sensation of
light. The prediction, which I made when this essay
was first published, that we shall return to a modified
form of the corpuscular theory with the electrified par-
ticle, the constituent of the atom, as an agent, has been
verified. The principle of relativity, recently an-
nounced by Professor Einstein, absolutely requires it.

If a general atomistic theory, which seems to be the
only practicable hypothesis, involves these inherent dif-
ficulties, and if it presents a real peril to correct scien-
tific thinking, the question arises, whether some general
mechanical explanation of all physical phenomena is
possible which is not so limited.

Rankine, in the same essay, proposes a method which
he calls the science of energetics. As we have been
able to frame with some success a theory of physics by
using a hypothetical method, we should have even more
success in combining all the branches of the science
into one general theory if the abstractive method were
extended and applied for the purpose. Instead of sup-
posing the various physical phenomena to be con-

SCIENCE AS A SYMBOL AND A LAW 21

stituted, in an occult way, of modifications of me-
chanical motion and force, let us attempt to frame laws
which shall embrace the properties common to any one
class. He finds energy, or the capacity to effect
changes, to be the common characteristic of the various
states of matter to which the several branches of
physics relate. If then we frame general laws regard-
ing energy, we ^I^A be able to apply them, with appro-
priate changes, to every branch of physics.

Rankine evidently denies the advisability of trying
to find the cause of the attraction of bodies for one
another, or the mechanism of the propagation of light
and heat through empty space. In all cases we have a
certain quantity of energy, acting in a specific manner.
Our aim should be to find by experiment the properties
of any such manifestation, and to combine all common
properties by general mathematical laws. Such was
the method of Newton when he established the law of
universal gravitation and refrained from publishing
how the forces of attraction could act through space,
and no discovery has aided science more. But after he
had determined experimentally many of the laws of
light, he advanced the hypothesis that these phenomena
were caused by motions of intangible corpuscles and he
ventured so far as to describe the shape and properties
of these hypothetical bodies. It is claimed, on good
grounds apparently, that his corpuscular theory retarded
the growth of the subject for more than a century, by

22 THE LIMITATIONS OF SCIENCE

preventing the adoption of the temporarily more con-
venient wave theory.

Whether or not it is advisable to substitute energy
for inertia, or mass, as the general attribute of matter
which will best serve for a fundamental unit, may be
open to discussion. But it seems certain to me, at
least, that the formulation of laws deduced mathe-
matically from experimental data alone, and not con-
jecture as to the causes of phenomena, is the true
province of science and the only method certain not to
lead us into vain metaphysical speculation.

Unfortunately, the restraint and clarity of thought
shown by Rankine are rare, and few are willing to
impose limitations on speculation or to forego the at-
tempt to create a subjective and metaphysical scheme
according to which nature shall work. In the hands
of his successors, notably Mach, Duhem, and Ostwald,
these barriers were cleared. They have endeavored to
give an objective reality to the mathematical equation
of energy. To make an entity of a symbol, to speak
of centers of force as if an intelligible image were
conveyed to the mind, to make matter and inertia an
attribute of energy, is even more metaphysical than
the concepts of atoms and ethers, which could, at least,
be likened to sensible objects. With Professor Ost-
wald, the most militant defender of the science of
energetics, matter disappears altogether; empty space
is known to us only by the quantity of energy necessary

SCIENCE AS A SYMBOL AND A LAW 23

to penetrate it, and occupied space is merely a group
of various energies. In his enthusiasm he does not
hesitate at difficulties. " When a stick strikes you,"
he exclaims, " which do you feel, the stick or the
energy?" One might as well ask the old question,
Which comes first, the owl or the egg? — a matter of
infinite dispute and no decision. Although Professor
Ostwald's work bristles with mathematical equations
and scientific terms, he asks us to return to the meta-
physical methods of the medieval schoolmen — to thrash
over again the endless verbal disputes of nominalists
and realists.

While mechanics is the only branch of physics which
has become a complete science through the use of the
inductive, or abstractive, method, just as soon as we
invent atoms and ethers, or consider an abstract quan-
tity, like energy, to be an entity, in order to explain
the modus operandi of matter and motion, and to serve
as connecting links in explaining non-mechanical
phenomena, such as electricity and light, mechanics
drifts at once into a highly metaphysical and subjective
study where each man's opinion is guided only by an
inward sentiment of knowledge. To what lengths
this can go, I shall show in a later chapter when I
present the confusion of thought of certain eminent
men of science who change impersonal mechanical
energy into a kind of vital and beneficent principle
ruling over the thoughts and actions of human society,

24 THE LIMITATIONS OF SCIENCE

or of Sir Oliver Lodge, who bestows on the ether the
ability to carry ghostly messages as well as light.

As a critical attempt, the school of energetics has
done good work by calling attention to the inadequacies
of atomic theories, yet as a positive method it has had
comparatively little effect until very recently, when it
has been pushed by a school of German physicists into
what can only be called an abyss of confusion where,
as in a sort of looking-glass world, all things tan-
gible become intangible and the abstract replaces
the concrete. But the majority of men of science still
rely absolutely on atomic hypotheses. Indeed, a fresh
stimulus has been given them by the efforts to explain
the experimental facts, recently discovered, concerning
Roentgen rays, the passage of electricity through gases,
and the properties of radium ; facts which will probably
do more, in the end, to discountenance mechanical
models of phenomena, by making them practically un-
manageable, than the theoretical criticisms of the fol-
lowers of the school of energetics.

So long as the hypothesis of an invariable and in-
divisible atom gave a reasonably simple and satisfac-
tory method of attacking the problems of physics,
even those men of science who were ready to acknowl-
edge the tentative character of the hypothesis and the
contradictory nature of its postulates were unwilling
to try other methods. But the phenomena mentioned
above do not fit into the general scheme, because the

SCIENCE AS A SYMBOL AND A LAW 25

mechanical atom does not explain such electrical
phenomena, unless we arbitrarily associate with it other
supposititious electrical fluids or else give it complex
and variable electrical attributes ; both of which defeat
the purpose of explaining all phenomena by means of
a single, invariable entity. Their explanation thus re-
quires us either to abandon the atomic theory or to
modify it radically; the latter has been done, and the
atom is now supposed to be a complex body composed
of an aggregation of invariable and indivisible par-
ticles, called electrons.

As might be supposed, some specious advantages
have been obtained. The chemists have long sought in
vain for a chemical element whose atom might be con-
sidered the primordial substance, and from which the
atoms of the other elements were derived. This new
idea of the atom offers a solution, for the chemists may
now construct the atoms of all the elements out of dif-
ferent combinations of corpuscles. Also the early
investigators in electricity, as Franklin and Du Fay,
were led to postulate the existence of subtile electric
fluids to explain the fact that electrified matter some-
times showed a force of attraction and sometimes of
repulsion. Later, in the theories of Faraday and
Maxwell, the hypothesis of fluids was abandoned
and the ends of the atom of matter were endowed
respectively with the properties of electrical attrac-
tion and repulsion. Now it is possible to discard this

26 THE LIMITATIONS OF SCIENCE

variability in the simple atom by supposing some of the
corpuscular elements of a complex atom to exhibit the
one kind of electric force, and others the opposite
kind.

In spite of these advantages and others which might
be cited, the prime fact remains that it is now neces-
sary to abandon the historic and hitherto invincible
atomic theory for another which is still more conjec-
tural. For the former element of matter, simple in
nature, we have substituted another, complex in char-
acter, and have thereby given up the chief and to many
the only value of an atomic theory.

The corpuscular theories advanced, almost simul-
taneously by Lorentz and Larmor, show this clearly.
Sir Joseph Larmor, in his treatise on JEther and
Matter, presents a view of the constitution of matter
which is sufficient over an extensive range of physical
theory, and which he trusts will not be made more
complex until it proves inadequate in some definite
feature. According to his hypothesis, the atom of mat-
ter is composed of a system, probably large in number,
of positively and negatively electrified protions (called
frequently by others corpuscles, electrons, or ions)
in a state of steady orbital motion around each other.
The passage of electricity through a conductor or from
one body to another is effected by a transference of
electrically charged protions from one atom to another.
The differences in the chemical elements, such as iron

SCIENCE AS A SYMBOL AND A LAW 27

or hydrogen, can be accounted for by ascribing them
to various aggregations of the protions. As for the
protions themselves, they are in whole or part nuclei
of intrinsic strain in the ether, places where the con-
tinuity of this medium has been broken and cemented
together again.

Such a theory is evidently, and in the highest degree,
artificial and metaphysical, and Sir Joseph Larmor
would be the last to assert that he has given a true
picture of the constitution of matter. Its value must
rest on the belief that it is the simplest theory avail-
able for explaining experimental facts. But the diffi-
culties inherent to the theory are insuperable. It is
almost inconceivable that our simplest idea of the ulti-
mate constituent of the chemical element should be an
atom, so bewilderingly complex in character. Each
atom of an apparently quiescent body is itself an
aggregation of particles, vastly more intricate than the
stellar systems, and whirling around each other with a
motion approximating a hundred thousand miles per
second. And although the atom itself still possesses
the attributes of matter, its constituents become merely
nuclei of strain in the ether. What must be the
structure of an ether which can maintain such a com-
plex of strains as all the countless atoms in the uni-
verse would require? If we can never be sure matter
is actually so constituted, it is unfortunate to create
a world so counter to our instinctive belief that in a

28 THE LIMITATIONS OF SCIENCE

correct definition a complex idea must be explained into
simpler parts.

The theory of Professor Lorentz is essentially the
same, although he does not attempt any speculations
as to the structure of the ether or atom. But he, too,
postulates the existence of small, electrically charged
particles in all bodies and deduces all electrical laws
from the positions and motions of these electrons.

It is not necessary to state that both these writers
develop their theories with great skill and from a pro-
found knowledge of the science. They have, perhaps,
achieved a closer unity in the branches of physics,
although I feel confident that they have really only
substituted an electrical atom which will not explain
matter for a material atom which would not explain
electricity. And to attain this ambiguous advantage
they have introduced postulates which lie still further
outside the domain of science and have, by fixing our
attention on a sub-atom, given an appearance of greater
reality to the relatively gross atom.

The influence of such abstruse and metaphysical
theories on scientific thought is already apparent in a
certain eagerness to advance startling hypotheses and
novel ideas. Many men of science of to-day have tem-
porarily put aside the sobriety and restraint which
should characterize scientific reasoning. The most
tremendous results are based on insufficient evidence,
and the simple statement that the cause of a phenom-

SCIENCE AS A SYMBOL AND A LAW 29

enon is to be found in electronic action is considered
satisfactory. Physicists in Germany are gravely dis-
cussing whether electrons are spheres or discs in shape.
The transmutation of the elements, a problem which
has baffled research for centuries, is announced as an
assured fact, because radium and a few other sub-
stances spontaneously give off energy. Electricity is
declared to be a substance and matter is said to be not
a substance, but an attribute of electricity, because an
electrified body has an apparent increase in its resist-
ance to motion; although we know nothing about the
nature of either matter or electricity. Others say that
the universe is a sort of modified ether; although we
never can have cognizance of an unmodified ether.
Surely matters of such infinite difficulty and of such
supreme importance should not be decided before the
most rigid elimination of more natural causes. The
fact is, all such statements as these are merely words
which convey no ideas; the problems involved are
entirely beyond our powers of solution either by
physical or by metaphysical methods. Such confusion
of thought and dissolution of the boundaries between
fact and fancy are deplorable, and if they create trouble
in the minds of scientific men, they have absolutely
bewildered the general public. Books of a popular na-
ture are constantly appearing which change these re-
sults of speculation into established fact, and their
readers naturally credit the most astounding state-

30 THE LIMITATIONS OF SCIENCE

ments. The day may come when a new war will arise
between science and religion on the issue that the de-
ductions of science are too metaphysical to be of value.

It may be necessary, when the laws and phenomena
of a science are vaguely known, to employ a hypothet-
ical method. And a hypothesis may then be of great
use in creating a certain unity amongst diverse ele-
ments. But the question may well be asked, whether
physical science has not outgrown a method proper for
the alchemist and the astrologer.

The attempt to unite the phenomena of all branches
of physics in a few general laws and to explain their
cause by the aid of atoms has engaged the attention
of the greatest men of science for more than a century.
They have spent upon these problems infinite thought
and pains, and in the end we have a body of laws firmly
established on experimental evidence, but the causes of
these laws are as hopelessly obscure as ever. The
atom has failed to satisfy the requirements, and now
the electron is added to explain new facts, an hypothesis
on an hypothesis. As our knowledge increases, who
can doubt but that these, in their turn, will give place to
others still more complex, if the same method is pur-
sued, until the succession of atoms and sub-atoms will
make the whole atomistic idea an absurdity ?

Just as we have, after centuries of incessant con-
troversy, been forced to accept the fact that we cannot
by reasoning from our consciousness obtain an ob-

SCIENCE AS A SYMBOL AND A LAW 31

jective knowledge of natural causes, so we must come
to realize that reasoning from experimental evidence is
subject to exactly the same limitations. Science, in
other words, like philosophy, has no ontological value.
Should not the men of science clearly recognize this
fact, and confine their effort to the legitimate function
of science — the discovery of natural phenomena and
their classification into general laws derived by logical
mathematical processes ?

CHAPTER II

THE METAPHYSICAL TENDENCIES OF
MODERN PHYSICS

Pero, signer Simplicio, venite pure con le ragioni e con le
dimostrazioni vostri o di Aristotile, e non con testi e nude
autorita, perche i discorsi nostri hanno a essere intorno al
mondo sensibile, e non sopra un mondo di carta. — GALILEO.

IT is a more or less simple thing to discover and
follow the main current of thought in a science like
physics, which must develop logically or not at all,
after the confusion of strife has passed away and only
the permanent additions to our knowledge remain.
This has been attempted in the former chapter, so far
at least as the atomic theory is concerned. It was
then shown that if we build up a homogeneous hypoth-
esis of the natural phenomena — heat, light, sound, and
electricity — from an analogy to mechanical laws, we
inevitably postulate the objective existence of matter,
and create a series of fictitious ethers, and of atomic, or
indivisible, elements of matter. The claim was also
made that this method which attempts to explain the
laws of nature not only fails to do so, but also pre-
vents the adoption of a better scientific procedure.

In the first place, it is difficult to point to any scien-

33

TENDENCIES OF MODERN PHYSICS 33

tific discoveries directly and inevitably produced by a
specific atomic theory. The contrary of this opinion
is very generally held, and many such discoveries in
chemistry and physics are laid at its door. The
chemist searches for and combines new compounds
of the elements, and bases his theory on the assump-
tion that each element is disintegrable only to a fixed
atom. But this means nothing more than to say that
the elements combine in definite proportions of mass,
and consequently does not bear on the question whether
matter is infinitely divisible. The chemist would have
been driven to the same laws of chemical combina-
tion if he had believed matter to be infinitely divisible.
This statement is true, because chemical analysis and
synthesis progress imperturbed and as rapidly now
when the chemical atom is supposed to be decompos-
able. And the same was true of chemical progress
before Dalton proposed his atomic theory, which be-
sides was so simple in form as to be little more than
the generalization, that from experience we may say
chemical substances unite in simple multiples of a unit
chemical mass, called the atom, instead of simple pro-
portions of mass. That is, Dalton's atomic theory was
more closely related to the abstractive than to the
hypothetical method and really has little in common
with the physical atomic hypothesis which gives defi-
nite and complex functions to the atom. As examples
in another field, we find the phenomena and laws of the

34 THE LIMITATIONS OF SCIENCE

double refraction and polarization of light were dis-
covered by Huygens before he, and later Fresnel,
attempted to explain them as a modification of me-
chanical waves in an elastic solid ether; and Newton
announced the laws of the interference of light which
occurs when there are reflections between thin films
before he pictured this phenomenon by his hypothesis
of corpuscles. To-day all these laws remain while the
specific hypotheses have been discarded. How can we
say the hypothesis of atoms and ether led to dis-
covery in these cases? The fact is just the contrary:
hypothesis, at least that part of it which consists in
developing a mechanical model of the action, follows
experimental discovery; it is the effort to explain or
visualize the unknowable processes involved in known
experimental facts and mathematical laws.

In the second place, these metaphysical hypotheses
progress from the simple to the complex. Each new
fact discovered adds its quota to the irreconcilable and
conflicting properties of the ether and the atom, and
these invisible links of the universal machine grow
more and more bewildering and complicated, until the
whole construction falls to pieces. Nor is this all ; the
man of science forgets that he is building toy houses,
and ends by believing in their reality. Even if hypoth-
esis does not carry him so far, it certainly has this
effect on others who accept the dogmas of science
without discrimination. It is no small danger thus to

TENDENCIES OF MODERN PHYSICS 35

confuse reality and imagination; a science, which be-
comes so hypothetical or so specialized as to be unin-
telligible to the educated man, is apt to become as sterile
as a religion which is in the sole possession of a hier-
archy.

This excessive use of hypothesis has developed a
sort of scientific cult which somewhat resembles a
religious dogma, in that adverse criticism of either
arouses a feeling of personal irritation. The rancor of
religious polemic is well known and is said to be due
to the fact that the believer of a religion relies on re-
vealed truth, to doubt which is sinful. The same oc-
curs with the supporters of a scientific hypothesis, who
declare their system to be founded on objective, experi-
mental fact, and to be developed by logical methods,
so that in doubting the hypothesis we are sinning
against truth and reason, — the gospels of science. On
the other hand, discussions in experimental science are
noted for their calmness, for then we are criticising,
not personal opinions but objective facts, and we care
comparatively little which way the matter ends. The
theorist, on the contrary, forgets that, while founded
on experience, his hypothesis is developed in one way
or another according to his own personal opinion;
for example, the same facts of light made Newton
believe in corpuscles and Huygens in waves, and so
tKe theorist injects into his discussions the bitterness
of personal defeat or the exultation of personal victory.

36 THE LIMITATIONS OF SCIENCE

There is yet another purpose in science which re-
quires simplicity instead of complexity. Physics, to be
something more than an intellectual puzzle for the
specialist, should enlarge our power over the external
world and increase our use of natural resources. Con-
sider how great an advance we might make in this
direction if hypothesis and occult causes were reduced
to a minimum. Instead of a mass of abstruse specu-
lations on the nature of ether and matter, our treatises
might present a clear and logical discussion of natural
phenomena and their laws. The work of Lord Kelvin
is typical. He has interspersed in his writings probably
a score of models of the atom: now it is a vortex or
whirlpool in a continuous fluid ether ; now, a box con-
taining gyrostats or wheels spinning on axes ; again, it
is a complicated structure of balls, strings, and springs.
No two of these agree in principle, and at best repre-
sent crudely a limited number of the properties of
matter and fail for others. Is there not, after all,
something almost pathetic in this incessant striving
of the greatest physicist of our times after the un-
knowable, building card houses which must be knocked
down to provide material for new ones? Certainly
more of his great and permanent constructive work
would be the property of the world if we had neglected
his hypotheses and developed more diligently his ex-
periments and his laws.

On the other hand, it is a serious matter to try to

TENDENCIES OF MODERN PHYSICS 37

sweep aside so large a part of scientific thought as
hypothesis has been, unless it is really parasitical, — a
hindrance rather than an aid to development. This
opinion as to the uselessness of hypothesis seems to be
gaining ground. Thus M. Duhem, in his Theorie
Physique, states that physical theories must have one
of two aims: either to explain laws which have been
established from experience, or to classify such laws
without giving any explanation. Of the two, the sec-
ond only is a legitimate scientific process, as the first
method makes physics dependent on metaphysics and
so introduces occult and unverifiable causes. A proper
theory should thus give us a classification of laws
and should point to new experimental methods, thereby
tending to intellectual economy in that we are per-
mitted to forget a multitude of details and otherwise
isolated facts in one common expression. He further
claims that the construction of a mechanical model
as an explanation of a law does not lead to such dis-
coveries, since these are really derived from abstract
principles, the model being invented afterwards merely
to make the law concrete. In this opinion he is sup-
ported by Hertz, who, after discovering experimentally
the electric waves predicted by Maxwell, found the best
statement in Maxwell's equations, and not in his model
of ethereal lines of force.

A ruthless and complete elimination of hypothesis is
undoubtedly impossible, and is not even desirable. We

38 THE LIMITATIONS OF SCIENCE

tend invariably to express our abstract conclusions in a
more or less concrete form. We shall always speculate
about the manner of the propagation of light to the
earth from the sun, and it is convenient to express this
transfer of energy either as a periodic disturbance
taking place in something filling space or as something
projected through space. Such indefinite speculations
are simple enough and allow us to state all that we
need in order to assume continuity of action in free
space. The obscurity and confusion in the science of
optics arise from the attempts to express in detail the
nature of the waves or of the particles of light. A
method where speculation is kept to its lowest terms is
quite different from the prevalent custom of spending
the greater part of our effort on the fictitious proper-
ties of the ether rather than on the phenomena and
laws of matter.

The problem of tracing the tendencies of thought
concealed in the conflicting data and opinions of the
present state of physics is difficult, and this difficulty
is increased by the unusual amount of new material
brought to light since the discovery of the X-rays by
Professor Roentgen in 1895. The phenomena con-
nected with the discharge of electricity through gases
and with radio-activity are obscure, and speculation
about them correspondingly bold. There is a desire,
quite common, to ignore the importance of the more
regular advance in other branches of physics and to

TENDENCIES OF MODERN PHYSICS 39

assume that the new methods of attack which have
arisen are essentially different from the thoughts and
speculations of former physicists and not subject to
their failure. This idea is brought out by Mr. Camp-
bell in his recent book on Modern Electrical Theory,
when he contrasts the work of Faraday, about 1830,
and his predecessors with that of living physicists:
" Men of his own and of the preceding era had founded
'natural philosophy'; they had made discoveries and
had elaborated theories which still form part of the
frame-work of the physical sciences. But their work
has little interest for us to-day. Their aims, their con-
ceptions, their whole attitude toward the problems
which they investigated differ so widely from our own,
that, while their results may be the basis of modern re-
search, their methods afford little inspiration for it."
This is far from being the case; if we can assign
definite periods to so continuous a development as the
history of science has shown, we should certainly date
modern physics from the seventeenth century when
Galileo introduced experimental methods and Des-
cartes applied analytical geometry to physics: human
thought does not progress at this late day by cutting
loose from the past ; especially when that past is said
to date from the middle of the nineteenth century.
Where the " new views " are not merely statistical
observations or fugitive models of some particular
phenomenon — that is, where there is a philosophical

40 THE LIMITATIONS OF SCIENCE

background to our recent work — we have abandoned
the ideas of the atomistic school of the nineteenth cen-
tury only to fall back on the doctrines formulated by
Descartes in the seventeenth, as Sir Joseph Larmor has
pointed out.

To show this connection, it is necessary only to out-
line and contrast briefly these two methods of scientific
procedure now, as I have already shown the tendencies
of the atomistic school and shall give, in the next chap-
ter, the ideas of Descartes. The followers of the
atomistic school believe natural phenomena to result
from the impact of atoms, possessing mass, figure or
extent, indestructibility, and the inherent property of
motion. Thus this idea, adopted by Huygens, agrees
in the main with that of Newton, except as it rejects
his hypothesis of the occult power of attraction of
atom for atom through space. With Descartes matter,
as a distinct and separate entity, disappears altogether,
and nothing is left but space and its variations. What
we call pure space or a vacuum is really a continuous
fluid plenum or ether, and material bodies are merely
places of permanent variation in this plenum. From
observing the persistence of whirlpools in water and in
the air, Descartes ingeniously concluded that all space
was filled with whirlpools or vortices of this plenum,
each having an axis which passes through one of the
stars. Unfortunately for the theory, these vortices and
material variations of space soon became so compli-

TENDENCIES OF MODERN PHYSICS 41

cated as to destroy its value. In the last century the
idea was revived by Lord Kelvin in his celebrated
vortical theory of matter. He used only the main ideas
of Descartes, and, from a better mathematical knowl-
edge of the properties of vortices, was able to sim-
plify their character and to account for many of the
attributes of matter. We may then say that the dis-
similarity in the two theories consists in the doctrine
that empty space is a vacuum or an imaginary entity
called the ether, as opposed to the postulate of Des-
cartes that space is true material substance ; while both
theories suppose that the smallest particles of sensible
matter are indivisible, the atomistic school considers
them to be atoms, inherently indivisible and essen-
tially different from space, but Descartes declared
them to be variations of a substance, itself infinitely
divisible, although they might not be further divisible
by our present experimental ability. With this under-
standing of Descartes's hypothesis, we are in a posi-
tion to show how closely modern views of matter and
electricity are concurring in this idea.

From the large number of physicists now writing on
the theory of physics, three names stand out promi-
nently as originators of the modern conceptions of
electricity and matter. Professor H. A. Lorentz, Sir
Joseph Larmor, and Sir Joseph Thomson are certainly
the men who will be most prominently associated with
this movement; others have aided, but mainly in the ex-

42 THE LIMITATIONS OF SCIENCE

tension or modification of their ideas. And of the
three, the most attention in an essay of this character,
which attempts a general discussion of the philosophical
basis of scientific theory, should be devoted to Pro-
fessor Larmor's ideas. In his treatise, &ther and
Matter, published in 1900, we have the rather rare
example of a scientific theory with a philosophical back-
ground clearly expressed and discussed.

The main thesis of his essay is that a purely me-
chanical theory of discrete atoms moving in empty
space has failed to account for the phenomena of
nature, and especially for the recent discoveries made
in electricity. We may, however, by altering this con-
ception of atoms, by separating electricity and matter
into two entities, or even by considering matter as an
attribute of electricity, again reconcile fact and hypoth-
esis. Since Faraday's time the drift of opinion has
been in the direction of this separation, so that it is
merely necessary to crystallize it into a definite scien-
tific postulate. No idea of finality is expressed in
Professor Larmor's theory, since he thinks it should
endure only so long as it agrees with facts in our
possession; on the other hand, he considers it not to
be effective criticism to make a charge of incomplete-
ness without indicating a better way, as an hypoth-
esis may be valuable not only when imperfect, but when
quite wrong, providing it serves as a useful instru-
ment for the progress of natural philosophy. As an

TENDENCIES OF MODERN PHYSICS 43

instance of this, he states that many of the most im-
portant discoveries in light were made when the er-
roneous corpuscular theory was still in vogue. But
does it necessarily follow that the theory prompted
the discoveries or led to their investigation because
they happened to be contemporaneous? It is difficult
to believe Bradley would have failed to obtain the
relation between the aberration of light and its finite
velocity if some other theory had been popular. Cer-
tainly the specific attributes assigned to light corpuscles
would have little influence in promoting such discover-
ies, since it was the habit to modify these without much
compunction if they did not square with observation.
And we are supported in this opinion by Professor
Larmor himself when he says : " At the same time all
that is known (or perhaps need to be known) of the
ether itself may be formulated as a scheme of differen-
tial equations, . . . which it would be gratuitous to
further explain by any complications of structure";
and again : " The ultimate inadequacy of a method of
treating material media, based on merely empirical or
speculative additions to the ascertained equations of
free ether, had indeed been clearly recognized by von
Helmholtz."

The questions, then, to be borne in mind while dis-
cussing these modern theories, are whether they involve
speculative additions to our equations and explanations
by complicated constructions, and whether they are

44 THE LIMITATIONS OF SCIENCE

essential to the progress of science. I shall try to show
that they are characterized by the same occult and
unverifiable assumptions as the older theories and are
really extra-scientific.

Professor Larmor, in the beginning of his essay,
recognizes that an hypothesis which supposes matter
to be constituted of an immense number of discrete
particles moving in empty space and incapable of fur-
ther subdivision has a philosophical objection too diffi-
cult to be overcome. In the first place, as Lord Kelvin
pointed out, the chemical atom cannot be the immeasur-
ably small body sometimes claimed by metaphysicians.
Both physical and chemical experience require the atom
to be a real portion of matter occupying a finite space,
and forming a not inappreciably small constituent of
any palpable body. The chemical molecule may be
decomposed into the atoms of hydrogen and oxygen,
and now these atoms are in turn divided into sub-
atoms. Even these also are by no means immeasurably
small; we are already calculating their size and their
mass. And we can think of no reason why matter
should have been created of this size rather than any
other. These minute grains still have much individual-
ity of their own in the way of attributes; if electrified,
their mass is supposed to change in quantity when they
move, as does also their shape; they must explain
electrical attraction and repulsion, gravitational at-
traction, cohesion, and a probable molecular repulsion

TENDENCIES OF MODERN PHYSICS 45

known as elasticity ; they must have a propensity which
makes them build geometrical crystals: in fact they
must be arbitrarily and occultly endowed with all the
attributes of ponderable matter which they were created
to explain. This sub-atom has many more duties to
perform, but sufficient have been given to show that
either it is excessively complex in essence or is en-
dowed with complex forces; so far, this is our arbitrary
resting point in the matter of subdivision, but it is
merely a temporary makeshift. But there is a still
more cogent reason for this philosophical objection
than the empirical ones given. The equally funda-
mental concepts of space and time are invariably con-
sidered as continuous or infinitely divisible functions,
and this theoretical difference assigned to matter, in-
troduces inevitable trouble in mathematical analysis.
The science of mechanics, in its theoretical aspect, may
be defined as the attempt to apply the laws of geometry
to real bodies, and while there is always an insurmount-
able break in thought between the laws of the imag-
inary bodies discussed in geometry and the concrete
ones of mechanics, we can, by the assumption of the
continuity and indefinite divisibility of matter, approxi-
mate as closely as we wish to the rigorous laws of
geometry. The geometrical point and line are re-
spectively abstract bodies of no, and of one, dimension ;
in experimental mechanics, they are both real bodies of
three dimensions, — the point is the atom and the line

46 THE LIMITATIONS OF SCIENCE

a succession of them. Theoretical mechanics is thus
the link between geometry and physics, for while it
deals with concrete bodies of real size, we eliminate
by the abstractive method all the variations which re-
sult from the finite size of bodies and then discuss them
as if they were theoretically simple bodies of no size.
That is, we divide a body into infinitesimal portions
and consider its effect as being due to the arithmetical
sum cf the effects of these parts. An example will
make this clearer; the attraction between two spheres,
which is one of the fundamental problems of physics,
can be solved rigorously only by the application of the
principle of centers of inertia, that the attractive force
of a sphere is the same as if its entire mass were con-
centrated at its mathematical center. As soon as we
apply this law of attraction to real spheres, even of
sub-atomic size, we introduce an appreciable error,
since the attractive force then produces strains and a
deformation of shape which reacts to change the force;
this error becomes negligible only when we consider
matter to be continuous and the sphere to be made up
of an indefinitely large number of indefinitely small
particles. We are thus brought to this dilemma; ex-
perimentally, matter is discontinuous and theoretically,
it is continuous, — hypothesis might be called the hope-
less effort to reconcile these irreconcilables.

Professor Larmor tries to avoid this pitfall, which
has caught the originators of atomic theories, and at-

TENDENCIES OF MODERN PHYSICS 47

tempts to reconcile the antagonistic ideas of continuity
and atomicity by placing himself squarely on the side
of Descartes. He does not regard space as mere
empty geometrical continuity. According to his no-
tion, the universe is a plenum or ether — that is, a con-
tinuous, frictionless fluid, everywhere uniform and
quiescent. This plenum constitutes what he calls true
matter. It is entirely unrecognizable by our senses
and cannot be brought to them by any experience. By
such a metaphysical hypothesis we may account for
the aberration of light and many other actions occur-
ring in free space. To provide for ordinary or sensible
matter,, making it at the same time discontinuous in
character, he supposes there exist in the plenum in-
numerable places of variation, which are uncreatable,
indestructible, and humanly indivisible, and by their
combination present to our senses all the phenomena
making up for us the material universe. These dis-
continuities are free to move without disturbing the
quiescence of the continuous medium, much as wind
blows through a forest. By this supposition we ac-
count for the experimental fact that motion of matter
does not affect the velocity of light in a vacuum. If,
however, the discontinuities show unbalanced electrical
force, then their motion causes real, although tempo-
rary, variations in the medium.

The next requirement in his cosmogony is to specify
what these variations in the supposititious plenum may

48 THE LIMITATIONS OF SCIENCE

be. This is the vital step in any process of reasoning
which attempts to link metaphysical assumption to
physical experience. Once taken without challenge, a
scientific theory may be developed logically. It is just
at this point that the Lucretian atom and the Cartesian
vortex fail. Here also Lord Kelvin failed. He proved
that no finite force could either create his tiny vortex
atom rotating in a f rictionless medium, or, once started,
could stop it. He showed it would act as if possessed
of many of the essential properties of matter. But, in
the process of elaboration, this atom, like all others,
became unmanageable from complexity; it failed to
account for the electric charges of matter, and finally
received a death-blow when Maxwell said a vortex
ring might be an analogy to the atom, but at best was
merely a mode of motion and not matter as we know it.
How, then, is this new protoplasmic element of the
universe to be defined so as to satisfy these criticisms,
and at the same time avoid making the speculative me-
chanical structures in an ether, which Professor Lar-
mor deprecates? The founders of the new electrical
theory of matter have studied profoundly the laws of
nature. They have made many permanent acquisitions
to our knowledge; they have elaborated their theory
with the greatest ingenuity, and yet the result has been
to show that their theory is merely the same as the dis-
carded ones, amplified and clothed in new names. The
additional complexity, due to the desire to be more

TENDENCIES OF MODERN PHYSICS 49

exact and more comprehensive, will do more than the
criticisms of its adversaries to hasten the time when
physicists will frankly avoid metaphysical explana-
tions and start from experimental axioms.

In order to be exact when defining this new idea of
the atom, I shall quote again from JEther and Matter:
" The protion (or sub-atom) must therefore be in whole
or in part a nucleus of intrinsic strain in the ether, a
place at which the continuity of the medium has been
broken and cemented together again (to use a crude
but effective image) without accurately fitting the
parts, so that there is a residual strain all round the
place." So far this might almost be interpreted as
the specification for a vortex atom; but, since such a
type of strain fails to provide matter with electric
charges, he diverges at this point and considers the
" ultimate element of matter to be an electric charge
or nucleus of permanent ethereal strain instead of a
vortex ring."

When discussing these definitions, we should bear
constantly in mind that the chief, if not the only, pur-
pose of an atomic theory or of a mechanical model is
to create a picture, however crude, of the constitution
of matter. I can form absolutely no mental image of
such a kind of matter as Professor Larmor proposes,
and although I have discussed this new theory many
times with its supporters, I have never found them able
to give any clear and simple idea of such a strain; it

50 THE LIMITATIONS OF SCIENCE

is certainly unlike any that we have encountered in ex-
perimental mechanics or electricity. Let us strip the
definition of technical intricacies, of such words as
protions and ethereal electric strains, which have the
power of confusing the mind and of making us accept
statements we do not quite understand. In the first
place, Professor Larmor's hypothesis is merely an
evasion of the old atomic theory. His continuous, true
matter which has absolutely no mechanical attributes
and indeed none of any sort, except what he calls the
ability to be modified by an electric charge, seems to
me, as a substance, but very little removed from my
idea of mere extent or abstract geometrical space.
Sensible matter which consists of discontinuous varia-
tions of this true matter, not of a mechanical nature
but of what he calls electrical strains, is to me less
substantial than extent or space; for, as difficult as it
may be, I can form some idea of space and I can com-
municate this idea to others, but I can make no mental
picture of an electrical strain in a non-mechanical
plenum; and such a strain certainly does not impress
me as being matter as I know it. I shall now form
these ideas into a chain: space is substance; matter is
a variation or strain in substance; a strain is an elec-
tric charge ; an electric charge is matter ; matter is sub-
stance; therefore an electric charge and matter are
both space, unless I can be persuaded that a variation of
an entity can change its essence, which is absurd. This

TENDENCIES OF MODERN PHYSICS 51

is a rather complicated syllogism, so it is better to
reduce it to simpler terms, as follows : true matter is a
plenum ; by definition, a plenum is that which is full of
matter; therefore matter is true matter. Such reason-
ing should convince anyone that, no matter how we
may wrap up our logic, we cannot explain those things
which we must use as a means of explaining other
phenomena. The ordinary man expresses this by the
saying, we cannot lift ourselves by our own bootstraps.
Are not such hypotheses in the same class as perpetual
motion and squaring the circle?

