which is derived from the apparent difference between matter as it
appears in physics and things as they appear in sensation. Men of
science, for the most part, are willing to condemn immediate data as
"merely subjective," while yet maintaining the truth of the physics
inferred from those data. But such an attitude, though it may be
_capable_ of justification, obviously stands in need of it; and the only
justification possible must be one which exhibits matter as a logical
construction from sense-data--unless, indeed, there were some wholly _a
priori_ principle by which unknown entities could be inferred from such
as are known. It is therefore necessary to find some way of bridging the
gulf between the world of physics and the world of sense, and it is this
problem which will occupy us in the present lecture. Physicists appear
to be unconscious of the gulf, while psychologists, who are conscious of
it, have not the mathematical knowledge required for spanning it. The
problem is difficult, and I do not know its solution in detail. All that
I can hope to do is to make the problem felt, and to indicate the kind
of methods by which a solution is to be sought.
Let us begin by a brief description of the two contrasted worlds. We
will take first the world of physics, for, though the other world is
given while the physical world is inferred, to us now the world of
physics is the more familiar, the world of pure sense having become
strange and difficult to rediscover. Physics started from the
common-sense belief in fairly permanent and fairly rigid bodies--tables
and chairs, stones, mountains, the earth and moon and sun. This
common-sense belief, it should be noticed, is a piece of audacious
metaphysical theorising; objects are not continually present to
sensation, and it may be doubted whether they are there when they are
not seen or felt. This problem, which has been acute since the time of
Berkeley, is ignored by common sense, and has therefore hitherto been
ignored by physicists. We have thus here a first departure from the
immediate data of sensation, though it is a departure merely by way of
extension, and was probably made by our savage ancestors in some very
remote prehistoric epoch.
But tables and chairs, stones and mountains, are not _quite_ permanent
or _quite_ rigid. Tables and chairs lose their legs, stones are split by
frost, and mountains are cleft by earthquakes and eruptions. Then there
are other things, which seem material, and yet present almost no
permanence or rigidity. Breath, smoke, clouds, are examples of such
things--so, in a lesser degree, are ice and snow; and rivers and seas,
though fairly permanent, are not in any degree rigid. Breath, smoke,
clouds, and generally things that can be seen but not touched, were
thought to be hardly real; to this day the usual mark of a ghost is that
it can be seen but not touched. Such objects were peculiar in the fact
that they seemed to disappear completely, not merely to be transformed
into something else. Ice and snow, when they disappear, are replaced by
water; and it required no great theoretical effort to invent the
hypothesis that the water was the same thing as the ice and snow, but in
a new form. Solid bodies, when they break, break into parts which are
practically the same in shape and size as they were before. A stone can
be hammered into a powder, but the powder consists of grains which
retain the character they had before the pounding. Thus the ideal of
absolutely rigid and absolutely permanent bodies, which early physicists
pursued throughout the changing appearances, seemed attainable by
supposing ordinary bodies to be composed of a vast number of tiny atoms.
This billiard-ball view of matter dominated the imagination of
physicists until quite modern times, until, in fact, it was replaced by
the electromagnetic theory, which in its turn is developing into a new
atomism. Apart from the special form of the atomic theory which was
invented for the needs of chemistry, some kind of atomism dominated the
whole of traditional dynamics, and was implied in every statement of its
laws and axioms.
The pictorial accounts which physicists give of the material world as
they conceive it undergo violent changes under the influence of
modifications in theory which are much slighter than the layman might
suppose from the alterations of the description. Certain features,
however, have remained fairly stable. It is always assumed that there is
_something_ indestructible which is capable of motion in space; what is
indestructible is always very small, but does not always occupy a mere
point in space. There is supposed to be one all-embracing space in which
the motion takes place, and until lately we might have assumed one
all-embracing time also. But the principle of relativity has given
prominence to the conception of "local time," and has somewhat
diminished men's confidence in the one even-flowing stream of time.
Without dogmatising as to the ultimate outcome of the principle of
relativity, however, we may safely say, I think, that it does not
destroy the possibility of correlating different local times, and does
not therefore have such far-reaching philosophical consequences as is
sometimes supposed. In fact, in spite of difficulties as to measurement,
the one all-embracing time still, I think, underlies all that physics
has to say about motion. We thus have still in physics, as we had in
Newton's time, a set of indestructible entities which may be called
particles, moving relatively to each other in a single space and a
single time.
The world of immediate data is quite different from this. Nothing is
permanent; even the things that we think are fairly permanent, such as
mountains, only become data when we see them, and are not immediately
given as existing at other moments. So far from one all-embracing space
being given, there are several spaces for each person, according to the
different senses which give relations that may be called spatial.
