Bertrand Russell.

Our knowledge of the external world, as a field for scientific method in philosophy online

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points, instants, and particles ; but I do not yet know to
what lengths this diminution in our initial assumptions
can be carried.





Among the objections to the reality of objects of sense,
there is one 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 sub-
jective," 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 know-
ledge 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 con-
trasted 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 sensa-
tion, and it may be doubted whether they are there wheq
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

But tables and chairs, stones and mountains, are not
quite permanent or guite 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 dis-
appear 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


eflFort 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, brealc 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 physi-
cists 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 chem-
istry, 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 rela-
tivity 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 dogma-


tising 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 be-
come 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 con-
struction 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 fluctuat-
ing hypotheses of physics, three main problems arise in
connecting the world of physics with the world of sense,
namely (i) the construction of permanent "things," (2)
the construction of a single space, and (3) the construc-
tion of a single time. We will consider these three
problems in succession.

(i) 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 Inter-
preting 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 con-j
trary, 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

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 legiti-
mate 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 with-
out 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 con-
tinuous 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 familiar7 If we
can state the laws according to which the colour varies,
we can state all that is empirically verifiable ; the assump-
tion that there is a constant entity, the wall-paper, which
" has " these various colours at various times, is a piece
Lof 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 o/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, j

The above extrusion of permanent things afFords an
example of the maxim which inspires all scientific philo-
sophising, 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 un-
warrantable 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 collec-
tions 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

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 con-
tinuous so far as our senses can perceive. We are thus
led to assume that, if we see two finitely diffi;rent appear-
ances 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 sup-


pose 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 '^hing."

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

(a) We have been considering, in the above account,
the question of the verifiability of physics. Now verifi-
ability 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 un verifiable : there are hypotheses
as to (a) how things would appear to a spectator <in a
place where, as it happens, there is no spectator ; (/3) how
things would appear at times when, in fact, they are not
appearing to anyone ; (7) 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.

(J?) 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 diflFerent 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 ^wbelieving
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 con-
sideration of space.

People who have never read any psychology seldom
realise how much mental labour has gone into the con-
struction 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 ^f 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 sensa-
tion 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 dis-
covered 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 in-
dependent 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

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Online LibraryBertrand RussellOur knowledge of the external world, as a field for scientific method in philosophy → online text (page 8 of 18)