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is wont to begin. This point is conceived as the inert and
rigid subject of possible motion, and in itself is so emptied
of all quality as to contain no ground of activity of any sort.
The deduction of the law from this conception is easy enough;
but this conception is a pure figment of the imagination.
As applied to a real element, even the first part of the law,
which asserts that a body at rest will remain at rest unless
moved by something outside of it, is not self-evident. It is
not self-evident that an element, if it could exist alone in
space, could not, whatever its nature, begin motion; for
motion, as we have seen, is but the spatial expression of an
internal state, and if that state were given, motion would
result. It is not self-evident that the inner changes of such
a thing could never result in that state which expresses it-
self in motion.

The common proof of the first part of the law consists in
bidding us conceive a single element in void space, and in
pointing out that there is no more reason why it should



MATTER, FORCE, AND MOTION 229

move in one direction rather than in another. Then the
conclusion is drawn that the element will remain at rest.
But the law of the sufficient reason, to which appeal is here
made, is a very treacherous ally. We could use it with
equal propriety to prove that the atom could not be in space
or in time. For every point of space or time is like every
other, and hence there is no reason why it should be in one
rather than in any other ; and hence it cannot be in either
space or time. It is well known that Leibnitz, the formu-
lator of this law, was perpetually on the verge of pantheism
because of its influence. But we may allow that there
would be no reason in space itself for motion in one direc-
tion rather than in another ; yet that would not prove that
there might not be a reason in the thing. In no case does
space determine the direction of motion ; this is due to the
interaction of things, and the point here is to know why
an element might not of itself pass into that internal state
which appears as motion. It is said that if it did, the mo-
tion would not arise from rest, but from an internal motion ;
but the series of metaphysical changes in things are mo-
tions only in a rhetorical sense. If, then, a thing could exist
alone and maintain a series of inner changes in its solitary
existence, it is not inconceivable that it should pass into mo-
tion alone. For all we can say, there might be a tendency
in things to seek a certain state, as in elastic bodies, where
any departure from equilibrium results in an effort to re-
store the balance. A better illustration is found in our own
mental life, where every state is not compatible with inner
harmony, and in which there is a corresponding effort to re-
store the internal equilibrium. Things, then, might be such
as to be in conflict with themselves when forced out of a
certain state, and hence they might have an inner tendency
towards that state, and this state might be one which should
manifest itself as either rest or motion, according to its nature.



230 METAPHYSICS

But it has been further said that motion could not result
even in this case, because direction is necessary to motion.
If, then, this state which implies motion should exist, it
could not produce motion because there would be nothing
to determine its direction. Motion would be possible in any
one of an indefinite number of directions, and as every one
would have as good a claim as every other, the motion could
not begin at all. This is a return to the doctrine of the
sufficient reason, and does not reach the difficulty. Since
motion involves direction, we should simply say that the
state supposed to be produced would be one which should
contain the ground of direction in it. Of course, the ques-
tion comes up, "Why one direction rather than another?
And the answer must be a confession of ignorance. But
for one who believes in the reality of space and time, the
same question would arise concerning the existence of the
element. It would be easy to develop a great astonishment
over the fact that the atom should be in any one point
rather than in some one of the countless other points, each
of which has as good a right to its presence. And this as-
tonishment would have as much ground as the wonder over
the atom's motion in space. Provided the existence of an
atom in space meant anything intelligible, its movement
and direction would be no more wonderful than its exist-
ence in a fixed point. The fact, whichever it might be,
would simply have to be admitted. Even in the actual sys-
tem we come down to the same difficulty. It might be
said that no thing can cause another to move by any attrac-
tive force, because the possible directions are infinite. The
word attraction must not mislead us into overlooking this
difficulty. It is by no means self-evident that motion must
take place along the line which joins the bodies. For all
we can say, it might be on any other line whatever. Hence
the attracting body must also determine the direction, and



MATTER, FORCE, AND MOTION 231

by the law of the sufficient reason this is impossible. But
by the law of fact the conclusion is absurd. Indeed, the
entire process by which this law is deduced is purely ficti-
tious. The single atom in void space is a contradiction, be-
cause the atoms have their existence and properties only in
the system of which they are parts or implications. The
sole use of such a fiction is to impress the law upon the im-
agination. It should never be tolerated for an instant as
an argument. But if we will resort to such a fiction, we
must declare that, for aught any philosopher or physicist
knows, a single element in space might be such as to set
itself in motion.