Experience teaches us to obtain one space from these by correlation, and
experience, together with instinctive theorising, teaches us to
correlate our spaces with those which we believe to exist in the
sensible worlds of other people. The construction of a single time
offers less difficulty so long as we confine ourselves to one person's
private world, but the correlation of one private time with another is a
matter of great difficulty. Thus, apart from any of the fluctuating
hypotheses of physics, three main problems arise in connecting the world
of physics with the world of sense, namely (1) the construction of
permanent "things," (2) the construction of a single space, and (3) the
construction of a single time. We will consider these three problems in
succession.
(1) The belief in indestructible "things" very early took the form of
atomism. The underlying motive in atomism was not, I think, any
empirical success in interpreting phenomena, but rather an instinctive
belief that beneath all the changes of the sensible world there must be
something permanent and unchanging. This belief was, no doubt, fostered
and nourished by its practical successes, culminating in the
conservation of mass; but it was not produced by these successes. On the
contrary, they were produced by it. Philosophical writers on physics
sometimes speak as though the conservation of something or other were
essential to the possibility of science, but this, I believe, is an
entirely erroneous opinion. If the _a priori_ belief in permanence had
not existed, the same laws which are now formulated in terms of this
belief might just as well have been formulated without it. Why should we
suppose that, when ice melts, the water which replaces it is the same
thing in a new form? Merely because this supposition enables us to state
the phenomena in a way which is consonant with our prejudices. What we
really know is that, under certain conditions of temperature, the
appearance we call ice is replaced by the appearance we call water. We
can give laws according to which the one appearance will be succeeded by
the other, but there is no reason except prejudice for regarding both as
appearances of the same substance.
One task, if what has just been said is correct, which confronts us in
trying to connect the world of sense with the world of physics, is the
task of reconstructing the conception of matter without the _a priori_
beliefs which historically gave rise to it. In spite of the
revolutionary results of modern physics, the empirical successes of the
conception of matter show that there must be some legitimate conception
which fulfils roughly the same functions. The time has hardly come when
we can state precisely what this legitimate conception is, but we can
see in a general way what it must be like. For this purpose, it is only
necessary to take our ordinary common-sense statements and reword them
without the assumption of permanent substance. We say, for example, that
things change gradually--sometimes very quickly, but not without passing
through a continuous series of intermediate states. What this means is
that, given any sensible appearance, there will usually be, _if we
watch_, a continuous series of appearances connected with the given one,
leading on by imperceptible gradations to the new appearances which
common-sense regards as those of the same thing. Thus a thing may be
defined as a certain series of appearances, connected with each other by
continuity and by certain causal laws. In the case of slowly changing
things, this is easily seen. Consider, say, a wall-paper which fades in
the course of years. It is an effort not to conceive of it as one
"thing" whose colour is slightly different at one time from what it is
at another. But what do we really _know_ about it? We know that under
suitable circumstances--_i.e._ when we are, as is said, "in the
room"--we perceive certain colours in a certain pattern: not always
precisely the same colours, but sufficiently similar to feel familiar.
If we can state the laws according to which the colour varies, we can
state all that is empirically verifiable; the assumption that there is a
constant entity, the wall-paper, which "has" these various colours at
various times, is a piece of gratuitous metaphysics. We may, if we like,
_define_ the wall-paper as the series of its aspects. These are
collected together by the same motives which led us to regard the
wall-paper as one thing, namely a combination of sensible continuity and
causal connection. More generally, a "thing" will be defined as a
certain series of aspects, namely those which would commonly be said to
be _of_ the thing. To say that a certain aspect is an aspect _of_ a
certain thing will merely mean that it is one of those which, taken
serially, _are_ the thing. Everything will then proceed as before:
whatever was verifiable is unchanged, but our language is so interpreted
as to avoid an unnecessary metaphysical assumption of permanence.
The above extrusion of permanent things affords an example of the maxim
which inspires all scientific philosophising, namely "Occam's razor":
_Entities are not to be multiplied without necessity._ In other words,
in dealing with any subject-matter, find out what entities are
undeniably involved, and state everything in terms of these entities.
Very often the resulting statement is more complicated and difficult
than one which, like common sense and most philosophy, assumes
hypothetical entities whose existence there is no good reason to believe
in. We find it easier to imagine a wall-paper with changing colours than
to think merely of the series of colours; but it is a mistake to suppose
that what is easy and natural in thought is what is most free from
unwarrantable assumptions, as the case of "things" very aptly
illustrates.
The above summary account of the genesis of "things," though it may be
correct in outline, has omitted some serious difficulties which it is
necessary briefly to consider. Starting from a world of helter-skelter
sense-data, we wish to collect them into series, each of which can be
regarded as consisting of the successive appearances of one "thing."
