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plane of perception to that of conception. I move
my hand ; my power to realize this motion depends
on my conceiving my hand bounded by a continuous
surface. If the physicist tells me that my hand is an

1 System of Logic, bk. i. chap. iii. That groups of sense-impressions
recur in a more or less permanent state is an experience we have every
moment of our lives. There is a " permanent possibility of sense-
impressions." We are not forced to assert anything about this possi-
bility residing in a supersensuous entity matter.



298 THE GRAMMAR OF SCIENCE.

aggregation of discrete molecules, then my idea of
the motion of the hand is thrown back on the motion
of the swarm of molecules. But the same difficulty
arises about the individual molecule. I may surmount
it by supposing the molecule to be in itself a corpora-
tion of atoms, but I cannot conceive the atom's motion
unless it be bounded by a continuous surface or else be
a point The only other way out of the difficulty is to
construct the atom of still smaller atoms (and there
are certain phenomena presented by the spectrum
analysis of the gaseous elements that might well
induce us to believe that the atom cannot be con-
ceived as the ultimate or " prime element of
matter ") but what about these smaller atoms, are
they geometrical ideals or are they built up of tinier
atoms still, and if so where are we to stop ? The
process reminds us of the lines of Swift :

" So naturalists observe, a flea
Has smaller fleas that on him prey ;
And these have smaller still to bite 'em,
And so proceed ad injinitum."

I am unable to verify Swift's statement as to the fleas,
but I feel quite sure that to assert the real existence
in the world of phenomena of all the concepts by aid
of which we scientifically describe phenomena
molecule, atom, prime-atom even if it be ad infinitum,
will not save us from having ultimately to consider
the moving thing to be a geometrical ideal, from
having to postulate the phenomenal existence of what
is contrary to our perceptual experience. This point
brings out very clearly what the present writer holds
to be a fundamental canon of scientific method,
namely : To no concept^ however invaluable it may be



MATTER. 299

as a means of describing the routine of perceptions > ought
phenomenal existence to be ascribed until its perceptual
equivalent has been actually disclosed.

Whenever we disregard this canon, when, for ex-
ample, we assert reality for the mechanisms by aid of
which we describe our physical experience, then we
are more likely than not to conclude with an antinomy,
or a conflict of rules. For such mechanisms are con-
structs largely based on conceptual limits, which are
unattainable in the field of perception. When we
consider space as objective and matter as that which
occupies it, we are forming a construct largely based
on the geometrical symbols by aid of which we analyze
motion conceptually. We are projecting the form
and volume of conception into perception, and so
accustomed have we got to this conceptual element
in the construct that we confuse it with a reality of
perception itself. When we go a stage further in the
phenomenalizing of conceptions, and postulate the
reality of atoms, the antinomy becomes clear. If
bodies are made up of swarms of atoms, how can they
have a real volume or form ? What is the volume
or form of a swarm of bees or a cloud of dust?
Obviously we can only give them shape and size by
enclosing them conceptually in an ideal geometrical
surface. Just as in a swarm of bees or a cloud of
dust odd members of the community near this imagi-
nary surface are continually passing in and out, so if
we phenomenalize conception we must assert that at
the surface of water or of iron odd molecules or atoms
are perpetually leaving or, it may be, re-entering the
swarm. Condensation and evaporation go on at the
surface of the water and iron has a metallic smell.
Now if the swarm be in this continual state of flow



3OO THE GRAMMAR OF SCIENCE.

at the surface we can only speak of it as having
volume or form ideally^ or as a mode of conceptually
distinguishing one group of sense-impressions from
another (p. 197). It is the conceptual volume or form
which occupies space, and it is this form, and not the
sense-impressions, which we conceive to move. If we
throw back the occupancy of space on the individual
members of the swarm, it is certainly not the
volumes or forms of the individuals, which we con-
sider as the volume or form of the material body, for
the former we treat as imperceptible and the latter as
perceptible. Further, we must then infer that the
unknown is ultimately unlike the known, that geo-
metrical ideals can be realized in the imperceptible.
This, however, is a distinct breach of the canon of
logical inference (p. 72).