The second part of the law is just as little an a/priori
truth on the current view of matter. To the unreflecting,
indeed, it even seems false ; but this is due entirely to the
bondage of the senses. First, the constant direction is no
necessity of thought. Direction itself is given from within,
and not from without. Of course, in reality the direction
is primarily determined from without, but only through an
internal state, so that the thing is not drawn, but driven
from within towards a certain point. The immediate reason
why a thing is moving in a certain direction and at a cer-
tain rate is not found in external things, but in its own inner
state. This is especially apparent on the current view that
if outer things should all fall away, the thing would con-
tinue to move in the same direction and at the same rate.
Direction, then, is finally given in the inner state of the
moving thing. There is, therefore, no absurdity in suppos-
ing that a thing should change its own direction. That it
does not do so is a fact, not a necessity. Here, also, appeal
is made to the principle of the sufficient reason, and it is
urged that there is no reason why the change should be on
one side rather than on the other, etc. Of course, there is
no reason in space, but to say that there is none in the



232 METAPHYSICS

thing is simply to beg the question. This part of the law
also is manifestly no necessity, but at most only a fact.

It remains to consider the last factor of the law of
inertia, the uniformity of motion when not interfered with
by external objects. This also follows necessarily from the
assumption that a material element cannot change its own
state; but it is no more a necessary truth than the other
factors of the law. But, curiously enough, a better argument
can be made for this part of the law than for the others. If
we assume that a finite change is reached only through suc-
cessive increments, and hence that a given change is only
the sum of the increments, then it is plain that there could
be no change without the law; and hence motion could
never begin nor end, as this beginning or ending would be
a form of change. If, then, motion can begin or cease, the
law of inertia must be admitted as an implication of this
fact. Taking the case of beginning motion, it is plain that
if every increment perished as fast as produced, there could
be no sum. Each new increment would begin with zero,
and could never get beyond it. Let us take the case of a
body falling from rest. At the end of the first unit of time,
which may be taken as infinitesimal, the body has a certain
velocity from gravitation. In the second instant, the body
is supposed to retain the velocity acquired in the first, and
to gain an additional increment; and so on in successive in-
stants. If, now, we suppose the acceleration uniform, the
velocity at the end of a given time will be the velocity ac-
quired in the unit of time multiplied by the number of
units. But it is plain that this could not be the case if the
law of inertia did not hold ; for the first increment of ve-
locity, dv, in the first instant, dt, would perish at once ; and
hence the next increment of velocity would begin not with
dv, but with plain zero. Hence at the end of any time, t,
the velocity would still be zero, and the body would not



MATTER, FORCE, AND MOTION 233

have moved. It may at first appear as if the body should
have moved some during the several instants, dt, but this is
seen to be a mistake, when we remember that as long as dt
expresses a real duration, we cannot assume that dv remains
constant through dt without assuming the law of inertia.
The untruth of the law would make even this impossible,
and hence each minimum increment of velocity would per-
ish as soon as born. While, then, we cannot directly prove
this part of the law of inertia, we can show that without it
no motion could ever begin.

Respect for those who have urged this argument would
incline us to accept it, if we held the realistic view, especial-
ly as it is by far the best argument advanced. It does not
aim to show that the law is a necessity of thought, but that
it is a necessary implication of admitted facts. It depends,
however, entirely upon the assumed truth of the law of con-
tinuity, or on the assumption that no natural force can in-
stantaneously produce or destroy a finite velocity. If, how-
ever, gravity were capable of instantaneously generating
any finite velocity, motion would be possible without the law
of inertia ; for velocity would be renewed as fast as lost, and
this would be equivalent to the constancy of the original
velocity. In a fountain under constant pressure the column
of water stands always at the same height. There is, in-
deed, incessant going, but there is also incessant coming;
and the one balances the other. If gravity were a constant
force, no acceleration could occur under such circumstances ;
but if gravity itself varied, variable velocity would result.
Nor would gravity in such a case be an infinite force ; for
it would never generate an infinite velocity. The summa-
tion of the finite velocities instantaneously produced into an
infinite sum would be impossible without assuming the law
of inertia. This law not holding, the velocity would remain
finite, and the present order would remain unchanged.



234: METAPHYSICS

There is no need to consider the pretended proof from
experience. Nothing remains at rest absolutely, and noth-
ing moves with uniform velocity in a straight line. If a
body be thrown into the air, it quickly loses its motion even
in the absence of that friction which plays so prominent a
part in the alleged experimental proofs of the law. As-
suming the law to be correct, we must account for these
variations by external forces ; and we throw on these forces
the burden of explaining the variations. But why might
we not assume the forces, and throw the burden of expla-
nation on the laws of motion ? Or might we not, in the
spirit of Leibnitz's monadology, find the ground of all
change in each element alone, so that they shall have vari-
ous laws of motion according to the demands of the system ?
In that case the laws both of force and motion would be
only the components into which the facts fall for purposes
of our calculation ; and the agreement of fact and calcula-
tion would only prove the practical validity of the laws,
not their reality. If things can exist independently, this
view is as good as any.