But even on the scientific side, this hypothesis is not
satisfactory. Every theorist acknowledges that sci-
ence is founded ultimately on our sense perceptions,
and this fact should warn us that the attribute elec-
tricity is not a substance. The phrase, to electrify
matter, has a well-defined meaning, because we know,
by experience, that a body when rubbed exhibits a
force which was not evident previously. We also know
that we may select two different bodies, which will
each show this electric force but of such opposite
characteristics that their mere contact reduces the
whole force to zero. Our knowledge of electricity
comes only by this manifestation of electric force, so
that if electricity were a substance we are reduced to
this anomaly, that the addition of substance to sub-
stance may result in less substance. This attractive
force is the simple and fundamental fact in regard to

52 THE LIMITATIONS OF SCIENCE

electricity and it is not proper to avoid it by speculating
on matter in a state so special and so removed from
common experience as when it is radio-active or highly
vacuous. Now experience teaches us that matter added
to matter is always more matter; thus satisfying our
prime requisite for substance. This difference between
electricity and matter is sufficient to explain why the
term electrified matter is a real idea, and why material-
ized electricity means nothing. There is no more
justification for calling electricity a substance than there
is for doing the same thing for any other attribute of
matter, such as color or temperature. The simple fact
that matter appeals directly to our sense organs and
electricity does not should be srfficient to convince any-
one that our interpretation of jature, because of our
material and mental organization, must be based for
all time on a foundation of material substance and
not of electrical substance. The postulate of the ob-
jective existence of matter is a necessary hypothesis
and that of electricity is not. Is it to be supposed that,
because certain learned men find difficulty in explaining
some of the obscure actions of matter, the human race
is to cast aside an instinctive and universally accepted
axiom, any more readily than it will discard the idea
that the straight line is the shortest distance between
two points ; that parallel lines never intersect ; or that all
bodies require three, and only three, dimensions in
order to locate them; — because a few modern ge-

TENDENCIES OF MODERN PHYSICS 53

ometers choose to advance other and contradictory
postulates as axioms?

Let us now turn to some of the specific difficulties
of this new theory. In addition to many absurd prop-
erties ascribed to the old elastic solid ether, its chief
defects were, that it must, at the same time, have
friction and not have friction, and that it could not
account for electricity. If it had friction, then the
ether would absorb light and heat energy, and the mo-
tion of bodies through it would affect the properties of
light in a manner which could be detected; both of
these have been found to be contrary to experience.
On the other hand, the ether must have friction to
permit the communication of atomic vibrations to it.
To escape these dilemmas, Professor Larmor supposes
the electro-magnetic ether to be without mechanical
friction and so to remain quiescent when any body
moves through it, but he apparently forgot that he had
assumed that the essence of substance is electricity.
If bodies are forms of electricity how can they move
through an electrical medium without disturbing it?
Since we have abandoned the theory that light and
heat are mechanical waves for the supposition that they
are electro-magnetic disturbances caused by periodic
variations of electric charges, the new ether must, in
some way, be modified by electric variations in order
to receive and to transmit light and heat. But anyone
can see we are just where we started. The electro-

54 THE LIMITATIONS OF SCIENCE

magnetic ether must have electro-magnetic friction, to
receive the electro-magnetic vibrations of the electric
atom and must be devoid of electro-magnetic friction
so as not to absorb electro-magnetic waves when in
transit. Again, he says the mechanical atom was de-
fective, in that it could not account for electricity, but
he also says that the electrical atom does not explain
cohesion, weight, and, I might add, any other me-
chanical property. Which shall we choose? Lastly,
not to prolong the discussion, just as the mechanical
ether and atom led us to such contradictory attributes
as enormous rigidity and inappreciable density, so the
electro-magnetic ether and atom require us to give the
latter an electric force whose magnitude is to that of
weight as ten raised to the forty-second power is to
one.

Temperamentally, Professor Thomson has little in
common with his colleague, Professor Larmor; as all
know, we owe to him a long series of most delicate and
profound experimental investigations in this field.
Like Lord Kelvin, he is usually content to construct a
model for each special phenomenon, and, as he is rather
indifferent whether these agree in operation, it is diffi-
cult to form any consistent idea of his theory. He
seems to regard matter as if it were a sort of building-
blocks which may be put together as fancy directs. His
best-known conception of matter and electricity is his
picture of an atom as a central sphere of uniformly

TENDENCIES OF MODERN PHYSICS 55

distributed positive electricity with points of negative
electricity so placed in it as to form the corners of
regular geometrical figures. He then calculates the
stability of each figure from the mutual attractions and
repulsions of the charges and supposes the chemical
elements to be conditioned by this stability. The
scheme is so frankly artificial and speculative that its
author can regard it only as an architect does his
sketch, as a symbol of a house. But in addition to his
pictorial representations of matter and phenomena,
which, if taken correctly, do not deceive anyone, he
subscribes to the hypothetical method and is a leader
in developing the electrical theory of matter.

If we now turn to a consideration of the ideas of
Professor Lorentz, we shall find a close agreement with
the hypothesis of Professor Larmor. We have been
led to the conception of electrons or protions, Professor
Lorentz says in his Theory of Electrons, by our de-
sire to understand the electrical properties of matter.
For, while we adopt the theory of Faraday and Max-
well that the space or electro-magnetic ether near an
electrically charged body is put in a certain state of
strain and never lose sight of this idea, yet we need
not form an image of it and really cannot say much
about it. In fact, these strains, as imagined by them,
cannot have a real existence without producing motion
in the ether, which is an impossible assumption. On
account of the difficulties into which such speculations

56 THE LIMITATIONS OF SCIENCE

lead us, there has been a tendency of late years to avoid
them altogether. But while this method is the safer one
and provides us with a set of correct formulae and laws,
yet we are compelled to introduce into these equations
unknown terms, called coefficients, which express the
individual properties of different kinds of ponderable
bodies. For example, the same magnetic force pro-
duces different magnetic effects in iron and copper. If
we wish to obtain a deeper insight into the properties of
matter, he says, we must not be satisfied with simply
introducing for each substance its special coefficient,
whose value is to be determined by experiment; we
must invent some hypothesis about the mechanism of
matter which causes such differences of behavior. It
is this necessity which has led us to the hypothesis of
the electron. He then defines these electrons as ex-
tremely small particles, charged with electricity, and
present in immense numbers in all ponderable bodies.
They are of two kinds, positive and negative, and are
free to move in conductors of electricity and bound
to points of equilibrium in non-conductors. Sometimes
he considers them to be rigid, and at other times as
deformable bodies. Their inertia, or mass, is, for the
most part, an effect of their electric charge, and the
negative electron is probably free electricity without
ponderable mass. Professor Lorentz assigns no
specific properties to the ether, but he is required to
assume that it can penetrate freely all parts of the

TENDENCIES OF MODERN PHYSICS 57

electron. It is evident that the philosophical ideas of
this theory are the same as those previously discussed.
We are driven in both to the supposition that the elec-
tron is a space modification of a universal medium and
that, in some way, neither electron nor ether is a ma-
terial substance, but a kind of transcendental entity
called electricity.

Of course we wish to obtain a deeper insight into the
properties of matter, and if we had discovered, or had
any means of discovering, a method to such a knowl-
edge, no amount of labor would be superfluous while
making an hypothesis. But we wish many impossible
things; we should like to be satisfied about the im-
mortality of the soul ; the causes and nature of life, and
a host of other problems. Now Professor Lorentz
says we know very little about the ether and the nature
of matter, and by very little, he means we know noth-
ing. What advantage, then, does he propose, when he
says: Come, let us invent something about these un-
knowable things, let us make an hypothesis that we
may seem to obtain a deeper insight into the mysteries
of nature ? He knows that the atom of iron is as mys-
terious as a ton of that substance, and that he does
nothing to explain the nature of iron by giving imagi-
nary properties to a sub-atom of iron ; he is aware that
he has not touched the reason why iron differs from
copper, and he ought to know that, by calling this sub-
atom a particle of electricity, he has only added con-

58 THE LIMITATIONS OF SCIENCE

fusion to our ignorance. What would he say of a
biologist who, growing tired of describing forms of
life which he can handle, gave the habits and appear-
ance of marine animals living beyond the reach of his
dredging nets? The security of experimental science
rests on the belief that, for the honor of science, no
one will tamper with what he has actually observed.
Why should more leniency be granted the theorist,
why should he be allowed to mix fact and fancy, law
and hypothesis, as he chooses, and not be called to ac-
count? It is just this restraint, this distinguishing
between what we know and what we desire, that con-
stitutes the value of science as a discipline of the in-
tellect ; and in the exercise of this restraint lies our in-
tellectual integrity. The gospel of science, for it has
one as truly as has religion, may be summed up in the
words of Goethe: " in restraint first shows himself the
master." What has it come to, when we can pass over
such false methods with a shrug? Huxley spent his
life, in season and out of season, waging battle with
bishops and laymen to convince them that religious
belief and religious theory must square with objective
fact. And he assured them that men of science could
provide a foundation of truth, and would not impose a
false one, so that all men might know and have a ra-
tional basis of life and belief. And how have we kept
the faith? We have given with equal emphasis our
speculations and our observations. Nor can Professor

TENDENCIES OF MODERN PHYSICS 59

Lorentz say he has kept in the certain path because he
has warned us in the beginning of his treatise that he
is dealing with glittering hypothesis. He takes all the
force out of the warning by using his genius to overlay
his speculations with a specious appearance of reality.
Let him try the opposite plan and actually convince a
class of students and educated men generally that his
hypothesis does not, and cannot, give any real insight
into the actual properties of matter, that he is talking in
a Pickwickian sense, and how much serious attention
would he attract? No, the world still believes in the
restraint of men of science and in their boast that they
will submit our vague longings to the test of experi-
ence. And it will be a bad day for science if this
belief is destroyed.

Nor is it proper to adopt an attitude of indifference
to these hypotheses as many experimentalists do, to
pass them by with a shrug or with the statement that
they cause little harm to the growth of science, how-
ever little they may aid it. If science were merely a
mental gymnastics, this indifference would be well
enough, but science is increasingly considered to be a
guide to conduct. We have no right to approve the
intellectual carelessness which has been so vividly ex-
pressed by M. Poincare in the preface to his Theorie
de la Lumttre: " It matters little to us whether the
ether really exists; that is the business of the meta-
physician to find out ; the essential thing for us is that

60 THE LIMITATIONS OF SCIENCE

everything acts as if it existed [?] and that this
hypothesis is convenient in explaining phenomena.
After all, have we any other reason for believing in the
existence of material objects? Is not that belief also
a convenient hypothesis; only we shall never cease to
make it, meanwhile the time will come, without doubt,
when the ether will be rejected as useless." Both ma-
terial objects and the ether may be only hypotheses, or
rather our knowledge of them is relative, but not in
the same way; the existence of material objects is
based on direct experience and the existence of the
ether is not. However we may argue, the objective
reality of matter is a necessary idea, fixed in our minds
and not to be dislodged.

Criticism is now often directed against the older
atomic theory because a given form of it no longer
accords with phenomena which have been lately dis-
covered. And it should be borne in mind that this new
theory of electrons has been developed with the main
purpose of supporting the atomic theory and making it
agree with our new knowledge of electricity. Thus
Professor Rutherford has recently performed a beau-
tiful experiment by which he detects electrically a por-
tion of helium gas, which he calculates to be of the
dimensions of a chemical atom. Here, he says, we
have at last an actual experimental proof of the reality
of the chemical atom. Does not this experiment show
just the reverse? The idea underlying all atomic

TENDENCIES OF MODERN PHYSICS 61

theories is that the indivisible unit of matter is so small
that it can be dealt with experimentally and mathe-
matically in aggregates only. So when he devises an
apparatus so delicate as to detect the action of a single
particle the size of the so-called chemical atom, he
forces us to adopt for the real atom a smaller unit
whose individual variations will be beneath our obser-
vation. The unit of matter becomes just one degree
further removed from matter as we know it. Instead
of squaring our hypotheses with the sensible proper-
ties of matter, we may thus more easily make matter a
purely transcendental quantity which we create ac-
cording to our own imaginations. Would it not be bet-
ter frankly to say the material universe is merely a
world of ideas, an embodiment of intangible motion,
energy, and electricity, rather than to keep up the
fiction that the electron is the ultimate unit of sub-
stance ?

Apparently the chemical molecule is a well-defined
point in the regular divisibility of matter where cer-
tain physical apparatus, as the balance, fail to record
variations in so small a body; but, by the use of
chemical appliances, we are able to take note of still
smaller masses, which have been named the atoms of
the chemical molecules. At this point these methods
become too gross, and we next have recourse to the
electrification of the gaseous atoms by the X-rays or
by radium, and can then detect variations in these

62 THE LIMITATIONS OF SCIENCE

particles by means of the electroscope. These smaller
portions of matter are called electrons or sub-atoms,
and for the time being we have rested here. But would
anyone say that new methods of analysis and new
apparatus of registration are an impossibility, and
that the electron will not in future be divided? On
the other side of the series the mote, dancing in the
sunbeam and disappearing when the light fails it, is an
indivisible atom to the unskilled man deprived of sensi-
tive apparatus. The fact is, the atom as an objective
unit of matter has no existence; we name that portion
of matter an atom when we have reached a limit of
appreciation of matter by our most sensitive apparatus.
If these fundamental and irrational assumptions of
plenum and sub-atom be once granted, then a me-
chanical explanation of many of the phenomena of na-
ture follows logically. But this is also true if we
postulate that matter is composed of the four es-
sences,— earth, air, fire, and water; and one has only to
recall the success of Descartes with his three elements.
The question is, are the postulates true? If we can-
not verify them by experiment, then science should
reject them. On this criterion the sub-atom is as
vulnerable as any other postulate. The conclusions,
deduced, may give a truly mechanical explanation ; for,
in spite of denying the existence of matter in the be-
ginning, the substitute electricity is at once endowed
with all the essential characteristics of the discarded

TENDENCIES OF MODERN PHYSICS 63

matter, such as inertia, conservation, gravitational at-
traction, extent, etc. Certain additional properties
add to its conquests, since, by splitting up the atoms, a
new set of pawns is available to the players of this
game of probability and chance.

The diversity of the chemical elements may be said
to result from the various stable combinations which
the sub-atoms may be made to assume. Professor
Rutherford developed his ingenious theory of radio-
activity by supposing certain elements to be in a state of
comparatively unstable equilibrium. A definite pro-
portion of their atoms explodes continuously, reduc-
ing the atomic weight of the parent body, and supply-
ing the spontaneous energy noted experimentally. This
process continues until a stable form is reached. But
does he not forget that one of the triumphs of the old
atomic theory, a proof that the chemical atom could
never be divided into sub-atoms, was that when an un-
stable compound, like gunpowder, exploded, the con-
stituents were found to be stable chemical atoms?

The phenomena of electricity are naturally the main
problems attacked. A current of electricity in this new
hypothesis becomes the flow of immaterial particles
of electricity in a metal conduit, carrying with them
their energy of motion. In non-conductors, like glass,
they may be heaped up into an excess of positive or
negative to provide a picture of the free charges on such
substances. Radiant light, heat, and electricity are

64 THE LIMITATIONS OF SCIENCE

the periodic disturbances produced in the plenum by the
oscillatory motions of the same particles about fixed
centers. These are said to be useful ideas and clear
explanations. But are they? Have we accomplished
anything more than to reaffirm the statement that a
current of electricity under certain conditions flows
through a wire, when we say a stream of charged par-
ticles moves through the wire? In the first place, we
create the particles, and next endow them with an
occult power of motion. Again, when zinc and cop-
per are placed in contact and separated, the zinc be-
comes positively charged with electricity, the copper
with negative, and the two attract each other. Do we
learn anything more when we affirm that an excess of
positive electrical particles passes into the zinc and
negative ones into the copper ? Why should they act so ?
In both cases we have merely stated an unknowable
cause in different words. The law remains the same
whether we say electricity or electrical particle, and
the former term expresses less pretense of knowledge.
Far more significant, and less justifiable even, is the
attempt to explain the mass of a body as an attribute of
€lectricity. Mathematical analysis shows that an elec-
trically charged body, moving with great velocity, has
a resistance to motion apparently greater than when
not so charged. Now, they say, continually diminish
the ponderable mass of the body and maintain the elec-
tric charge constant ; the electro-magnetic mass, as this

TENDENCIES OF MODERN PHYSICS 65

effect of electricity is called, becomes proportionately
greater and greater. Continue this process indefinitely,
and at last all the matter is gone, and there remains a
free electric charge, an immaterial point of electricity,
moving and possessing inertia or mass. And just here
lies the greatest danger of all such hypothesis — a total
confusion of fact and fancy. In the first place, it is
not even based on experience, since the most rapidly
moving bodies of a sensible size have a velocity far
too little to make this effect noticeable. But, what
is more important, it is a method of thought to be used
with the utmost caution even in experimental processes.
The warning against such extra-polation is metaphor-
ically displayed in every physical laboratory. How we
would scorn the unscientific conclusions of the meta-
physicist who reasoned in the same way ! Let us
imagine one saying that goodness is an attribute of
small, as well as of large men; now diminish the size
of a man and let his quality of goodness remain con-
stant, then we shall have an entity, concrete goodness,
left when the man shrinks to nothing. It is not neces-
sary to use such an absurd example, as a parallel case
exists in physical phenomena. A sphere, moving in
a fluid, experiences a like increase in apparent mass,
due to the necessity of imparting energy to the fluid.
Now decrease continually the density or mass of the
body and maintain its volume and velocity constant;
the hydrodynamic mass becomes proportionately

66 THE LIMITATIONS OF SCIENCE

greater. Continue this process until the matter is all
gone, and there is left a sphere of something with an
apparent mass still moving through the fluid. Will
it not be difficult to persuade anyone that the something
moving did not vanish simultaneously with the ma-
terial sphere — that the attribute did not vanish with
the entity? It will be just as hard to convince the
future scientist, when the vogue of the electrical theory
departs, that an electrical charge remains after the elec-
trified matter is reasoned away. Such ideas leave us
in the same foolish state as the hunters of the Snark,
who, after incredible labors, came to the place where
a Snark should be, and found it was a Boojum which
vanished silently away.

If I am correct in believing the fallacy to lie in try-
ing to explain natural laws, it is not pertinent to
inquire further into the working of this electrical
hypothesis. The essential point is whether physics has
anything to do with the nature of matter and elec-
tricity. Atoms and ethers of any kind are metaphys-
ical creations; the mechanical models built on such an
unsubstantial foundation require a god to set them go-
ing, and are, at best, an ineffectual means of describing
phenomena previously observed, and not finger-posts
to new discoveries.

The claim, that such arguments as this are ineffectual
criticism because they tend to destroy the scientific
method most used and offer nothing better in its stead,

TENDENCIES OF MODERN PHYSICS 67

is frequently made by scientific theorists who recognize
the artificiality of their hypotheses but who feel that, in
some way, they tend to good. They forget that the
growth of science has always been largely due to the
discovery and the elimination of error. If we wish to
make a garden, the first necessity is to clear away the
weeds, and the same is true of science; it is as impor-
tant to know what is wrong as what is right. But
even this claim is not correct, the better method is
known and is in use. Have they forgotten the work of
Galileo, of Newton, of Franklin, and of many others,
who employed the abstractive method, or, at least, kept
their hypotheses well in the background? Nor is it
difficult, if one studies the history of physics, to out-
line the basis of a method in harmony with my ideas,
as I shall do in a later chapter.

Nothing has been more convincing to me of the
advantages of the abstractive over the hypothetical
method than a study of Descartes's Principia Naturae.
Modern theorists have acknowledged their debt to
him ; how great is this obligation can be seen from the
discussion of Descartes's system which follows. A
comparison of his postulates and conclusions with
those of our modern theory shows them to be almost
identical, if we change his antiquated knowledge and
his discarded metaphysical language into modern
terminology. And lastly we should compare Descartes
with modern physicists ; his knowledge of the phenom-

68

THE LIMITATIONS OF SCIENCE

ena and laws of nature is insignificant, so great has
been our progress in this respect, but as a metaphys-
icist he is still the master of modern scientific hypoth-
esis, so little has been accomplished in that field in two
hundred years.

CHAPTER III

DESCARTES AND HIS INFLUENCE ON
RECENT SCIENCE

De s'6garer avec m^thode. — MICHBLET.

IF it be true that the permanent advances made in
science have been the result of observing phenomena
and of classifying them in laws which are as often as
possible to be expressed by mathematical formulae ; and
if it be also true that we have persisted in the effort
to explain the causes of phenomena without really
advancing knowledge; then it will be most useful to
compare our present state with that of an earlier time.
For this purpose, I have chosen to sketch the scientific
system of Descartes. In the first place, there can be
no doubt as to the enormous increase in our positive
knowledge of phenomena and natural laws since his
time; the difference is so great that there is no need
to dwell on it. And yet, if we consider the history of
Descartes's hypothetical cosmogony, we learn that it
was discarded only to have a revival at the present
time. The advantage of reviewing the system of Des-
cartes is all the greater because it seems apparent that
many of those who are quoting his authority have not

an accurate knowledge of what he taught.

69

70 THE LIMITATIONS OF SCIENCE

So far as I can see the hypothetical method has its
most illustrious example in Descartes, and instead of
aiding us to gain real and clear ideas, he has burdened
science with useless and complicated metaphysical sys-
tems. Instead of being a symptom of power, the reluc-
tance to recognize the limits of science comes rather
from a certain intellectual cowardice which refuses to
acknowledge the truth, that we cannot attain any knowl-
edge of things themselves but only of their attributes
as they affect our senses. If we really face the ques-
tion; strip our scientific hypotheses of their technical
phraseology and complex logic, and try to get a clear
and simple idea of what they mean, we find that we
have been deceiving ourselves. In the first place, we
use words, which ordinarily convey definite ideas, in a
sense purely symbolical, and then confuse the image
and the reality. For example, when we define space
or the ether as a perfect fluid, we deceive ourselves
into believing that we have gained a clearer idea of
space by applying to it a term which signifies the
mobility of matter. But this attribute can be applied
only to a material fluid whose change of position may
be measured, and such a fluid appeals to us as some-
thing essentially different from immaterial space. Nor
do we overcome this difficulty by qualifying space as
a perfect fluid; any fluid is perfect which satisfies the
laws of its nature, and we practice deception when we
inject the ethical meaning of perfect, as being some-

INFLUENCE ON RECENT SCIENCE 71

thing above ordinary criticism, into the scientific
definition of a fluid. We have also constructed a sym-
bolic language, called mathematical analysis, whose
characters and terms are so removed from ordinary
speech that it imposes on our minds an impression of
not being limited by the bounds of logic. Thus, if we
derive a mathematical formula for the quantity of
heat or electrical energy which passes through free
space, we deceive ourselves by thinking that we have
an expression not only for a quantity of energy, but
that also we have in some unaccountable way gained
a knowledge of the nature of energy and of the at-
tributes of space. And we slur over the scientific
axiom, that since these mathematical symbols did not
express in the beginning something concrete, they can-
not after any manipulation give a result which is other
than imaginative. Again, we postulate some entity
such as matter, energy, or electricity, as a foundation
and attempt to derive logically from it all the phe-
nomena of nature, and ignore the plain fact that
nature, as a whole, reveals itself to us as a succession
of events, either not connected at all in a logical se-
quence of cause and effect, or at least in such an intri-
cate tangle as to defy our powers of analysis.

During the last two decades, there have been dis-
covered an unusually large number of physical phe-
nomena, and it is no exaggeration to say that we have
mastered them with surprising rapidity and with great

72 THE LIMITATIONS OF SCIENCE

ingenuity. At the same time we have turned to these
new manifestations of matter and energy with the
hope that in them we have at last found the materials
for a new and lasting scientific cosmogony. But the
edifice differs in appearance only from that built
long ago by Descartes; and the materials in both
are the same, changed in name but not in sub-
stance.

By a scientific cosmogony, as distinguished from
revelation and from metaphysics, is here meant that
we first postulate an archetypal form of substance and
certain fundamental forces, few in number and in-
herent in this entity, and that then the universe, as it
now exists, follows as the result of the continued
action of these forces on this substance. That is, the
state of the universe may be expressed at any time
subsequent to the initial action of the forces by a set
of mathematical or verbal formulae. And if we could
actually, as we can theoretically, reverse the action of
these forces in time and in direction, the primal
condition of the universe would again result. It is
furthermore postulated that this archetypal substance
existed originally in the form of minute particles,
separate from each other and exactly similar in char-
acter, and that the forces acting on these particles were
in such perfect balance that the total value of their
effect was zero. From some cause, generally unex-
plained, this balance was destroyed and, like a clock

INFLUENCE ON RECENT SCIENCE 73

when its pendulum has once been jogged, the panorama
of cosmical history unrolls itself inexorably. Thus
the universe becomes a sort of machine whose parts are
mechanically driven, not by some external motive force,
but by the mutual reactions of its parts, and so destined
in time to run down when this internal and available
energy shall have exhausted itself. And when we
speak of the universe, all that part of it designated
as living bodies and vital forces is to be included, be-
cause of the belief that they also can be considered as
ponderable masses subject to physical and chemical
forces.

As an original hypothesis the work of Lucretius is
of no consequence. In fact his atomic theory was
taken almost entirely from Democritus, and it was
rather by the vision of the poet than by the logical
analysis of the man of science that he developed these
ideas into a picture of the nature of our world. His
theory was, in brief, that the universe contained in an
otherwise empty space an indefinite number of indivis-
ible and immeasurably small particles, called atoms,
which differed only in size, position, and shape. These
atoms were indestructible and by their combination
and separation formed all natural bodies. The motion
of the atoms did not arise from external forces but
was an inherent property of their nature. With a com-
mon impulse, they all moved toward the center of the
universe, but in addition they possessed an individual

74 THE LIMITATIONS OF SCIENCE

power of irregular deflexion which introduced variety
in matter. By their union they formed bodies; and by
their impact and rebound they caused vortical motions
which now find expression in our term, energy. As an
explanation of natural phenomena the theory has no
value," as it originated long before the mathematical
laws of forces had been formulated or the phenomena
of matter had been accurately observed; but as a guide
to thought it has been the basis of most of the later
scientific theories. Gradually elaborated by Gassendi,
Newton, Boyle, Kant, Laplace, Dalton, and others,
this atomic theory is still the touchstone of modern
chemistry and physics.

Possibly the vastest consequence of the atomic
theory is the nebular hypothesis developed independ-
ently by Kant and Laplace. Essentially this theory
is a restatement of the ideas of Democritus and Lucre-
tius, yet the discovery by Newton of the mathematical
law of the force of gravitation permitted for the first
time a true scientific method. Thus, while they were
compelled to assume, as arbitrarily as did Lucretius, an
initial state of chaos when matter was scattered in
atomic masses throughout space, they nevertheless had
a cause when for any reason the original balance of
forces was disturbed, experimentally verified and
mathematically expressed, to account for the gradual
agglomeration of atoms into larger masses at definite
places, from the fact that any two masses of sensible

INFLUENCE ON RECENT SCIENCE 75

size were known to have a mutual attraction varying
inversely as the square of the distance between their
centers. The active attribute of matter, ruling and
guiding its motion, thus became independent of fancy
and subject to experimental verification. The nebular
hypothesis has remained more or less a fragment,
limited to the determination of the sizes, masses, and
positions of celestial bodies and systems. Neither Kant
nor Laplace, except for a discussion of temperatures,
included in their scheme of the evolution of inorganic
matter the causes of the complex forms and forces
of matter now observed on the earth or stars. Nor
beyond assuming that matter was determined by mass
and an inherent power of attraction, did they make any
attempt to explain how this occult force acted through
a distance. And from this simplified idea of matter
without variety and without complexity, they were
able to deduce mathematically and logically the idea of
the evolution of cosmical matter, from a condition of
primitive distribution, at least to its segregation into
cosmical systems: suns, planets, and satellites. And
if we remember that Kant approached the problem
from the standpoint of the metaphysician and Laplace
from that of the pure mathematician, we can readily
understand why they both were satisfied to take such an
abstract view of the universe, and also the simplicity
and the insufficiency of such a method. Astronomy is
the one science, because of the comparatively enormous

76 THE LIMITATIONS OF SCIENCE

magnitude of its units, which permits such an abstract
simplification of matter as to consider it merely in the
form of masses concentrated at mathematical points.
Where we deal with bodies measured in millions of
tons and with distances in millions of miles, such varia-
tions as are found in the laboratory sink into com-
parative insignificance and we can deal with averages
instead of particulars. On the whole their attempt was
a success since we can find few flaws in the general
conception of a nebular hypothesis, however we may
differ as to details. And just because the phenomena
discussed are so few in number and so general in char-
acter, there was not the need for supposititious causes
and fictitious attributes, provided we grant their initial
state of the universe and the first cause contributing to
irregularity and the beginning of motion. These pos-
tulates are of course entirely arbitrary and require
us to assume an existence previous to time, since time
has no meaning in a universe which is everywhere in a
state of perfect equilibrium and rest. Undoubtedly
the reason why this hypothesis persists in its principal
features to the present time, in spite of constant
attacks, is just because its authors exercised self-
restraint, holding to general laws and avoiding specific
details. Some form of cosmical evolution is now gen-
erally granted and the heavens are swept by gigantic
telescopes which linger on the nebulae, in the hope that
accurate measurement will show that these apparently

INFLUENCE ON RECENT SCIENCE 77

chaotic masses are slowly changing into the more stable
form of stellar systems.

Side by side with the belief in atoms, separated from
each other in empty space, had grown up the directly
contrary idea that substance is continuous and space
is a plenum. This doctrine permits us to make no
essential difference between space and matter. Space
becomes a continuous substance unvaried, and so im-
perceptible to our senses, while matter is merely a
localized variation of this same substance of such a
nature as to make it perceptible. And it is significant
of these two systems, that although they begin with
contradictory premises, they both lead to the same
conclusions after apparently rigorous deductions.

The doctrine of continuity owes its rise to Hera-
clitus and, amongst the Greeks, was most highly de-
veloped by Aristotle. They announced this postulate
because the notion that a body can attract another
through an intervening vacuum and cause it to move
introduces an occult or inexplicable idea. Our experi-
ence teaches us that motion results only from a push or
impact between bodies actually in contact. But it is
quite evident, that in refusing to accept a force which
acts contrary to our experience, which all goes to show
that a material link is necessary to produce motion
between bodies, they fell into as serious a difficulty,
for they were compelled to create an occult substance
to serve as the material link between bodies, and occult

78 THE LIMITATIONS OF SCIENCE

variations in it for the bodies themselves. As explana-
tions of phenomena both ideas are occult, but not to
the same degree. We know, for a fact, that there is
an attractive force between bodies of sensible size,
although we cannot explain its cause, and we can
in our imaginations transfer a like form to bodies of
an insensible size with some probability of truth. But
the postulation of a plenum of continuous substance and
of variations in it, which affect us as matter, is wholly
occult since we have no experience from sensible mat-
ter to guide us ; in fact, both plenum and its variations
always have characteristics assigned to them directly
contrary to the evidence of our senses.

The history of scientific theory is a record of the
conflict between these rival ideas of continuity and dis-
continuity of substance. While the atomistic school
has frequently had the advantage, since the time of
Descartes the doctrine of the continuity of matter has
persisted in some form, and at the present time is
again established as the basis of physical theory.
Nevertheless, the cosmical system as deduced by Des-
cartes from this hypothesis of a plenum has suffered
shipwreck and comparatively few think it profitable to
study it in detail. Before we adopt his principles and
discard his conclusions, it is at least advisable to see
whether his errors lie in the principles themselves or
in the inability of Descartes to derive true conclusions
from correct principles. Fortunately, we have in the

INFLUENCE ON RECENT SCIENCE 79

Disc ours de la Methode, in the Principia Naturae, and
in the many letters of Descartes an unusually com-
plete record of his principles, his method, and his con-
clusions.

In character, training, and opportunities, few if any
philosophers have been better equipped for their task
than Descartes. As has been said of him, " he is a
type of that spirit of science to which erudition and all
the heritage of the past seem but elegant trifling." He
believed and acted on the opinion that no scientific
knowledge is attainable unless men doubt ; unless they
put aside authority and rely on their own experience.

Descartes has in his Principia Naturae set forth
with specious simplicity the causes, laws, and the phe-
nomena of the universe as he finds them. Geometry
is to be the ruler or at least the vicegerent, and no
substance will be discussed except such as may be
divided, figured, and moved according to the laws
which geometers hold to govern quantity, nor will
any proposition be considered proved unless it has
been deduced with such evidence as would suffice for a
mathematical demonstration. With vexatious incon-
sistency, he then destroys the force of this admirable
introduction by carefully warning us not to consider
his premises true or his conclusions conformable to
fact, since his scheme is really an hypothesis or sup-
position as to what might be and not what is. This
caution is usually attributed to his fear lest he should

80 THE LIMITATIONS OF SCIENCE

arouse the hostility of the Church and suffer a penalty
similar to that which had just overwhelmed Galileo.
His own plea was that he valued peace more than the
spread of his opinions and also that he had always
been a good Catholic and bowed to the authority of
the Church, even when its decrees were contrary to his
reason. But it is also possible that doubts arose in
his own mind as his system developed and that when
he found it necessary to compromise with the rigorous
principles he had announced, he tried to disarm criti-
cism by the plea that after all he was really concerned
only with a fictitious world.

At all events, while the laws of the heavens were
under consideration, he permitted this veil of unreality
to remain very thin; for he knew the Church wisely
allowed considerable latitude of thought concerning
those regions of space which apparently contained no
subjects to Catholicism, and he felt scientifically safe
in a field where verification by experiment was only
beginning to be advocated. But the case was altered
when he came to discuss terrestrial laws and phe-
nomena, for here both Church and experience held
sway and must be conciliated. In this field Descartes,-
mindful probably of both of these perils, relied on the
same hypothesis, but to placate the Church he insisted
that it was to be understood only in a most figurative
sense, because we know that God created the earth,
finished and perfect, as revealed in the Mosaic account;

INFLUENCE ON RECENT SCIENCE 81

and to disarm scientific criticism, his postulates he de-
clared to be fictions, but in some way without depart-
ing from correct mathematical deductions, his conclu-
sions were similar to experience.

It would be difficult to understand from these con-
tradictory statements what was Descartes's real opinion
of his scheme. But he has this answer in another part
of his Principia, an answer which carries conviction.
Since we have an idea of perfection, we have also
the certainty of the existence of God, or an all-perfect
Being. And because this God is justice itself, if the
principles laid down by him are evident, if the con-
sequences are founded on mathematical laws, and if
the deductions agree with experience, it would be
ascribing injustice to God to believe that the causes of
the effects are false. Now observe how far Descartes
believes he has fulfilled these conditions: " je ne pense
pas qu'on doive recevoir d'autres principes en la
Physique, ni mesme qu'on ait raison d'en souhaiter
d'autres, que ceux qui sont icy expliquez."

Descartes has recorded for us how he arrived at the
postulates from which he developed his natural laws.
Having previously laid aside preconceived ideas, he
found that to doubt is the first and only means of
knowledge; we can doubt the existence of everything
except that which doubts, therefore that which doubts
or thinks, exists. Whence he derives the principle
that our thoughts and the things we have an idea of,

82 THE LIMITATIONS OF SCIENCE

are real and objective to us. However, by such a proc-
ess we do not obtain a knowledge of things themselves,
but only of their attributes. Hence, the final reality
must be those attributes which are inseparable from our
conception of all phenomena, and there should be
some one essential attribute which may be used to
designate things in general. Thus hardness, while it is
an attribute, is not essential, for a body moving at
the same speed as ourselves does not give us the sensa-
tion of hardness. After careful consideration he found
that simple extent in length, breadth, and thickness is
the one attribute common and essential to all mat-
ter. Not only is this true, but the extent of matter is
identical with the extent of space : " The same extent in
length, breadth, and thickness, which constitutes space,
constitutes a body; and the difference between them
lies in this, that we attribute to a body a particular and
limited extent which changes position with the body as
it moves, and that we attribute to space an extent so
general and so vague that when we remove from a cer-
tain space the body which occupied it we do not think
we have transported the extent with it ; meanwhile the
extent of the body remains of the same size, of the
same figure, and has changed position with respect to
the body only as we determine position by other
bodies."

The reason, according to Descartes, why we have
been led to believe that substance is different from

INFLUENCE ON RECENT SCIENCE 83

space, and that it consists of atoms either in a vacuum
or in a non-material medium, is the property known as
expansion and contraction. As an illustration, he in-
stances a sponge, which changes size but not character
when its pores are filled with water. Here we have a
change of size from the change of position of sponge-
matter, the two kinds being of the same essence. So
the change of volume of any body is due to a change
of position of matter-substance produced by a change
of space-substance, which also are essentially the same
and differ only in accidental qualities.

Furthermore, since we cannot imagine a space so
great that there cannot be a greater, or so small that
it cannot be divided, then as matter is essentially the
same as space, it too must be indefinitely great in ex-
tent and indefinitely divisible.

This is a very complicated way of getting back to
one's starting point. He says first, that substance is
extension and then that space is extension, but since
extension is everywhere and space is nowhere vacuous,
a body is a body.