So far, then, our analysis of the physicist's defini-
tions of matter irresistibly forces upon us the following
conclusions : That matter as the unknowable cause
of sense-impression is a metaphysical entity x as
meaningless for science as any other postulating of
causation in the beyond of sense-impression ; it is as
idle as any other thing-in-itself, as any other projection
into the supersensuous, be it the force of the mate-
rialists, or the infinite mind of the philosophers. The
classification of certain groups of sense-impressions as
material groups is, on the other hand, scientifically of
value ; it throws no light, however, on matter as
that which perceptually moves.

Conceptually all motion is the motion of geometrical
ideals, which are so chosen as best to describe those

1 The scientific reader must for the present have at least sufficient
confidence in the author not to believe that mass is thrown overboard
with the fetish matter.



MATTER. 301

changes of sense-impression which in ordinary lan-
guage we term perceptual motion.

5 . The " Common-sense" View of Matter as Impenetrable and

Hard.

Now the reader may feel inclined, on the basis of
his daily experience, to assert that both the physicists
above referred to and the author are really quibbling
about words, and that we can sufficiently describe
matter by saying that it is impenetrable and hard.
Now these terms describe important classes of sense-
impressions, and the sense-impressions of impenetra-
bility and hardness are very frequently factors of what
we have called material groups of sense-impressions.
But it is very doubtful whether we can consider them
as invariably associated with these material groups.
At any rate if we do we shall find ourselves again
involved in the antinomies which result when we pass
incautiously to and fro from the field of perception to
that of conception. When we say a thing is impene-
trable, we can only mean that something else will not
pass through it, or that there are two groups of
sense-impressions which, in our perceptual experience,
we have always been able to distinguish under the
mode space. Impenetrability, therefore, can only be
a relative term ; one thing is .impenetrable for a
second. When we say that matter is impenetrable
we cannot mean that nothing whatever can pass
through it. A bird cannot fly through a sheet of
plate glass, but a ray of light does penetrate it per-
fectly easily. A ray of light cannot pass through a
brick wall, but a wave of electric oscillations can. In
order to describe the motion of these luminous and
electric waves the physicist conceives ether to pene-



302 THE GRAMMAR OF SCIENCE

trate all bodies and to act as a medium for the transit
of energy through them. Matter cannot therefore be
looked upon as the thing which is absohitely impene-
trable.

Or, are we missing the point of what is meant, when
it is asserted that matter is that which is impenetrable ?
Are we to postulate the real existence of atoms and
then to suppose the individual members of the swarm
impenetrable ? Here again a difficulty arises. There
is much that tends to convince physicists that the
atom cannot be conceived as the simplest element of
the conceptual analysis of material groups. Just as
a bell when struck sets the air in motion and gives a
note, so we conceive an atom capable of being struck,
and of setting not the air but the ether in motion, of
giving, as we might express it, an ether note. These
notes produce in us certain optical sense-impressions
for example, the bright lines of the spectrum of an
attenuated gas. As without seeing two bells we
might, and indeed often do, distinguish them by their
notes, 1 so the physicist distinguishes an atom of
hydrogen from an atom of oxygen, although he has
never seen either, by the different light notes which
he conceives to arise from them. But as the bell to
give a note must be considered as vibrating changing
its shape or undergoing strain so the physicist prac-
tically finds himself compelled to conceive the atom
as undergoing strain, or changing its shape. This
conception forces us to suppose the atom built up
of distinct parts capable of changing their relative

1 The householder is generally able to distinguish the sound of the
back-door from that of the front-door bell, although, probably, in
ninety-nine cases out of a hundred he may never have seen the bells in
his house.



MATTER. 303

position. What are these ultimate parts of the atom,
by the relative motion of which we describe our sense-
impressions of the bright lines in the spectrum ? We
have as yet formed no conception. Does the ether or
anything else penetrate between these ultimate parts of
the atom ? We cannot say. In the present state of
our knowledge it is impossible to tell whether it would
or would not simplify things to conceive the atom as
penetrable or impenetrable. Hence, even if we go
so far as to give the concept atom a phenomenal
existence, it will not help us to understand what is
meant by the assertion that matter is impenetrable.