Thus far we have considered this law from the common
stand-point of a real space with things moving in it. This
view we have found to involve some peculiar paradoxes
concerning the relation of space to motion and direction.
In addition we have found reason to complain of the meth-
od of proof. This consists in setting the moving subject
apart in unreal abstraction, and then deducing laws for
reality from purely fictitious and impossible cases. Thus
the idea of a system is overlooked entirely, and the attempt
is made to find the laws of the system by denying in effect
that a true system exists. The individual has been assumed
as capable of existing by itself ; and against this view our
previous criticisms are valid. Of such elements, one law
would antecedently be no more probable than another ; and



MATTER, FORCE, AND MOTION 235

the validity of a law up to a certain point would be no war-
rant for its universality. If any deduction of this law is
possible, it must be from considering the nature of the
system and not from reflecting on those parts which have
been hypostasized into an unreal and impossible indepen-
dence. It may, then, be allowed to inquire whether any
rational insight into this law of motion can be reached from
the general character of the system.

Cosmology deals only with the system of nature, or with
what we mean by the physical system. But in discussing
interaction we have seen that it is impossible to construct
a system out of mutually independent elements. The nat-
ure and action of each thing must be determined by the
nature and idea of the whole. But this idea itself can de-
termine nothing except as it is set in reality. Hence the
logical implications of the idea are realized in the actual
members of the system; and the demands of the whole
upon each are realized through the mutual interaction of
the members. Each, then, is what it is, and does what it
does, because all the rest are what they are and do what they
do. Interaction in general means simply the determination
of one thing by another ; and in a system where there is
nothing but interaction the activities of each thing are nec-
essarily objective, and the determinations of each thing are
necessarily from without. But this is the conception we
must form of the physical system. In it we know of noth-
ing but interaction, or mutual determination. There is no
ground for affirming any subjectivity or self-determination
in them ; and they are members of the system only as each
is what the system demands. If in addition to their cos-
mological activity they also maintain an inner life, they be-
long by this element to the realm of psychology and not to
cosmology. But a cosmology is possible only as the mem-
bers interact and determine one another. Law and svstem



236 METAPHYSICS

would not otherwise exist. Hence the law of inertia in its
fullest extent must reign in such a system. No element
can change its own state whatever it may be; but the
ground of change must always be found outside of the ele-
ment itself. If it were otherwise, then the state of an ele-
ment at any moment would not be an expression of the
demands of the system upon it; and this is contrary to
the notion of a system. Not even the suggestion already
made that things may tend to a certain state can be longer
allowed ; for things have no right to any state on their own
account, but only to such as the state of the system as a
whole demands. Hence change of any and every kind in a
physical element must be referred to external causes. This
is the law of inertia in its very broadest sense ; and its ap-
plication to motion is only a special and limited case. And
we reach this conclusion not by considering such hyposta-
sized impossibilities as the existence of a single element in
void space, but by reflecting on the demands which a phys-
ical system must make upon each of its members. In so
far as any of them are capable of independent action, they
become rebels against the system or seceders from it. These
considerations do not, indeed, prove the law to be an onto-
logical necessity, for the system itself is no necessity ; but
they do prove that there can be no physical system without
the law. "We need not, then, doubt this law because we
know nothing about the mysterious nature of things ; for
the existence of a system at all implies the law. Nor need
the conclusion be confined to the physical elements alone.
Even the finite spirit, to a very large extent, comes under
this law ; and so far as it does not, it exists in relative inde-
pendence of the physical system. If the mental life were
absolutely determined by our interaction with the system,
the law of inertia, in its broadest sense, would be absolute
for mind as well as for matter.



MATTER, FORCE, AND MOTION 237

The law of inertia is the basal law of motion. In addi-
tion, two others are commonly given, which are as much
laws of force as of motion. The first of these, the second
law of Newton, is that the amount of motion is propor-
tional to the moving force, and is in the direction of its
action. The first part of this law is simple enough. Mo-
tion being an effect, must of course vary with its cause;
and, besides, the intensity of the force is measured by the
motion it causes. This part of the law could hardly fail to
be exact. But the second part of the law contains implicitly
the doctrine of the parallelogram of forces, and this is not so
self-evidently true. "We postpone its consideration, and pass
to the next law, Newton's third law of motion, the equality
of action and reaction. This is not properly a law of mo-
tion, but of action. In speaking of being, we pointed out
that there can be no action without reaction. In such a
case the object would in no way determine the agent, and
the effect would be created outright. Hence all interaction
involves reaction, and we may lay it down as an axiom of
metaphysics that there can be no action without reaction.
But this axiom in no way determines the nature and form
of the reaction, and is far from giving us the third law of
motion. This law of motion is, besides, thoroughly ambigu-
ous, and is self-evident only in one, and that its least impor-
tant, sense. The action and reaction may be purely static,
as when one thing rests on another. In this sense the law
is a necessity of equilibrium. If the table did not press up
as much as the weight on it presses down, it would be broken.
The foundations must meet the downward pressure of the
building by an equal upward pressure, or motion and col-
lapse will result. But action and reaction may be dynamic
also, as when the earth attracts the sun and the sun attracts
the earth ; and in this case the law is no self-evident neces-
sity. It is common to speak of this as a case of tension, and