Having discussed the nature of matter in general,
he then finds that diversity in matter and also its dif-
ferentiation from space can consist only in variations
of position and motion of small parts of space which
are themselves exactly similar. As corollaries to this
definition, it follows that there can be neither absolute
position nor absolute motion. To determine the posi-

84 THE LIMITATIONS OF SCIENCE

tion and motion of a body we must use some other body
as a point of reference. But in this system, all space is
capable of motion and, in fact, is in rapid motion, and
with no possible stationary reference point all positions
and motions are merely relative. This question of abso-
lute motion has been the subject of much discussion in
the last few years, as certain phenomena of light re-
quire that granting a luminiferous ether, it must be
absolutely stationary. And experiments have been de-
vised to determine whether we can measure the absolute
velocity of matter with respect to the ether. As in all
experiments involving the ether, the results are
nugatory.

Nor, in the theory of Descartes, can there be action
at a distance, for matter is continuous and all motion
is the result of a push or impact. Motion, therefore,
he defines as the transference of a part of matter or of
a body from the neighborhood of those which touch it
immediately, and which we consider at rest, to the
neighborhood of others. And since all space is full
of matter, or rather is matter, each body is so fashioned
that it can never occupy a greater or a less space, nor
can any other body occupy the space while it is there;
therefore if a body move to another position, it must
displace an occupant; and this, another; so that every
motion results in a closed ring of moved bodies, each
finally occupying the space left by its previous occu-
pant.

INFLUENCE ON RECENT SCIENCE 85

These postulates of Descartes, that space is a plenum
and motion the result of an impact, required him to
oppose such theorists as Gassendi who were advocat-
ing the atomic theory and an occult attractive force in
matter as its cause of motion. It thus became of prime
importance for him to formulate laws of impact and
motion. This was an extremely difficult problem, espe-
cially so as the available knowledge of the phenomena
of impact and motion was very deficient and, such
as it was, indicated that friction produced an uncom-
pensated diminution of velocity. With great care and
in minute detail, he announced such laws as would, in
his opinion, maintain constant the total quantity of
motion or momentum of the universe in spite of fric-
tion. That is, such laws as would transfer the loss of
motion of one body by impact to an equivalent increase
of another. These laws are:

God in his omnipotence created matter with motion
and rest.

If a body move twice as fast as another twice as
great, the quantity of motion of the two is the
same.

All bodies, which move, tend to move in straight
lines and can change their direction only by encounter-
ing others.

If a moving body strike another of greater mo-
mentum (plus fort) than itself, it loses none of its
motion and if it strikes another with a less momentum

86 THE LIMITATIONS OF SCIENCE

(plus foible) which it can move, it loses as much mo-
tion as it gives to the other.

Then seven other laws of impact of less importance
follow, which it is not necessary to quote, as Huygens
later showed that all eight were, for the most part,
erroneous.

In sprte of the fact that Descartes, without verifica-
tion, invented the laws of motion of bodies and of
their impact, yet we must recognize that he sought
and found one of the great scientific principles ; that un-
less the universe is tending to a state of uniform rest
through dissipation of motion by friction, some active
property of matter must be conservative in addition to
its quantity. While his particular law of the con-
servation of momentum was erroneous, yet it is un-
doubtedly the progenitor of the law finally enunciated
by von Helmholtz and now generally accepted, that the
total quantity of energy remains constant.

With these general principles settled, the nature of
space and matter, and its conservation of quantity and
action, we shall defer criticism and describe the vari-
ous kinds and phenomena of matter as nearly as pos-
sible in the sense of Descartes.

We are to suppose that, in the beginning of time,
God divided all space or substance into equal parts,
which, contrary to the chaos pictured by poets and
philosophers, had been previously in perfect uniformity
and rest. Out of these primordial particles of space

INFLUENCE ON RECENT SCIENCE 87

were fashioned all the small constituent parts of mat-
ter which now compose not only all terrestrial and
celestial bodies but also the interstellar spaces. While
we do not know the actual size of these particles, as
they were originally or as they are now after they have
suffered changes, some growing smaller by division and
others larger by the accretion of many into one from
causes which will be described later; yet their first
size must have been the exact average of all the con-
stituent particles now comprising the universe. God
also caused these primordial particles to move, and
with equal force in two diverse fashions : each to rotate
about its own center to form the constituent elements
of the interstellar spaces, or, as Descartes calls them,
the fluid body of the heavens, and many to revolve to-
gether about common axes, creating vortices whose
centers are the nuclei of the sun and fixed stars in the
heavens. The velocity of this uniform motion was the
average of all the diverse motions existing now,1 so
that the quantity of motion or momentum has remained
constant throughout all time.

Although these primordial particles were of equal
size and motion, they could not have been spherical in
shape, since a pile of spheres does not fill a space and
there must be no vacuum. But whatever their initial
figure may have been, they have in the course of time
become exact spheres. The cause of this change of
shape is, that the force, by which they were first moved,

88 THE LIMITATIONS OF SCIENCE

was sufficiently great to separate them from each other,
and was therefore great enough to knock off their
angular edges and corners because of the concussions
of their future impacts. The result of such a constant
attrition is well known to be that the body approaches
the figure of a sphere, just as the pebble on the seashore
becomes round from the grinding of the waves and its
fellows.

This action gives rise to three forrns of matter which
constitute the universe, and whose various forms of ag-
gregation and proportions of mixture, with their re-
sulting varieties of motion, account for all the diversi-
fied kinds and attributes of matter and space.

The first kind of matter is the cosmic dust of attri-
tion or the little fragments resulting from the above
mentioned collisions. They are excessively small and
have acquired enormous velocities, because the larger
particles, from which they were split off, have con-
strained them to move faster than themselves through
the narrow and tortuous paths formed by their inter-
stices, just as air in a whistle moves the faster, the
smaller the orifice from which it issues. They are
also so numerous, so various in size, and so irregular
of shape, that there are always sufficient of them ready
to hand to fill exactly any space which might other-
wise be left vacuous by the arrangement and motion of
their parent sphericules.

The second elementary kind includes all the rest of

INFLUENCE ON RECENT SCIENCE 89

matter and space, whose least parts are spheres and
smaller than any body we know, but they are much
larger than matter of the first kind.

There is also a third kind of matter formed by con-
glomerate masses of the other two kinds, which have
become so linked and interlaced together as to be in-
separable, at least by human means. The pores of
these masses are filled with the spheres of the second
kind and the fragments of the first kind.

The first kind of matter forms the sun and the fixed
stars ; the second kind is the material for the so-called
empty spaces of the heavens ; and the third is the basis
of the diversified bodies composing the earth, the
planets, and the comets.

As stated before, this elementary matter was origi-
nally endowed with two kinds of motion: the rotation
of each particle about its own axis and the revolution
of many about a common axis, forming a vortex or
whirlpool. Descartes then portions out the heavens
so that the axis of a vortex will pass through the center
of each star, including the sun. The outer limit of
each vortex extends so far in every direction as to
touch the confines of each of the neighboring star-
vortices ; in this manner all space is occupied by them,
rushing about their several axes with a velocity de-
creasing as the distance from the axis increases. It
is naturally a problem of great intricacy to place these
immense vortices so that they will not interfere with

90 THE LIMITATIONS OF SCIENCE

each other's motion, and he spends much labor and
great ingenuity in describing the possible inclinations
of axes and directions of motion of such a system,
but not satisfactorily!

The sun and stars, as they now are, were not created
contemporaneously with the vortices but were a gradual
growth from them. When more dust of attrition was
ground from the rotating matter of a vortex than was
sufficient to fill the interstices of this matter, it began
to flow toward the center and along the axis of the
vortex, gradually forming there a nucleus, ires subtil et
trts liquide; namely, a luminous star. According to
Descartes's idea, which in spite of his contempt for au-
thority he borrowed from Aristotle and the schoolmen,
these stellar masses, consisting of matter of the first
kind exclusively, are pure celestial fire, which is thus
an entity and of all things the most fluid and so vio-
lently agitated as to be able to disintegrate the most
solid bodies. Fire of itself does not need to be replen-
ished but only seems to need replenishment, because the
particles of a terrestrial fire are constantly flying
away and being dissipated, and so must be renewed by
others derived from the pores of gross combustible
bodies and of air; but in celestial fires there is no need
of external replenishment because the steady stream
of fire-substance, flowing of its own accord to the
center of the vortex, maintains a constant supply.
Alas, that the spectroscope should show us that our sun

INFLUENCE ON RECENT SCIENCE 91

and the stars are not this pure elemental fire but merely
heated matter of a terrestrial nature. Such havoc does
experiment play with a grandiose hypothesis. We
may, however, pass over difficulties impossible to have
been foreseen by Descartes, since many men of science
still think an hypothesis valuable if it escapes con-
temporaneous troubles, and of these there are always
an abundance.

Between these star centers lie the great interstellar
spaces which some believe to be vacuous but which
Descartes supposes are packed with matter of the sec-
ond kind. The interstices, which would otherwise
exist between these little spheres, are filled with matter
of the first kind. And all together they rush around
common axes to form the vast heavenly vortices with
a velocity enormous but less than that of the celestial
fire of the stars.

This accounts for all the universe except those parts
occupied by terrestrial and planetary bodies, which
are composed mostly of matter of the third kind. The
constituent parts of this kind of matter, as stated be-
fore, consist of agglomerated masses of the other two
kinds, whose pores are filled with matter of the first
and second kinds still in their simple state. Accord-
ing to the relative proportions and various arrange-
ments of these three constituents, we distinguish all the
different bodies which are classed as solids, liquids,
and gases. Of these, solid bodies are those whose least

92 THE LIMITATIONS OF SCIENCE

parts are made of closely packed and intricately ar-
ranged particles, which can move with respect to each
other but very slightly, if at all. The spaces between
the constituent parts of a liquid are greater and contain
a larger proportion of the subtle elements than solids ;
while gases have their particles so separated that they
approach fire in their freedom of motion. As he
quaintly puts it : a body is a fluid when it is divided in
many little parts which are free to move separately in
various ways, and it is hard when all its parts are so
interlaced that there is no action capable of separating
them. Cohesion in hard bodies is caused by the lack
of motion of their constituent parts, for no cement
could be harder than rest, which is the quality the most
contrary to motion. He does not tell us how to inter-
lace and twist a number of spheres and irregular
fragments together, so as to form compact and in-
extricable units of matter. To anyone but a great
philosopher they would remain ropes of sand.

Descartes had spent much time investigating the ex-
perimental laws and phenomena of light and with
notable success. One of his greatest ambitions was
evidently to explain the nature of light and the mode of
its transmission, for he discusses these in great detail
in his Prlndpia and refers to his solution of the prob-
lem constantly in his letters with much complacency.

As noted, the substance of the sun and stars is like
fire in respect to its motions; for there is nothing

INFLUENCE ON RECENT SCIENCE 93

more agitated than fire which can disintegrate even
solid matter into its smallest parts, and then carry them
away. So we should believe that the matter of the
sun is celestial fire, very fluid and agitated, carrying
off with it particles of the heavens. Although matter
of the first kind is constantly rushing along the axis
toward the center of the vortex, yet, when it approaches
that point, it experiences a tendency to fly out to the
equatorial surface because of its centrifugal force.
The effort, not only of the little spheres of the second
kind but also of the fragmentary particles of the first
kind, to leave the center of a stellar vortex, constitutes
light. While all particles of a vortex may tend to
move away from the center because of their cen-
trifugal force, yet, since they are packed like balls in
a cup, they cannot really move and so only tend to
move. Just as when a sufficient hole is made in the
bottom of a cup filled with balls, one of them drops
through and all the balls lying within an inverted cone
settle down; so it is with light, if any particle in space
tends to move, this tendency or pressure is instantly
transmitted to any distance along straight lines, which
come not only from the center of a luminous body but
also from all points in its superficies. If we attempted
to discuss details, we should find ourselves worried
and baffled between this tendency to move in a plenum
and the real motions of balls in a cup containing free
spaces between them. But there is little use in fretting

94 THE LIMITATIONS OF SCIENCE

over such a detail, when the entire conception is not
light nor anything resembling light. Descartes may,
perhaps, prove that this tendency to move proceeds
in straight lines and would be reflected and refracted
in agreement with the laws of light; that the inter-
stellar spaces would be transparent; that terrestrial
bodies would vary from transparency to opacity ac-
cording to the greater proportion and complexity of
matter of the third kind in their composition; but the
mechanism of all this is far more obscure and com-
plicated than the phenomena it attempts to elucidate.

This theory of light advanced in the Principia was,
in a sense, supported by the rather meager experimental
knowledge then existing, and seems at first plausible.
But examined critically, and with the mind no longer
awed, or perhaps hypnotized, by Descartes's sweep of
imagination and his power of making words seem to
express clear ideas when they really do not, his cause
of light is found to be as arbitrary as the fiat lux of a
God, and its effects mere confusion. In fact, it is the
unavoidable weakness of any such hypothesis, and a
very irritating and tantalizing weakness, that the words
used apparently express things we can understand, and
yet when we try to visualize these things, stripped of
technical and intricate verbiage, the mind has received
no clear impression.

And here we have a splendid example of an hypoth-
esis, whose foundations now seem ridiculous; whose

INFLUENCE ON RECENT SCIENCE 95

laws are not correct generalizations; and whose con-
clusions are unlike the phenomena of nature; which,
nevertheless, anticipates an idea to be advanced again,
after a century and a half. This hypothesis of light
contains, as a corollary, the germ of the kinetic theory
of heat. He discards the notion, which then generally
prevailed, that heat was a sort of mysterious substance
called caloric, for which indeed there was no place in
his universe, and defines it as the oscillatory agitation
of terrestrial particles, set up by the pressure of light.
The pores of such bodies are tortuous, and the pressure
of light on one end of such a gross and irregularly
shaped particle may be greater than on the other end
and so cause a tipping motion. Such a tilt would give
an oscillatory motion to a particle, similar to a violin
string when bowed, and he believed its momentum
affects us as heat. An oscillation of this sort would
communicate itself to neighboring particles and there-
fore explains the conduction of heat from one part of
a body to another; also, it accounts for the expansion
of bodies by heat, since vibrating particles usually re-
quire more space than quiescent ones; but, on the
other hand, they might be so shaped and arranged as to
bccupy less space, when in motion, and such a body
should contract if heated. Such an effect was unknown
at that time, but we ought to claim that it was bril-
liantly verified when, in later years, water was ob-
served to contract when heated from zero to four

96 THE LIMITATIONS OF SCIENCE

degrees Centigrade. Not to contradict known phe-
nomena, and to anticipate some unknown ones, is held
to be the justification of such hypotheses; by this
standard Descartes was successful as few others have
been. Yet, if we compare the splendid advances which
he made in science by his experimental discoveries and
his application of mathematics to physical laws, to the
mass of falsehood in his metaphysical schemes by
which he dominated science and which still flourish
in the metaphysical theories now in vogue, we can
hardly tell whether he has benefited or done harm to
science by his labors. Possibly no labor is too great,
if by it we arrive at ever so little truth, but no one can
believe that this medieval conception of light and heat
induced his successors to seek for a possible, but unex-
pected, contraction of water. Surely the converse is
the case and his metaphysical divination was purely
specious ; the phenomena were discovered without any
reference to his theory and probably without even a
knowledge of it, and now, if we wish, we may use them
as a buttress for Descartes's tottering edifice.

The fourth and last book of the Principia is devoted
to an explanation of the natural phenomena of the
earth. At first the earth was a small stellar vortex,
composed of matter of the first kind only, and was one
of fourteen satellary nuclei located in our larger solar
vortex. Gradually the less subtile parts of its mass
attached themselves together and formed spots or

INFLUENCE ON RECENT SCIENCE 97

crusts on its surface, similar to sun-spots, a phe-
nomenon then recently made known by the telescope.
Sun-spots, because of the superior agitation of solar
matter, are broken up and disappear, but the earth-
spots formed more rapidly than they dissipated, finally
covering its surface with a thick crust of many layers,
composed of what he called matter of the third kind.
This crust diminished the motion of the terrestrial
vortex and finally destroyed it altogether, so that the
earth with its atmosphere and its obscure bodies de-
scended toward the sun to the place it now occupies.

With the earth in its proper position and with the
beginnings of diversity in its composition, Descartes
was free to employ the remainder of his treatise to the
description of the character of each aggregation of
elementary matter necessary to form the various
chemical substances; the proportions and velocities of
the three kinds of matter to produce forces, such as
cohesion, weight, etc., and the different geo-physical
phenomena, such as winds, rain, and earthquakes. It
is amazing how much he passes before our eyes, and
how ingeniously he links his ideas, giving to them the
appearance of the greatest plausibility.

There is little profit in discussing these at length,
for if the conclusions of the hypothesis were absurd
when applied to those regions of space about which we
even yet know little, they become grotesque when con-
nected with matter which we can investigate experi-

98 THE LIMITATIONS OF SCIENCE

mentally. Besides our thesis is with such methods in
general, and in this respect only is a study of Des-
cartes's system useful, as it is his method which still
flourishes in the theories of physics and of other sci-
ences. He is to be admired in this respect; when
he had once outlined his premises and his method, he
deduced his conclusions as rigorously as possible, and
compared them consistently with experience; whereas
it has become the custom now to alter postulates when-
ever their conclusions point to error, with the result
that it is most difficult to outline a consistent and in-
vidual modern theory. If we study modern scientific
theories we find that the postulates are as metaphysical,
if not more so, than those of Descartes. They are
stated with much assurance, but as the conclusions un-
fold themselves, we begin to notice a certain hesitation
and a desire to limit the discussion to a small and re-
lated class of phenomena. Or if an excursion is made
into a wider field, lack of confidence increases and usu-
ally results in a modification and confusion of the
postulates. If Descartes's theory may be illustrated as
a tree with all its conclusions branching out from a
single idea as a stem, our present state of physics is
like a thicket of bushes with many stems so concealed
and interwoven that the parent stem of any branch
cannot be distinguished.

I have sketched the most elaborate and comprehen-
sive hypothesis ever developed in the name of science,

INFLUENCE ON RECENT SCIENCE 99

which, if it means anything to mankind, is his best
expression of verity and fact. Yet we see Descartes,
an illustrious man of science, devoting his talents to
the exposition of an openly confessed fiction. And his
reputation rests on the belief that he has spun a web
of fancy so subtly that it could deceive us. While
additional knowledge has been acquired by us, no one
has shown that modern theorists have discovered a
method different and more trustworthy than that of
Descartes. We recognize that many of the laws he
formulated are false and that most of his facts have
been corrected or disproved, but we should remember
that modern hypotheses also are developed as a means
of attacking unexplored regions of science where our
own knowledge is either meager or false. For ex-
ample, he felt it necessary to find a cause for the
recently discovered sun-spots and then extended its
action so as to change a vortex into a primitive ter-
restrial planet. A better knowledge of these spots on
the sun proves that his whole reasoning was false, or
shall I say childish. But was it less plausible at that
time or even less childish than is now our most recent
theory; that an atom of matter is a system of cor-
puscles, each of which is a unit of free negative elec-
tricity moving with the velocity of light, and that this
denatured bit of electricity is nothing but a localized
strain in an ethereal plenum. Let us examine such a
postulate as we would a similar statement if it had been

ioo THE LIMITATIONS OF SCIENCE

made by Descartes. We may admit with Lord Kelvin
that we know nothing about the real nature of elec-
tricity. We do know experimentally that electricity
seems to be associated always with matter ; the greatest
velocity we have caused or observed any body of an
appreciable size to have, is one thousand eight hun-
dred times less than the speed of light. An ethereal
plenum is certainly only a matter of imagination, and
the conception of matter as a strain in this imaginary
plenum is hardly a clear idea. So it seems that the
facts supporting our modern postulates regarding the
nature of substance are as meager and doubtful, and
our ideas as obscure for our purpose, as those of Des-
cartes were for his.

On the contrary, it is no exaggeration to say that
there probably never lived a man better equipped than
Descartes to make and to defend an hypothesis; his
scientific skepticism, his freedom from the trammels
of authority, his devotion and skill in experimental
work, his determination to submit his id 'as to the
rigorous logic of mathematical analysis in which he
was the leader of his age, were admirable qualities for
such a purpose. A man who doubts even his own
existence, is not likely to adopt other ideas lightly. To
strip matter of every quality except mere extension; to
abolish every cause of phenomena except linear mo-
tion and the impact of bodies, both of which are
capable of the most accurate experimental investiga-

INFLUENCE ON RECENT SCIENCE 101

tion; is to attempt the limit of simplicity in scientific
procedure. Why Descartes chose such a postulate as
the criterion of matter, is directly traceable to his
fundamental dictum: cogito, ergo sum. If his own
existence is real only because of thought, and if mind
or thought be the criterion of all reality, form replaces
substance, and the extent of matter is its essential
quality. Although Descartes went further in this di-
rection than most men of science are willing to go,
yet he has imposed his method on science to the present
day and we are still industriously building worlds as we
think them to be.

Dazzling as the system of Descartes appears when
viewed as a whole, it has a foundation of sand and an
imaginary rather than a substantial superstructure.
Consider his statements: space or matter is infinite in
extent and continuous in character, and in the begin-
ning it was divided in equal parts which were then
moved with a force sufficient to separate them. If
matter fills all space, or rather is space, where was the
additional space to permit of this separation and what
then filled the interstices between the separated parts?
Again, the impact and grinding of particle on par-
ticle are supposed to have reduced them to uniform
spheres and the dust of this attrition then served to
fill the spaces left in such a pile of spheres. This
dust is of all shapes and so fine that there is always
at hand just the proper quantity to fill any space be-

102 THE LIMITATIONS OF SCIENCE

tween the spheres. It really amounts to endowing
these cosmic fragments with the intelligence of Leib-
nitzian monads; if impact and grinding produced them,
why are they also not true spheres ? The sand on the
seashore is as spherical as the pebbles. Then too, if
the original parts of space were reduced in size by at-
trition, why did they attain a certain size and then
cease to be worn away? Or are we to suppose that
the whole universe — earth, stars, and interstellar spaces
— are still grinding themselves away until some day all
its parts will be reduced to the size of the cosmic dust
which he calls fire ? We might go still further and let
the universe actually grind itself into nothing, and
simply vanish.

But even if we showed, step by step, that the scheme
not only was not true, but even not capable of resisting
the most cursory criticism, we should be met by the
answer; that as knowledge increases, details which are
erroneous will be abandoned and new ones substituted
which better approximate to the truth. This counter-
criticism seems aside from the question; it would be
strange if the efforts made to discover new phenomena
and laws, and to correct false ones, did not increase our
knowledge. But is this aim furthered by such hypo-
thetical systems, which attempt to describe the mechan-
ism of these phenomena and laws, and which, at bot-
tom, assume that their authors are the creators of the
universe and not observers of one whose laws and

INFLUENCE ON RECENT SCIENCE 103

phenomena are independent of them; a confusion of
subjective ideality and objective reality? Also how-
ever it advances, our knowledge of nature will always
be so inadequate that the very announcement of a
system of nature should cause us to suspect it of being
etched out by fancy, and to be useless as an aid to
scientific investigation. Nor can we find a system
which does not transgress constantly the limitations of
science, and it is safe to say none will ever be proposed
which will not transgress them, because it is the desire
for such a system that is false, and not its develop-
ment.

On the other hand, the discovery and verification
of phenomena should be unreservedly advocated, also
their classification into laws and even the restricted use
of hypothesis. But the latter has come to have two
meanings in scientific usage. The word hypothesis
very frequently signifies a law which has been pretty
accurately expressed and verified by available experi-
ence, but which still does not embrace some phenomena
believed to be related to it, or is contradicted by some
others ; for example, the law of conservation of energy
was an hypothesis in this sense, until the discovery of
the mechanical equivalent of heat proved that the me-
chanical energy, apparently lost in every action by
friction, was accurately balanced by the thermal energy
produced by the friction. Such hypothetical reason-
ing is quite warranted ; in fact a law or hypothesis of

104 THE LIMITATIONS OF SCIENCE

this sort should always be announced as soon as a con-
siderable number of facts point to its probable truth;
such tentative laws always direct attention to the phe-
nomena involved and stimulate research.

But hypothesis in the other sense does not gradually
crystallize into law as our knowledge increases. No
information, however greater than ours at present,
will ever advance Descartes's hypothesis a step closer
to a law. We shall never have any data about his
three kinds of matter, his nature of free space, etc.; we
learn constantly more about the action of light but
we still drift confusedly and without a guide between
his apparatus of pressures, Newton's corpuscles, and
Huygens's waves; the latest treatise on optics now
states that we may have to mix together all three of
them.

The system of Descartes will fascinate anyone who
surrenders himself to its spirit and scope, but illusion
is not the function of science. Nor can I find any more
accurate and just criticism of this and all other
hypotheses than that given by Bolingbroke : " The
notion Descartes entertained and propagated, that there
is, besides clear ideas, a kind of inward sentiment of
evidence, which may be a principle of knowledge, is,
I suppose, dangerous in physical inquiries as well as
in abstract reasoning. He who departs from the
analytic method, to establish general propositions con-
cerning the phenomena on assumptions, and who rea-

INFLUENCE ON RECENT SCIENCE 105

sons from these assumptions, afterwards on inward
sentiments of knowledge, as they are called, instead of
clear and real ideas, lays aside, at once, the only sure
guides to knowledge. This Descartes did very widely
in his construction of a world, and yet by dint of genius
he gave a great air of simplicity and plausibility to his
hypothesis, and he knew how to make even geometry
subservient to error. . . . The plenum of Descartes
is well-nigh destroyed ; many of his laws of motion are
shown to be false; the mills that served to grind his
three elements are demolished : and his fluid matter in
which, as in a torrent, the planets were carried around
the sun, whilst a similar motion in the particular vortex
of every planet impelled all bodies to the center, is
vanished. Notwithstanding all this, how slowly, how
unwillingly have many philosophers departed from
the Cartesian hypothesis?"

That Bolingbroke was mistaken when he says that
the plenum, the vortices, and all the other apparatus
of Descartes have been destroyed, can be readily seen
by reading any modern treatise on physics.

But he was vividly correct in the larger and more
important part, when he finds that all such hypotheses
are based on an inward sentiment of truth and not on
clear and real ideas. An inward sentiment of knowl-
edge is and must be the final guide of anyone who em-
ploys this hypothetical method, for how can anyone
have clear and real ideas about such things as tran-

io6 THE LIMITATIONS OF SCIENCE

scend experience? And amongst the many following
this method, what man can be the arbiter to declare
which one has been gifted by a divine power with the
true inward sentiment of knowledge ?

CHAPTER IV

THE SCIENTIFIC METHOD

The truth of science has ever had not merely the task of
evolving herself from the dull and uniform mist of ignorance,
but also that of repressing and dissolving the phantoms of the
imagination. — FARADAY.

IF we are compelled to revert to old and supposedly
discarded systems of thought when we attempt to
make new hypothetical systems, we should inquire
whether we are really advancing the theory of science
by that method. Is it true that Descartes reaches in
his wonderful clarity of expression the highest attain-
ment in speculative thought? Even in the then little
cultivated subjects of electricity and magnetism, his
imagination did not fail him and he drew a picture of
the field of force about a magnet which is strikingly
like those in modern treatises. And to explain elec-
trical attraction, he supposed bodies to contain little
filaments of his elementary matter which were crowded
out when the bodies were rubbed together. These fila-
ments attached themselves like lines of force to neigh-
boring bodies. When the rubbing was stopped they
retracted and so drew the electrified bodies together.

If we modernize this explanation, we have a fair state-

107

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ment of Faraday's lines of force. Faraday believed
that when a body is electrified the space about it is
filled with lines of electric force which are stretched in
the direction of their length and experience a pressure
at right angles to their direction. This idea, or rather
the modification of it by Maxwell, who was able to as-
sign quantitative values to those forces which corre-
spond with the laws of electrical attraction and repul-
sion, is expressed more precisely. But qualitatively:
that is, in telling us what electricity is ; why it is pro-
duced by friction; and what lines of force are; the
modern statement is no more definite than that of Des-
cartes. It is a mistake, however, to suppose he pos-
sessed a unique power of formulating hypothesis ; other
early writers attained eminence in this respect. Thus
Sir Thomas Browne thought that electric effluvia (the
prevailing name for force) behave like threads of
syrup which elongate and contract and so produce at-
traction; Von Guericke stated that bodies contain efflu-
via which emanate from them according to their nature
and form an electric field of force. In agreement with
these opinions, we are taught to-day that the best way
to consider lines of force is to picture an electrified
body as one surrounded by stretched elastic bands. As
a diagram to show the direction of motion of an at-
tracted body, and as a name for the quantity of force,
this conception of elastic lines of force is accurate and
convenient. But Faraday and Maxwell went far be-

THE SCIENTIFIC METHOD 109

yond this, as they gave to them a concrete reality.
This conception still persists, although Sir J. J. Thom-
son showed years ago that no known system of me-
chanical forces would keep such a system of force-lines
in equilibrium and Professor Lorentz now says they
cannot really exist but are fictions of the imagination.
It seems rather futile, if such be the normal his-
tory of hypothetical models, to inflict on us the labor of
learning abstruse hypotheses which continually revamp
old metaphysical terms and merely dress them up in
new transcendental symbols. It is a valuable exercise
to strip hypotheses of their technical phraseology; to
change those words which deceive our minds into be-
lieving that a clear idea has been conveyed, when, in
fact, they have merely been wrenched from any real
significance. Thus Sir Oliver Lodge says that the
ether is very massive. This definition at once increases
our belief in its reality since it conveys the impression
that the ether is tangible and impenetrable, something
like a vast globe of rock. And we must stop to think
before we realize that whatever the ether may be, it
must be just the opposite to our ordinary ideas of mas-
sive things. Or what clear idea is conveyed by Pro-
fessor Einstein's definition that vacuous space contains
radiant energy which is an entity of the same kind as
matter? Does he not add to the difficulty when he says
further, that the difference between a vacuum and the
ether is that the latter is a vacuum transmitting radiant

i io THE LIMITATIONS OF SCIENCE

energy and possesses a light vector. What right has he
to insinuate into our minds that a vacuum may contain
something and still be a vacuum? He does this by a
play on the word " energy," which he permits us to
think of in the ordinary sense as an attribute of matter
and at the same time states implicitly to be a distinct
entity. We are inclined to pass lightly over the second
statement because we tacitly think of a light vector as
a geometrical line; the substance of such a line is too
intangible to give a distinct shock to the reason. But
if we put this definition to a simple test, we easily see
how futile it is. Say to anyone, that a golf ball in its
flight is not a thing of rubber and paint but a complex
of energy; and, that this is true because the moving
golf ball has a motion vector and consequently changes
vacuous space into ether. How quickly such a state-
ment about a familiar action would be recognized as an
absurdity. I presume that the reason why we like to
indulge in these phantoms of the imagination is be-
cause we still hate to confess our ignorance. But it is
a pity that science thus lurks in the mists.

We can easily follow modern hypothesis as it pro-
gresses into transcendental symbolism. Sir Joseph
Larmor and Professor Lorentz wish to define elec-
tricity so that it may be measured. They adopt the
hypothetical method to a limited degree. Thus, they
each postulate the atom of matter. They next assume
each atom to consist of a multitude of positively and

THE SCIENTIFIC METHOD in

negatively electrified particles which revolve in orbits.
Except to say that these particles may be a modifica-
tion of an ether, they avoid explicit details. Their
method of exposition is still the classic method of
mechanics. When they try to explain certain lately
discovered and obscure phenomena, they merely show
that they could be satisfied by supposing the dimen-
sions of bodies to be influenced by their motion. At
this point they wisely refrain from further explana-
tions. Next we find that Professor Einstein definitely
changes electrical particles into particles of electricity
and matter into complexes of energy. He speaks so
confidently of his ability to visualize electricity and
energy that we feel our own inability to do so results
from a pitiful lack of intelligence. At this point he
clinches the whole matter and explains the changes of
the dimensions of moving bodies by introducing the oc-
cult idea that light is an entity which moves in space
with a constant velocity. It is a far cry from the induc-
tive method of science which attempts to build general-
izations on experience, thus to make the whole concrete
world conform to so abstract an idea as the constancy
of the velocity of light in space. Nor does he hesitate
to found physical science on the paradox, that motion
cannot be absolute but the motion of light is absolute.
Then Professor Minkowski goes a step further. He
accepts all these ideas and then treats them symbol-
ically. To deduce conclusions from these postulates,

112 THE LIMITATIONS OF SCIENCE

he uses mathematical equations as if there were four
dimensions to space. The mathematician can employ
equations which contain four or any number of vari-
ables, but the physicist who desires to deal with an
objectively real universe and also to be intelligible is
forced to limit himself to the three dimensions which
correspond to his powers of measurement of length,
breadth, and depth. Lastly, Professor Lewis confuses
scientific method utterly by arbitrarily assuming which
quantities in an equation shall be treated as variable
and which as constant. Thus he says, if the mo-
mentum of a body changes, let us suppose that this
happens not because its motion changes but because we
shall consider its mass variable. Of course anyone
can say, let us consider the universe to act as he wishes.
But, after all, what is the use when no one believes it
does ? Is it any wonder that a gulf is growing not only
between men of science and the rest of the world, but
also between theorists and those who are still willing
to submit their imagination to experience? Such a
gulf is certain to continue so long as theorists are
willing, and even anxious, to ignore common sense and
the facts gained by patient and exact experimenta-
tion.

It is true that my criticism of scientific method has
been so far purely destructive. And in that admission
may lie the ineffectiveness of the argument to many.
Some will say that however weak and vacillating the

THE SCIENTIFIC METHOD 113

hypothetical method may have been, yet it is the custom
of thought and in spite of it or even, in some way, be-
cause of it, scientific truth has nobly expanded, dis-
pelling ignorance and subjugating natural forces. But
because knowledge advances, objection should not be
made to a protest against what tends to embarrass a
more rapid advance. Such a protest is the value of
destructive criticism. The reason why scientific knowl-
edge advances in spite of hypotheses, those phantoms
of the imagination, is because hypothesis rarely pre-
cedes experiment. If we examine the work of the
experimenter of to-day, we find he still goes on calmly
working with apparatus and using it with the common
sense idea that he is using real objective matter in spite
of the attempt of the theorist to make it an attribute
of energy or electricity. The conclusions derived from
experiment and laws may be discussed and condemned
or approved according as they support a fashionable
hypothesis, but scientific hypothesis is much like re-
ligious dogma : although it may protest, yet in the end
it swerves around to accept all new facts. And in a
short time the despised fact is cited as a pillar, or at
least as a flying buttress of the hypothesis.

While it is not possible to draw a definite boundary
line between the regions of physics and metaphysics,
still we may do so in a general way by saying that the
domain of physics is concerned with the discovery of
phenomena and the formulation of natural laws based

114 THE LIMITATIONS OF SCIENCE

on postulates which are determined by experience and
generally accepted as true; the causes of phenomena
and the discussion of the postulates of science lie in the
province of the metaphysician. This differentiation in
method of thought cannot be rigidly adhered to since
the boundary line is more or less obscure, and is liable
to considerable displacement as a science advances ; but
the acceptance of this principle would prevent much of
the confusion which has been introduced into science
by writers who have not recognized it to be a general
rule. For example, the principle of relativity is not
strictly a physical law but the expression, in mathe-
matical symbols, of the general philosophical law of the
finite nature of the human mind which has been ac-
cepted for centuries. Again, the discussion of the
shape of the atom or electron is not a physical prob-
lem, as it is incapable of verification by experience.
This does not mean that such questions should not be
discussed, but the method of their discussion and the
results obtained are properly the method and results
of metaphysics and are not in the category of physical
phenomena and laws.

In the first place, men of science must accept the
existence of an objective universe, whose phenomena
and laws are external to our intelligence and will.
But, since the interpretation of phenomena is sub-
jective and thus conditioned by our intelligence and
will, scientific laws are governed by the mathematical

THE SCIENTIFIC METHOD 115

theory of probability, or the consensus of opinion of
the greatest number, working with the greatest care.

The basic laws of physics are the laws of continuity
and conservation, and the law of cause and effect.
Unless we believe that something, matter, energy, or
both, remains unchanged in amount and has a continu-
ous existence however changed in appearance, and un-
less phenomena can be repeated, we have no certainty
of knowledge and no means of communicating ideas
to others. The discussion of the reality of these laws
may be left to the philosopher, but I dare say, however
he decides, they will continue to be accepted by man-
kind generally.

The universality and application of these and other
laws should be rigidly limited to experience by the
physicist. The law of conservation requires that the
quantity of matter and energy is either infinite, which
means nothing, or that there is an exact interchange
in quantity in every action. This belief is expressed
in Newton's law that to every action there is an equal
and contrary reaction. But it is evident that conserva-
tion, as a scientific law which may be verified, is limited
to a very small category of observations and is only ap-
proximate for them. Thus we know nothing of the
total amount of energy radiated from the sun or where
it goes. Hypothesis here shows considerable vacilla-
tion. Some assert that the universe is infinite and so
the radiation never reaches a boundary; others say

ii6 THE LIMITATIONS OF SCIENCE

that the universe is so filled with matter that no straight
line can be drawn from the sun without reaching an
obstacle and so radiant energy is reflected back and
forth ; again the universe may be finite in size and its
boundary may be a reflecting surface. These hypotheses
are evidently futile speculations and no support to the
law which we have been driven to accept and shall
continue to accept until personal observation shows re-
sults which increasingly depart from the law.