There is, to begin with, some conflict between what common sense regards
as one thing, and what physics regards an unchanging collection of
particles. To common sense, a human body is one thing, but to science
the matter composing it is continually changing. This conflict, however,
is not very serious, and may, for our rough preliminary purpose, be
largely ignored. The problem is: by what principles shall we select
certain data from the chaos, and call them all appearances of the same
thing?
A rough and approximate answer to this question is not very difficult.
There are certain fairly stable collections of appearances, such as
landscapes, the furniture of rooms, the faces of acquaintances. In these
cases, we have little hesitation in regarding them on successive
occasions as appearances of one thing or collection of things. But, as
the _Comedy of Errors_ illustrates, we may be led astray if we judge by
mere resemblance. This shows that something more is involved, for two
different things may have any degree of likeness up to exact similarity.
Another insufficient criterion of one thing is _continuity_. As we have
already seen, if we watch what we regard as one changing thing, we
usually find its changes to be continuous so far as our senses can
perceive. We are thus led to assume that, if we see two finitely
different appearances at two different times, and if we have reason to
regard them as belonging to the same thing, then there was a continuous
series of intermediate states of that thing during the time when we were
not observing it. And so it comes to be thought that continuity of
change is necessary and sufficient to constitute one thing. But in fact
it is neither. It is not _necessary_, because the unobserved states, in
the case where our attention has not been concentrated on the thing
throughout, are purely hypothetical, and cannot possibly be our ground
for supposing the earlier and later appearances to belong to the same
thing; on the contrary, it is because we suppose this that we assume
intermediate unobserved states. Continuity is also not sufficient, since
we can, for example, pass by sensibly continuous gradations from any one
drop of the sea to any other drop. The utmost we can say is that
discontinuity during uninterrupted observation is as a rule a mark of
difference between things, though even this cannot be said in such cases
as sudden explosions.
The assumption of continuity is, however, successfully made in physics.
This proves something, though not anything of very obvious utility to
our present problem: it proves that nothing in the known world is
inconsistent with the hypothesis that all changes are really continuous,
though from too great rapidity or from our lack of observation they may
not always appear continuous. In this hypothetical sense, continuity may
be allowed to be a _necessary_ condition if two appearances are to be
classed as appearances of the same thing. But it is not a _sufficient_
condition, as appears from the instance of the drops in the sea. Thus
something more must be sought before we can give even the roughest
definition of a "thing."
What is wanted further seems to be something in the nature of fulfilment
of causal laws. This statement, as it stands, is very vague, but we will
endeavour to give it precision. When I speak of "causal laws," I mean
any laws which connect events at different times, or even, as a limiting
case, events at the same time provided the connection is not logically
demonstrable. In this very general sense, the laws of dynamics are
causal laws, and so are the laws correlating the simultaneous
appearances of one "thing" to different senses. The question is: How do
such laws help in the definition of a "thing"?
To answer this question, we must consider what it is that is proved by
the empirical success of physics. What is proved is that its hypotheses,
though unverifiable where they go beyond sense-data, are at no point in
contradiction with sense-data, but, on the contrary, are ideally such as
to render all sense-data calculable from a sufficient collection of data
all belonging to a given period of time. Now physics has found it
empirically possible to collect sense-data into series, each series
being regarded as belonging to one "thing," and behaving, with regard to
the laws of physics, in a way in which series not belonging to one thing
would in general not behave. If it is to be unambiguous whether two
appearances belong to the same thing or not, there must be only one way
of grouping appearances so that the resulting things obey the laws of
physics. It would be very difficult to prove that this is the case, but
for our present purposes we may let this point pass, and assume that
there is only one way. We must include in our definition of a "thing"
those of its aspects, if any, which are not observed. Thus we may lay
down the following definition: _Things are those series of aspects which
obey the laws of physics._ That such series exist is an empirical fact,
which constitutes the verifiability of physics.
It may still be objected that the "matter" of physics is something other
than series of sense-data. Sense-data, it may be said, belong to
psychology and are, at any rate in some sense, subjective, whereas
physics is quite independent of psychological considerations, and does
not assume that its matter only exists when it is perceived.
To this objection there are two answers, both of some importance.