6. Individuality does not denote Sameness in Substratum.

Shall we, however, be more dogmatic still, and,
denying that ether is matter, assert that matter is
impenetrable relative to matter ? In order to give
any definite answer to this question we have again
to pass from the perceptible material group to its
supposed elementary basis, the atom, and to ask
whether we have any reason for conceiving atoms as
incapable of penetrating each other. In the first
place the physicist, although he has never caught an
atom, yet conceives it as something which is incapable
of disappearing it continues to be. In the next place,
if we conceive it as entering into combination with a
second atom, although we have no reason for asserting
that the two atoms do not mutually penetrate, we are
still compelled, in order to describe by aid of atoms
our perceptual experience, to conceive that, out of the
combination, two separate atoms can again be obtained
with the same individual characteristics as the original
two possessed. What right have we to postulate
these laws with regard to atoms when atoms are, even



304 THE GRAMMAR OF SCIENCE.

if real, still absolutely imperceptible to us, when we
are absolutely unable to observe their mutual action ?
We have exactly the same logical right as we have to
lay down any scientific law whatever. Namely, we
find that these laws as to the action of single atoms,
when applied to large groups of atoms, enable us to
describe with very great accuracy what occurs in those
phenomenal bodies, which we scientifically symbolize
by groups of atoms ; they enable us to construct
without contradiction by perceptual experience, those
routines of sense-impression which we term chemical
reactions.

The hypotheses that the individual atom is both
indestructible and impenetrable suffice to elucidate
certain physical and chemical properties of the bodies
we construct from atoms. But the continued existence
of atoms under physical changes and the reproduction
of their individuality on the dissolution of chemical
combination might possibly be deduced from other
hypotheses than those of the indestructibility and
impenetrability of the individual atom. It does not
follow of logical necessity that because we experience
the same group of sense-impressions at different times
and in different places, or even continuously, that
there must be one and the same thing at the basis of
these sense-impressions. An example will clearly
show the reader what we mean and at the same time
demonstrate that however useful as hypotheses the
indestructibility and impenetrability of the atom may
be, they are still not absolutely necessary conceptions ;
so that even if we do project our atom into an imper-
ceptible of the phenomenal world, it will not follow
that there must be an unchangeable individual some-
thing at all times and in all positions as the basal



MATTER.



305



element of a permanent group of sense-impressions.
The permanency and sameness of the phenomenal
body may lie in the individual grouping of the
sense-impressions and not in the sameness of an
imperceptible something projected from conception
into phenomena.

The example we will take is that of a wave on the



WAVE




FIG. 19.

surface of the sea. The wave forms for us a group
of sense-impressions, and we look upon it, and speak
of it, as if it were an individual thing. But we are
compelled to conceive the wave when it is fifty yards
off as consisting of quite different moving things to
what it does when it reaches our feet the substratum
of the wave has changed. Throw a cork in ; it rises

21



306 THE GRAMMAR OF SCIENCE.

and falls as the wave passes it, but is not carried along
by it. The wave may retain its form and be for us
exactly the same group of sense-impressions in
different positions and at different times, and yet its
substratum may be continually changing. We might
even push the illustration further ; we might send two
waves of different individual shapes (Ffg. 19) along the
surface of still water in opposite directions (a), or in the
same direction if the pursuing wave had the greater
speed. One of these waves would meet or overtake the
other (&) ; they would coalesce or combine (<:), pro-
ducing in us for a time (which depends entirely on their
relative speeds), a new group of sense-impressions dif-
fering totally from either individual group ; but they
would ultimately pass each other (d) and emerge with
their distinct individualities the same as of old (e).
Throughout the whole of this sequence the substrata of
the two individual waves are changing and for the time
of the combination their substratum is identical, and
yet the waves are able to preserve their individual
characteristics, so far as reappearing with them after
combination is concerned. 1 Thus sameness of sense-
impressions before and after a combination is seen
from a perceptual example not to involve of necessity
a sameness of substratum.