So, too, the law of cause and effect is a generaliza-
tion from few observations and neither supports nor is
supported by hypothesis. While we can never hope to
establish such a law, it is nevertheless a necessary gen-
eralization, or scientific deduction becomes meaningless.
The fact is, the phenomena of the universe do not re-
veal themselves, as a whole, in any regular sequence
of cause and effect ; and our theories, based on such a
law, show such a complex tangle as to be quite beyond
our power to interpret. The law involves time, and
past time at that ; and the successive causes of an ob-
served phenomenon, if carried back in any logical
sequence, soon widen out into an incomprehensible
maze and vanish in the obscurity of the past. The
most beautiful and perfect example of this law is the
belief in organic evolution. Yet on what meager and
inaccurate observations it rests. Everyone believes in
some such law, but no one can point out the sequence
of cause and effect, and its rigorous development leads

THE SCIENTIFIC METHOD 117

to absurdity. Mathematically it is a law of geometri-
cally decreasing types which reduce finally to a single
protoplasm. If we adopt the hypothetical method, we
should discuss the origin of this protoplasm. To say
it was made by God, is not scientific. Lord Kelvin
offers an hypothesis (although one would suppose he
was joking if the context were not so serious) when
he suggests that the original protoplasm may have
fallen on the earth from some celestial body! How-
ever we are to consider such an extraordinary state-
ment, we do know that Maxwell tried to support the
hypothesis of pangenetic evolution by the futile
method of estimating the number of molecules in a
germ. The question with him was whether there were
enough molecules to form miniature organs and parts
of the mature object into which the germ would ex-
pand.

Another illustration may be given to show that as
soon as we extend our laws beyond the point where
verification is possible, we merely cause confusion.
Certain experiments indicate that the apparent mass of
a body changes when it moves in an electric field. The
law shows that the mass should become infinite when
the velocity equals that of light. This conclusion has
been accepted as the basis of an hypothesis that the
velocity of light is a maximum limit to motion. Such
a belief is not only pure hypothesis but it is contrary
to the conclusions of other hypotheses. If this hypo-

ii8 THE LIMITATIONS OF SCIENCE

thetical method is generally applicable it is necessary
to explain gravitational action also as due to some
form of motion; Laplace has shown that the motion
involved requires a velocity many times that of light.

Our most fundamental perception of an external
universe seems attainable from our sense perception of
force. The muscular sense of effort is apparently the
simplest and most general mechanical notion we have,
and in the opinion of the masters of the science our
idea of force is adequate to serve as the basis of so
exact a science as physics. Yet, when we attempt to
make force serve as a fundamental measure of phe-
nomena, we have found, since the time of Newton, that
it is not so convenient as mass and acceleration. Mo-
tion is further divisible into a measurement of length
and time. It is therefore customary to reduce all our
complex observations into combinations of the funda-
mental units of mass, length, and time instead of force.
The idea of force being thus associated in our minds as
an attribute of matter, we postulate the objective
reality and conservation of matter and assume the
fundamental attribute of matter to be its mass or
inertia. M. Hannequin expresses this idea clearly
when he says that nothing in a mechanical sense exists
except masses in motion.

We shall next assume length, mass, and time to be
the fundamental units of measure. These quantities
are continuous or, at least, are indefinitely divisible.

THE SCIENTIFIC METHOD 119

The continuity of space and time is generally accepted ;
without this belief it is impossible to establish the
geometrical laws of figure founded on the point, line,
and surface or the analytical laws "of motion derived
from the calculus. The only exception I know to
this postulate is Professor Planck's theory of quanta,
in which motion may occur in jumps. But the divisi-
bility of matter is not usually supposed to be infinite.
Indeed, the denial of this assertion is the foundation
of all atomic theories. Yet it is difficult to see how
mathematics can be anything but abstract logic, or how
it can be applied to physical problems unless this third
fundamental quantity, which is, as it were, the con-
necting link between the abstract and the concrete, be
also indefinitely divisible. It is only by the postulate
of the indefinite divisibility of mass that we may pass
from the mathematical laws of pure motion (kine-
matics) to the physical laws of the motion of bodies
(dynamics). How, otherwise, can we replace finite
bodies by mathematical centers of inertia? In this
connection Sir Joseph Larmor says : " The difficulty of
imagining a definite uniform limit of divisibility of
matter will always be a philosophical obstacle to an
atomic theory, so long as atoms are regarded as dis-
crete particles moving in empty space. But as soon as
we take the next step in physical development, that of
ceasing to regard space as mere empty geometrical
continuity, the atomic constitution of matter (each

120 THE LIMITATIONS OF SCIENCE

ultimate atom consisting of parts which are incapable
of separate existence, as Lucretius held) is raised to
a natural and necessary consequence of the new stand-
point." This is clearly an attempt to reconcile the two
antinomies of continuity and discontinuity, which are
usually attached to the names of Descartes and Lucre-
tius. This Sir J. Larmor tries to do by postulating
the existence of a true matter, which is a continuous
plenum and imperceptible to our senses, and relegat-
ing sensible matter to the role of a mere variation in
this otherwise changeless plenum — making it an at-
tribute rather than an entity. If this definition denies
the infinite divisibility of matter, it apparently accepts
its indefinite divisibilty ; the atom, as a variation limited
only by our power of observation, must become smaller
with each advance in the refinement of our apparatus.
Such a plenum must remain a pure creation of the
imagination, and its existence is not determinable by
physical or experimental methods; it must therefore
be classed as a problem for the metaphysician. The
distinction between atoms continually diminishing in
size and the infinite, or at least indefinite, divisibility
of matter is here a question of words — the definition of
what matter is.

Few things have been brought out more clearly by
modern physicists than that, if we accept the doctrine
of the continuity and conservation of energy, either of
the two, matter or energy, may be considered as the

THE SCIENTIFIC METHOD 121

fundamental unit from which the other can be derived.
This undoubtedly follows from the fact that we have
no conception of matter without energy or of energy
without matter. But while it is thus possible mathe-
matically to make either of them a starting-point for
the explanation of phenomena, the advocates of ener-
getics apparently soon develop a pronounced tendency
to prefer the abstract to the concrete and to subtilize
objective facts into metaphysical ideas. A science like
physics, to be useful and not merely an intellectual
gymnastics, should preserve in all its speculations a
close touch with the practical and the concrete — a cer-
tain common sense. The history of the science shows
these advantages have been obtained most frequently
by those who maintain matter and not energy to be
a fundamental entity. The failure of the mechanistic
school has arisen from the attempt to explain the na-
ture of matter, the cause of its forces, and the proper-
ties of atoms. However we may try to reason away
the belief in the objective reality of matter, our minds
persistently cling to the advantage, and even neces-
sity, of such a postulate, and we consciously or uncon-
sciously endow any substitute of it with all the prop-
erties of matter, excepting its name.

Energy is to be considered then as an attribute of
matter and may be defined as the power to do work.
It is customary and convenient to divide energy into
two classes, potential and kinetic, according as the mat-

122 THE LIMITATIONS OF SCIENCE

ter concerned appears to be at rest or in motion. Since
attractive forces exist between all bodies, we find that
the idea of work is involved whenever the distance
between bodies is altered and we denote this potential
energy as the force of attraction times the distance be-
tween them. I accept frankly the idea of action at a
distance, not because it seems reasonable, for my ex-
perience teaches me that to cause motion I must con-
struct a link between two bodies ; but the fact remains,
that both gravitational and electrical attractions seem
to act at a distance and all attempts made to explain
them have so confused the mind that the occult phe-
nomenon is less perplexing than the occult explanation.
In the majority of such problems we can go no further;
but in certain cases, as for instance the theory of
gases, a portion of the potential energy due to the pres-
sure of gases may be ascribed to the impact of small
moving masses of gases. Even here, a portion of the
energy of the gas must be considered as potential and
incapable of further explanation. Kinetic energy is
the power of work due to the motion of bodies. Its
measure is one half the moving mass into the square of
its velocity. These two kinds account for all the energy
of material bodies; they are mutually interchangeable
and their sum is a constant.

A third class of energy remains to be discussed. It
is called radiant energy; its difference lies in the fact
that it is not associated with material bodies. Cer-

THE SCIENTIFIC METHOD 123

tain forms of the energy of bodies which we name
heat, light, etc., are observed to appear in other bodies
although the space between them is devoid of matter.
We suspect that the amount of this energy disappear-
ing in the emitting bodies is equal to the amount ap-
pearing in the receiving bodies and that time elapses
between the emission and the reception of the energy.
On these ideas we have built the theory that energy
travels through immaterial space and in its transit we
call it radiant energy. The conception of radiant
energy in a vacuum is a useful one if we limit it to a
mere quantitative idea. For this purpose it suffices to
state the facts in a mathematical formula which ex-
presses a continuous passage of a quantity of energy
through space equal to the amount lost by the emitting
body. We thereby generalize the laws of continuity
and conservation and of cause and effect. This is not
the custom; it is usual to try to explain the nature and
mechanism of radiant energy. This requires either
that space be filled with an ether to serve as the vehicle
of energy or that energy be regarded as itself an
entity.

It has been the persistent attempt of physicists for
centuries to explain this radiant energy by mechanical
models. And this effort has fastened on the science
an interminable series of impossible fictitious ethers
and mechanical atoms. The most indefatigable labors
of the greatest minds have been spent to construct an

124 THE LIMITATIONS OF SCIENCE

atom, which would serve satisfactorily as a source and,
at the same time, as a receptacle of radiant energy and
an ether which would transfer it. Not one of these
models has been even partially adequate ; the course of
the development has been steadily from the simple to
the complex, from the concrete to the abstract, from
the physical to the metaphysical, until the most recent
atom is a complex more intricate than a stellar cos-
mogony, whose parts are an entity called electricity, and
the ether is an abstraction devoid of any mechanical
attributes. Out of all this controversy we have gained
the following facts : — Heat, light, and electrical energy,
originating in one body, may be assumed to pass
through space undiminished and unaugmented to an-
other body. We can also express this energy as kinetic
energy while it is associated with matter. In transit,
since our experience gives us no clew or criterion, we
can assume as a formula for the energy, either a
periodic motion of an hypothetical something, called
an ether, or a projectile motion of an hypothetical mass-
particle. In either case, all we really do is to divide
the initial or final material energy into two mathe-
matical quantities, one a mass-factor and the other a
velocity-factor, and give to each such a value as to
make their product remain a constant. As a rule, we
make the mass-factor so small that we can shut our
eyes to its existence and imagine anything about it
we please. The time relation is fixed by experiment.

THE SCIENTIFIC METHOD 125

For the purposes of theory, although this energy ap-
peals to our senses in the three forms of heat, light,
and electricity, which in their qualitative aspects are
each fundamental and not referable one to another, we
fortunately find that quantitatively all three are satis-
fied by one dynamic formula. We have therefore ob-
tained an adequate quantitative knowledge of energy,
but not an inkling of the qualitative coefficients in this
formula.

The hypothesis of the ether is an attempt to accom-
plish the impossible. And while it is now generally
admitted that we cannot create such a substance as will
satisfy the physical requirements of a transmitter of
radiant energy, still the ether is claimed to be a useful
hypothesis. This utility is said to consist in giving us
a crude image, in a mechanical way, of what occurs.
In other words, it supports our innate dislike to con-
fessing complete ignorance, and it provides a set of
concrete analogies for abstract statements and equa-
tions. Now the old elastic solid and mechanical ether did
afford us a concrete image of a mechanism for radiant
energy, and we could speak of it with some intelligence
to one another, because everyone has a conception of
an elastic solid. To be sure, this solid ether became a
grotesque. It permitted the transference of heat and
light energy, but only at the expense of creating a kind
of matter entirely outside of, and contradictory to,
anything in our experience. We have only to recall the

126 THE LIMITATIONS OF SCIENCE

properties ascribed to this ether to find that it operated
equally well if it had a density indefinitely great or one
indefinitely small; if it were rigid or if it were col-
lapsible, etc. As certainly as one physicist endowed it
with a property, another arose who showed that just
the opposite property was equally efficient. Yet we
might still be staggering along with the conviction that
somehow this supposititious stuff was of use to us; at
least it gave us a set of words conveying some meaning.
But when Maxwell proved mathematically that a third
kind of radiant energy of an electrical type should be
looked for, and when Hertz demonstrated its existence,
no elastic solid would serve for all three kinds ; and so,
for a time, we were taught simultaneously the proper-
ties of two coexistent ethers. An elastic solid and a
so-called electro-magnetic ether in a single space were
impossible, and the former soon collapsed since it was
more concrete and thus more vulnerable to criticism.
Maxwell's idea produced a revolution in the theory
of physics; heat and light remained no longer a form
of mechanical waves but became electro-magnetic
waves of a special periodicity. By a progressive sub-
tilization we have now arrived at Sir J. Larmor's cele-
brated definition of a medium which will satisfy all
forms of radiant energy. The ether is " a plenum with
uniform properties throughout all extension, but per-
meated by intrinsic singular points, each of which
determines and, so to speak, locks up permanently a

THE SCIENTIFIC METHOD 127

surrounding steady state of strain or other disturb-
ance." This ether is unaffected by any type of me-
chanical action since ethereal strains are of an unknown
kind responding only to electro-magnetic stresses.
This definition seems general enough to satisfy the
most critical, but Professor Einstein goes much fur-
ther. He says we must abolish the ether because the
only difference between empty and occupied space is
that the latter is the seat of an entity, energy, and
contains a light vector. Such a definition, in the sense
of explaining a complex idea in terms of simpler ones,
is wholly incomprehensible and at the same time ap-
parently denies and affirms the existence of the ether.
But Professor Einstein is not averse to paradoxes.
These ideas evidently reduce matter to an attribute of
electricity, and make all forces of the type called elec-
trical forces. But if electricity is everything, we must
inevitably some time explain pure mechanical actions
in terms of this electrical substance. Sir J. Larmor
clearly foresees this, as shown by his statement : " The
electric character of the forces of chemical affinity was
an accepted part of the chemical views of Davy, Ber-
zelius, and Faraday ; and more recent discussions, while
clearing away crude conceptions, have invariably
tended to the strengthening of that hypothesis. The
mode in which the ordinary forces of cohesion could
be included in such a view is still quite undeveloped."
He thus rather leaves this question in the air by con-

128 THE LIMITATIONS OF SCIENCE

eluding that a complete theory is not necessary. But
the history of science shows that we shall soon create
two media or try to give properties to one which will
include electrical, chemical, and material forces; in-
deed, this latter is already being attempted. If the
conception of an elastic solid ether was admittedly a
fiction of the mind, and one impossible to align with
any known kind of matter, the electro-magnetic ether is
so esoteric, so subtilized from all substance, that it
merely provides a nomenclature for a set of equations
expressing the propagation of radiant energy. We
may well go still further, for I believe the time is
rapidly approaching when all scientific discussion of
the nature of the ether will be considered futile.

In accordance with my view no hypothesis will be
made to express properties of a medium, whose exist-
ence is itself incapable of scientific proof. It is, at
the same time, perfectly proper to distinguish space
through which we say radiant energy passes by a
special name such as the ether. The amount of
radiant energy in transit is best given by an equa-
tion expressing conservation of energy and con-
taining a velocity and an inertia factor. The
velocity factor of this equation most conveniently
takes the form of a periodic motion, but no assump-
tions need to be made as to the nature of the periodicity
or of the inertia factor, since they also are not subject
to experimental verification.

THE SCIENTIFIC METHOD 129

Such a revolution as has occurred in the ideas of
the ether requires a like one in our ideas of matter.
The most notable effort in theoretical physics, at the
present time, is the hypothesis that the ultimate ele-
ment of matter is not a material atom, a sort of micro-
cosm of sensible matter, but a free electrical charge,
considered to be an entity for the purpose; added to
this are the dependent ideas that inertia and all other
properties of matter are attributes of electricity. This
hypothesis can mean nothing else than that the Lu-
cretian atom, the centers of force of Boscovich, the
vortices of Kelvin, and all the atomic models (made
of weights and springs and strings), have failed and
become useless as aids to the imagination.

Sir J. Larmor defines this new atom as a protion,
" in whole or in part a nucleus of intrinsic strain in
the ether, a place at which the continuity of the me-
dium has been broken and cemented together again (to
use a crude but effective image) without accurately
fitting the parts, so that there is a residual strain all
round the place." This strain is not of the character
of mechanical elasticity, since the " ultimate element of
material constitution is taken to be an electric charge
or nucleus of permanent ethereal strain instead of a
vortex ring." Sir J. J. Thomson pictures the atoms of
the various chemical elements as nuclei of free positive
electricity holding in electrical equilibrium free nega-
tive charges, placed in various geometrical designs.

130 THE LIMITATIONS OF SCIENCE

The degree of stability of each system is determined by
the radio-activity of its element. Professor Lorentz
considers the protion to be a small particle charged
with electricity and probably a local modification of
the ether ; but his work on electro-magnetic mass leads
one to the opinion that he believes electricity to be the
real essence of the material universe. The modern
school of German physicists is frankly endeavoring to
give a purely electro-magnetic foundation to the
mechanism of the electron and to mechanical actions
in general.

Now to me, and I believe to many men of science, the
chief and indeed only value of an atomic theory is to
give a concrete, though crude, image of matter reduced
to its simplest conditions. The word electricity gives
me no such image of matter; it conveys absolutely no
idea of materiality nor even of space or time rela-
tions. What the originators of the electrical atom
have done is apparently to transpose the words, matter
and electricity, tacitly giving to the latter all the ideas
usually associated with the former. We may as well
take the next step at once and raise the objective uni-
verse on the Leibnitzian monad or on Schopenhauer's
philosophy of " Die Welt als Wille und Vorstellung."

Again, the law of the conservation of matter has
been one of the most fertile ideas in science; according
to this law at least one attribute, inertia, remains con-
stant however all others may change, thus giving con-

THE SCIENTIFIC METHOD 131

tinuity to material bodies as well as to space and time.
It is quite possible to imagine an element of this new
electric matter to be composed of equal quantities of
positive and negative electrons, whose motions are so
balanced as to make all material attributes vanish and
produce a quasi-annihilation of matter.

Lastly, when the statement is made that the electron
is merely a local modification of the all-pervading
ether, some idea should be given us as to the nature of
this modification. If it is of the character of a strain,
no meaning is conveyed unless this strain is subject to
the laws of static or kinetic mechanics. But we have
no knowledge of a static strain which fulfils the re-
quirements of matter, especially that it must be localized
at definite points and must be uncreatable and inde-
structible; of kinetic strains, the only one at present
available is the vortex ring of Helmholtz and Kelvin.
To imply that matter is electricity and that electricity is
a static strain or a vortex ring, is to make an impossible
assumption and is reasoning in a circle. If the vortex
ring of matter failed chiefly because Maxwell said:
" That at best it was a mode of motion and not matter
as we know it," what chance has this new type to sur-
vive criticism?

Although matter appears to us as a continuous quan-
tity or at least as divisible far below our present
methods of experimentation, still it is convenient to
give to the smallest observable portion of matter some

I32 THE LIMITATIONS OF SCIENCE

such name as protion. This unit of matter must be
reduced in size as refinement of observation increases,
so that we may always be able to discuss it mathe-
matically in the aggregate only. It must also be en-
dowed with the same attributes which we recognize in
gross matter.

At the present time this protion is the electron, and
the only attributes necessary to assign to it are inertia
in the Newtonian sense, a force of gravitational attrac-
tion and a force of electrical attraction, either positive
or negative in sign. No causes for these attributes
can be given, as they are fundamental. If the experi-
ments of Kaufmann, which show that an electrified
particle in motion has an apparently increased mo-
mentum, are cited as supporting the view that inertia
is a function of velocity and should be considered as
an attribute of an invariable quantity, the electrical
charge, I hope to show that it is possible to accept
Kaufmann's results and at the same time the invari-
ability of inertia. Before proceeding further with this
discussion it is convenient to assemble the foregoing
ideas in a more concise form.

We have first postulated a real and objective uni-
verse and assigned to matter rather than to energy the
role of being an entity. The fundamental attribute of
matter which makes it recognizable by our senses is
force.

We next assumed that quantitatively all phenomena

THE SCIENTIFIC METHOD 133

may be expressed in mechanical ideas and that the
fundamental units of measurement are mass, length,
and time. These are continuous functions and con-
sequently indefinitely divisible.

While matter, as measured by mass and extent, is
indefinitely divisible, it is convenient to adopt as a
scientific unit of mass a quantity so small that it is
inferior to our powers of observation and so must be
treated mathematically only in aggregates. As this is
a general definition, the name protion has been given
to this unit in order to avoid confusion with the chem-
ical atom and the electron. At the present time the
protion is the electron.

The general laws governing actions are the laws of
continuity and conservation and the law of cause and
effect. These are generalizations from experience and
cannot be extended beyond possible experience without
great precaution.

Energy is defined as the power of doing work and is
held to be an attribute of matter. True or observa-
tional energy is always associated with matter and is
divided, for convenience, into potential and kinetic
energy.

A third and hypothetical kind of energy is assumed
in order to extend quantitatively the laws of continuity
and conservation, and of cause and effect, to the
apparently well-founded interchange of energy of
two bodies situated in a vacuum. This energy is named

134 THE LIMITATIONS OF SCIENCE

radiant energy and, in order to link it with kinetic
energy, its quantity is expressed as the product of a
" mass " and a " velocity " factor. Its velocity is
naturally taken to be the distance between the bodies di-
vided by the observed time. It is most conveniently
expressed as a periodic motion with a translational
velocity equal to 3 x io10 centimeters per second. No
hypothesis is made in regard to the nature of the mass
factor; it is taken merely as a coefficient to maintain
conservation.

As no attempt is made to account for the mechanism
of radiation, no attributes need be assigned to an ether.
In fact no ether need be postukted, although it is
advisable to use the name to differentiate space when it
is occupied by radiant energy.

Action at a distance is a matter of experience and
cannot be denied until some reasonable proof is found
to account for force by some other means.

So far these ideas have had the approval of some
acute men of science, however they may be disapproved
of by others. Those which follow are more novel and
need to be supported.

Since mechanical explanations are to be avoided, it is
necessary to endow the electron with all the attributes
of gross matter. For example, the protion of oxygen
has a different density, force of cohesion, etc., from
that of hydrogen. In this discussion, it is necessary
to discuss only a few of these attributes.

THE SCIENTIFIC METHOD 135

I shall, therefore, assume that the electron has a
constant mass, m, and that it possesses a force of gravi-
tational attraction for all other electrons which is
determined only by their masses and the distance be-
tween them.

The electron, in addition to gravitational attraction,
has a power of electrical attraction. To measure this
force, I shall assume that it possesses a quantity of
electricity, e. Electrical force obeys the same law as
gravitational force, since it is conditioned by the quan-
tity of electricity and the distance between electrons.

The electrical property of matter is also manifested
to us by the experimental fact, that an electrified body
apparently possesses a greater mass when in motion
than an unelectrified body. A similar effect is noticed
when a body is moved in a fluid. As the apparent in-
crease in mass is there due to the resistance of the
medium, it is called hydrodynamic mass, we may call
the apparent increase in mass of a moving electron, its
electro-magnetic mass me. The total or effective mass
is therefore m"^- me.

Since the total mass is found to vary with the
velocity of an electron, two suppositions are possible.
Most physicists now assume that the mass, m, is a
variable and that the mass, me, is constant. It seems
to me more rational and more convenient to adopt the
converse idea that the electro-magnetic mass, like the
hydrodynamic mass, is a variable. I shall, therefore,

136 THE LIMITATIONS OF SCIENCE

assume that the electrical charge on matter is a quan-
tity varying with the velocity of a body.

So great a revolution in thought as to consider
inertia a variable quantity and to substitute electricity
for matter as the substance of the universe, would only
have been undertaken from a fancied necessity. A
mere matter of convenience would scarcely warrant
the labor of revising the work of the past and of dis-
carding what has been considered, until lately, as
definitely established. The need for some such radical
change in theory is based on the experimental facts dis-
covered in connection with the passage of electricity
through highly rarefied gases, and with radio-activity.

We may consider it established that the phenomena
noted, when electricity is discharged in a high vacuum,
are most readily explained by supposing the current
due to a stream of electrified particles moving with a
velocity comparable to light. The experiments of Sir
J. J. Thomson and C. T. R. Wilson go to show that
the masses of these projectiles, when charged nega-
tively, are about the one-thousandth part of the mass
of a hydrogen atom, provided the charge on each is
assumed to be the same and equal to that of the hydro-
gen atom. Those charged positively are comparable to
the various chemical atoms.

Radio-activity, on the whole, is best explained by the
projection of positive and negative electrons from a
certain class of bodies.

THE SCIENTIFIC METHOD 137

And lastly, Kaufmann has shown by a delicate ex-
periment that the apparent mass of an electron is a
function of its velocity. This conclusion has been con-
firmed by others, although in minor points there is a
considerable difference in results and opinions.

It must not be lost sight of that all these experiments
deal with quantities of matter, supposing it to exist,
too small to be appreciable by either chemical analysis
or mechanical apparatus, such as the balance. They
are ultimately measured by the force of electrical at-
traction of an electrical charge. We are, therefore,
experimenting with matter which appeals to us through
only one of its attributes. Is it not almost inevitable
that an exclusive attention paid to this single attribute
is likely to exalt it into an undue prominence? We
have had, in the past, examples of much the same sort
of reasoning. When the phenomena of light were
predominantly discussed, physicists drifted into the
opinion that this property of matter could be explained
only by creating a light substance. Again, this process
of reasoning occurred when heat was first investi-
gated; we had the creation of caloric. And now we
are asked to do the same thing with electricity. It
is safe to predict that history will be repeated again,
and that electrical charges and their forces will also
sink into the condition of an attribute of matter.

It might certainly be true that two experiments
showing equal electrical charges would, if we could

138 THE LIMITATIONS OF SCIENCE

measure the amount concerned, provide us with un-
equal quantities of matter, just as conversely equal
quantities of matter might show different quantities
of electricity. The hypothesis of equivalence of elec-
trical charge and matter rests solely on an analogy to
electrolysis, where matter is in a quite different state
and also where the equivalence may be only approxi-
mate. Matter, on the other hand, in a solid state shows
no connection between volume and density and elec-
trical charge. In dealing with electricity we should not
forget the immense superiority of electrical detectors
in delicacy to those for mechanical quantities, so that
we can appreciate far smaller quantities of electrified
than of neutral bodies.

There is no doubt, from the quotations given, that
theorists are basing their work on the assumption of
the electron as the unit of matter. And they give to it
the following properties: Its mass is wholly electro-
magnetic; the motive forces are electric forces; and
the laws of mechanics are to be deduced from the laws
of electro-magnetism.

At first sight, it would seem to be a simple matter to
devise an experiment which would decide whether the
mass or the electrical charge of matter is constant.
But so far these two quantities have not only been
found to be inseparable but they invariably enter as a
simple ratio, whose value decreases with increasing
velocity. Such a relation can, of course, be satisfied

THE SCIENTIFIC METHOD 139

by assigning a proper variation either to the numerator
or the denominator. It therefore becomes a mere mat-
ter of expedience which of the two quantities, mass or
electrical change, shall be supposed constant. In addi-
tion, the quantity, e/m, is itself a constant for all
velocities which can be attained by bodies which are
appreciably large. So the whole question of variation
is more or less academic, in that it does not become
important unless we are discussing hypothetical atomic
systems.

To say that e is a constant is an assumption based
solely on an analogy to the experimental laws of elec-
trolysis; but in electrolysis, when we obtain equal
electrical charges we also find equivalent masses of
matter. In the discharge of electricity through gases
and in radio-activity the matter deposited is too small
to be measured. This is a fundamental difference and
vitiates an analogy between the two. For example, we
measure the amount of current in a vacuum tube by an
electrical device, and at the same time we measure the
deflection of the current by an electric and magnetic
field; in other words, all quantities and forces are
electrical, and we say that equal currents in this case
require equivalent quantities of matter. But it has
not been shown to be impossible or even improbable
that electrons, associated with equal quantities of mat-
ter but having different velocities, might show different
electrical charges; or that electrons producing equal

140 THE LIMITATIONS OF SCIENCE

electrical charges, might deposit different amounts of
matter if it were sufficient in quantity to be detected by
chemical or mechanical reactions.

As an hypothesis, I propose that, in order to make
the ratio ^ agree with the experimental evidence of its
value and to account for electro-magnetic mass, we
consider m to be the mass of a particle of matter in
the Newtonian sense, of constant and small value, and
e, the electrical charge, to be a force attribute of mat-
ter which varies with the velocity of the particle.

However novel this hypothesis may be, I have not
been able to find any experimental facts more difficult
to explain by it than by any of the other hypotheses
which have been recently advanced ; and, on the other
hand, it apparently accounts for much of the modern
work in terms of old and well-established ideas.

From the very nature of my conception of the limits
which should be imposed on scientific inquiry, I make
no attempt to explain the cause for this electrical prop-
erty of matter any more than I should for its gravita-
tional attributes. Both are fundamental phenomena to
be accepted as experimental facts until we gain con-
trary knowledge. Indeed, I have ventured to indulge
in this speculation rather with the idea of showing
that the recent hypotheses for electricity and matter;
for the ether, protions, and corpuscular light ; for the
electro-magnetic and other non-Newtonian mechanics,
are not necessary. We may still account as adequately

THE SCIENTIFIC METHOD 141

for all our experimental facts by a simple addition to
the attributes of matter and continue to base our
theories on mechanical laws.

So long as the measurement of physical qualities be-
comes ultimately a matter of measuring mechanical
forces, it is advisable to express quantitative physical
laws in terms of mechanical formulae. For this rea-
son electricity should be considered a function of me-
chanical energy rather than the converse. If it be
possible to place mechanics on an electro-dynamic basis,
it is certain that we may always explain electricity in
terms of pondero-dynamic laws. As both are possible,
it seems far more natural and more rational to con-
sider electricity as an attribute of matter than matter
as a phenomenon of electricity.

CHAPTER V

THE CLASSICAL AND THE NEW
MECHANICS

Mathematics, quae philosophiam naturalem terminate, non
generate aut procreare. — BACON.

So far the hypothetical method has been discussed
in its broader aspects. It is my purpose now to out-
line its effect on science and on men of science by con-
sidering certain special cases. I know of no better
way to point out the influence of this method on sci-
ence than to contrast the classical mechanics, founded
on the work of Galileo, Descartes, and Newton, and
developed in accordance with the abstractive or real-
istic method, with the new mechanics which is based
on electricity as a substance and on electro-dynamic
energy, and which is pronouncedly speculative in char-
acter.

All phenomena of a mechanical nature can be re-
duced ultimately to modifications of inertia, velocity,
momentum, and energy. Theories of mechanical ac-
tion have, in addition, this common property; they
begin with the postulate of an entity which possesses
inertia and velocity. Various names have been at-

142

CLASSICAL AND NEW MECHANICS 143

tached to this entity, but whether it be called an atom,
an ether, a vortex, electricity, or energy, its function
is the same. While there is little difference in the
nature of this entity or substance, yet there are two
diametrically opposite ways of considering its space
attributes which give rise to two irreconcilable schools
of thought. One of these considers the primordial sub-
stance to be discontinuous with its parts separated by
vacuous spaces, and the other school just as con-
fidently assumes that there can be no empty spaces,
and that all space is therefore continuous. Arguments
for and against these two views have been unceasing
and are likely to continue, so long as hypothetical
methods remain in vogue. The problem is quite in-
capable of solution because the postulate of continuity
or discontinuity is a matter of conviction rather than
of reason. The fact is, we believe one or the other to
be true and that is the end of it. In such discussions
where a postulate is beyond our powers of verifica-
tion by experience, each contestant chooses his starting-
point, and this once chosen, his argument in favor of
it is as sound as that of his opponents. And the truth
of this assertion is evident, because from these dia-
metrically opposite postulates, conclusions which are
quite identical are deduced by equally logical argu-
ments; witness the controversy between the atomists
and the Cartesians which see-saws through all scientific
theory and is as far from settlement to-day as it was

144 THE LIMITATIONS OF SCIENCE

centuries ago. This dualism, as it may be called,
is not confined to science; it is but one phase of that
larger dualism of philosophy and ethics which has
come down to us from the Greek thinkers ; the claims
of two opposing schools of thought are always present
to show us that, if the mind can develop a system from
one set of postulates, the same results can be obtained
from their contraries.

If then our conception of the nature of things is
but a matter of personal conviction, what value is
there in the opinion of Professor Lorentz, which I
have already quoted, — if we wish to obtain an in-
sight into the mysteries and operations of nature, we
must make hypotheses? If such hypotheses are not
capable of proof then they must rest on what Boling-
broke so aptly calls our inward sentiment of knowl-
edge. The experimentalist who described phenomena
from his inward sentiment of what they should be
rather than from observations of what they are, would
be classed as a nuisance. Such a one not only does not
advance our knowledge but he actually retards it, since
his work must be repeated before the truth can be
known. So, too, the theorist, who relies on his per-
sonal conviction and not on facts and laws, builds a
structure which is not only temporary and false but
must be torn down. If we relegate to metaphysics so
large a part of what is commonly called physics, what
is left to the science of physics? The answer probably

CLASSICAL AND NEW MECHANICS 145

is to be found in the saying of Lord Kelvin, that no
scientific statement is understood until it is measured.
If we grant this, then we must first examine, in such
a discussion as this, our methods of measurement.

The statement of a phenomenon invariably contains
two terms, called qualitative and quantitative factors;
the former expressing " what kind " and the latter,
" how much." Thus, when we speak of a distance as
ten centimeters, we mean that we are to consider a
quantity, ten, of the quality, length. Now it is not
really the province of science to seek for absolute
knowledge of either qualities or quantities, and the
attempt to do so is the excuse for hypothesis. What
science is concerned with is the relative knowledge, or
comparison, of different quantities of any quality and
the reduction of complex qualities into combinations
of simpler ones.

It thus becomes of prime importance to settle on the
simplest and most fundamental qualities which may
serve as a foundation for our system of measurement.
Because of the fact that mechanical motions and me-
chanical forces are the most readjjy perceived by us
and are most easily expressed in mathematical for-
mulae, the fundamental units of quality are always
selected from mechanical concepts. Of these, length,
time, and mass or inertia, are found to be incapable
of further simplification and have been adopted as the
units of measurement. As these qualities must enter

146 THE LIMITATIONS OF SCIENCE

into all equations quantitatively and as we can have
no conception of an absolute quantity, we have by
statute fixed upon certain arbitrary standards of quan-
tity, such as the centimeter and foot for length, the
gramme and pound for mass, and the second for time.
From these prime standards, all other quantities of a
mechanical nature may be readily derived, as for ex-
ample : velocity is the quotient of a given length by a
time; momentum is the product of a mass and a
velocity ; energy, one-half the product of a mass and a
square of a velocity, etc.

As I have already pointed out, the science of me-
chanics is the only branch of physics which has a
completely developed theory. Not only is this the case,
but the other branches of physics have been developed
from a mechanical basis, in so far at least as the meas-
urement of all phenomena is now made in terms of
these mechanical units. This coordination in physics
has the great advantage of making it possible to express
what are apparently unrelated phenomena by using
combinations of only three standards of measurement
and by a few general equations of mechanics. And
we attain the additional advantage of expressing all
these phenomena in the most concrete form imagi-
nable. But, on the other hand, this method produces
a serious break between physics and certain other sci-
ences, especially those which rely more exclusively on
the sense perceptions as criteria for classification of

CLASSICAL AND NEW MECHANICS 147

phenomena. Thus, to the physicist light of different
kinds is distinguished only by the three qualities pos-
sible in a mechanical wave; its wave-length, the
amplitude of its disturbance, and the complexity of its
form. These same qualities must also serve to dis-
tinguish sounds, water waves, and many other types of
this kind of motion. For the biologist and psychol-
ogist, light is distinguished by its tint, intensity, and
saturation, the three qualities which affect the sense of
sight, and sound is determined by pitch, loudness, and
timbre, which affect the auditory nerve. And as there
is no relation between the sensations of sight and hear-
ing, so there can be no connection between light and
sound. While the method of the physicist has the
great advantage of unity, yet it suffers from its arti-
ficiality, as it tends to bring into undue prominence the
mechanical energy involved in producing light and
sound and ignores the more important property of
these phenomena: their effect on our senses.