238 METAPHYSICS

to illustrate by a tense cable. If a person in one boat pulls
at another boat, each boat moves towards the other, and ac-
tion and reaction are equal. At any point whatever in the
cable there is equal tension in both directions. But this il-
lustration is of no use until it is shown that attraction takes
place through a cable. There is no difficulty in conceiving
that a magnet should attract iron without being attracted
by it. The magnet causes in the iron a state which tends
to translate itself into motion towards the magnet, but this
in no way implies that the iron must cause a similar state in
the magnet. Neither act implies the other. The same is
true for attraction in general. The attraction of any one
element does not imply the attraction of any other. This
is all the more evident from the fact that many physicists
have spoken very freely of repulsive elements which meet
attraction with repulsion. It is, indeed, a grave misuse of
language to speak of anything as reaction which is not di-
rectly elicited by the preceding action. Eepulsion due to
pressure, or to repulsive forces called into play by previous
motion, is properly described as reaction, because it results
from the previous action ; but the attraction of one element
upon another is in no sense a reaction from the attraction of
the other upon it. This confusion of so many things under
a common term is what makes this law such an inexhaus-
tible mine of truth in the view of English physicists. That
the law, in this wide sense, is based entirely upon induction
needs no further proof.

The next law of motion which calls for consideration is
that relation to the composition of motions. This law is
implicit in Newton's second law of motion. If the abstrac-
tions of kinematics were realities, we might at once allow
the parallelogram of motions to be a rational necessity. If
the tendency to move in each of two directions is to be sat-
isfied, it can only be as the motion is along the diagonal of



MATTER, FORCE, AND MOTION 239

the parallelogram on the lines representing the tendencies
and directions. But, in reality, it is not a question of com-
pounding motions, but of finding the resultant of forces
which tend to cause the motions; and this introduces new
difficulties into the question. The law is sufficiently justified
in practice to exclude any doubt of its validity in all molar
motions. Its necessity, however, is quite another thing, and
depends on certain assumptions which are far from self-
evident. The chief one is that each force shall have its full
and proper effect in a crowd as well as when acting alone.
Thus if A and B both attract <7, the law assumes that each
shall have its proper influence without regard to the other.
On this assumption the resultant must be represented by
the diagonal of the parallelogram on A and JS. But this is
so far from necessary that it is antecedently improbable. It
would seem as if the effect of a new impulse ought to de-
pend on the previous state of the subject. This is the case
in the only subject of which we have direct knowledge.
The effect of a new thought or desire depends very largely
on the character of the thoughts and desires already in the
mind. The same thing affects us diversely according to our
mood or preoccupation. It is, therefore, a surprise to find
that the elements are never preoccupied, but are always
open to any new impulse whatever. This is so strange, and
from the stand-point of the mental life so paradoxical, that
we can allow the law only as a fact, and only so far as it is
justified by experience. It is possible that in the molecular
realm, especially in chemistry and biology, the law may be
modified.

Another assumption is commonly read into this law which
does not belong in it. The law itself says nothing of the
nature or origin of the forces, but views them all alike as
moving forces. They may be qualitatively distinct other-
wise ; but as moving forces they all stand on the same plane,



METAPHYSICS

and their effects are combined according to the parallelo-
gram of motions. But it is generally further assumed that
the forces themselves act in the same way, whether singly
or in a crowd. The action of a given element is not affected
by aggregation, but only by its own position in space. The
same amount of matter, at the same distance from the earth,
will attract with the same intensity whatever its form may
be. But this also is no necessity of thought, and from the
stand-point of human experience it is antecedently improb-
able. If such variation were allowed, it would, indeed,
increase the difficulty of calculation indefinitely; but this
proves nothing. As it is, we regard the action of a com-
pound as the sum of the acts of the components, and we
reach the total action by summing up the effects of the sep-
arate factors. If it were otherwise, we should have a prob-
lem immeasurably more complex than that of three bodies.
In the latter case we have to find the positions of bodies
from forces which depend on the positions which are to be
found; but in the former case we should have the addi-
tional difficulty of not knowing even the law of the forces.
The parallelogram of forces might still be valid, but it
would be useless. The actual forces would depend upon
the aggregation or velocity of the elements, and could be
known only from their resultant. Nevertheless, the inde-
pendent action of each element as assumed in mechanics is



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