Now we have cited this example of the wave
for two reasons. In the first place it shows us
that it is possible to conceive atoms as penetrable
by atoms, and as varying from moment to moment

1 If analogy were to be sought to the sameness of total weight before,
during, and after combination, it might be found in the sameness of the
volume of fluid raised above the sea-level, before, during, and after
coalition. Thus sameness of weight does not in conception necessarily
involve sameness of substratum.



MATTER. 307

in their substratum, without at the same time
denying the possibility of their physical perma-
nency and individual reproduction after chemical
combination. To consider an atom as consisting
always of the same substratum, and as impenetrable
by other atoms, may help us to describe easily certain
physical and chemical phenomena ; but it is quite
conceivable that other hypotheses may equally well
account for these phenomena, and this being so we
have clearly no right first to project special conceptions
into the world of real phenomena, and then to assert
on the strength of this that matter, penetrable in itself,
is impenetrable in its ultimate element, the atom.
Clearly impenetrability is neither in perception nor
conception a necessary factor of material groups of
sense-impressions. Further, the permanence and
sameness of such a group do not necessarily involve
the conception of a permanent and same substratum
for the group.

My second reason for citing this wave example lies
in the light it throws on the possibilities involved in
the statement : "Matter is that ivhich moves" The wave
consists of a particular form of motion in the sub-
stratum which for the time constitutes the wave. This
form of motion itself moves along the surface of the
water. Hence we see that besides the substratum
something else can be conceived as moving, namely,
forms of motion. What if, after all, matter as the
moving thing could be best expressed in conception
by a form of motion moving, and this whether the
substratum remain the same or not ? To this sugges-
tion we shall return later, as it is one extremely
fruitful in its results.



308 THE GRAMMAR OF SCIENCE.

7. Hardness" not Characteristic of Matter.
It remains for us now to deal with the other cha-
racteristic, hardness, which is popularly attributed to
matter. There are certain persons who, when men's
ignorance as to the nature of matter is suggested to
them, are content to remark that one has only to knock
one's head against a stone wall in order to have a
valid demonstration of the existence and the nature of
matter. Now if this statement be of any value, it can
only mean that the sense-impression of hardness is the
essential test of the presence of matter in these persons'
opinion. But none of us doubt the existence of the
sense-impression hardness associated with other sense-
impressions in certain permanent groups ; we have
been aware of it from childhood's days, and do not
require its existence to be experimentally demon-
strated now. It is one of those muscular sense-
impressions which we shall see are conceived by
science to be describable in terms of the relative
acceleration of certain parts of our body and of
external bodies. But it is difficult to grasp how the
sense-impression of hardness can tell us more of the
nature of matter than the sense-impression of soft-
ness might be supposed to do. There are clearly
many things which are popularly termed matter and
are certainly not hard. Further, there are things
which satisfy the definitions of matter as that which
moves or as that which fills space, but which are very
far indeed from producing any sense-impression of the
nature of hardness or softness ; nor would they even
satisfy our definition if we said that matter is that
which is heavy, heaviness being certainly a more widely-
spread factor of material groups of sense-impressions
than hardness. Between the sun and planets, between



MATTER. 309

the atoms of bodies, physicists conceive the ether to
exist, a medium whose vibrations constitute the
channel by means of which electro-magnetic and
optical energy is transferred from one body to another-
In the first place, the ether is a pure conception by
aid of which we correlate in conceptual space various
motions. These motions are the symbols by which
we briefly describe the sequences and relationships we
perceive between various groups of phenomena. The
ether is thus a mode of resuming our perceptual
experience ; but like a good many other conceptions of
which we have no direct perception, physicists project
it into the phenomenal world and assert its real
existence. There seems to be just as much, or little,
logic in this assertion as in the postulate that there is
a real substratum, matter, at the back of groups of
sense-impressions ; both at present are metaphysical
statements. Now there is no evidence forthcoming that
the ether must be conceived as either hard or heavy, 1
and yet it can be strained or its parts put in relative
motion. Further, from Professor Tait's standpoint, it
occupies space. Hence those who associate matter
with hardness and weight must be prepared to deny
that the ether is matter, or be content to call it non-
matter. It is worth noting, at the same time, that the
metaphysicians whether they be materialists asserting
the phenomenal existence both of space and of a
permanent substratum of sense-impression, or " com-
mon-sense " philosophers asking us to knock our