(a) We have been considering, in the above account, the question of the
_verifiability_ of physics. Now verifiability is by no means the same
thing as truth; it is, in fact, something far more subjective and
psychological. For a proposition to be verifiable, it is not enough that
it should be true, but it must also be such as we can _discover_ to be
true. Thus verifiability depends upon our capacity for acquiring
knowledge, and not only upon the objective truth. In physics, as
ordinarily set forth, there is much that is unverifiable: there are
hypotheses as to (A) how things would appear to a spectator in a place
where, as it happens, there is no spectator; (B) how things would appear
at times when, in fact, they are not appearing to anyone; (C) things
which never appear at all. All these are introduced to simplify the
statement of the causal laws, but none of them form an integral part of
what is _known_ to be true in physics. This brings us to our second
answer.
(b) If physics is to consist wholly of propositions known to be true, or
at least capable of being proved or disproved, the three kinds of
hypothetical entities we have just enumerated must all be capable of
being exhibited as logical functions of sense-data. In order to show how
this might possibly be done, let us recall the hypothetical Leibnizian
universe of Lecture III. In that universe, we had a number of
perspectives, two of which never had any entity in common, but often
contained entities which could be sufficiently correlated to be regarded
as belonging to the same thing. We will call one of these an "actual"
private world when there is an actual spectator to which it appears, and
"ideal" when it is merely constructed on principles of continuity. A
physical thing consists, at each instant, of the whole set of its
aspects at that instant, in all the different worlds; thus a momentary
state of a thing is a whole set of aspects. An "ideal" appearance will
be an aspect merely calculated, but not actually perceived by any
spectator. An "ideal" state of a thing will be a state at a moment when
all its appearances are ideal. An ideal thing will be one whose states
at all times are ideal. Ideal appearances, states, and things, since
they are calculated, must be functions of actual appearances, states,
and things; in fact, ultimately, they must be functions of actual
appearances. Thus it is unnecessary, for the enunciation of the laws of
physics, to assign any reality to ideal elements: it is enough to accept
them as logical constructions, provided we have means of knowing how to
determine when they become actual. This, in fact, we have with some
degree of approximation; the starry heaven, for instance, becomes actual
whenever we choose to look at it. It is open to us to believe that the
ideal elements exist, and there can be no reason for _dis_believing
this; but unless in virtue of some _a priori_ law we cannot _know_ it,
for empirical knowledge is confined to what we actually observe.
(2) The three main conceptions of physics are space, time, and matter.
Some of the problems raised by the conception of matter have been
indicated in the above discussion of "things." But space and time also
raise difficult problems of much the same kind, namely, difficulties in
reducing the haphazard untidy world of immediate sensation to the smooth
orderly world of geometry and kinematics. Let us begin with the
consideration of space.
People who have never read any psychology seldom realise how much mental
labour has gone into the construction of the one all-embracing space
into which all sensible objects are supposed to fit. Kant, who was
unusually ignorant of psychology, described space as "an infinite given
whole," whereas a moment's psychological reflection shows that a space
which is infinite is not given, while a space which can be called given
is not infinite. What the nature of "given" space really is, is a
difficult question, upon which psychologists are by no means agreed. But
some general remarks may be made, which will suffice to show the
problems, without taking sides on any psychological issue still in
debate.
The first thing to notice is that different senses have different
spaces. The space of sight is quite different from the space of touch:
it is only by experience in infancy that we learn to correlate them. In
later life, when we see an object within reach, we know how to touch it,
and more or less what it will feel like; if we touch an object with our
eyes shut, we know where we should have to look for it, and more or less
what it would look like. But this knowledge is derived from early
experience of the correlation of certain kinds of touch-sensations with
certain kinds of sight-sensations. The one space into which both kinds
of sensations fit is an intellectual construction, not a datum. And
besides touch and sight, there are other kinds of sensation which give
other, though less important spaces: these also have to be fitted into
the one space by means of experienced correlations. And as in the case
of things, so here: the one all-embracing space, though convenient as a
way of speaking, need not be supposed really to exist. All that
experience makes certain is the several spaces of the several senses,
correlated by empirically discovered laws. The one space may turn out to
be valid as a logical construction, compounded of the several spaces,
but there is no good reason to assume its independent metaphysical
reality.
Another respect in which the spaces of immediate experience differ from
the space of geometry and physics is in regard to _points_. The space of
geometry and physics consists of an infinite number of points, but no
one has ever seen or touched a point. If there are points in a sensible
space, they must be an inference. It is not easy to see any way in
which, as independent entities, they could be validly inferred from the
data; thus here again, we shall have, if possible, to find some logical
construction, some complex assemblage of immediately given objects,
which will have the geometrical properties required of points. It is
customary to think of points as simple and infinitely small, but
geometry in no way demands that we should think of them in this way. All
that is necessary for geometry is that they should have mutual relations
possessing certain enumerated abstract properties, and it may be that an
assemblage of data of sensation will serve this purpose. Exactly how
this is to be done, I do not yet know, but it seems fairly certain that
it can be done.