It is generally conceded that we have no abstract or
absolute knowledge of a quantity of length, time, or
mass. In other words, we can express any of these
three quantities only as a numerical ratio with respect
to a predetermined standard of the same quantity, such
as a yardstick for length, a pound for mass, and a
given motion of a clock-hand or of the rotation of
the earth for time. And, from this fact, it is often
argued that we cannot form any idea of the qualities,

148 THE LIMITATIONS OF SCIENCE

space, time, and matter, except as they are individually
and concretely measured. Kant, to be sure, main-
tained that we were endowed with an innate and inex-
plicable, but sufficient idea of pure space and time.
These qualities are, however, by themselves inappreci-
able to our senses. To make them sensible, we need
a third, which he calls the Ding an sich, corresponding
in the external world to what we call the entity,
matter.

However vulnerable and unsatisfactory the doctrine
of innate ideas may be, yet it seems to me that by the
abstractive method as used in the science of mechanics
we do obtain a real and adequate idea of these three
fundamental postulates. If we have not such a power
of abstracting real ideas from our concrete observa-
tions of phenomena, then it is difficult to believe that
the conclusions of Euclidean geometry and of mathe-
matical analysis in general are rigorous. Thus, in
mathematical definitions, space is a mere volume en-
closed in an imagined boundary which may be con-
ceived as of any extent from the indefinitely small to
the indefinitely large. And this imagined bounding
surface bears no closer relation to a concrete material
envelope than does an image in a mirror to its object.
It seems to me that I have an adequate idea, for
instance, of the space in an empty room and that I
can abstract all the properties from my concrete per-
ception of the material walls of this room except the

CLASSICAL AND NEW MECHANICS 149

one fact that they inclose this space. By deduction
and by experience I am convinced that this space is
not empty, but contains air. But it is really more
difficult to appreciate the existence of the air, if it be
at rest, than its non-existence. This belief is borne
out by the slow advance in the conception of the exist-
ence of gases. And it also seems true to me that I
have an adequate idea 'of an area inclosed in a tri-
angle, because I can think of the area inclosed by three
abstract lines and refrain from thinking of the con-
crete volume of any real lines drawn with a pencil.

As for the concept time, we have a twofold sense
of it; one is the coincidence of an event with the posi-
tion of the hands of a clock or of the earth. But we
have, in addition, a much more general idea of time,
as mere succession of events without any reference to
such a standard of measurement as the second or
minute. This might be called our belief that events
entirely unconnected with our own experience occur
successively just as those events do which we com-
pare with a clock. We have, on awaking from sleep,
a distinct and clear idea that events have transpired
successively during our unconsciousness and without
any reference to a measured interval of time. This
general knowledge of " before and after " is appa-
rently possible to an animal ; a dog will with certainty
expect a reward after the performance of a trick and
not before or during it.

150 THE LIMITATIONS OF SCIENCE

As for the third postulate, which is called matter, it
may be taken in the most general sense as the some-
thing which makes space and time concrete or sensible.
The necessity in science for such a postulate is clear,
for science deals with the phenomena of an objective
world. Even those men of science most opposed to
the idea that mass is the measure of matter still
postulate an entity identical with matter, as just de-
fined, although they may call it by a different name,
such as energy or electricity. And the distinction be-
tween mathematics and science lies in the conception of
this third postulate. In pure mathematics, matter be-
comes the abstract postulate, quantity. When discuss-
ing velocity abstractly there is then no need to con-
sider the properties of the thing moving, but in physics
there is such a need. Or again, when dealing with
space relations the mathematician is in no way limited
to the restricted number of three dimensions which our
sense perception of the material universe imposes on
science.

The supreme value of mathematics to science is due
to the fact that scientific laws and theories have their
best, if not their only complete, expression in mathe-
matical formulae; and the degree of accuracy with
which we can express scientific theory in mathematical
terms is a measure of the state of a science. Thus
it is possible to classify sciences according to their
development, from the accumulation of statistics of

CLASSICAL AND NEW MECHANICS 151

phenomena to the generalization of these phenomena in
comprehensive and rigorous laws. In such a classi-
fication, sociology or the study of existing society oc-
cupies the lowest rank, since true laws can be derived
only from actions whose completed consequences are
known. Sociology therefore attempts to found its
laws on the data of history, the study of past society;
history must in the same way rely on psychology,
which deals with the actions of the individuals of
society; psychology relies on biology; biology, on
chemistry ; chemistry, on physics ; and physics, on pure
mathematics. While each science thus strives to found
its laws on the conclusions of the following science,
each succeeds only partially; this leads us to a paradox.
The goal of science is mathematics, and while mathe-
matics may be said to be the only true science since it
has the only true scientific method, mathematics is not
a science because it deals with abstractions and ignores
concrete phenomena.

As stated before, all quantities in mechanics may
be expressed by combining the fundamental units,
length, mass, and time, in simple ratios and products.
And, while the phenomena of light, heat, and elec-
tricity do not manifest themselves qualitatively to
our senses in any manner which may be coordinated
with mechanical actions, yet we endeavor to measure
them quantitatively in physics as if they were wholly
mechanical in nature. Thus we speak of the velocity

152 THE LIMITATIONS OF SCIENCE

of light from the sun to the earth, as if we were
considering a real mechanical motion of a ponderable
body, although in the intervening space there is no
matter. The only thing we have been able to observe
is, that light emitted from the sun appears on the earth
some time later. Light, as a phenomenon, does not
exist unless it is associated with matter; we can no
more discuss the amount of light or its velocity in
vacuous space than we can speak of the temperature
of such space. Light has a true mechanical velocity
when passing through space occupied by matter, for
then we can observe and measure its path as well as
the time function and so obtain a value for velocity.
From observations on the velocity of light in matter
and from analogy to the phenomena of sound trans-
mission, which takes place only in spaces occupied by
matter, we by the hypothetical method transfer the
measurements and laws of light in transparent bodies
to space not occupied by matter. The very assump-
tion of a light velocity in immaterial spaces requires
us also tacitly to assume that something, in a mechan-
ical sense, is moving. Once we have granted that light
is something moving, then all the other phenomena of
light permit of a hypothetical mechanical explanation,
and we have the right to speak of the momentum and
energy of this light something, whether it be corpuscles
or waves. But it is the easiest thing in the world to
forget that we can never obtain any real knowledge

CLASSICAL AND NEW MECHANICS 153

of this something we have called light. It is sur-
prising that men of science should believe that they
have proved the existence of the ether, as when Sir
Oliver Lodge states that it is the most massive thing
imaginable; or that space is occupied by energy, an
entity possessing inertia and probably gravitational
force, as Professor Einstein announces: they should
see that such statements are not deductions made from
our experimental knowledge of light, but are already
contained in the postulate that light is mechanical and
has a mechanical velocity.

It is instructive to consider, in this connection, how
we also have attached hypothetically the science of
electricity to mechanics. The fundamental phenome-
non observed, when bodies are electrified or magnet-
ized, is that they attract or repel each other with a
mechanical force which, like the force of gravitation,
varies inversely as the square of the distance between
them. In our fundamental units this mechanical force
is equal to a mass times a length and divided by the
square of a time. Now Coulomb, who discovered
and measured the law of electrical attraction, believed
that electricity was a kind of fluid substance, such as
was always introduced when phenomena were obscure ;
and with this idea in his mind, he employed the term
quantity of electricity to indicate an analogy with a
quantity of matter. On this supposition, a quantity
of electricity expressed in mechanical units is equal to

154 THE LIMITATIONS OF SCIENCE

the square root of a length times a mass. Now it is
quite certain that a quantity of electricity has nothing
in common with length. Taking a step further, we
find that the resistance of a conductor to an electrical
current may be expressed as a velocity. Yet it would
be absurd to attach any concrete relation between elec-
trical resistance and mechanical velocity.

These three examples of velocity illustrate quite
clearly the difference between the abstractive and hypo-
thetical methods. From the definite and clear idea of
the mechanical velocity of a concrete body, we pass to
an indefinite idea of the velocity of light in empty
space and in order to link this idea to mechanical
notions, we assign to light a hypothetical material
existence. But our mathematical equations lead us a
step further and we can derive a purely f ormular rela-
tion between mechanical velocity and electrical resist-
ance; in this case analogy between physics and mathe-
matics entirely fails and no idea, even hypothetical,
has been attached to the result.

The principles of the science of mechanics, on which
the theories of the other branches have been built,
date from the time of Galileo and Newton. As they
had withstood the searching criticism of the masters
of the science for centuries without having been shown
to be either false or inadequate, the belief grew that
however other theories of physics might change, the
laws of mechanics as stated by Newton were prob-

CLASSICAL AND NEW MECHANICS 155

ably final. But it is inevitable that if we found the
laws of light and electricity on mechanics, the time will
come when the accumulation of knowledge will in-
crease the discrepancies which must always exist be-
tween any two branches of science and which will
eventually require a thorough revision of one or the
other. If the attention be directed more toward dis-
covering the phenomena and laws of light and elec-
tricity than of mechanics, as it is to-day, these
discrepancies will probably be laid to the laws of
mechanics and their revision will be attempted to
insure agreement. This has occurred in the last few
years, and the mechanics based on material bodies is
being replaced by a mechanics of electricity or by one
of energy, if the terms be permissible.

The mechanics of material bodies, to which the name
of Newton is generally attached, was based on the ob-
jective reality of matter, whose quantitative measure
was inertia or mass. Newton evidently considered
inertia as a fundamental attribute of matter, and thus
invariable and inexplicable; something to be accepted
and determined solely by experiment. Thus he says
in his Principia: " Haec (materiae vis) semper pro-
portionalis est suo corpori, neque differt quicquam ab
inertia massae, nisi in modo concipiendi. Per inertiam
materiae fit, ut corpus omne de statu suo vel quiescendi
vel movendi difHculter deterbetur." This postulate may
be freely translated to mean that the force of attrac-

156 THE LIMITATIONS OF SCIENCE

tion of matter is always proportional to the amount of
matter acting, and does not differ in any way from the
inertia of mass except in our method of apprehending
it. By inertia of matter is meant, that a body can be
changed from its previous condition of rest or motion
only by this material force. It is evident that he
regarded inertia as an inherent and inalienable prop-
erty of a body, independent of the influence of any
other body or ether, and forming the connecting link
between ourselves and the external world. Such being
the case, how may we decide what is the mass of any
particular body? If a number of individuals measure
experimentally a mass, or even if one of them measures
it several times, no two observations will agree. Which
observation gives the correct value? Newton would
have answered, none of them. Data of objective phe-
nomena can never be known exactly ; each value we ob-
tain approximates to the truth, and the approximation
is the closer, the greater the number so obtained and
the greater the care exercised. The final result must
be deduced from all the observations, according to a
well developed mathematical theory of errors. The
same reasoning was held to apply to observations on
the space dimensions of a body and on the time occur-
ring during any event.

While the idea was advanced in this mechanics that
the position and motion of any body could be deter-
mined only from the position of some other body,

CLASSICAL AND NEW MECHANICS 157

supposed for the time being to be at rest, or that posi-
tion and motion were relative and not absolute; yet it
was not explicitly stated that there could not be absolute
rest or motion, such as would occur if the motion of a
body were referred to an absolutely fixed center of the
universe or to an ether which was incapable of motion.
For all practical problems, Newton's third law of mo-
tion, which states that to every action there is an
equal and oppositely directed reaction, announces the
universality of relativity.

We should finally note, that mass, dimensions, and
time were held to be unaffected by the motion of a
body. Newton expresses this by saying that force
actions of matter, or the science of dynamics, are inde-
pendent of its initial state of rest or motion.

The first serious criticism of these postulates was
made by a number of physicists, forming what is often
called the school of energetics, who proposed to sub-
stitute energy for mass as the fundamental attribute
of matter. At the time, the change was rather imma-
terial as we were accustomed to think that mass and
energy were coexistent and that either one was unin-
telligible without the other. As I have said before, it
was the same kind of a problem as deciding which came
first, the owl or the egg; the answer to which is we
know nothing about the matter.

The discrepancies between electricity and mechanics
did not prove to be embarrassing until certain problems

158 THE LIMITATIONS OF SCIENCE

connected with light and electricity became pressing.
Of these, three stand out most prominently.

The phenomena associated with electricity when it
passes through very high vacua and with radio-active
bodies like radium are now explained as being due to
the action of excessively small particles, carrying a
charge of electricity and moving with a velocity com-
parable to the velocity of light, or about one hundred
thousand miles per second. These particles, both be-
cause of their smallness and because of their velocity,
are in an entirely different class from the bodies
previously considered in mechanics which have a sen-
sible mass and whose greatest velocity is less than one
hundred miles per second. Errors in mechanical laws
which would otherwise be inappreciable may easily
assume large proportions when applied to such ex-
treme cases. The hypothesis of the electron has
profoundly modified the conception of the atom, and
the nature of matter and motion.

In the second place, recent experiments lead to the
belief that matter is always electrified; that light is
due to electrical variations; and that the amount of
electricity associated with a given amount of matter is
a fixed and invariable quantity. It is further shown
by theory and confirmed by experiment that if an
electrified body be moved, the ratio of its electrical
charge to its apparent mass must vary with the velocity
of its motion; and since the electrical charge is assumed

CLASSICAL AND NEW MECHANICS 159

to be a constant, there remains only the alternative of
considering the mass of a body as a variable. This
evidently strikes at the very root of Newtonian me-
chanics. The effect of motion on mass is found to be
inappreciable until the velocity approximates to that of
light, so the discussion would have remained a purely
academic one, if the creation of the electron had not
brought us suddenly face to face with bodies which
are supposed to have a velocity great enough to affect
experimentally their mass. A further consequence of
this theory is that mass becomes infinite when the
velocity of light is reached. While that velocity has
always been considered enormous and beyond our
power to attain, such a result was entirely unsuspected.
The laws of mechanics of bodies at rest could evidently
no longer be held to be the same as those for bodies in
motion.

Lastly, various experiments have been made to find
an effect due to the mutual relations of the ether and
matter. None could be found. One in particular, de-
vised by Professors Michelson and Morley, has proved
to be the hardest problem in modern physics to explain.
Calculation showed that certain properties of light
which depend on its velocity should be affected appre-
ciably by the motion of the earth through space, but
the experiment proved beyond doubt that such was not
the case. The first attempt at a reconciliation was
made by assigning certain complicated motions to the

160 THE LIMITATIONS OF SCIENCE

ether which would annul the effect the motion of the
earth should produce; but it was shown that unless the
ether remains absolutely at rest worse difficulties re-
sult. Then the bold assumption was made, often
called the Fitzgerald-Lorentz effect, that the dimen-
sions of bodies in motion were so changed by their
motion as to neutralize the effect of the earth's motion
on the phenomena of light. Every body would, accord-
ing to this idea, grow shorter, the faster it moved;
and would flatten out to a disc of no thickness if it
could attain a speed equal to the velocity of light.

One of the results of this criticism of mechanics has
been to change profoundly our hypothesis of the ether.
As is well known, the early conception of the ether was
a kind of material substance possessing properties in-
compatible with those of any other kind of matter. A
large part of the effort of theorists down to the middle
of the nineteenth century was devoted to inventing
attributes for it which would enable it to fulfill its func-
tion as the medium for the transmission of light. At
this time, Faraday discovered an effect in electricity
which required an entire change in our ideas of the
ether. When he found that static electric charges and
forces were dependent on the characteristics of the
material substance in which electrified bodies were im-
mersed, and when later Maxwell predicted and Hertz
showed experimentally that electro-magnetic energy
passed through vacuous space, and that this form of

CLASSICAL AND NEW MECHANICS 161

radiant energy was undoubtedly of the same type as
light and heat; then it was found that no material
ether could be imagined which would perform these
new duties, especially as it was already staggering
under the burdens of the old ones. Faraday proposed
as a substitute, that we should no longer imagine the
medium to be a substance having material or mechani-
cal properties, but one responding to electrical and
magnetic actions. He was far in advance of his time
and to be acceptable the hypothesis needed the mathe-
matical development which was so skillfully accom-
plished by Maxwell. Both Faraday and Maxwell,
while really destroying the material nature of the ether,
strove to maintain at least a partial connection between
electro-magnetic and mechanical attributes. For this
reason they supposed that electro-magnetic stresses
manifested themselves by creating mechanical strains in
the ether and in matter immersed in it. Such strains
must produce actual physical deformations of size and
shape in all electrified bodies. It has been shown ex-
perimentally by the writer that such deformations are
not produced in electrified matter and lately Professor
Lorentz has stated, that since Helmholtz proved these
stresses would cause the medium to move, and since no
experiment has ever shown us a trace of a motion in the
ether, we must deny the real existence of such stresses.
The effect of such a denial is to separate all attributes
of the ether from concrete realities and to class them

1 62

as abstract symbols. Professor Lorentz is quite ex-
plicit on this point, as he holds that, " while thus deny-
ing the real existence of ether stresses, we can still
avail ourselves of all the mathematical transformations
by which the application of the formula (for these
stresses) may be made easier: . . . and for conveni-
ence's sake we may continue to apply to the quantities
occurring in this integral the name of stresses. Only,
we must be aware that they are only imaginary ones,
nothing else than auxiliary mathematical quantities."
This dematerialization of the ether, when it was once
found that light and heat still managed to come to us
from the sun although we had given its medium of
transmission such a rude shock, has progressed rapidly
until to-day many accept the postulate that there is no
difference between absolutely vacuous space and the
ether, except that the latter is the temporary seat of
radiant energy and possesses a light vector. If this
definition of space means anything, it implies that light
has the power of changing a vacuum into a substance.
When we stop to think that a vacuum means absolute
negation of everything, we realize what an extraordi-
nary thing light is in modern physics. Just consider
this statement of Professor Einstein, which is con-
sidered almost authoritative, " the places in space
where these electro-magnetic actions (i.e., light) occur
are here considered not as states of a sort of matter,
but as self-existing things which are similar to ponder-

CLASSICAL AND NEW MECHANICS 163

able matter and in common with it have the character-
istic of inertia." One has merely to ask, what becomes
of these self-existing things when light ceases to go
through a certain space and it slips back into its state
of vacuity?

Without going into details, we find a like trend in
the hypothesis of the nature of matter. It began with
the atom as a minute simulacrum of ponderable bodies,
and then we proceeded to strip away one concrete at-
tribute after another until for a brief interval matter
was a manifestation of an entity, electricity. But
even this idea was too concrete, too material, to serve
and now the objective universe is the symbol, energy.

If we finally subscribe to these ideas, are we not
really acknowledging that hypothetical science has
failed as the interpreter of an objective world? It
seems to me the guides to knowledge are now to be
found in those subjective impressions which must
depend on the individual and vary with him. Scientific
laws are thus not facts to be discovered but the tempo-
rary consensus of opinion of a number of individuals
who, for the time being, find themselves in agreement.
The classical natural philosophy of Newton and Gali-
leo has drifted into that transcendental symbolism
which is apt to take place when German thinkers be-
come the leaders in philosophy.

Evidently an almost chaotic condition had de-
veloped in our ideas of space, matter, and electricity.

164 THE LIMITATIONS OF SCIENCE

Each theorist advanced an hypothesis of the most
tentative character which all felt to be inadequate.
Yet, in spite of the confusion, three points of agree-
ment may be noted. In the first place, the ether as a
material substance is impossible and even useless; the
name, it is true, is left but it expresses now but the
shadow of a reality. When the ether is called an
electro-magnetic something, or a space differentiated
only by the transient presence of energy, the name may
signify something but it is hardly intelligible except as
a mathematical symbol. Secondly, these theories
agree in assuming electricity to be an entity; that is,
we are to suppose that it is not due to a state of mat-
ter, manifested by a special mechanical force, but a
substance like matter, divisible into atomic elements
and having inertia. Thirdly, the mass inertia of mat-
ter is not an invariable quantity but changes with the
velocity of a body; thus it is the measure of matter
only while there is no motion.

Such was the state of physical theory when Professor
Einstein announced, in an article published in the
Annalen der Physik for the year 1905, a new scientific
principle which he believes will reconcile the contra-
dictions of our new hypotheses; satisfy the three con-
ceptions mentioned; and correct and amplify the New-
tonian mechanics so that it will again harmonize with
modern science. Whether this Principle of Relativity
will accomplish all that its discoverer hopes can be

CLASSICAL AND NEW MECHANICS 165

decided only after an exhaustive trial. But there is no
doubt as to the startling effect it has produced on scien-
tific theory nor of the far-reaching importance of its
conclusions. For example, Professor Planck of Berlin
is said to have declared that this new idea of time and
space surpasses in boldness anything that has appeared
up to the present time in speculative science.

The name, Principle of Relativity, is derived from
Professor Einstein's first postulate, which is as fol-
lows: the idea of absolute rest or absolute motion is
an impossibility to the human mind, and not only in
mechanics, but also in electro-dynamics corresponds
to no properties of phenomena.

In addition he announced as a second postulate that
the velocity of light, V, in empty space is an absolute
constant of nature. Hence this velocity, contrary to
all others, is independent of the motion of the body
emitting and of the one receiving the light. The
startling nature of this postulate is readily under-
stood when we remember that the closest analogue to
light is sound, the velocity of which is known by ex-
perience to be dependent on these quantities.

He has recorded for us, that he became convinced of
the necessity for these postulates, because the theory
of electro-dynamics developed by Maxwell leads to
an asymmetry, when applied to moving bodies, which
is not true experimentally. For instance, when a mag-
net and an electric conductor are moved with respect

166 THE LIMITATIONS OF SCIENCE

to each other, the phenomena of the forces developed
are observed to depend only on the relative motion of
the magnet and the conductor, but Maxwell's theory-
requires a different explanation, according to which is
moved and which remains at rest. Besides this dis-
crepancy between observation and theory, experiments,
devised with sufficient accuracy, fail to show any effect
of the earth's motion through space on the phenomena
of light.

It will be convenient to grant these postulates and
follow Professor Einstein's deductions before attempt-
ing any criticism. In the first place, their adoption
does away with the possibility of an ether and revives
the postulate of space as a vacuum. Both theory and
experiment show that an ether, if there be one, must
be in absolute rest with respect to the motion of the
earth, and the first postulate denies the possibility of
absolute rest and motion. Again, the failure of New-
tonian mechanics lies in the assumption, which is
always tacitly made, that moving bodies are subject
to the same mechanical laws as those at rest. As I
have already pointed out, the modification to be made
in the laws for ordinary bodies is very minute and
would probably never have become of importance if
modern theory had not been interested in the properties
of bodies moving with velocities approximating that of
light.

The root of the error in the mechanics of moving

CLASSICAL AND NEW MECHANICS 167

bodies, Professor Einstein believes, lies in our deter-
mination of time, and clear thinking in regard to time
is nearly all that is necessary to clear up the trouble.
Suppose a body or a material point to be at rest rela-
tively to a coordinate system of three rectangular lines,
then its position can easily be determined by the ordi-
nary geometrical method of measuring its distance
from each of the lines by rigid measuring-rods. But
if the point is in motion with respect to the reference-
system, its position depends on time and cannot be
determined by the geometrical method. Our idea of
time is usually defined by what we call isochron-
ism; we say an event occurs at seven o'clock,
when the occurrence of the event and the position of
the hour-hand of a clock at seven are simultaneous.
But suppose the clock were at some distance from us,
then we could observe the hand to be at seven only
after it had passed beyond that figure, since it would
take some time by any method of transmission for the
intelligence to reach us. As the velocity of light is the
greatest of all known motions, the least discrepancy
would be caused by using light signals as the mode
of transmitting such intelligence. Also, if we accept
the second postulate, our intelligence will be still more
accurate because the velocity of light is unaffected by
other motions and we thus avoid the difficulty caused
by the question whether any relative motion between
us and the clock is an approach or a separation. To

168 THE LIMITATIONS OF SCIENCE

illustrate further our confusion as regards the measure-
ment of time, suppose two persons wish to record two
events, which we shall grant to be simultaneous,
but which occur at different places, A and B. An
observer at A records the event, when it occurs at A,
as being at TA time by his clock, and instantly signals
the fact to an observer at B. Whatever the means of
signaling, a certain time will elapse before the ob-
server at B is cognizant of it. For the reasons given,
we shall adopt light signals as the best method. B
observes the signal as TB time by a clock placed at
B and immediately reflects it back to A, who receives
it at T'A time by his clock. Although we have granted
that both events were simultaneous, it is evident they
will not be so recorded by the two observers. B will
record the event at A as being later than the one at B.
But if the velocity of light be absolutely independent
of all conditions, then we should find that the differ-
ences of time going and returning are the same, or
TB— TA = T'A— TB. This relation is satisfied by any
two events occurring at a distance from each other,
is Professor Einstein's definition of simultaneous
events or isochronism. The definition may be put in
this form; two events are simultaneous, if the differ-
ence of time to flash a signal there and back is equal
to twice the distance between the two positions divided
by the velocity of light, V.

Not only does this limitation in our ability to meas-

CLASSICAL AND NEW MECHANICS 169

ure time affect our ideas of time, but it also has an
important and unsuspected influence on our ideas of
the size and shape of a body. This may be shown by
an example. Suppose we wish to measure a rigid rod
of length, I, moving in the direction of its axis with
a velocity, v, then there are two methods of measuring
this length and they do not give concordant results.

First an observer may move with the rod and meas-
ure its length by applying directly to it a measuring-
rod. He will evidently obtain the same result as if both
he and the rod were at rest.

A second method is possible and is frequently em-
ployed. An observer remains at rest and notes the
positions of the two ends of the rod, at a certain time,
t, which he determines by means of clocks, also at rest
and tested for synchronism. These two points are
dependent on our ability to record simultaneous events ;
if the rod were at rest the problem would be the one
already discussed, but in this case the rod has a velocity,
v, and consequently the time used in signaling in one
direction involves, V — v, and in the other, V + v.
So when he measures the distance between the two
points, which may also be called the length of the
rod, he will find it not equal to / as determined by the
first method, if he still regards his clocks as isochro-
nous; or if he determined two positions whose
measured distance is / then his clocks will no longer be
isochronous.

170 THE LIMITATIONS OF SCIENCE

Now our measurements of length are usually made
under the condition that we, clocks, and rods are all
moving with the earth and so relatively at rest. Our
measurements of length of bodies on the earth are
thus different from those which would be made on the
same bodies by an observer if he could be stationed
with his clocks in the moon. Also if an object on the
earth is measured while it is moving with respect to
the observer, it will appear to have a different length
from that which it has when relatively at rest. Thus
the dimensions of a body are dependent on its velocity,
and Newtonian mechanics, which assumes the con-
trary, must be modified when applied to bodies in
motion.

Professor Einstein then derives a set of equations
which will express the dimensions of a moving body
as they appear to a stationary observer. These show
that the length of every body moving with a velocity,
v, is diminished in the direction of its motion by the
fraction

and that its dimensions at right angles to its mo-
tion remain unchanged. Thus a sphere in motion
becomes an ellipsoid flattened in the direction of
its motion by an amount equal to the above frac-
tion. It is proper to say, that this effect is quite
inappreciable at ordinary velocities. This is true even

CLASSICAL AND NEW MECHANICS 171

of so great a velocity as that of the earth around the
sun. This velocity is about thirty kilometers per sec-
ond while V is 300,000 kilometers per second. One
diameter of the earth would thus, to an observer in
the sun, appear shortened about 7.5 centimeters, or
three inches. But this effect becomes quite important
for velocities approaching one-tenth of V. And a
velocity equal to that of light is absolutely unattain-
able because the length of the moving body would
then be reduced to zero. So we have the curious
anomaly of a finite velocity producing an infinite
effect.

The same equations also show that if1 one of two
clocks, which are synchronous when at rest, be moved
with a velocity, v, the stationary clock will run faster
each second than the moving one. The maximum
value of the difference is when one clock runs infinitely
faster than the other.

We must not lose sight of the fact that this discus-
sion, so far as mechanical bodies and motions are con-
cerned, is purely academic, because for them the ratio
v/V is too small in any known case to have an appre-
ciable effect. The Principle of Relativity has its great-
est significance when applied to problems in electricity,
provided we accept the theory of electrons. // the
atom of matter be composed of particles of electricity,
if the inertia of matter be variable and due to elec-
trical reactions, and if the velocity of the electron

172 THE LIMITATIONS OF SCIENCE

approaches that of light, then the effect of its velocity
on its shape, size, and mass is an important matter.
For, let m be the mass of an electron at rest, from
Professor Einstein's formulae, its apparent mass in the
direction of motion is

m

and its mass at right angles to the motion which would
make it resist change of direction is

Thus we have the unusual result of not only a variable
mass, but also a difference in mass according to the
direction considered.

Another consequence of the hypothesis is, that mass
also depends on energy. This result is of extraordi-
nary importance, for it means we have no ability to
distinguish between the inertia of a physical system
of bodies and its energy; in other words, between the
inertia of a body and the energy content of the space
surrounding it. When we recall Professor Einstein's
conception of space and energy, which I have quoted,
most persons will become convinced that no idea of
the nature of matter could be more abstract. The
mass of a single body thus remains constant only when

CLASSICAL AND NEW MECHANICS 173

its energy remains constant. If it gives out heat,
light, or electro-magnetic energy, or if it even moves,
its mass continually decreases, until, theoretically at
least, it would melt away into a complex of energy : I
know oi no name to designate so immaterial a thing
as this complex of energy located somewhere in vacu-
ous space. To be sure, this interchange between mass
and energy is very slow, so slow that ordinary minds
grow skeptical of its existence. Thus a body radiat-
ing enough heat to warm a kilogram of water, one
degree Centigrade, would decrease in mass only about
4.6 X io~~" grammes. It is fortunate that mass dis-
sipates so slowly or we should indeed be things dreams
are made of.

The last deduction I shall note is that the tem-
perature of a moving body is less when measured by
a moving observer than by one who is stationary.

Such are some of the more startling conclusions
which have been derived from the Principle of Rela-
tivity. If they can be established, and men be per-
suaded that the universe is, or even may be, as they
indicate, a revolution has been accomplished in scien-
tific thought. If we are to criticise the conclusions of
this hypothesis, and they are opposed to what seems
reasonable, it must be done by examining the postu-
lates; in them, as in all hypotheses, lies the real
strength or weakness of the system.

Professor Einstein asks us to accept two postulates.

174 THE LIMITATIONS OF SCIENCE

The first is; we have no ability in us to determine
absolute rest or motion. We can say only that one
body is at rest or changes position with respect to
others. Phenomena are conditioned entirely by the
relative positions of bodies and we can gain nothing
toward an explanation by introducing the idea of abso-
lute position. The second postulate is; the velocity
of light, V, is a universal and absolute constant.

Apparently no objection has been made to his state-
ment that these two postulates are sufficient from
which to derive all the conclusions mentioned. But it
seems to me, at least two more independent postulates
are advanced in the memoir on relativity, which must
also be granted. I shall propose as a third, Professor
Einstein's definition of time, and as a fourth, the as-
sumption of the atomic nature of electricity. The
fourth postulate carries with it as corollaries, that the
amount of electricity per atom, or the electron as it is
called, is a universal constant, and that the mass of the
electron is variable. My excuse for offering them is,
they cannot be derived from his postulates, and his con-
clusions require them.

The first postulate can be granted at once and unre-
servedly for all purely mechanical motions of bodies.
These involve merely changes of position and do not
affect the nature of bodies nor their phenomena. But
it must be accepted with limitations when in addition
to mechanical motion, and by mechanical motion I

CLASSICAL AND NEW MECHANICS 175

mean a mere change of position, one body is emitting
energy in the form of heat, light, or electricity, and the
other receiving it. True relativity requires a strictly
symmetrical arrangement Now the mechanical mo-
tions of two bodies with respect to one another are
symmetrical. If a body has a velocity, vlf to the right
and another a velocity, v2, to the left, they approach
each other with a velocity, Vi '+' v2. The same result is
obtained if the velocities of the bodies are interchanged.
This symmetry is not true if the first body is emitting
energy and the second receiving it. The behavior of
each is then conditioned by the behavior of the other
and in an asymmetrical manner. As an illustration:
let a body by a periodic disturbance of its parts send
out a wave of heat; this proceeds, according to theory,
through space in all directions and on encountering a
second body produces a periodic disturbance in it. The
effect of this energy is twofold; the motions of the
parts of the two bodies are symmetrical but the wave
itself does not proceed from the second body in all
directions but only in the one already impressed upon
it by the first body. To make this clearer, we may start
a wave along a stretch of string by plucking aside one
part of it; the wave will travel from the initial point
along the string in two directions, causing successive
parts to vibrate symmetrically, but these parts will
send the wave in one direction only. So we may say
the velocities of two bodies are relative because the

176 THE LIMITATIONS OF SCIENCE

quantities appear in the mathematical expression in a
symmetrical manner ; so also are their momenta or their
masses multiplied by their velocities. But this is not
the case for energy since it involves the square of the
velocity. The squared velocity remains positive al-
though we change direction and the composition of two
energies is always an addition. For true relativity, a
change in direction must be accompanied by a change
in sign. The extension of the idea of relativity to in-
volve cases of radiant energy is partly responsible
for the conclusion that mass is a function of energy.

Professor Einstein's second postulate has been
widely discussed and many attempts have been made to
interpret it. At first sight it seems absurd to say that
the mechanical motion of a body emitting light
does not affect the velocity of the light emitted. But
the fact remains that all our experiments, and they
have been most accurate and searching, fail to find
any difference in the velocity of light whether the
sources and the recipient are at rest or in motion. As
we have seen, Professor Einstein, with admirable
directness, goes straight to the point: he accepts the
reliability of these experiments; assumes the constancy
of V as a postulate, determines its effect on the space
dimensions of bodies and on time, and finds that we
must change our previous ideas of these radically. Let
us, when discussing V, consider it under two heads :
first, when light passes through transparent material

CLASSICAL AND NEW MECHANICS 177

bodies and is subject to experimental verification; sec-
ondly, when it passes through space absolutely de-
prived of material bodies and so is not subject to
experimental evidence.

In the first case, we know that there is a true path
and that light moves very approximately in straight
lines, and we have quite accurately measured the time
light requires to move from one place to another
through various substances. V is here the length of
path divided by the time, — a true velocity. We know
that this V is a variable; it is less in water than it is in
air, and still less in glass. It is also less in dense air
than in rarefied air. Not only does V vary with the
kind of matter through which light passes, but it also
depends on the motion of the medium as shown in the
experiments on the velocity of light passing through
columns of moving water made by Fizeau and repeated
by Professor Michelson. The velocity of light in
material media is therefore subject to all the variations
which influence the velocity of sound and other types
of motion and evidently cannot be the V assumed by
Professor Einstein to be an absolute constant.

He must then limit his postulate strictly to what is
called the velocity of light in absolutely immaterial
space. There are two methods of obtaining this value.
We observe the difference in time between the cal-
culated eclipse of some satellite and the recorded ob-
servation of the event or we use other stellar phe-

i;8 THE LIMITATIONS OF SCIENCE

nomena. If we know the distance and the time, we
say the velocity of light in empty space is the quotient
of the two. Such observations are quite inadequate
to settle experimentally the question of the constancy
of V. Our measurements of the distances are crude
for such a purpose, and also the light must travel part
of the way through a material medium such as the air.
Neglecting such astronomical methods, we have left
only determinations of V made on the earth where
the path is necessarily through matter. Here, what we
are to call the constant V can be found only by extra-
polation. For example, we find that the ratio of the
velocity in air and in water is about four to three and
agrees with their refractive indices. We find also that
the velocity in different gases as they are reduced in
density tends to a common value, which is independent
of the kind of gas and approaches the value 3 x io10
centimeters. If we take this extrapolated value of
3 x io10 centimeters for the velocity of light in empty
space and assume the refractive index of space to be
one, then we may calculate back and by this method we
find the absolute refractive index of air at ordinary
pressure to be 1.0002. Such an experimental method
and such reasoning are highly unsatisfactory. In the
first place, we start with measurements of lengths and
time which are subject to experimental verification and
calculate V, from these we pass to a supposititious V
where only one factor, the time, is subject to experi-

CLASSICAL AND NEW MECHANICS 179

mental proof and the other factor, the length, is not, as
we cannot experiment on the path of light in free space.
But passing this objection, we have calculated from
length and time determinations a value for V and Pro-
fessor Einstein declares it to be an absolute constant.
He then reasons backward that the length of a body
and time determinations must be variables with motion,
in order to keep V constant. Of course, if Professor
Einstein wishes to look on the universe as a purely ab-
stract conception; and if he wishes to make what we
sometimes call concrete or objective phenomena cor-
respond to his preconceived idea of the universe, he
can assume V in a vacuum to be a universal and ab-
solute constant and no one can disprove it sci-
entifically. But there are some who still cling to
the idea that dimensions of bodies and time are
not subject to our fancy, and who believe that
if any quantities must vary, it should be those
which we have no means of determining directly.
And after all it is asking a great deal of us, to
upset our ideas in order to explain at bottom a
single experiment, that of Michelson and Morley, how-
ever accurately it has been performed and however
puzzling its results may be. He has not even the
justification his predecessors would have had. When
the ether was believed to be a crystalline solid which
vibrated with the passage of light rays, V had a real
meaning although we could not determine it directly.

i8o THE LIMITATIONS OF SCIENCE

When the ether was a substance which periodically
varied electro-magnetically, we could still say that V
had a possible meaning. But the latest definition, that
the ether is absolutely quiescent space to be distin-
guished from vacuous space only by the fact that it is
the seat of an entity, called electro-magnetic energy,
and contains a light vector, makes the word velocity
when applied to V absolutely without meaning in any
ordinary sense of the term. To speak of a motion in
an absolutely quiescent space is a rather startling state-
ment. The ether also becomes a local affair, shifting
back and forth in vacuous space according as light is
present or not. The feeble light of a candle, appa-
rently, changes nothing into something.