1 I venture to think Sir William Thomson's attempt to weigh ether a
retrograde step (see his Lectures on Molecular Dynamics, pp. 206-8,
Baltimore, 1884). If the ether be a sufficiently wide-embracing con-
ception, gravitation should flow from it, and this certainly was Sir
William's view when he propounded the vortex atom.



316 THE GRAMMAR OF SCIENCE.

heads against stone walls reach hopelessly divergent
results when they say that matter is that which moves,
that matter occupies space, and that matter is that
which is heavy and hard.

8. Matter as non- Matter in Motion.

There is, however, a still greater dilemma in store
for the " common-sense " philosophers. We have not
yet reached a clear conception of what the ether, the
non-matter of our philosophers, consists in. There
are in fact two, at first sight, completely divergent
ways in which the ether is reached as a conceptual
limit to our perceptual experience (see p. 217), but it is
the great hope of science at the present day that "hard
and heavy matter " will be shown to be ether in motion.
In other words, it is well within the range of possibility
that during the next quarter of a century science will
have discovered that our symbolic description of the
phenomenal universe will be immensely simplified, if
we take as our symbolic basis for material groups of
sense-impressions a type of motion of the conceptual
ether ; in other, more expressive if less accurate,
language, if we treat our friends' matter as their non-
matter in motion. We shall then find that our sense-
impressions of hardness, Weight, colour, temperature,
cohesion, and chemical constitution, may all be
described by aid of the motions of a single medium,
which itself is conceived to have no hardness, weight,
colour, temperature, nor indeed elasticity of the
ordinary perceptual type. This would mean an
immeasurably great advance in our scientific power
of description. Yet if physicists even then persist in
projecting the conceptual into the sphere of sense-
impression, and in asserting a phenomenal existence



MATTER. 311

for the ether, we should still be ignorant of what it is
that moves, of what ether-matter may really consist
in.

Our analysis, therefore, of the various statements
made by physicists and common-sense philosophers
with regard to the nature of matter, shows us that they
are one and "^metaphysical- that is, they attempt to de-
scribe something beyond sense-impression,beyond per-
ception, and appear, therefore, at best as dogmas, at
worst as inconsistencies. If we confine ourselves to the
field of logical inference, we see in the phenomenal uni-
verse not matter in motion, but sense-impressions and
changes of sense-impressions, coexistence and sequence,
correlation and routine. This world of sense-impression
science symbolizes in conception by an infinitely ex-
tended medium, whose various types of motion corre-
spond to diverse groups of sense-impressions, and enable
us to describe the correlations and sequences of these
groups. The moving elements of this medium can in
thought be conceived of only as geometrical ideals, as
points or continuous surfaces. To make our symbolic
chart or picture agree the better with perceptual experi-
ence, we find it necessary to endow these geometrical
ideals with certain relative positions, velocities, and ac-
celerations, the correlations of which are expressible
in certain simple laws termed the laws of motion (see
the following Chapter). If we choose to term the
moving things of the conceptual chart matter, there
can be no objection to the term, provided we carefully
distinguish this conceptual matter from any meta-
physical ideas of matter as the substratum of sense-
impression, as that which perceptually moves, as that
which fills space, or as that which can be defined as
heavy, hard, and impenetrable. Conceptual matter is



312 THE GRAMMAR OF SCIENCE.

thus merely a name for the geometrical ideals endowed
with certain correlated motions by aid of which we
describe the routine of our external perceptions. It
is in this sense that we shall use the term matter for
the remainder of this work, unless we are expressly



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