But aside from these considerations, which lie in the
debatable land and which will be decided largely by the
temperament of the individual, there seems to be an
absolute contradiction between the first two postulates
as I understand them. If V be the value of the velocity
of light in an absolutely quiescent ether and itself a
constant, then the velocity of light in a material me-
dium, such as air, is an absolute velocity or motion
when referred to V. Now the first postulate declares
that we can have no knowledge of absolute motion
and, in addition, that the explanation of phenomena is
not conditioned by absolute motion.

The third postulate, which I have proposed as neces-
sary for the system proposed by Professor Einstein,

CLASSICAL AND NEW MECHANICS 181

is his definition of time. He says, — our idea of time
is defined by synchronism or the simultaneous occur-
rence of an event and the position of the hour-hand
of a clock at a certain position, the number seven for
example. This is certainly not our idea of time but
merely our method of measuring it quantitatively. If
we did not have an adequate idea of time as the mere
succession of events, we should have no conception of
what simultaneous occurrences are nor of how to
measure time. His definition gives me the feeling
that if I could make clocks go slower my life would
become longer. In the review of his memoir, it was
pointed out that his definition of simultaneity or isoch-
ronism, when combined with the constancy of V, led
to the conclusion that two clocks which were syn-
chronous, when relatively at rest, would not remain so,
if one of them were given a velocity. Moreover the
length of a body in motion decreases with respect to
its length when at rest. It is certain that these re-
sults depend on the constancy of V. If we are willing
to rest our knowledge of time and space on a value
which by the nature of things can never be put to a
direct test, I am convinced of the theoretical correct-
ness of these results. But I am not willing to do this.
I prefer to trust to the invariability of time and space
phenomena, even if it requires V to be a variable and
time measurements to contain an unavoidable dis-
crepancy. By so doing, I am aware that I forfeit an

182 THE LIMITATIONS OF SCIENCE

explanation of the Michelson-Morley effect and of
some others, but this loss is not overwhelming and we
can afford to wait for an explanation until a future
time.

I am the more willing to take this attitude, because
I can see no means of applying the Principle of Rela-
tivity to the test of experience. As we have seen, the
velocity of light in any material medium is a variable
and can be no more trusted than the velocity of sound.

Perhaps this illustration may make my meaning
clearer. Suppose a race of men to exist who are blind
and have no knowledge of electro-magnetic radiation,
but who wish to measure the lengths of moving bodies.
They will undoubtedly be compelled to get this in-
formation and that of the synchronism of clocks by
sound signals. It is evident that observations car-
ried out under conditions similar to those imposed by
Professor Einstein would indicate that the length of
a moving body underwent changes. And while they
could make corrections for some of the effects, because
sound waves are largely affected by the motion of
media and of sonorous bodies, yet they would undoubt-
edly come to the conclusion that the dimensions of a
moving body depended to some extent on its motion.
Now, if we should bestow sight oh one of these men, he
would be able to correct their measurements; as he
could by his immensely more rapid light signals gain a
much more nearly instantaneous value for synchronism.

CLASSICAL AND NEW MECHANICS 183

We are, at present, in the condition of this man. As we
improve in our ability to measure the velocity of light
under different conditions we shall, Professor Ein-
stein thinks, get closer to the knowledge of the abso-
lute V and to the relations for space and time which
he has derived. But we may suppose men will some
day find a kind of radiation which has a velocity
greater than V (for example, the transmission of
gravitation), and by its aid remove the conviction re-
maining in our minds that motion affects length and
time. Calculation may show that material bodies can-
not attain this velocity, but we are speaking of an
immaterial radiation. To say that such a radiation is
impossible is as futile, at least as unscientific, as for a
race of the blind to say that there is no light.

Since the motion of any ponderable body is too slow
to make the ratio r/v an appreciable quantity, the only
supposable case, where this ratio can enter as a deter-
mining factor, is in problems of radio-activity and the
discharge of electricity through gases. In these, the
particles of matter are supposed to be so small and to
have a velocity so great that their mass and size are
measurable functions of their velocity. But to limit
the applicability of the principle of relativity to such
supposititious bodies as electrons, is to rob it of its im-
portance, and we should hardly consider it one of the
great principles of nature.

But even this is not all: if we wish to apply the

184 THE LIMITATIONS OF SCIENCE

principle to electrons, we shall need a fourth postulate.
We must assume that a quantity of electricity is
atomic in character; either the charge of electricity
associated with what we call an atom of matter is an
invariable, or, as it is now usually expressed, elec-
tricity is an entity which may be divided into invariable,
equal, and indivisible parts called electrons. As a
corollary to this postulate, the ponderable mass of an
atom is a variable depending on its velocity. It has
been shown that the constancy of electric quantity and
the variability of mass is not a necessary assumption.
All experiments, which involve both these quantities,
include them in the form of a simple ratio, e/m ; where
e is the quantity of electricity and m the mass of the
electron. It is evident that any value may be given
to this ratio by supposing either one of its members
to remain constant and the other to vary, or by sup-
posing both to vary in opposite fashions, and it is just
as reasonable to keep m constant and to let e vary with
the velocity, as to make the contrary assumption. This
is certainly possible until we have experimental evi-
dence which will determine our decision, and this evi-
dence is not likely ever to be at our disposal.

If we attempt to estimate the results which follow
from the postulates of relativity, the first would be that
Professor Einstein has proved that we cannot theoret-
ically measure in space and time moving bodies exactly
by the laws which apply to bodies at rest. The first

CLASSICAL AND NEW MECHANICS 185

postulate will be accepted for all mechanical motions
and no further attempts should be made to find experi-
mentally an absolute motion. But the second postulate
contradicts the principle of relativity, if by V we mean
the absolute motion of something, — matter, energy,
or light through quiescent space. If, on the other
hand, V is understood to be the velocity of light in
space containing matter, then it cannot be taken as
a universal constant. The third postulate concerning
time should not cause us to change our belief that the
dimensions of a body and the unit of time are inde-
pendent of velocity, but it should show us how to cor-
rect our measurements of moving bodies, as we must
correct all subjective measurements of objective phe-
nomena.

If we grant the assumptions of Professor Einstein,
the theory of relativity is a perfectly logical system so
long as we apply it to abstract systems moving with a
constant velocity in a straight line. But I can find no
evidence that the postulates agree with experimental
facts and certainly, to the present time at least, its
conclusions will not affect experimentally the laws of
mechanics. Also its theoretical conclusions are limited,
as yet, to the rare cases when there is neither any
change of speed nor of direction. We should remem-
ber before we abandon or modify Newtonian mechanics
that mathematicians have devised numerous systems
which point to different mechanical laws. If we pos-

186 THE LIMITATIONS OF SCIENCE

tulate a fourth dimension to space we can deduce per-
fectly logical laws for a mechanical system that are
quite different from the laws of ordinary mechanics.
And the universe, constructed on this principle, is a
very beautiful and interesting one. It is the privilege
of mathematicians to deal with symbols; the physical
universe is no more important to them than any other
universe which can be developed symbolically. The
trouble occurs when the distinction between the real or
physical universe and symbolical or metaphysical uni-
verses is obliterated in the minds of men of science.

CHAPTER VI

E egli questo un far loro oracolo una statua di legno, e a
quella correr per i responsi, quella temere, quella riverire, quella
adorare. — GALILEO.

THE intellectual habits of men have a very decided
effect on their characters, and it is evident that Galileo
had met with contemporaries who carried their devo-
tion to the hypothetical and dogmatic scientific method
of Aristotle to a state of idolatry, accepting on faith
that which should be submitted to experience. The
quotation, from his Dialogues on the Two Principal
Systems, which I have given expresses his opposition to
such idolatry in no uncertain language. It is fortunate
for me that I wrote this chapter as an essay with the
same title before I had read Galileo's comment, because
the quotation is so ben trovato that otherwise I should
have been accused of fitting an argument to a title.

Men of science have two principal functions to per-
form: first to observe the phenomena of the world;
and when certain connections and differences are
found in these phenomena, to classify them under laws.
The conclusions, thus derived, have been used with
great success to enlarge our intellectual life; to modify

187

188 THE LIMITATIONS OF SCIENCE

our environment; and to promote our comfort and
power. But, allured by their great and legitimate suc-
cess in these two fields of activity, they have also tried
to discover the hidden causes of phenomena, with the
result that a sort of fictitious world has been created
by them, in which the laws of objective, or physical,
phenomena are inextricably confounded with the de-
ductions of subjective psychology. Science is made
metaphysical, and at the same time pretends to sup-
plant metaphysics.

This encroachment, naturally, has not been accom-
plished without a sharp conflict, and the history of
the nineteenth century is permeated with the struggle
of science against religion and philosophy. The issue
was clearly in favor of science, which has not only
gradually become a dominating influence in education
and in thought, but has also changed our attitude to-
wards history, politics, and social life to such an extent
that these subjects are now classed as sciences. Even
philosophy and religion were unsettled by its growing
power; instead of basing character on attributes pecu-
liar to man and designated by the name of spiritual
powers, many now include man with the rest of organic
life as subject only to the statistical and impersonal
laws of heredity and environment: metaphysics tends
towards a philosophy of science; religion to eugenics.

Both the conflict and the victory were no doubt in-
evitable. But the results have not been on the whole

SKEPTICISM AND IDOLATRY 189

beneficial either to society or to science. It would be
difficult to prove that the acceptance of the belief that
man has no divinity, in at least the sense of super-
natural powers, and no innate standards of right and
wrong — in other words, that he is merely the most
complex machine in a world governed exclusively by
physical and chemical laws — that such a belief has not
sunk him to a lower plane of morality and induced
in him a resigned weariness towards such a fate.
The victory has not only reacted on science in such a
way as to give the world a too implicit confidence in
its hypotheses, but it has also made men of science
dogmatic and rash in proposing bold and unsupported
speculations, — impatient of criticism of themselves and
hypercritical towards religion, philosophy, and all
other methods of human thought. Thus the most
urgent need is a severe and just criticism, not of our
experimental observations or of our logic, but of our
hypotheses. One of the greatest difficulties in de-
veloping such a criticism lies in the fact that so few
men of science leave any record of their intimate and
personal convictions as to the limitations and the pos-
sibilities of their field of action. They content them-
selves, for the most part, with a mere statement of
experimental results, or they develop speculative
theories without much consideration whether they are
fanciful or whether their influence will be good or
pernicious. Such criticism as there may be is directed

190 THE LIMITATIONS OF SCIENCE

towards checking the accuracy of observation and the
logic of deduction. As for hypothesis, there is a gen-
erally accepted and naive belief that any such endeavor
is beneficial.

The writings of men of genius in science frequently
exhibit this sort of naivete in method of thought. And
probably a too critical attitude would be a hindrance
to their creative powers as they must look at problems
intensively, and exclude the many complexities and
doubts which would tend ito embarrass them in their
special work. It would be foolish to say " thus and
thus only shall a man work out his ideas." We have
an Ampere who develops the laws of electro-dynamics
from the experimental facts of electricity, and quite in-
dependently of the prevailing hypothesis of the nature
of electricity; and, on the other hand, a Lord Kelvin
who could not work until he had first visualized a
problem, and usually he put this image into a concrete
form, making for the purpose many different models
of atoms out of sticks and strings, to illustrate the
properties of matter.

But science has other functions in addition to the
attack and solution of problems by the creative power
of the individual : phenomena and laws must be taught
in detail to the specialist; general conclusions must be
given to the world in order that they may become a
part of the general intellectual life; and finally dis-
coveries are to be applied to social and industrial needs.

SKEPTICISM AND IDOLATRY 191

Thus, not only the results obtained by creative minds,
but also the methods of obtaining them, are important,
because they will ultimately be interpreted and pro-
mulgated to others. The harm done by a vicious
method of thought may outweigh the benefits of a
useful discovery happened upon in spite of them.
There is always this danger in the hypothetical method;
the man who assists his intellectual labors by the help
of crude mechanical models undoubtedly tries to keep
distinct in his mind the real actions of nature from
the properties of his model, let us say of the atom.
But in imparting his results to others, this model is
made to assume an aspect of reality in the written word
which was not in his own mind. Baffled by the diffi-
culty of expressing complicated ideas, he paints his
metaphorical pictures too vividly. The process grows
more pronounced as the idea passes from mind to
mind; the fictitious model grows progressively more
and more concrete, until to the student and to the world,
it is at last the concrete model of the atom that be-
comes the reality, while real matter dissolves into an
abstraction. And if words can be relied on to express
ideas, the creator of the atom himself is a believer
in the reality of that creation of his imagination, the
model.

This sort of speculation is probably least dangerous
in pure mathematics. The mathematician looks upon
the world symbolically. He studies its laws from pos-

192 THE LIMITATIONS OF SCIENCE

tulates which are given to him by others, or assumed
by himself. Thus he may derive the laws of mechanics
from a postulate that bodies have three spatial dimen-
sions, which is verified by observation; but he is also
interested in the mechanics of bodies which would
prevail if there were four dimensions to space, a pos-
tulate not verifiable. He develops a geometry which
requires the axiom that parallel lines do not inter-
sect ; and at the same time he studies another geometry
based on the axiom that parallel lines do intersect. He
finds it no more important as an exercise in analysis
to study a solar system which is subservient to forces
of attraction, than one which obeys a law of repulsion.
That is, he is not limited at all to what we call the
reality of an objective and material world, and mathe-
matical deductions regarding an imaginative world will
have very little influence on society. So, also, the
purely hypothetical parts of such abstract subjects as
physics, chemistry, and astronomy are not very influ-
ential in a direct manner, but indirectly they have had
an enormous influence since they have been taken
as an example for the development of biology and that
class of sciences known as political and social. Specu-
lations in these subjects have a direct and intimate
bearing on the character of the individual and on so-
ciety. Thus a ready proneness to accept hypothesis
and speculation as well as observation has resulted
in the crude laws and dogmas of eugenics, and has put

SKEPTICISM AND IDOLATRY 193

government under the necessity of hearkening to the
dilettante of the slums, and the feminist; all of whom
are preaching the scientific basis of their nostrums. It
is not then a matter of indifference what the hypotheses
of even the abstract sciences may be, or how we attempt
to solve their problems.

Two books * have recently appeared most oppor-
tunely, which record the mature beliefs of two con-
spicuous men of science concerning the value and
necessity of scientific hypothesis. We could scarcely
have two authors more widely contrasted in tempera-
ment and in opinions than Poincare and Sir Oliver
Lodge; the one, a skeptic who views with detachment
the efforts of men to penetrate the mysteries of nature,
and the other, a credulous believer with equal convic-
tion in matter and ether and spirits.

Before discussing their views, we should call to
mind that Poincare began his career and attained his
greatest eminence as a pure mathematician; that he
later critically examined the theories of physics; and
finally turned to philosophy for the purpose of examin-
ing the foundations of science. Sir Oliver Lodge has

* The Foundations of Science. By H. Poincare. An author-
ized translation by George Bruce Halsted of " Science and
Hypothesis," "The Value of Science," and "Science and
Method," with an introduction by Professor Royce. (The
Science Press.)

Continuity. The Presidential Address to the British Asso-
ciation for the Advancement of Science for 1913. (Putnam's.)
By Sir Oliver Lodge.

194 THE LIMITATIONS OF SCIENCE

worked mostly from the experimental side. With an
early tendency toward speculation, he wrote several
books which aimed to give a most concrete, and even
crude, picture, of natural phenomena. His present
position as executive head of a university has thrown
him into the practical affairs of life. And probably
his chief trait of mind is the belief that all things, from
engines to souls, are best considered as manifestations
of a luminiferous ether which has the characteristics
of a jelly.

It will be best now to let Poincare state his ideas
regarding the scientific method in his own words : for
he has done so most lucidly and vividly. The quota-
tions are from Professor Halsted's authorized trans-
lations :

" Experiment is the sole source of truth. It alone
can teach us anything new; it alone can give us cer-
tainty. But then, if experiment is everything, what
place will remain for mathematical physics? What
has experimental physics to do with such an aid, one
which seems useless and perhaps even dangerous ? And
yet mathematical physics exists, and has done unques-
tionable service. We have here a fact that must be
explained. The explanation is that merely to observe
is not enough. We must use our observations, and
to do that we must generalize. This is what men have
always done; only as the memory of past errors has
made them more and more careful, they have

SKEPTICISM AND IDOLATRY 195

observed more and more, and generalized less and
less."

" It is often said experiments must be made without
a preconceived idea. That is impossible. Not only
would it make all experiment barren, but that would
be attempted which could not be done. Everyone
carries in his own mind his own conception of the
world, of which he cannot so easily rid himself. We
must, for instance, use language; and our language is
made up only of preconceived ideas and cannot be
otherwise. Only these are unconscious preconceived
ideas, a thousand times more dangerous than the
others."

And he goes on to show how barren would be the
mere accumulation of experimental facts, and how
the master minds group them into generalizations and
laws which make them fit for use. Out of complexity
they achieve simplicity and order. And he warns us
that even in this true phase of science, lurk the dangers
of preconceived ideas, and of inaccuracy of expression.
Having pointed out the proper path, he then enters the
more debatable field of hypothesis:

" All generalization," he says, " is a hypothesis.
Hypothesis, then, has a necessary role that no one has
ever contested. Only, it ought always, as soon as pos-
sible and as often as possible, to be subjected to verifi-
cation. And of course if it does not stand this test it
ought to be abandoned without reserve. This is what

196 THE LIMITATIONS OF SCIENCE

we generally do, but sometimes with rather an ill
humor."

" The firm determination to submit to experiment is
not enough ; there are still dangerous hypotheses ; first,
and above all, those which are tacit and unconscious.
Since we make them without knowing it, we are power-
less to abandon them. Here again, then, is a service
that mathematical physics can render us. By the pre-
cision that is characteristic of it, it compels us to
formulate all the hypotheses that we should make with-
out it, but unconsciously."

It is just here that I think Poincare begins to leave
sure ground, and by a confusion of thought and terms
he falls into what seems to me an impossible posi-
tion. He first stated that a generalization is an hypoth-
esis. It is true that every generalization is speculative
to the extent that we cannot verify it by experiment
with absolute accuracy or in all possible cases. For in-
stance, no one supposes we can ever record all the
changes of energy which occur in the universe, yet we
state with great confidence that energy is conservative.
The justification for our belief is simple. All the
cases we have measured confirm the law. And this
law is of the kind that can be frequently and readily
put to the test of experimental verification; until
future experiments shall show it to be in error, we
have the right to believe the law correct. But hypoth-
esis has a wide range of meanings besides that of

SKEPTICISM AND IDOLATRY 197

signifying a tentative generalization which will ulti-
mately be accepted as a law or be rejected because of
its increasing disagreement with observations and, un-
fortunately, it is used very loosely. It frequently
means those speculations in which we indulge when
we attempt to define the causes of phenomena; when
we create fictitious substances, as an atom or ether;
and when we construct models to illustrate the actions
of forces. None of these cases is a generalization in
the sense of Poincare's first statement, because it can-
not be verified by experiment. It would greatly sim-
plify thought if we would confine the term hypothesis
to these speculative ideas, and use the words law or
theory for those generalizations which are based on
experimental observations of a material world. One
has only to note Poincare's own confusion of thought;
if we must generalize, and if our generalizations are
hypotheses which are subject to, and must be verified
by, experiment, then such hypotheses are the truth,
so far as can be determined by scientific methods. We
certainly have the right to ask : how can they be dan-
gerous and how can there be a too great multiplica-
tion of them, if they are the truth? If they can be
subjected to experiment, then as soon as one is dis-
proved, it would necessarily be abandoned. The reason
for his caution to us is that Poincare knows that the
great majority are incapable of verification, since they
deal with purely metaphysical ideas. His own words,

198 THE LIMITATIONS OF SCIENCE

quoted from the introduction to his Theorie de la
Luwviere, will prove this:

" It matters little to us whether the ether really
exists; that is the business of the metaphysician to
find out; the essential thing for us is that everything
acts as if it existed, and that this hypothesis is con-
venient in explaining phenomena. After all, have we
any other reason for believing in the existence of ma-
terial objects? Is not that belief also a convenient
hypothesis ; only we shall never cease to make it, mean-
while the time will come, without doubt, when the ether
will be rejected as useless."

See what an advance in confusion of thought we
have now! Hypothesis is no longer a necessity, it is
a convenience. If those of the ether (and no idea has
been more fruitful than the ether) cannot be verified
by experiment, how can they be convenient, because he
says unverifiable hypotheses are dangerous; and if they
can be verified, how can we reject the truth, whether
they are convenient or not? Again, how can every-
thing act as if the ether existed, unless it does exist?
Is not that our definition of existence? And lastly, one
would suppose that if we shall never cease to postulate
the existence of matter, we have come as near making
matter a certainty as we can ever attain to any cer-
tainty.

The unfortunate feature of such statements is that
they constantly rise to trouble their makers. We shall

SKEPTICISM AND IDOLATRY 199

see later that Poincare absolutely reverses this opinion,
rejects matter and clings to the ether; meanwhile, both
of his opinions are unsupported by experimental evi-
dence, which he has declared to be the touchstone of
truth and usefulness for hypotheses. Not only does
Poincare drift in this hopeless fashion between matter
and ether, but the founders of the New Mechanics are
at sea as regards the existence of the ether. One
school of thought claims that all substance is but a
differentiation of the ether, which thus becomes uni-
versal substance; the other school is just as positive in
its belief that the ether is a wornout fiction. In spite
of this trifling difference in their points of view, both
schools arrive at much the same conclusions. At
least they give us a good illustration of the power of
mind to modify matter. During the recent conference
at Brussels for the purpose of discussing the new con-
cepts of matter and mechanics, Poincare suggested
that it was unfortunate that physicists were using the
ether when they needed it, and were discarding it when
it proved troublesome. Curiously, no one in the con-
ference seemed to find the situation of the New Me-
chanics in the least embarrassing or humorous; the fact
is, the consequences announced at the conference were
so unintelligible that a sense of humor would have
been out of place.

Although Poincare says that we must generalize,
and that every generalization is an hypothesis, still

200 THE LIMITATIONS OF SCIENCE

he finds he must distinguish between different kinds,
and must warn us against their indiscriminate use:
" It is important not to multiply hypotheses beyond
measure, and to make them only one after the other.
If we construct a theory based on a number of hypoth-
eses, and if experiment condemns it, which of our
premises is it necessary to change? It will be impos-
sible to know. And inversely, if the experiment
succeeds, shall we believe that we have demonstrated
all the hypotheses at once ? "

This is excellent advice, but when he makes hypoth-
eses, he does not heed his own warning and neither
does anyone else. Imagine a physicist saying to
another, yours is dead, now let me have a turn
with one. But let us follow Poincare's classification
further :

" There are first those which are perfectly natural
and from which one can scarcely escape. It is diffi-
cult not to suppose that the influence of bodies very
remote is quite negligible. . . . They are the last that
ought to be abandoned.

" There is a second class of hypotheses, that I shall
term neutral. In most questions the analyst assumes
at the beginning of his calculations either that matter
is continuous or, on the contrary, that it is formed of
atoms. He might have made the opposite assumption
without changing his results. He would only have
had more trouble to obtain them ; that is all. If, then,

SKEPTICISM AND IDOLATRY 201

experiment confirms his conclusions, will he think that
he has demonstrated, for instance, the real existence of
atoms? "

' These neutral hypotheses are never dangerous, if
only their character is not misunderstood. They may
be useful, either as devices for computation, or to aid
our understanding by concrete images, to fix our ideas
as the saying is. There is, then, no occasion to ex-
clude them.

" The hypotheses of the third class are the real gen-
eralizations. They are the ones that experiment must
confirm or invalidate. Whether verified or condemned,
they will always be fruitful. But for the reasons that
I have set forth, they will only be fruitful if they are
not too numerous."

It would seem to almost anyone that the first and
third classes are so different from the second class,
that it is advisable to call them laws, and limit the
term hypothesis to the speculative second class. The
class of neutral hypotheses is evidently the melting-pot
for the bewildering ethers, atoms, subtile fluids which
abound in the physical sciences, and which have their
analogues in all the others. Poincare teaches us that
we shall never acquire any definite knowledge from
them, and then he makes the amazing statement that
there is no need to exclude them if they are not mul-
tiplied, if they are made one after the other, and if
their character is not misunderstood. Anyone in the

.202 THE LIMITATIONS OF SCIENCE

least conversant with their history knows that their
number is great, and that they are not proposed con-
secutively. As for their character, he evidently means
that they are dangerous if we forget they are mere
conveniences, fictions, not to be taken too seriously. It
is perfectly safe to say that there is scarcely a text-
book or a treatise in any science which does not state
explicitly that the sort of things classed by Poincare
as neutral hypotheses, are realities and not conjectures.
Before showing how Poincare and Sir Oliver Lodge
confirm this opinion, let me quote two statements of
Sir J. J. Thomson:

" The ether is not a fantastic creation of the specu-
lative philosopher; it is as essential to us as the air we
breathe. . . . The study of this all-pervading sub-
stance is perhaps the most fascinating and important
duty of the physicist."

" The possession of a charge by the ions increases
so much the ease with which they can be traced and
their properties studied that, as the reader will see, we
know far more about the ion than we do about the un-
charged molecule."

Evidently convenience of computation and an aid to
our understanding by concrete images are not at all in
the minds of even eminent physicists when they indulge
in neutral hypotheses of ethers and atoms.

Now let us return to Poincare, and see how he heeds
his own warning. But first notice how clear and how

SKEPTICISM AND IDOLATRY 203

vivid his thought is when he is not involved in these
pitfalls to accurate reasoning: " Is not each great ad-
vance accomplished precisely the day someone has
discovered under the complex aggregate shown by our
senses something far more simple, not even resembling
it — as when Newton replaced Kepler's three laws by
the simple law of gravitation, which was something
simpler, equivalent, yet unlike ? "

To this excellent question, he gives the following
lamentable answer :

" One is justified in asking if we are not on the eve
of just such a revolution or one even more important.
Matter seems on the point of losing its mass, its solid-
est attribute, and resolving itself into electrons. Me-
chanics must then give place to a broader conception
which will explain it, but which it will not explain. . . .
The ether it is, the unknown, which explains matter,
the known; matter is incapable of explaining the
ether."

How can Poincare justify himself? When we re-
call how Newton refrained from giving any hypoth-
esis regarding the cause or nature of gravitational
force, because he felt such an hypothesis would be out-
side the field of science; and how the subsequent veri-
fication of the law of gravitation by innumerable
experimental observations has established it as one of
the few great and universal laws; and when we recall
what Poincare says about electrons, the ether, and

204 THE LIMITATIONS OF SCIENCE

neutral hypotheses in general, how can we be expected
to see any similarity in these two revolutions? The
two, on the contrary, are diametrically opposed to
each other. Does Poincare really mean that it is to be
the function of science to resolve matter, which he
said we must always assume to be an objective reality
whether we can prove it or not, into electrons, an
hypothetical component of the hypothetical atom, the
assumption of whose reality should be a mere fugitive
matter of convenience ? And does he believe the boast
of science, that it shall rest on the objective experi-
ence of our sensations rather than on the subjective
proof of our imaginations, can be maintained, if we
admit for an axiom, that henceforth it shall be the
aim of science to explain the known by the unknown ?
He might have pursued this revolution further; the
dissolution of matter into the electron is but the first
step in the confusion of ideas, those who are promoting
it are further transforming the electron into a strain
in the ether of a type unknown to experience, and the
most advanced are dissolving the ether into nothing.
The process of explaining the known by the unknown
is complete; matter to atoms; atoms to electrons; elec-
trons to ether; ether to nothing. Truly, philosophy
and theology are gross materialism compared with
such a science. Can he so quickly and completely for-
get his wholesome, skeptical, and critical attitude,
merely because he also is tempted to indulge in specu-

SKEPTICISM AND IDOLATRY 205

lation? As an example of what absurdities are ad-
vanced in speculative physics, I give his final utterance
on the existence and nature of matter, which he de-
livered in a lecture on the " New Mechanics " : " We
can almost say that there is no longer matter, but only
holes in the ether; and in so far as these holes seem to
play an active part, it consists in the inability of these
holes to change their location without influencing the
surrounding ether which exerts a reactive influence on
such changes."

What to make of such a statement passes under-
standing. There was once a man who pestered the
students in Baltimore by giving them tracts which
proved in fifty-seven or more different ways that the
earth was hollow, and that we lived on the inside, and
so in a hole. But not even he was so confused as to
contend that we were holes living on the outside of a
hole. Poincare has, of course, no resemblance to that
man and yet, unless he means something by the word
" hole " which is understood exclusively by himself and
a small coterie of physicists who write in the same
absurd fashion, there is no more sense in his definition
of matter. If there were any connection between
the words and the idea — that is, if he were trying to
define the word matter so as to express our experience
of it, then his statement makes matter the answer to
the old conundrum : " What is it, the more you take
from it, the more it be ? " I admit matter is not ether ;

206 THE LIMITATIONS OF SCIENCE

but if it is a hole, then a hole in the ether is just the
contrary to a hole. Holes never even seem to play an
active part in anything; they show no inclination or
ability of themselves to change their location; and
nothing, except an ether, has ever been conceived of as
able to react on a hole. The simple fact of the case
is, such statements are attempts to do just what Poin-
care said they were, — attempts to explain the known by
the unknown. The pity of it is that science is filled
with just such attempts; we recognize the words used,
but their sense is so twisted that they really express
no clear idea. In comparison with such quibbles and
such verbal distortion, the action of Dr. Johnson,
when, in answer to the similar logic of a metaphysician
of the Berkeleian type, he kicked a stone as our ulti-
mate proof of the existence of matter, is true science —
at least it is organized common sense. It is comical
to read the opinions, concerning the essence of matter,
of those modern physicists who have succumbed to the
fascination of explaining the known by the unknown.
Led by a small band of German physicists, they use
mathematical symbols and scientific phrases; and yet
they are explaining phenomena in quite the approved
medieval fashion of transcendental symbolism. It is
perfectly easy to match their statements with the ab-
stract theorems of an Albert Magnus or a St. Thomas
Aquinas. In other words, modern science has sud-
denly taken a leap into pure metaphysics, while, at the

SKEPTICISM AND IDOLATRY 207

same time, it persists in the habit of sneering at meta-
physical methods.

It was with the greatest regret that I found Poincare
had given in to this form of idolatry of the graven
images of science. His mathematical writings, his
physical theories, and his critical spirit had always
impressed me as models of clear and vivid thinking.
And the statements I have quoted show that he did not
adopt this other mode of messy thinking without
reluctance. His ideas no longer are unqualified: he
is willing to admit only that things seem to point this
way or that, as if he had been caught and entangled in
this German school of transcendental symbolism, and
could not see his way out.

Sir Oliver Lodge has no such scruples. He rejoices
in his beliefs, and delights in promulgating a clear
knowledge of all the unknowable things in the universe
just as he sees them ; especially by popular essays ad-
dressed to those whose lack of technical training makes
them unable to discriminate between real and sham
science. In his recent presidential address on " Con-
tinuity," he tries to accept at once the modern me-
chanics and Newtonian mechanics, continuity and dis-
continuity, and scientific laws for bodies both mortal
and immortal. But with all the trouble which this
reconciling of irreconcilables gives him, he always
finds comfort and refreshment in his " fervent belief in

208 THE LIMITATIONS OF SCIENCE

the Ether " : in some way it will solve our difficulties.
This is his creed :

" The Ether is the universal connecting medium
which binds the universe together, and makes it a co-
herent whole [not hole] instead of a chaotic collection
of independent isolated fragments. It is the vehicle
of transmission of all manner of force, from gravita-
tion down to cohesion and chemical affinity ; it is there-
fore the store-house of potential."

In short, the Ether, not being matter, is for Sir
Oliver pretty nearly everything else; almost, if not
quite, God, even to the use of the reverential capital
initial. More specifically, he considers it the principle
of continuity, and in continuity he finds a scientific
proof of immortality. If he had based a belief in the
immortality of the soul on an analogy with the con-
tinuity of existence of matter and energy, I think many
persons would agree that he was expressing one of our
most certain reasons for such a hope. It is difficult
to suppose that the quantity of matter and energy in
the universe is unchangeable, and yet to maintain that
thought and emotion, which have so many of the char-
acteristics of durability, end with death. On the con-
trary, " we * do see the sum of mind increasing every
time two old thoughts coalesce into a new one, or even
every time matter assumes a new form before a re-
ceiving intelligence." But such an intimation of im-
* Unpopular Review, April, 1914.

SKEPTICISM AND IDOLATRY 209

mortality is a very different thing from assuming a
body of postulates and creating a de facto science of
psychic phenomena, as Sir Oliver Lodge does. Science
must deal with material things, and must be confined to
our sense perceptions. So that, whether immortality
and psychic phenomena be ultimately accepted or not,
the proof must be expected by other than scientific
methods, unless we give to these words a totally dif-
ferent significance from what they had in the past.
Omitting all other difficulties, one wonders how imma-
terial intelligences can make material noises, for, if
they do, what becomes of our law of conservation of
energy which accounts for all material motion by ma-
terial causes? Of course he falls back on his omnipo-
tent Ether :

" The evidence to my mind goes to prove that dis-
carnate intelligences, under certain conditions, may
interact with us on the material side, thus indirectly
coming within our scientific ken; and that gradually
we may hope to attain some understanding of the
nature of a larger, perhaps ethereal, existence, and of
the conditions regulating intercourse across the chasm."

Science is still burdened with the inexplicable mys-
tery of the material world, and it should not open the
doors of its temple for the worship of graven images,
even if the idol is the great god Ether. Sir Oliver
Lodge's speculations are not even qualified by logical
methods. His reasoning is apparently a mere play on

210 THE LIMITATIONS OF SCIENCE

words: Immaterial spirits are not material bodies, the
ether is not matter; therefore spirits may be ethereal
bodies. It does considerable harm when he uses his
official position and, as it were, makes the British As-
sociation indorse such foolish views.

Sir Oliver Lodge still believes with the past genera-
tion of physicists that science has discovered a path
to positive knowledge : " Many scientific men," he says,
" still feel in pugnacious mood towards Theology, be-
cause of the exaggerated dogmatism which our prede-
cessors encountered and overcame in the past. They
had to struggle for freedom to find truth in their own
way; but the struggle was a deplorable necessity, and
has left some evil effects." It has left evil effects, and
the chief of them is Scientific Dogmatism.

In spite of our self-confidence, we cannot be too
sure that hypothetical science has not traversed the
same path as dogmatic theology. We have a fairly
large and clearly defined body of moral facts. And
we have generalized from them rather consistent moral
laws. It is inevitable that we shall always speculate as
to the causes of these moral facts and laws, and it is
probable that most men will continue to fashion an
image of their idea of God, more or less anthropo-
morphic and concrete. But unfortunately for religion,
many will not stop at this point of pure speculation, or
the worship of God in spirit and in truth, but they will
carve for themselves images in wood and stone, and

SKEPTICISM AND IDOLATRY 211

bow down and worship these images as realities. So
also there are the many who will not stop at the great
and scientific work of discovering phenomena and
laws, but they will speculate on natural causes and
mechanisms. If they do this with an open mind, per-
haps no harm is done as Poincare says, and possibly the
imagination may be healthfully stimulated. How few
stop at this point may be imagined from the examples
I have given ; a large and increasing number have be-
come idolaters, and are worshiping the graven images
of science with dogmatic fervor.

CHAPTER VII

SCIENCE AS THE ARBITER OF ETHICS
Sire, in this system there is no need of a God. — LAPLACE.

WHEN Renan wrote that humanity must, in future,
look to science for what it craves in the way of a law
and symbol, science was in the full swing of conquest.
The war between it and religion was believed to be all
but over. The law of evolution was accepted not only
in its general aspects, but also it was believed that in
natural selection a cause had been discovered which
would permit us to trace the progress of the organic
world from the simple protoplasm to the most complex
forms of life. Search was made for the missing link
between man and the lower animals, and those at-
tributes which an earlier age was content to group as
spiritual powers were abolished as unscientific. It was
inevitable that philosophers like Renan and Spencer
would propose an evolutionary law for society, and
that even religion would fall in line and make of God a
sort of omnipotent and beneficent natural force which
gently led man up to ever higher types of perfection.

And while to-day those who cultivate the more exact
sciences have come to believe that the objective and

212

THE ARBITER OF ETHICS 213

subjective worlds are governed by different forces, the
wave of evolutionary philosophy, under scientific domi-
nation, has spread to the students of political and
social history who are trying to devise a state which
shall evolve toward better conditions by natural means.
The result is that the attitude of thoughtful people
toward the moral questions of the day is one of more
or less perplexity. Few of them are willing to accept
the doctrine that human nature is essentially good and
that the only need of society is to remove all restraint.
In the past, the majority of men experienced this neces-
sary restraint in the conviction of personal respon-
sibility to a God, who actively interfered in their
thoughts and deeds, and who rewarded or punished
according to a revealed standard of righteousness.
But with the growth of knowledge and especially with
the impersonal attitude assumed in scientific inquiry,
the impression has become widespread that mankind
has been left to work out its own destiny. So, as I
have said, thoughtful people are perplexed to know
where to turn to find an inner check which can replace
that sense of personal responsibility to a God which,
however men might rebel, did exert a steady and po-
tent influence upon them. Some still cling to the idea
that the Christian church will ultimately discover again
the guiding principle for society; that a new reforma-
tion from within is all that is necessary. But the diffi-
culty is graver than in the past, as such reformations

214 THE LIMITATIONS OF SCIENCE

involved matters of doctrine rather than a change in
fundamental ideas. Many are simply drifting; but
an increasingly large number are frankly turning to
scientific doctrines in the hope that a deeper experi-
mental knowledge of the laws of man's individuality,
of his social relations, and of his environment will
bring with it the solution of the problem. And in
spite of our very deficient acquaintance with such laws,
some are proclaiming that this naturalism is the
surest guide for us in evolving a society nearer to the
ideally good. Apparently, they have the idea that
accurate observations and statistical records, which
may be formulated into scientific laws, are sufficient
as guides to conduct.

A curious feature of the discussions, which have
arisen about these new systems of scientific ethics, is
that almost no attention is paid to the fundamental
question whether the deductions of science are suitable
to serve as an ethical principle for society; or even
whether science, except indirectly, concerns itself with
character; yet character, or the judging between right
and wrong, is necessarily the essence of all systems of
ethics. Now I think it can be shown that the pursuit
of science has for its aim to acquire power; that is, we
seek through science to learn the facts of nature and to
interfere with natural forces so as to make them se"ve
man's desires. As an illustration of the mixture of
truth and fallacy, which is typical of many who advo-

THE ARBITER OF ETHICS 215

cate scientific ethics, consider this statement of a writer
on genetics which merely reflects a widespread opinion :
" Human civilization goes hand in hand with the de-
gree of successful interference which man exerts upon
the natural forces surrounding him." The truth of
this statement lies in the correct view that the pur-
pose of scientific inquiry is not only to discover the
forces of nature but to interfere with them so as to
increase man's dominating power; the falsehood con-
sists in assuming that civilization is based on, or even
necessarily runs with power. Everyone knows that
power may make for evil as efficiently as for good;
the ethical standard of a civilization depends on the
will of its individuals to choose between right and
wrong. To deny this, is to refuse the attributes of
the noblest civilization to Jesus, to Buddha, to Socrates,
each of whom was quite ignorant of science, and lived
in times when men exerted themselves but little to
interfere with natural forces. Nor could we to-day, in
the midst of an earnest scientific endeavor, deny that a
civilization higher than our own would be possessed
by a community formed of men like to them.

The greatest difficulty encountered, if the attempt be
made to determine the ethical value of science, is, as I
nave said before, the lack of a spirit of serious criti-
cism amongst men of science, with the consequent
absence of critical data on the aims of science and on
the effect which scientific activity has had on society.

216 THE LIMITATIONS OF SCIENCE

Before much can be done to find out what the influ-
ence of science on morals has been, a school of critics
of men of science must be created. I am quite aware
that this opinion is counter to the general belief that
science is the most critical of all human endeavor. The
results of experimental investigation and the mathe-
matical laws formulated from them seem so positive,
so subject to minute and patient scrutiny, that it may
well seem that men of science are critical. But this
form of criticism is limited to the mere question of
accuracy of observation and logic. Before the sub-
jective influence of science on character can be deter-
mined, the postulates of science and the scientific
method itself must be outlined clearly and discussed
critically; it is this higher criticism which is lacking
in men of science.

If such a body of criticism existed it is probable
that a philosophy of science could be created. But the
present method of educating men to engage in scientific
work is little likely to foster the critical or even the his-
torical attitude. In fact, most men of science know
so little of metaphysics or even of the historical de-
velopment of science that they are quite ignorant of
how metaphysical their sciences are. If they were
conversant with the history of scientific thought, they
would see that while scientific laws are as positive and
as objective as human knowledge has been able to
attain, yet the hypotheses of science, which aim to dis-

THE ARBITER OF ETHICS 217

cover the causes of phenomena and to simulate the
mechanism of natural forces, are as subjective and as
dependent on human opinion as any other form of
knowledge. And it is just these subjective and meta-
physical aspects of science which are concerned in the
question of the relation of the external world of
phenomena to our internal world of ideas.

One would naturally turn to the histories of science,
not only for the data of scientific experience, but also
for that larger aspect of the question, the discussion
of the relations between scientific thought and other
forms of human activity. But almost without excep-
tion our histories of science are mere chronicles of
scientific experiments and hypotheses. The work of
each man of science is outlined in as great detail as the
scope of the history permits, as if everything done in
the name of science were important. What we should
have, is a discussion of the development of the sub-
ject and of the relations between the intellectual forces
of a given epoch and the scientific activity of the same
period ; for example, there should be shown the relation
of the ideas of Galileo, Copernicus, and Descartes to
the Renaissance ; at a later date there is a similar close
connection between the rise of electricity, the skeptical
spirit of the mathematical physicists, and the revolu-
tionary and democratic ideas which were prevalent at
the beginning of the nineteenth century.

The most striking evidence of the ineffectiveness

218 THE LIMITATIONS OF SCIENCE

of scientific histories is, however, their attitude toward
hypothesis. Such hypotheses are clearly subjective in
character and are to be criticised in accordance with
the same standards as a philosophical system of Plato
or Kant. Instead of this they are invariably treated as
if they dealt with phenomena verifiable by experi-
ment.

In our histories of science a number of things about
scientific hypotheses might have been brought out. In
the first place, all of them rest on mechanical analogies
and attempt to make of the world, both inorganic and
organic, a vast machine whose parts grind out motions
which reveal themselves to us as heat, light, thought,
and whatever else we are cognizant of. That is, a
mechanical explanation of phenomena is considered to
be the simplest and most satisfactory one that can be
given. But we know there is no criterion which will
distinguish the truth between many rival mechanical
hypotheses. Thus the explanation of phenomena is
dependent on subjective interpretation, and is in the
end a matter of personal opinion. Nor does the recent
attempt to replace matter by electricity escape this
difficulty since the principles governing electrical
forces and energy are the same as those controlling
matter. The restrictions pointed out are still in force,
with the substitution of the word electricity for matter.

It is also evident that, however logically a scientific
hypothesis may be developed, we can never say that

THE ARBITER OF ETHICS 219

it is anything more than our idea of the world; thus
scientific hypothesis stands on the same ground as any
other kind of logical thought. Criticism of hypotheses
should therefore be directed principally to their postu-
lates.

In the next place, the postulates of science are al-
ways metaphysical in character since we must assume
initial conditions of space, time, and substance which
are not subject to experimental verification and which
are contradictory to our experience of the present
state of those quantities.

We imagine a simple primordial universe which is
crudely fictitious, and start it going on its complicated
career by the action of some universal force which un-
balances and unlocks its internal actions and reac-
tions.

Then we assume the existence of fictitious sub-
stances, atoms, which we deliberately fashion so small
as to be below the limit of observation. We endue
them with as many different and contradictory at-
tributes as may suit our convenience in order to
fashion the diverse forms of bodies by their combina-
tion.

And lastly, if we are to attempt to include in the
name of science all laws, we must provide portions of
this machine with life, thought, and self-consciousness
as a form of mechanical forces.

Evidently, the postulates of science are as complex,

220 THE LIMITATIONS OF SCIENCE

as subjective, and as debatable as the postulates of
religion and philosophy. And they also lack the sim-
plicity and generality which have made the postulates
of geometry universally acceptable and have given to
them the appearance of finality. And from these meta-
physical postulates of natural science, the scientific
conclusions follow which somehow impress us as being
positive knowledge not subject to human opinion.

Since most of our scientific postulates and the
hypotheses which are developed from them are not
questions of objective facts, they must have an influ-
ence which may be helpful, harmful, or indifferent.
And it should be the chief duty of the historian and
the critic to trace this influence. Instead of this
critical spirit, it is only too common for men of science
to insist that all hypotheses are meritorious. This
opinion is so widespread, that it is frequently stated
that even if a hypothesis be entirely false, yet it may
be useful. The reason for this lack of discrimination
lies probably in the fact that science has gradually
created two worlds connected by only a slender thread ;
one the experimental world of our sensations, and the
other a fictitious world of our imagination. What-
ever the prevailing hypothesis may be, the experi-
mentalist continues his work, confident in the belief
that if his results agree with a hypothesis they will be
taken as a confirmation of it; and if they disagree, then
he may be sure that the hypothesis will be modified so

THE ARBITER OF ETHICS 221

as to conform to them. Thus the phenomena and laws
of light continue to unfold themselves in a consistent
progress in spite of the fact that now one, and now
another, contradictory hypothesis of the mechanism of
light and its transmission through space is uppermost.
This is the explanation of the reason, so puzzling to
the layman, why two conflicting hypotheses, explaining
the same class of phenomena, can be maintained and
cultivated at the same time. There is no telling when
new facts will be discovered which will bring an al-
most discarded hypothesis back into favor. The fic-
titious worlds of natural science bear a close analogy
to those hypergeometrical realms of the mathematician
which, while logical and interesting, do not rest on
experience and so do not exist. Such mathematical
worlds of the imagination are invented as a sort of
intellectual game and can have no influence on human
actions and society; so also the hypothetical properties
ascribed to nature by the physicist cannot affect our
relations to our environment.

This neglect of the critical field by men of science
has resulted in leaving to metaphysicians the discus-
sion of scientific methods and the development of what
now passes under the name of scientific philosophy.
Whatever the influence of this criticism may have been
on philosophy and on thought generally, it is safe to
say that it has had little on science; its conclusions
have not engaged the attention of men of science very

222 THE LIMITATIONS OF SCIENCE

seriously. The reason for their indifference is two-
fold. Rightly or wrongly, it is felt that the meta-
physicists are too engrossed in the exact definitions of
terms and in the niceties of verbal expression. They
thus miss or confuse the real issue of science, which is
to discover the significance and influence of objective
facts rather than of words. This does not mean that
the careful use of words is not important in science.
It is only too apparent that many of the battles of
science are waged over the meaning of words and not
of phenomena.

The other reason for the ineffectiveness of this sci-
entific philosophy as developed by the metaphysicists
is that they are not disciplined by labor in the labora-
tory nor trained in the analysis and technique of
scientific theory. They must thus depend on elemen-
tary treatises, which are rarely the work of master
minds; or they can approach the great thinkers only
through the medium of popular expositions in which
the most scrupulous are somewhat relaxed. To con-
trast the opinions of Plato with Ganot does not com-
mand respect ; and to depend on the popular addresses
of a Helmholtz or a Lord Kelvin is not to know their
real thought. The first leads to frequent errors and
the second to sweeping conclusions. If we are to
develop a satisfactory scientific philosophy it seems
requisite to have it done by men trained in science and
conversant with philosophy ; this combination has been

THE ARBITER OF ETHICS 223

a rare one, of which the greatest examples are Aris-
totle, Descartes, and possibly Kant.

It is difficult to see how this combination of science
and philosophy is to be obtained with the present sys-
tem of training men in our graduate schools. The
prospective man of science is 'taught laboratory methods
and becomes, thanks to it and to his research work, a
rather skillful manipulator of apparatus, but he rarely
is required to trace back the gradual development of
the subject on which he is working. It remains in his
mind as a more or less isolated fragment, since he is
quite ignorant of the work of the master minds of
science of the past. When he leaves the school, he is
impressed by 'the head of his department with the
opinion that he must continue his research work; left
to his own devices he casts about for new problems,
and, in despair of ideas, continues some of the minor
points left unsolved in his thesis. A second article
appears and then the curtain drops. In addition to
his laboratory work, the student attends lectures in
theoretical science and passes rigid examinations which
are for the most part exercises in ingenuity in mathe-
matical and logical exposition of the most modern and
abstruse parts of the science. The lectures treat the
science as a modern and fully developed theory devoid
of continuity of background. Hypothesis is mixed
with fact, and fugitive speculations with permanent
laws; his texts are largely confined to purely specula-

224 THE LIMITATIONS OF SCIENCE

tive philosophy and fail to contrast the limitations and
the permanent achievements of science; no connection
with past thought is drawn and the probable aspects
of future thought are not shown. Indeed, no mention
is made of the prime fact that human thought has been
concerned with these fundamental problems for so
many centuries, and methods of scientific attack are
so limited in number, that no new theory or hypothesis
can be developed; witness our present return to Car-
tesianism. At most, what we call modern thought is
but a recrudescence of past thought dressed in new
clothing. The see-saw of the time-worn antinomies
constantly recurs. Since the historical and critical
attitude toward science is almost wholly neglected, the
student enters his life work innocent of the limitations
and powers of his science; practiced in modern text-
books and ignorant of the masters of the subject.
Some teachers of science realize this vaguely and ad-
vise their students to take a minor in philosophy. Now
the philosophers, not knowing science, have introduced
certain emasculated courses under the name of scien-
tific philosophy or scientific methods for just such
students. One has merely to read the texts used and
learn the views of the expositors to find that the texts
are written, and the courses delivered, by men who
know nothing of science at first hand. Thus the course
merely discourages the student and gives him a con-
tempt for philosophy as a juggling of words and quite

THE ARBITER OF ETHICS 225

different from the exact and virile sciences. If stu-
dents of science are ever to attain to the wide outlook
which the dignity of science deserves, teachers of sci-
ence must themselves first learn the historical and
critical development of their subject, establish its rela-
tion to other knowledge, and then impart this spirit to
their neophytes.

If the postulates of science are doubtful and con-
tradictory, what is likely to be the effect on science
and thought in general of the hypotheses derived from
them? The very general belief that any hypothesis,
whether false or not, is useful to science puts us in
a curious attitude in respect to other methods of
thought. Evidently, it is a doctrine which does not
hold elsewhere; the theologian, the philosopher, or the
historian who ventured the same opinion would quickly
be attacked; and yet science is supposed to be the
search for objective truth. The reason for this pecu-
liar attitude of men of science is due to the fact that
the real work in science is connected with phenomena
and laws, and this true aim of science has never really
been lost sight of, however much the hypothetical
method may have distorted it.

I suppose it may be granted that hypotheses should
be divided into the three general classes of the good,
the false, and the indifferent.

Good hypotheses are those which are known as laws.
They are generalizations from such necessary postu-

226 THE LIMITATIONS OF SCIENCE

lates as the conservation of matter and energy, or they
are advanced as tentative laws when a certain number
of phenomena can conveniently be classified; they be-
come steadily more exact as our knowledge of the sub-
ject increases and are finally accepted as laws; such
has been the history of the second law of thermo-
dynamics, of the law of evolution, and numerous
others. The difference between these proper hypoth-
eses or laws and other hypotheses is that a law does
not attempt to explain the mechanism of nature as an
hypothesis does. That is, laws may be readily recog-
nized because they deal only with sensible matter and
its attributes and can thus be subjected to a rigid
test of their truth; all other hypotheses, since they at-
tempt to explain natural actions, must create fictitious
substances and attributes and when they are found to
depart from facts they are not discarded but are merely
modified by arbitrarily altering the fictitious substances
on which they depend. This difference is shown clearly
by Darwin's law of evolution and his hypotheses of
natural selection and pangenesis, or by Newton's law
of gravitation and his hypothesis of light corpuscles.
The history of science points to no more certain conclu-
sion than that laws persist and hypotheses decay. For
this reason, I have emphasized the distinction between
the two and have limited the term, hypothesis, to those
scientific theories which require the creation of fictitious
substances and occult forces and whose use has caused

THE ARBITER OF ETHICS 227

us to cross those boundaries which properly limit sci-
ence.

As for false hypotheses, it would seem to be self-
evident that they should be abandoned as soon as a
postulate or conclusion was shown to be wrong. It is
just as important to discard error in science as it is in
anything else. And it is besides an added and con-
fusing burden to the student to keep these false hypoth-
eses in treatises on science; they should be relegated to
histories of criticism whose chief purpose is to show the
progress of science in its devious path toward the
truth.

Unfortunately, most hypotheses cannot be readily
classed as either true or false since they involve pos-
tulates which can neither be denied nor affirmed from
scientific criteria; thus in themselves they are fitly
classed as indifferent. Yet they may indirectly either
benefit or obstruct the progress of science. So long
as we keep clearly in our minds and in our statements
the fact that such problems as a nebular hypothesis, the
condition of prehistoric life, radiation in interstellar
space, the ultimate constitution of matter, etc., arc
pure speculations, I do not suppose any serious harm
is done. But the hypotheses which we have created
with respect to atoms, the ether, natural selection,
mutations, and the like, have a much more subtile in-
fluence, and they have been used in such a fashion as
to confuse knowledge.

228 THE LIMITATIONS OF SCIENCE

Indifferent hypotheses will have a pernicious influ-
ence if by their use the deductions of science become
increasingly complex. Since hypotheses deal with con-
fessedly fictitious substances, it seems rather futile to
create things which add to the difficulty of a problem.

Again we find our hypotheses are becoming so ab-
struse that they require a prolonged technical training
and specialization before they can be understood; thus
the science itself is restricted to a few specialists and
loses much power. These abstruse hypotheses are
producing a breach even between theoretical and ex-
perimental science. So marked is the difference be-
tween these two aspects of the same science that they
have little in common and are frequently hostile.

But the most inevitable and dangerous influence of
the free use of indifferent hypotheses is the breaking
down of the scientific method by carrying science into
fields where it has no business to be. I have tried to
show what the limitations of science are and why the
obliteration of its boundaries is prejudicial to it. In
what has gone before, the discussion has been limited
to excursions into what may be called pseudo-science.
Encouraged by lack of criticism, there is now a desire
to go much further and to claim that science is the
sovereign of all knowledge. Thus, the example given
in the last chapter of Sir Oliver Lodge's attempt to
include the phenomena of immortality in the field of
science is undoubtedly made possible by the steady

THE ARBITER OF ETHICS 229

and gradual trend toward treating matter symbolically.
The step between considering matter as tangible reality
and as Poincare's hole in the ether is really greater
than passing from material to immaterial phenomena
or than maintaining that science is the guide of char-
acter and the arbiter of ethics. In this way scientific
naturalism is more dangerous than the easily refuted
outbreak of Sir Oliver Lodge.

Any system of ethics must aim to develop character;
it must establish a standard of good and evil; it must
judge actions according to this standard and provide
an inner check which will restrain the will of the indi-
vidual. But scientific experimentation and theory do
not directly consider character at all. The attempt is
there made to discover objective facts and laws which
have no character in themselves and to manipulate
or interfere with natural forces so that they will
add to our knowledge and power. No one would
hesitate to say that the discovery of the laws of
heat and their application to steam power were prob-
lems definitely in the field of scientific investigation or
that they had added enormously to our power.
They have in fact changed civilization, and yet
we cannot deduce from science whether or not
this acquisition of power has been accompanied
by a beneficial effect on civilization. That can
be determined only by the moral effect of the
expansion of industrialism on the inner life and

230 THE LIMITATIONS OF SCIENCE

thoughts of men, and science has no criteria for these.
The man of science is thus trained to discover new
things. He may point out their dangers and advantages
but the restrictions to be placed upon their use is not
his affair.

If we were to trace the growth of the idea that the
scientific method is our best means of obtaining in-
formation not only of objective facts but also of the
motives of human thought and character, it would re-
quire a detailed history of science. But without under-
taking so laborious a task, certain prominent factors
in the rise of science can be indicated. In the first
place we may assert that the guide of science during
the early and medieval periods was the Organon of
Aristotle. And we can also state pretty accurately
that the revolution in science against the Aristotelian
domination was accomplished under the leadership of
Albert of Saxony, Leonardo da Vinci, Copernicus,
Galileo, and Descartes.

The aim of these revolutionists was to replace the
metaphysical method of Aristotle by the physical or
experimental method. To put the issue simply, the
purpose of the Aristotelian philosophers was to form
a comprehensive and logical system of the universe
as they conceived it should be, a philosophy in which
experimental observation and inductive reasoning
played but a minor role; the scientific method of the
new school aimed to determine the laws of a universe

THE ARBITER OF ETHICS 231

which would be in accord with the phenomena dis-
covered by experiment. Naturally the division was not
sharp; even to Galileo, and especially to Descartes,
much of the Aristotelian method still clung.

Just as the Organon of Aristotle absorbed the sci-
entific spirit of the Greeks, so we have in the Novnm
Organum of Bacon an explicit attempt to crystallize
the new knowledge into a scientific method. To make
his purpose quite clear he invented for it a new name,
natural philosophy, so as to separate it from the meta-
physical philosophy of the Greeks. This natural
philosophy, if carried out logically, would limit us to
the laborious and careful accumulation of experimental
facts, out of which would grow true natural laws.
And, further to show the break he would make with
the Peripatetic school, he states that any further gen-
eralization which would lead to the consideration of
formal and final causes must require a hypothetical
method proper only to metaphysics. His criticism
of Greek philosophy is characteristic of his attitude.
Thus he gives his well-known opinion that the Greeks
were a vain and disputatious people, whose desire to
shine, whose taste for dispute, and whose mania for
new systems of thought multiplied error, leading them
to forsake observation for the more facile triumphs
of speculation. Nor did he spare the greatest, when
he declared that Plato subordinated the world to ideas ;
and Aristotle, ideas to words. The one corrupted sci-

232 THE LIMITATIONS OF SCIENCE

ence by theology and the other by dialectics, as later
Proclus did by mathematics. And while we have
learned by experience that scientific laws are not to be
discovered by such a regulated system of induction
because science does not rest on a single broad founda-
tion which rises uniformly, like an Egyptian pyramid,
to a point that signifies a single dominant force, yet
Bacon's inductive philosophy is still our authoritative
scientific method. In this opinion we have the un-
qualified statements of such men as Newton, Huygens,
and Laplace. Thus Laplace expresses most clearly
what men of science even now generally admit : " La
methode la plus sure qui puisse nous guider dans la
recherche de la verite consiste a s'elever par induction
des phenomenes aux lois et des lois aux forces. Les
lois sont les rapports qui lient entre eux les phenomenes
particuliers : quand elles ont fait connaitre le principe
general des forces dont elles derivent, on le verifie soit
par des experiences directes, lorsque cela est possible,
soit en examinant s'il satisfait aux phenomenes connus;
et si par une rigoureuse analyse, on les voit tous
decouler de ce principe, jusque dans leur moindres
details, si d'ailleurs ils sont tres-varies et tres-nom-
breux, la science alors acquiert le plus haut degre de
certitude et de perfection qu'elle puisse atteindre.
Telle est devenue 1'astronomie par la decouverte de la
pesanteur universelle."

It is natural that, if observation is the only sure

THE ARBITER OF ETHICS 233

guide to natural philosophy and if knowledge must
finally rest on the sensations, Bacon would be consid-
ered by many as the founder of the doctrine elaborated
by Locke, Hobbes, Hume, and others that there is noth-
ing in the intelligence which has not previously been a
matter of the sensations. But as de Remusat * points
out: "To say that in life all knowledge is derived
only from the data of experience, and to say that
everything which is in the intellect has been a matter
of the senses, is to say two immensely different things.
And Bacon has not said the second of these two things ;
he has not even said absolutely the first; he admits in-
spired knowledge." That is, Bacon apparently divided
knowledge into classes, the physical and the metaphysi-
cal, and based the former only on the sensations. In
confirmation of this opinion Bacon took a positive stand
against atheism : " No one denies the existence of the
gods, except him to whom it is serviceable that the
gods do not exist. To deny God, is to destroy the
nobility of the human race."

There seems then good reason for considering the
Novum Organum as the starting-point of modern sci-
ence, as in it is developed the doctrine which still pre-
vails, that science must depend on observation, and
that scientific theory must conform to the data of
experience.

* V(t de Bacon, p. 266.

234 THE LIMITATIONS OF SCIENCE

While it is true that Bacon maintained a distinction
between those things which are proper for scientific
elucidation and those things which are not; and al-
though he avoided a universal philosophy of the sensa-
tions; yet his predilection for the scientific method and
his inclusion in it of such subjects as history, which
in spite of time and effort has made little progress as
a science, pointed the road to that philosophy. So also
some believe him to be the originator of the idea of
applying the scientific method to society and ethics.
Such does not seem to be correct and I think it is not
possible, because the rule of science over life could not
have been accomplished until a great accumulation of
scientific observations had been made. No such ac-
cumulation had been undertaken before the last cen-
tury. In Bacon's time only a few enlightened minds
were convinced of the need of systematic experimental
knowledge. Even the British school of philosophers,
known as rationalists, materialists, or atheists, who
were more or less followers or supposed to be followers
of Bacon, was a school of metaphysicians and not of
scientists.

Of these philosophers, Hobbes undoubtedly had more
of the scientific closeness of reasoning than the others.
He based all knowledge on the sensations and in so
far seems to exalt science to be the arbiter of life, but
nothing could be less scientific than the postulates and
the conclusions of his philosophy. He had little reali-

THE ARBITER OF ETHICS 235

zation of, and much contempt for, experimental knowl-
edge. He assumed certain abstract definitions as uni-
versal postulates and from them derived all his con-
clusions by pure ratiocination without any regard as
to whether these conclusions conformed to objective
facts. A brief glance at some of the definitions and
deductions, which may be found in his Leviathan, will
show that he was advancing a purely metaphysical sys-
tem of thought. Thus, every part of the universe is
body. Bodies comprise those things which are formed
by nature and commonly called bodies and those formed
by the human will which we call societies; this latter
idea still lingers in the phrase, the body politic. Mo-
tion is the cause of all things, even of the human pas-
sions, etc. The small beginnings of motion within the
body of man before they appear in walking, speaking,
striking, and other visible actions, are commonly called
endeavor. Endeavor, when it is toward some thing
which causes it, is called appetite, or desire. He dis-
tinguishes in the following and entirely arbitrary
fashion between the sensations. Heat is motion re-
sulting from the light endeavor; hearing is generated
by the motion of the medium, but not in the same man-
ner as seeing. Sight is an endeavor from pressure
produced by the luminous body on the retina of the eye,
and by the pressure on that part it will be propagated
to the heart, the innermost organ of sight and of all
the senses; and from the reaction of the heart, in which

236 THE LIMITATIONS OF SCIENCE

reaction consisteth the nature of sense, there will pro-
ceed an endeavor back to the retina. This endeavor
outwards is the thing called light, or the phantasm of a
lucid body. From this utter confusion of bodies,
subjective and objective, physical and political, and
motions, real and occult, proceed his deductions. It is
no wonder that he had continual controversies about
scientific questions, in which he was always worsted.
One of the most famous resulted from his explanation
of the barometer. In his desire to assume body for
everything he was forced, as was Descartes, to include
space in the category of substance. So to account for
the space above the mercury, he asserted that air passed
in and out through the mercury because he had pre-
viously stated that a vacuum was a body which could
not be increased or diminished. Enough has been
given to show that Hobbes was not a man of science
and that his method was not the scientific method;
and the same can be shown with certainty of all
philosophers who flourished previously to the nineteenth
century. It was not until then that a systematic and
large accumulation of scientific observations of all
sorts was at hand. Even now, the biological sciences
are the only ones possible as a guide to ethics because
the mathematical sciences, physics, astronomy, and
chemistry, are too remote from human passions and
emotions to be serviceable.

Apparently in the biological sciences it was neces-

THE ARBITER OF ETHICS 237

sary to wait for the promulgation of the law of evolu-
tion before a nexus could be formed between the ma-
terial and spiritual aspects of nature. For it seems
clear that such a system of ethics must substitute the
worship of nature for the worship of God if science
is to become the guide to conduct. That is, some prin-
ciple of nature, subject only to physical laws, must
work toward perfection in man in the ordinary sense
of guiding his aspirations toward absolute goodness,
and thus supply a check and interference to his actions ;
a check which metaphysical systems have always ac-
complished by assuming an outside and supernatural
force, which is not restricted by natural law.

On first sight, the biological sciences, with evolu-
tion as a guiding principle, offer a promising field for
a system of ethics which shall depend on natural law
and be positive in that it does not introduce the occult
and supernatural. It seemed necessary, during the
Victorian age, only to have implicit confidence in evo-
lution and to let the machine work out its own destiny,
confident that all was well. Thus we have doctrines
of humanitarianism and evolution in the poetry of
Tennyson who trusts to that " one far-off divine event,
to which the whole creation moves." We have the same
confidence shown by Wordsworth who sucks his moral-
ity from flowers and stones, or by Fiske who writes his
moral confession in an essay entitled " Through Na-
ture to God." But all is not so simple or even so

238 THE LIMITATIONS OF SCIENCE

scientific as Spencerian philosophy would have us be-
lieve.

The doctrine of evolution, as a strictly scientific law,
states merely that the different species of animals and
plants were not created as distinct types but that they
have gradually changed by a progressive modification
until each existing species is the last surviving branch
or twig of the biological tree. Evidently, then, all life
can be traced back, if we could gather up the tangled
and broken skein of life, either to one or at least to a
few prototypes. Now the law of evolution takes no
account of good or bad, of high or low, or of the
method by which one species has changed to another.
According to it, each type has maintained its continued
existence simply because certain of its attributes have
given it an advantage over its competitors. From
observation we find that those types, we think to be
primitive, are simpler in construction and functions
than are those we suppose to be later. But it is by
no means a universal law that simple types change
to complex ones, witness the persistence of microbes
and bacilli. The law of evolution is thus a scientific
law which attempts to generalize a set of phenomena
observed objectively and has nothing to do with ethics
or what I have called character.

What may be called the ethical aspect of evolution
has been injected into it by hypothetical or metaphysical
reasoning. Darwin and his successors, generally, have

THE ARBITER OF ETHICS 239

attempted also to find the causes of evolution and the
mechanism of heredity. And here all is confusion,
and, as occurred in the physical sciences, each theorist
sets up his own scheme of natural selection, of pan-
genesis, of mutation and what not, and the battle
without an issue rages fiercely. In the first place, a
purely anthropomorphic aspect is given to evolution by
the unjustifiable use of the terms higher and lower
forms of life. These words can signify merely the
comparison between two types as regards their com-
plexity of functions. It is only by regarding man as
the goal toward which all creation tends, that we can
call those types the highest which most nearly resemble
man. The final step is easy and the word " high " in
evolution is transferred to the derived sense of mean-
ing noble and good. It would be a most interesting and
useful work to trace back this curious and persistent
habit of linking high and low as space attributes, to
high and low as ethical concepts. Much of our con-
fusion of thought comes from such loose use of words,
and few of us can quite rid our minds of the impression
that hell and evil are beneath us, and heaven and joy
above us. At all events, the metaphorical use of these
words seems to have done much to change the imper-
sonal law of evolution into a sort of deity which de-
velops the lowly algae into a choir of angels.

If we attempt to discover, in a general way, the
cause of evolution, we must ascribe it either to a super-

240 THE LIMITATIONS OF SCIENCE

natural or to a natural force. The variation of species
may be due to a supernatural power which created a
protoplasm and then guided organic life through the
slow developing ages. But to us such a form of
creation is as little scientific as the cosmogony of the
Book of Genesis. Scientific hypotheses must avoid the
supernatural and, however they differ in details, they
must base evolution on the natural laws of probability
and chance, using these words in their technical sense
of expressing the statistical actions of physical, chem-
ical, or biological forces on molecular masses. In
natural or scientific law there can be assumed no escape
from the calculable action of a force. Given effects fol-
low from given causes and these must precede each
other with uniform regularity, back as far as we care
to carry the law. In this manner we have formulated
a law of evolution without introducing the idea of
ethics at all. And so far as the question concerns
ethics it is restricted to a minute province, man, in the
vast empire of life. Thus we have made an absolute
break in the law of evolution; on one side is the un-
moral development of all the universe, and on the other
side is the moral growth of man. At least in our
egotism we reserve the attribute of character, or of
judging actions as good or evil, to ourselves. It is
almost useless to add that a law of continuous develop-
ment, like evolution, with such a break in it is far from
perfect.

THE ARBITER OF ETHICS 241

We shall therefore confine ourselves to the law of
evolution only so far as it relates to man. And let us
in the first place reject rigorously the sentimental
opinions of a class of writers who twist the laws of
nature into a kind of beneficial providence. The inex-
orable forces of nature teach us the survival of the
strong and the elimination of the weak; the fatal
progress of the inanimate universe riding over and
crushing whatever disobeys its laws, without hate but
without ruth, is not calculated to inspire an enlightened
and exclusive student of science to regard with con-
sideration this personification of nature as a type of
human love which would cherish the sick and teach
self-abnegation to the strong.

Nor can we discover, during historic times, much
change in the physique or in the character of men. And
we are forced to agree with Huxley, who believed that
the laws of natural evolution ceased to be operative on
man when self -consciousness became developed in him.
In the prolegomena to Evolution and Ethics he intro-
duces a vivid picture in which he portrays natural
evolution of animals and plants as life in a forest. The
characteristic feature of this life is an intense and
unceasing competition in the struggle for existence.
In the untamed forest, the cosmic forces use unre-
stricted multiplication as their principal aid ; for every
violet or for every oak that grows, thousands die,
crushed without a compunction. There must be

242 THE LIMITATIONS OF SCIENCE

strength and flexibility and good luck that plants and
animals may attain congenial places and invade suc-
cessfully large areas. On the other hand, the habita-
tion of man may be considered as life in a cultivated
garden, where the gardener restricts multiplication,
gives each plant space and nourishment, and shields it
from the vicissitudes of climate. He uproots the nat-
ural inhabitants, modifies the soil and conditions to
suit exotics, and gives the weak equal advantages with
the strong. As a result, natural evolution has become
so modified and weakened that man is in a class by
himself, and develops under different laws from the
rest of the world.

So far as I can see, nothing in biology has been dis-
covered which contradicts this opinion of Huxley. It
is, however, difficult to see how and when a break of
so fundamental a nature between man and the rest
of life could occur in a continuous evolution in which
man is included. But it seems certain that man has
attained to so complex and rich a character, his aims
are so diversified, that any law of evolution of his
future development simple enough for us to compre-
hend is out of the question. Where any such a law
would operate to emphasize a certain attribute, it would
diminish another which would be considered by many
to be equally important. Instead of strength, flexi-
bility, and good-luck only, there are a thousand other
influences to be balanced.

THE ARBITER OF ETHICS 243

If we are to found ethics on biology and evolu-
tion we are driven to inventing a sort of spiritual evo-
lution which is best expressed by the term naturalism.
And if anyone will consider the systems of this kind
which are proposed as guides to society, I think he will
find that they may all be included in this one general
type. There seem to be four possible ways of account-
ing for an evolution of the race. Humanity may be
guided to a goal of perfection by some divine and
omniscient external power which imposed certain initial
laws of nature and permits a subsequent evolution to
progress without interference; humanity may contain
in itself such a directing force; it may be constrained
toward a future condition by the conscious effort of
a set of judges who will determine and enforce the
manner of its evolution; lastly, society may divide
into two classes, those who by superior knowledge and
power fulfill their destiny at the expense of the op-
posite class of the ignorant and weak.

If we bear in mind that science is not only the study
of natural law as an objective series of events, but
that, if it is to have any application to the needs and
desires of society, the natural balance and operation
of forces and energy must be interfered with, then it
is easy to see that the first two doctrines of naturalism
are not scientific. To say that the human race is
guided to a goal of perfection, previously determined,
by either an external and divine power or by some

244 THE LIMITATIONS OF SCIENCE

omniscient power existing in society itself, is to deny
and abstract from the individual the basic axiom of
science that the laws of nature may be interfered
with.

The third class, which leaves the guidance of the
evolution of the race more or less under the control
of individuals composing it, is properly a scientific
method, because it postulates an objective world sub-
ject to laws and permits of their modification. This
type of naturalism has already, under the name of
eugenics, attained a very considerable vogue, and it
is heralded as the long sought guide to righteousness.
It is worth while to consider its claims both as a
science and as a system of ethics.

Since the science of physics has developed the sci-
entific method more consciously and more accurately
than any other of the sciences, we may turn to it for
an illustration of the method to be followed by eugen-
ists. In the first place, the experimenter puts himself
in the position of being external to the phenomena he
expects to investigate. He also decides beforehand
on the object of the experiment; that is, he has some
definite idea which he wishes to confirm or contra-
dict. He then observes and tabulates the phenomena
which are relative to the problem and abstracts from
them all the actions which complicate the result and
are not essential to it. But as he invariably finds that
the free and unconstrained phenomena are too com-

THE ARBITER OF ETHICS 245

plex to be manageable he must interfere with natural
actions and rearrange them. Lastly, his observations
are to be classified by a logical process into laws.

To apply this scientific method to the development
of an ethical system which shall conform to the con-
clusions of biology, certain individuals or a class of
individuals must act as experimenters, distinguish
themselves from the rest of society, and regard its
actions as objective phenomena which do not apply,
for the time being, to themselves. These experimental-
ists must acquaint themselves with the object of their
experiment and interfere with the unconstrained ac-
tions of society by providing constraints which shall
control and direct its complex course into simpler chan-
nels; and finally they must coordinate the effects of
these constraints.

Such should be the aim of what is popularly known
as the science of eugenics. By derivation, eugenics
means to be born well, and since the results of good
birth may be counteracted by the subsequent life of the
individual, a second science has been added currently
under the title, euthenics, which may be defined as the
science of living well. For the sake of simplicity let us
use the word, eugenics, to include this entire system of
scientific ethics. And let us put out of our minds im-
mediately the idea that the eugenists are concerned
with the simpler problem of the well-being of the in-
dividual; like all avowed men of science, they attempt

246 -THE LIMITATIONS OF SCIENCE

to deal with classes of phenomena. In this instance,
the object is to mold the whole human race, with its
immensely complex and diversified desires and actions,
its egotisms and its sympathies, into a homogeneous
society which shall progress toward a standard, previ-
ously determined, of a noble and god-like humanity.
The reward to be expected by the individual who is
born and lives well is that intense feeling of satisfac-
tion he will have that the race as a whole has been
carried a little closer to a distant and vague goal of
perfection because of his submission to the laws of
eugenical righteousness.

We can now define the eugenists, if our ideas be cor-
rect, as a band of human beings who shall be the ar-
biters of right and wrong. This band must be small
because it is difficult to find even two persons who have
the same standards; it must be select as there is at
present no known way for a person to exercise a choice
in his parents and it will need judges of superior
ability to pick out those who are worthy to be parents
and to live. Parentage under eugenical guidance is
certain to be a very serious matter and I imagine that
we should expect a rather large diminution in the
human race for a few centuries until the system is
running smoothly. At present, we cannot leave the
regulation of life after birth according to euthenic
standards to the ordinary person, because we should
then not have euthenics at all, but the present hap-

THE ARBITER OF ETHICS 247

hazard society. So we must take it for certain that all
people must be born and live according to the regula-
tions of a band of superior human beings.

Having thus settled on the organizers of experiments
for this science, their next step will be to arrange
the experiments and to carry them out. They will
first, in order to work intelligently, decide what are the
qualities of human perfection. I cannot discover that
this has been done. There seems to be just as great
diversity of opinion as to what constitutes the perfect
man among the eugenists as there is among ordinary
men. We meet so-called eugenic babies and euthenic
adults, but as standards they are rather disappointing
and do not seem to be sufficiently differentiated from
other people. Perhaps this is to be expected, for true
eugenics is a slow process. With the goal established,
the experimenters must then find some scientific way
of propagating the race eugenically and of determin-
ing and applying constraints or checks on our free
manner of life which will make all individuals live
euthenically.

If such a scientific method were practicable, it would
seem to a physicist that a system of ethics could be
established by it. But it is a question whether such a
system, minimizing as it must the check of personal
responsibility, would not fail because it would result in
a form of intellectual slavery. So far the doctrines of
modern eugenics have not shown the slightest indica-

248 THE LIMITATIONS OF SCIENCE

tion of scientific method; they are vague and char-
acterized by a lack of any accurate thinking. Indeed,
it is difficult to obtain an idea of what the eugenists
aim to do or how they expect to work. Curiously
enough, considering his lack of scientific training, Plato
seems to be the one who saw the problem clearly and
attempted a real solution. His belief, that every per-
son desired to be born well and to live well if only
he knew how, appeals to one as an explicit statement
of eugenics. That is, if we could eliminate ignorance
and regulate our passions, society would advance to
an ideal state, and in his Republic, Plato sketches
such a polity in detail. The failure, for failure it was,
came from his inability to define what ignorance is or
how to check our passions. His ideal state is not only
impracticable, but if adopted would result in political
slavery.

If we examine somewhat in detail what is being done
to make a science of eugenics and to apply it to regu-
late the affairs of men, we shall find that it is in no
sense a science and is singularly unfit to accomplish
such a purpose.

In the first place there are no judges who are ac-
cepted, or likely to be accepted, as having any unanimity
of purpose or plan. Ethical systems, in the past, have
been born in the heart and mind of a single man, who
was recognized as one endowed with a peculiar power
of righteousness and whose life had become an ex-

THE ARBITER OF ETHICS 249

ample. So necessary was it to have an example of per-
fection which should not be subject to the waywardness
of human passions, that without exception all religions
assign divine attributes to their founders. And in
order to maintain the integrity and the unanimity of
belief in even a sect, the rest of society, with its con-
flicting purposes, has always been explicitly banished
from communion with the faithful.

The case of eugenics is quite different. To be a sci-
ence it must deal with the race and not with indi-
viduals; instead of a founder, to whom are ascribed
divine or at least superhuman powers and who makes
an appeal to sympathy, it must rely on a body of judges
who appeal to law and reason, and who have discarded
the powerful check of personal responsibility and per-
sonal reward. Instead of choosing individuals from
society to form a more or less cohesive sect, the eu-
genists must constrain all individuals to forsake their
personal desires and attempt to bind these hetero-
geneous units into a homogeneous race. And who are
intellectually wise enough to be the arbiters of fate?
The clinging of man to the idea of corporal manifesta-
tions of divinity is a confession of the impotence of
man to grasp the problem of humanity. Huxley stated
this difficulty unanswerably long before eugenics came
to life. He, the evolutionist and biologist, warns us:
" I doubt whether even the keenest judge of character,
if he had before him a hundred boys and girls under

250 THE LIMITATIONS OF SCIENCE

fourteen, could pick out, with the least chance of suc-
cess, those who should be kept, as certain to be service-
able members of the polity, and those who should be
chloroformed, as equally sure to be stupid, idle, or
vicious. The * points ' of a good or bad citizen are
really far harder to discern than those of a puppy or a
short-horn calf; many do not show themselves before
the practical difficulties of life stimulate manhood to
full assertion. The evil stock, if it be one, has had time
to multiply, and selection is nullified."

Instead of a sober and careful study, with a full
realization of the almost hopeless difficulties of the
problem, we have a number of people, mostly of a very
restricted outlook, who say with conviction that man is
mentally defective, man is diseased, man is criminal.
And they say vaguely, these misfortunes must be
stopped. But how is any one of these to be remedied
or how are we to weigh or balance them ? A man may
be a criminal and otherwise a perfect physical creat-
ure; a man may be diseased and yet be intellectually
and morally a giant ; in fact, Lombroso claims that all
those we most reverence for morality or intellect were
diseased and quite unfit to be progenitors of the race.
And while this doctrine of Lombroso, that intellectual
and moral genius is a symptom of physical degeneracy,
is a monstrous falsehood, yet it is certain that those
who possess great powers themselves frequently do not
transmit their excellent qualities. And these are only

THE ARBITER OF ETHICS 251

the simplest attributes of a good citizen to be con-
sidered.

So far eugenics has limited itself to a trite formula
that only the fit should be permitted to have children.
This battle-cry has been sung loudly and it has gath-
ered together a motley band who would interfere with
the laws of nature and reform civilization overnight.
They have no clear idea who are the fit or how the unfit
are to be restrained. They busy themselves collecting
statistics, but for the most part these are undigested,
or are drawn from questionnaires scattered broadcast
and inviting inaccuracy, and frequently they are not
even honest. Books also are written and as an exposi-
tion of an ethical system they give the impression that
the writers' loftiest aim is to turn the human race
into a stock-breeding farm. The chief argument and
the complaint is that men can breed cattle, dogs, and
plants eugenically but not themselves. But what an
absurd attitude this is ! The breeder of dogs and cattle
stands in a relation to them much as a god would to
us. Dogs and cattle are bred to bring into prominence
some trait which will suit the purpose or pleasure of
their master, not of their own. No one supposes that
the monstrous nose of the pug dog or the inflamed liver
of the Strassburg goose was developed with any regard
to those unfortunate animals. The whole point has
been missed. Man cannot be bred like animals be-
cause he has no apparent master. If we could be

252 THE LIMITATIONS OF SCIENCE

content to believe that the destiny of man is under
divine control, we can have hope; and if it is left to
the rough methods of nature, which sooner or later
blot out the degenerate and the weakling, there is
some possibility of achievement.

In spite of much noise about the science of eugenics,
the eugenists know that at most it is but a police regu-
lation. Society has always assumed the right to pro-
tect itself by isolating or by punishing, even with death,
those it considers dangerous to its stability. The eu-
genists are advocating the same thing and have so far
limited their efforts to prevent children from criminals,
imbeciles, drunkards, and syphilitics. The methods of
society to accomplish this safeguard have been crude,
but they have been sufficiently effective to prevent any
notable deterioration of the race, and it is safe to say
there has been improvement. If the eugenists would
try to improve the methods of the past to some extent,
something might be done. But there is reason for be-
lieving that even this good is likely to be stifled by
the outcries and rash heedlessness of the overzealous.

To prevent the strains of disease, imbecility, and
criminality from continuing in the race, we now have
the proposed surgical remedy of vasectomy. As an
efficient preventative it must be a failure. No society
would countenance such an operation except for cases
of hopeless degeneracy. While it might reduce some-
what the number of degenerate offspring, we would

THE ARBITER OF ETHICS 253

still have the children of the less degenerate, who
may inherit the weakness of the parent in an intensified
form. No good arguments can be given against the
more humane method of the separation of sexes in
institutions. This method requires merely a reform
in such institutions as already exist in order that their
inmates may be provided with as free and useful life as
is possible. The argument is frequently given that the
cost of this method is great. But a strong and vigorous
community may well blush at such a motive; certainly
the care of its unfortunates is a solemn duty and it
should be undertaken with as much solicitude as a man
would shield a weakling child. And as for the plea
that, after this operation, the individual loses only the
power and not the desire to procreate, it strikes one as
simply disgusting. Is it not giving a license to the
degenerate and to the man of loose morals to be as foul
as he pleases if only his sins end with himself? It
would be far more manly, if the plan of isolation can-
not succeed, to put degenerate children and adults to
death and at least preserve some self-respect for the
dignity of human life.

Another plan proposed to promote eugenics is to
rely on the legislator and the clergy to prohibit mar-
riage, unless the contracting parties show certificates
of fitness from a physician. Without the least knowl-
edge of what effect such a regulation would have, the
state of Wisconsin has recently passed a law of this

254 THE LIMITATIONS OF SCIENCE

character. The result so far has been ridicule and a
marked decrease in marriages. The absolute inability
to carry out the purpose of such a law does not seem to
have occurred to its promoters. If it were enforced
over a wide area, the youth would certainly dispense
with the ceremony of marriage rather than to debase
their ideals of love. And one can imagine the con-
sternation of physicians if they were forced to decide
when people were fit to marry. Very few of them
know anything about the laws of heredity, and those
that do know the laws of heredity also know that they
are so complex and so obscure that only a few extreme
cases can be trusted. As Huxley said, the points of
a good citizen are more difficult than those of a puppy
or a short-horn calf.

A third class of eugenists consists mostly of the
hysterical element of the social workers who sob over
the sins of society and sob over the innate purity of
the harlot, who weep over the heartlessness of the law-
abiding and weep over the innate nobility of the crimi-
nal. So far as one can make out from their incoherent
utterances, they wish to put all the sins of the individual
on society, without comprehending that society is a col-
lection of individuals. Whatever good they may ac-
complish, no one in the least conversant with science
will concede that they are advancing an ethics in con-
formity with scientific methods; for if science makes
any one thing clear, it is that the actions of the indi-

THE ARBITER OF ETHICS 255

vidual must bring their reactions also on the same in-
dividual.

Now it seems to me that in eugenics of the simplest
type there is a possible good. If the advocates of good
breeding, and everyone is that to some extent, will
work quietly and systematically on the problems of
heredity; if they will try to find the effects of criminal-
ity and of disease on posterity, we shall then have some
reliable facts to work on. We may then hope to ac-
complish some more decent plan of isolating the worst
of such cases than we have now. And we are sure of
the help of society itself, for we know that the human
race contains in itself the power of gradually eradicat-
ing defective stock from the simple fact, that if it did
not possess this power, it would have hopelessly de-
generated long ago. But this natural process is slow
and if it can be accelerated and guided, eugenics will
be valuable.

There are many of these patient and accurate in-
vestigators of the laws of heredity but there are also un-
fortunately others, classed professionally as eugenists,
whose methods are not so reliable. From their bureaus
issue questionnaires which are spread broadcast. The
statistics which result are mostly useless and often
false, as they are given by untrained people. And
they are especially obnoxious as they too frequently
make a direct appeal to the morbid. Their so-called
laws are based on insufficient evidence. Apparently

256 THE LIMITATIONS OF SCIENCE

the only two examples which have been worked out
in America are the Jukes and the Edwards families.
The first has shown itself to be an undesirable and
the other a desirable strain. But curiously enough the
first ancestress in America of each of these families
was not a moral woman. It is sufficiently easy to look
back and decide what characteristics proved to be un-
desirable, but it is a very different thing to look for-
ward and determine who should establish a family
and who should not. Not even the most enthusiastic
eugenists can hope to unravel the genealogies of more
than a small proportion of families. And it would
require accurate genealogies of many families, not
only of successive generations but also of the char-
acteristics of its members, to settle whether a strain
of immorality came simply from an excess of vitality
or was the result of degeneracy.

If eugenics is a problem too complex for solution,
its companion, euthenics, is an example of trying to
assign to science a problem it has no means of solving.
Science knows no method of constraining an indi-
vidual to conduct himself so as to further the exist-
ence of a perfect race. The greatest difficulty in all
ethical systems is to provide an efficient check on the
passions. The strongest check is evidently the belief
that disaster to himself will result from disobedience
of the laws of right conduct. And yet the man is rare
who can by his will refrain from those habits and

THE ARBITER OF ETHICS 257

passions which he knows to be injurious to him-
self or to those nearest and dearest to him. What
more ineffective system of ethics could be imagined
than euthenics, which bases its claim on the plea that
a man should so live that the race may move forward
to some unknown goal of perfection? And he is not
even to have the satisfaction of seeing the progress of
the race, as little improvement is to be expected for a
hundred or so of generations.

The average man is too busy with his own con-
cerns even to consider those of a distant posterity, of
whose needs he can know nothing. He is convinced
that future generations cannot be controlled by him and
that they must solve their own problems; and he is
also conscious that he is not altogether degenerate
although he is the result of a long line of careless an-
cestors, heedless of him and ignorant of eugenics and
euthenics. However traits of heredity may affect
immediate posterity, it must be recognized as a general
principle that the race has attained a normal develop-
ment, which can change but slightly and very slowly ;
disease and vice must disappear just as abnormal excel-
lences must decay. We find but little that is essentially
different in the moral character of ourselves and that
of persons who formed the ancient civilizations. The
eugenists forget that the great majority of all men, and
a still greater majority of those of influence, lead for
the most part decent, law-abiding lives, and this quiet

258 THE LIMITATIONS OF SCIENCE

and unobtrusive power of example is far more potent
for righteousness than a propaganda led by enthusiasts.

Side by side with the doctrine that human sympathy
is the controlling factor of ethics, and this belief is
evidently the basis of eugenics, there has always per-
sisted the contrasted doctrine that the state of man is
one of warfare, a survival of the fit. This school
evidently relies on a law of natural evolution based
on the motive of egotism. It is thus my fourth class
of naturalism.

Of all those who have advanced this motive of
egotism, none has done so as explicitly, or has made of
it so complete a philosophy as Hobbes. " In the first
place," he says, " I put forth, for a general inclination
of all mankind, a perpetual and restless desire of
power after power, that ceaseth only in death." This
is, I think, the direct influence of science unqualified
by character and piety. It is not my purpose to follow
this doctrine down to the present time but it can be
shown that Nietzsche, with his ideal of the Superman,
is the logical successor of Hobbes. Both the strength
and weakness of this form of philosophy have been
contrasted in a recent essay : *

" Nietzsche regarded the self-assertive Superman
as a true reaction against the prevalent man of sym-
pathy, and as a cure for the disease of the age. That

* Essay on Nietzsche. By Paul Elmer More. Shelburne Es-
says; Eighth Series.

THE ARBITER OF ETHICS 259

much of Nietzsche's protest against the excesses of
humanitarianism was sound and well directed, I for
one am quite ready to admit. He saw, as few other
men of our day have seen, the danger that threatens
true progress in any system of education and gov-
ernment which makes the advantage of the ordinary
rather than the distinguished man its first object. He
saw with terrible clearness that much of our most ad-
mired art is not art at all in the higher sense of the
word, but an appeal to morbid sentimentality. . . .
But the cure Nietzsche proposed for these evils was it-
self a part of the malady. The Superman, in other
words, is a product of the same naturalism which pro-
duced the disease it would counteract ; it is the last and
most violent expression of the egotism, or self-interest,
which Hume and all his followers balanced with sym-
pathy, as the two springs of human action."

If the predominant object of science is to acquire
power, how can we escape the conclusion that if it
should become the arbiter of ethics, society would tend
to a condition closer to the ideals of Nietzsche than of
sentimental eugenics? Can we look with complaisance
on the unrestricted development of either of tlu-^c
ideals? Nietzsche teaches a gospel of scientific evolu-
tion when the restraints are removed from the free
exercise of self-interest. The gospel of the Superman,
when transferred to the ambitions of a nation, as has
been done by Treitschke, shows its results in that doc-

260 THE LIMITATIONS OF SCIENCE

trine of necessity of the Germans which has plunged
Europe into war. No "individual and no nation can
believe for long that in him or in it rest the culture
and the power of the world without resorting ulti-
mately to the arbitrament of force to overcome opposi-
tion. And on the other hand, the ideal of a world
governed by human evolution and depending on
brotherly love — a world under a banner floating from
a Peace Palace of The Hague — is a dream of sentimen-
tality. And yet, one or the other seems to me the goal
of eugenical righteousness. But because science is not
concerned primarily with problems of character, it
does not follow that its pursuit does not promote char-
acter. We certainly enrich the character by the larger
acquisition of power which results from the modifying
and dominating of our environment. This is true, if
side by side with increased power to do things, we
also learn to use it for the benefit of humanity; that
is, when it is regulated according to the inner check of
piety, as taught by those in whom we recognize the
mysterious power of righteousness.

If I have made myself clear, the limitations of sci-
ence are due solely to the fact that there are, in addi-
tion to material forces, others of an essentially dif-
ferent kind which may be called, for lack of a better
name, spiritual powers. And so long as men of sci-
ence restrict their endeavor to the world of material
substance and material force, they will find that their

THE ARBITER OF ETHICS 261

field is practically without limits, so vast and so numer-
ous are the problems to be solved. And it should dis-
tress no one to discover that there are other fields of
knowledge in which science is not concerned; on the
contrary, the fact that the range of science is limited
should encourage us to greater hopes, because our
freedom of action is still far greater than our powers
of accomplishment. After centuries of effort, the
ocean of the unknown lies before us unexplored.

INDEX

Abstractive and hypothetical
methods, 13; outlined by
Rankine, 20.

Action at a distance, 84, 134.

Ampere, abstractive method,
190.

Aristotle, continuity, 77; dic-
tator of Greek and medieval
science, 230; spirit of Greek
science, 231 ; ideas as logic,
231-

Astronomy, its relation to hy-
pothesis, 76.

Atomic, Kelvin's models, 36,
190; nature of electricity,
138.

Atomic theory, defined, 8; its
axioms, 11; failure, 24; not
an aid to discovery, 33 ; in-
adequacy of, 44; modern and
classic, 49 ; its nature, 73 ;
its philosophical weakness,
119; its value, 130.

Atoms, nature of, 10; Lar-
mor's definition, 26, 49; nec-
essary attributes, 44; sub-
divided, 44; modern concep-
tions, 129.

Axioms, of atomic theories,
1 1 ; see Postulates.

Bacon, Fr, natural philosophy,
121 ; province of mathemat-
ics, 142; on the sources of
knowledge, 233 ; on the ex-
tent and limit of science,
234-

Biology, as the basis of ethics,
236.

Bolingbroke, Lord, critique of
Descartes's cosmogony, 104,
144.

Boscovich, atomic theory, 8.

Bradley, discovery of the aber-
ration of light, 19.

Browne, Sir Thomas, nature
of electricity, 108.

Campbell, Norman, division of
past and present science, 39.

Celestial matter, nature of, 90.

Character, not the aim of sci-
ence, 229.

Clifford, W. K., plurality of
ethers, n.

Cohesion, cause of, Descartes,
92; Larmor, 127.

Continuity and discontinuity
of matter, contrasted, 3, 119;
as a dualistic principle, 40,
44; ideas on, 77; its history,
77; conflict between, 78; in-
ability to decide between,
'43.

Cosmogony, of Laplace and
Lagrange, 7; Larmor's, 47;
requirements for a scientific,
72; nebular hypothesis, 74;
as a scientific convenience,
80; Descartes's, 82 el seq.;
revealed and natural, 240.

Coulomb, nature of electricity,
153-

d'Alembert, laws of motion, 6.
Dalton, atomic theory, 33.
Darwin, law of evolution, 226,

238.
Democritus, atomic theory, 8,

73-

Descartes, influence on science,
3. 5, 39. 40. 67, 101, 142, 224;
theory of matter, 40; the
plenum. 40, 78; example of
hypothetical method. 70; ex-
ponent of continuity of mat-
ter, 78; scientific principles,
79; revelation, 80; attributes
of substance, 82; action at
a distance, 84; laws of tno-

263

264

INDEX

tion and impact, 85 ; classi-
fication of matter, 86; vor-
tices, 89; cohesion, 92; light,
92 ; heat, 95 ; the earth, 96 ;
his consistency of thought,
98; critique of his cosmog-
ony, 101, Bolingbroke's
opinion, 104; nature of elec-
tricity, 107; space as sub-
stance, 236.

Dufay, fluid theory of elec-
tricity, 25.

Duhem, on science of ener-
getics, 22; on theories of
physics, 37.

Egoism, as a scientific system
of ethics, 258-

Einstein, definition of space,
109, 127, 153; electricity and
energy as entities, in.

Einstein's Principle of Rela-
tivity, to harmonize modern
and Newtonian mechanics,
164 ; its postulates, 165 ; meas-
ure of time, 167 ; measure
of length, 169; variability of
mass, 172; mass and energy,
172; its postulates, 174; re-
striction of the relativity of
motion, 175 ; absolute veloc-
ity of light, 177; velocity of
sound and light, an illustra-
tion, 182; atomic nature of
electricity, 184; logical but
false, 184.

Electricity, an entity, 42, 51,
63, 65, 107, 1 10, 184; the
basis of mechanics, 158.

Electrons, nature of, 55, 60,
131, 135, 138.

Energetics, definition, n, 20;
value of, 24.

Energy, the basis of science,
22; conservation of, 120, 128;
classification, 122, 133.

Ether, a mechanical link, 10;
need for more than one, u;
and matter, 42; its prop-
erties, 43 ; elastic-solid and
electromagnetic, 52; massive,
109; recent ideas of, 109; a

confession of ignorance, 125 ;
a plenum, 126; a new con-
ception of the, 162 ; a con-
venience only, 198; as a
reality, 202; as the explana-
tion of matter, 203 ; the re-
ductio ad absurdum, 204;
Lodge's definition, 208; as a
psychic medium, 208; as a
quasi-deity, 209.

Ethereal, see Vortices.

Ethics, present perplexity, 213;
science as the basis of, 214;
lack of criticism of sci-
entists, 215; effect of hy-
pothesis on, 225; material-
ism, 233 ; atheism, 233 ; sys-
tem of Hobbes, 235 ; science,
the guide to conduct, 237;
law of evolution not eth-
ical, 238 ; evolution and,
241 ; classification of natural-
ism, 243; egoism, 258; rela-
tion of science to, 260.

Eugenics, as a science, 245 ; as
a system of ethics, 249; as
a police regulation, 252;
under guidance of physi-
cians, 252; under guidance
of legislators and the clergy,
253 ; under the social work-
ers, 254; lack of influence,
257-

Eugenist, defined, 246.

Euthenics, defined, 245; its
failure, 256.

Evolution, as a law, 116; so-
cial, 212; discussed, 237; its
causes, 239; natural and re-
stricted, 241 ; spiritual, four
types of, 243.

Experience, the basis of sci-
ence, 233.

Experimentum crucis, 18.

Fallacies, in Descartes's sys-
tem, 98.

Faraday, the duty of science,

107; theory of electricity,

108; effect of dielectrics,

160; nature of the ether,
161.

INDEX

265

Fire, Descartes's conception

of, 90.

Fiske, John, naturalism, 237.
FitzGerald-Lorentz, effect of

motion on matter, 160.
Fizeau, the velocity of light in

moving media, 177.
Force, as the basis of science,

118.
Foucault, velocity of light in

transparent media, 19.
Franklin, Benj., fluid theory

of electricity, 25.

Galileo, on sensation as the
postulate of science, 32;
founder of experimental sci-
ence, 39, 187; classical me-
chanics, 142.

Gassendi, atomic theory, 8, 85.

Genealogies, eugenics, 255.

Generalization, a necessity, 194.

Geometry, its postulates com-
pared with those of experi-
mental science, 12 ; the basis
of science, 79.

Goethe, restraint in science,
58.

Guericke, von, theory of elec-
tricity, 108.

Hannequin, atomic theory, I ;

definition of mechanics, 118.

Heat, Descartes's hypothesis,

95-

Helmholtz, von, conservation
of energy, 86; vortex rings,
131 ; stagnant ether, 161.

Heraclitus, continuity of mat-
ter, 77.

Hertz, H., opinion of Max-
well's equations, 37 ; electro-
magnetic waves, 160.

Histories of science, their de-
ficiencies, 217.

Hobbes, on the sensations, 233,
234 ; metaphysical system,
235; °n the barometer, 236;
egotism of mankind, 258.

Hume, on the sensations, 233;
egotism and sympathy, 259.

Huxley, on evolution, 241 ; on
eugenical selection, 249.

Huygens, atomic theory, 8, 40;
theory of light, 19; correc-
tion of laws of impact and
motion, 86.

Hypothesis, its danger, 16;
elimination not desirable, 37 ;
utility of, 42; apology for,
57 : not an indifferent sub-
ject, 59; Descartes's, the
most complete, 98; good and
bad aspects, 103; Boling-
broke on, 104 ; and symbol-
ism, no; a tentative hypoth-
esis of electricity, 140; its
value, 144; effect on society,
192; as generalization, 195;
Poincare's classification, 200;
and ethics, 225.

Hypothetical method, 13; its
deceptions, 70.

Idolatry of scientists, 209.
Impact, Descartes's laws, 85.

Johnson, Samuel, reality of
matter, 206.

Kant, axioms of mechanics, 6;
nebular hypothesis, 74; space
and time, 148.

Kaufmann, variation of mass
with velocity, 132, 137.

Kelvin, Lord (Sir Wm. Thom-
son), models of atoms, 36,
190; theory of vortex atoms,
41, 48, 131 ; size of atoms,
44; origin of life, 117;
quantitative measurements,
MS-

Lagrange, axioms of mechan-
ics, 6; equilibrium of bodies,
6; Mecanique analytique, 7;
no criterion for truth, 18.

Laplace, Systeme du monde, 7 ;
materialistic attitude, 8, 212;
his mechanistic theory, 9;
nebular hypothesis, 7.)
locity of propagation of
gravitational energy, 118; on
the inductive method, 232.

Larmor, Sir Joseph, properties
of the ether, 19, 53. "°;

266

INDEX

corpuscular theory of mat-
ter, 26, 27, 41, 42, 44, no;
value of speculative hypoth-
esis, 43; continuity of mat-
ter, 46; his hypothesis does
not avoid former difficulties,
50; divisibility of matter,
119; definition of ether, 126;
electrical theory of mechan-
ics, 127 ; definition of the
atom, 129.

Laws, difference between hy-
pothesis and, 104; continuity,
causal, 115.

Leibnitz, invention of the cal-
culus, 5.

Length, a function of motion,
169.

Lewis, G. N-, confusion of
fact and fiction, 112.

Light, theories of, 19; Des-
cartes's hypothesis, 92; its
velocity, an absolute con-
stant, 165; its velocity in
vacuous and in occupied
space, 177; its velocity not a
maximum, 182.

Limits of science, 113.

Locke, on the sensations, 233.

Lodge, Sir Oliver, the ether
as a medium for psychic
phenomena, 24; ether mas-
sive, no, 153; presidential
address on Continuity, 193;
his scientific credulity, 194;
his scientific confusion, 207 ;
his ideas of the ether as om-
nipotent and omniscient,
208; as a quasi-deity, 208;
as a soul-body, 209; his
speculations not logical, 209;
war between science and the-
ology, 210; as an example
of scientific dogmatism, 210.

Lombroso, the imperfection of
the genius, 250.

Lorentz, H. A., his corpus-
cular theory of matter, 26,
28, 41, 55, no, 130, 144;
properties of the ether, 56;
apology for the hypothetical
method, 57; ethereal stresses

not realities, 109; contrac-
tion of matter, 160; ether
stresses, 161.
Lucretius, atomic theory, 73.

Mach, Ernst, science of ener-
getics, 22.

Mass, as an attribute of elec-
tricity, 64, 117, 135, 171; as
a fundamental unit, 145, 148,
J53 ; Newton's conception,
155; as dependent on en-
ergy, 172.

Mathematics, as a scientific
language, 71; its value, 150;
a paradox, 151 ; not subject
to the restrictions of science,
185.

Matter, real and hypothetical,
17 ; continuous or discontin-
uous, 40, 44; modern defini-
tions, 50; identity of space
and, 82; fundamental attri-
bute of, 82; three primordial
kinds, 88; terrestrial, 96;
confusion with electricity,
no; its divisibility, 119;
true and sensible, 120; as
Ding an sich, 148; our con-
cept of, 150; as an ethereal
strain, 161 ; Poincare's defini-
tion, 205.

Maxwell, J. C, theory of light,
19, 160; theory of electrifi-
cation, 25, 108; discredit of
vortex theory, 48, 131 ; ori-
gin of life, 117; nature of
the ether, 161.

Mechanical, rise of principles,
5; theories have no criterion
of truth, 18; models do not
lead to discoveries, 37; the-
ories, their weakness, 62.

Mechanics, dominance over
science, 4 ; axioms, 6 ; its
metaphysical basis, 12 ; the
only complete theory, 13 ; its
failure as a method, 146;
Newtonian, 154; the new,

159.

Mechanistic idea of the uni-
verse, 8.

INDEX

267

Metaphysical theory, Larmor's,
27 ; Lorentz's, 28 ; influence
on thought, 28.

Metaphysics, definition, i.

Method, of physics a model,
3 ; abstractive and hypo-
thetical, 13; Rankine's, 20;
the author's outline, 115;
Laplace's opinion, 232.

Michelet, 69.

Michelson, A. A., ether drift,
159. 179; velocity of light in
moving media, 177.

Minkowski, four dimensional
space, in.

Models, for radiation, 123 ; see
Atoms.

Moral influence of science,
213.

More, L. T., outline of a sci-
entific method, 115; on ether
stresses, 161.

More, P. E., on Nietzsche and
the doctrine of egoism, 258.

Morley, Edward, on ether
drift, 159, 179.

Motion, real and hypothetical,
152.

Naturalism, as social evolu-
tion, 243.

Nebular hypothesis, 74.

Newton, on hypothesis, title
page; calculus, 5; law of
gravitation, 6, 21, its appli-
cation to atoms, 7, 40, 74;
hypothesis of light, 19, 21,
226; action and reaction, 115;
classical mechanics, 142, 154
el seq.; on mass, 155; re-
placing Kepler's laws, 203.

Nietzsche, Fr, reaction against
humanitarianism, 258.

Occult, substances and forces,

Organon of Aristotle, the text
for Greek and medieval sci-
ence, 230.

Organum Novum of Bacon,
the authority for modern
science, 231.

Ostwald, W., science of ener-
getics, 22.

Peripatetic school, 231.

Philosophy, metaphysical
teaching of scientific, i.
of Greeks characterized by
Bacon, 231; of Hobbes, 234;
scientific, 236 et seq.

Physical theory, nature of, 12;
aims of, 37; originators of,
41.

Physics, has best scientific
method, 2; relation to meta-
physics, 3; dates from, 39.

Planck, Max, quantum theory
of discontinuity, 119; on
principle of relativity, 165.

Plato, the world as idea, 231 ;
and eugenics, 248.

Plenum, 40; Larmor's 46;
Descartes's, 83.

Poincare, H., on hypothesis of
ether, 59; The Foundations
of Science, 193 ; as a skeptic,
193 ; on the scientific method,
194; on generalizations, 194;
on hypothesis as a conveni-
ence, 198; classification of
hypotheses, 200; the new
mechanics, 203 ; the func-
tion of science, 204; defini-
tion of matter, 205. 219.

Postulates of science, their
truth, 81 ; extent, as a fun-
damental attribute, 82; of
Descartes, 85, 148; of Ein-
stein, 165; of the new me-
chanics, 174; their sub-
jectivity, 219.

Power, the aim of science,
214; as the desire of man-
kind, 258, 260.

Primordial space and time, 72,
86.

Principia Naturae of De»-
cartcs, 79 et sea.

Principle of Newton, title
pane, 155.

Proclus, science as mathemat-
ics, 232.

268

INDEX

Radiant energy, nature of,
122; and its medium of
transmission, 123, 128.

Rankine, on energetics, 1 1 ; on
physical theories, 12; out-
line of abstractive and hy-
pothetical methods, 16, 21.

Relativity, Principle of ; see
Einstein.

Relativity, of motion and posi-
tion, 83; Descartes's doc-
trine, 83 ; of knowledge,
147; of mechanical motions,
175; not applicable to radi-
ant energy, 175; an aca-
demic question, 182; limited
to hypothetical cases, 184.

Remusat, C. de, Vie de Bacon,

233- .

Renan, Ernest, science as sym-
bol and law, 2, 212; social
evolution, 212.

Roentgen, W. C., discovery of
X-rays, 38.

Rutherford, Sir Ernest, ex-
perimental evidence for at-
oms, 60; theory of radio-
activity, 63.

Science, as a guide, 2, 58; its
limits, 30, 113, 228; cata-
logue of, 151; its functions,
187 ; its domination of mod-
ern thought, 188; its dog-
matism, 189; lack of crit-
icism, 189, 215; as a meas-
ure of civilization, 215;
overthrow of Aristotelian,
230; its aim to acquire power
and not character, 229; and
ethics, a modern combina-
tion, 234; its ethical bearing,
259 ; its true aim, 260.

Scientific, method, i ; cult, 35 ;
and religious polemic, 35 ;
skepticism and credulity,
193 ; dogmatism, 210 ; eth-
ics, feasibility of, 214.

Scientists, effect of hypoth-
esis on, 28; German school
of, 206, 207; education of,
223.

Sensations, not criteria of
phenomena, 8.

Sentiment, as the basis of hy-
pothesis, 105.

Space, and matter, 83; our
concept of, 148.

Spencer, Herbert, evolution as
a social law, 212, 238.

Superman, as the contrast to
eugenics, 259.

Symbolism, the end of hy-
pothesis, no; of the new
mechanics, 206.

Tennyson, Lord, humanitari-

anism, 237.
Theology and science, 30, 35,

58, 210.
Theory, need at present time,

3-

Thomson, Sir J. J., properties
of atom, 17; theory of mat-
ter, 41, 54, 129; on electricity,
109; mass of electron, 136;
artificiality of his hypoth-
esis, 202.

Time, our idea of, 149; meas-
urement of, 167; a property
of space, 168; variability
with motion, 171 ; Einstein's
idea of, 181.

Transcendental symbolism of
German physicists, 206, 207.

Treitschke, doctrine of neces-
sity, 259.

Units, of measure, 118.
Universe as a machine, 9, 18,
72, 185.

Velocity of light, its signifi-
cance in the modern ether,

179-

Vortex, Kelvin's theory, 48;
Descartes's theory, 87.

Wilson, C. T. R., mass of the

electron, 136.
Wordsworth, William, human-

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