No More Learning

No two of these people have exactly the same sense-data,
yet there is sufficient similarity among their data to enable them to
group together certain of these data as appearances of one "thing" to
the several spectators, and others as appearances of another "thing. "
Besides the appearances which a given thing in the room presents to
the actual spectators, there are, we may suppose, other appearances
which it would present to other possible spectators. If a man were to
sit down between two others, the appearance which the room would
present to him would be intermediate between the appearances which it
presents to the two others: and although this appearance would not
exist as it is without the sense organs, nerves and brain, of the
newly arrived spectator, still it is not unnatural to suppose that,
from the position which he now occupies, _some_ appearance of the
room existed before his arrival. This supposition, however, need
merely be noticed and not insisted upon.

Since the "thing" cannot, without indefensible partiality, be
identified with any single one of its appearances, it came to be
thought of as something distinct from all of them and underlying them.
But by the principle of Occam's razor, if the class of appearances
will fulfil the purposes for the sake of which the thing was invented
by the prehistoric metaphysicians to whom common sense is due, economy
demands that we should identify the thing with the class of its
appearances. It is not necessary to _deny_ a substance or substratum
underlying these appearances; it is merely expedient to abstain from
asserting this unnecessary entity. Our procedure here is precisely
analogous to that which has swept away from the philosophy of
mathematics the useless menagerie of metaphysical monsters with which
it used to be infested.


VI. CONSTRUCTIONS VERSUS INFERENCES

Before proceeding to analyse and explain the ambiguities of the word
"place," a few general remarks on method are desirable. The supreme
maxim in scientific philosophising is this:

_Wherever possible, logical constructions are to be substituted
for inferred entities. _

Some examples of the substitution of construction for inference in the
realm of mathematical philosophy may serve to elucidate the uses of
this maxim. Take first the case of irrationals. In old days,
irrationals were inferred as the supposed limits of series of
rationals which had no rational limit; but the objection to this
procedure was that it left the existence of irrationals merely
optative, and for this reason the stricter methods of the present day
no longer tolerate such a definition. We now define an irrational
number as a certain class of ratios, thus constructing it logically by
means of ratios, instead of arriving at it by a doubtful inference
from them. Take again the case of cardinal numbers. Two equally
numerous collections appear to have something in common: this
something is supposed to be their cardinal number. But so long as the
cardinal number is inferred from the collections, not constructed in
terms of them, its existence must remain in doubt, unless in virtue of
a metaphysical postulate _ad hoc_. By defining the cardinal number of
a given collection as the class of all equally numerous collections,
we avoid the necessity of this metaphysical postulate, and thereby
remove a needless element of doubt from the philosophy of arithmetic.
A similar method, as I have shown elsewhere, can be applied to classes
themselves, which need not be supposed to have any metaphysical
reality, but can be regarded as symbolically constructed fictions.

The method by which the construction proceeds is closely analogous in
these and all similar cases. Given a set of propositions nominally
dealing with the supposed inferred entities, we observe the properties
which are required of the supposed entities in order to make these
propositions true. By dint of a little logical ingenuity, we then
construct some logical function of less hypothetical entities which
has the requisite properties. This constructed function we substitute
for the supposed inferred entities, and thereby obtain a new and less
doubtful interpretation of the body of propositions in question. This
method, so fruitful in the philosophy of mathematics, will be found
equally applicable in the philosophy of physics, where, I do not
doubt, it would have been applied long ago but for the fact that all
who have studied this subject hitherto have been completely ignorant
of mathematical logic. I myself cannot claim originality in the
application of this method to physics, since I owe the suggestion and
the stimulus for its application entirely to my friend and
collaborator Dr. Whitehead, who is engaged in applying it to the more
mathematical portions of the region intermediate between sense-data
and the points, instants and particles of physics.

A complete application of the method which substitutes constructions
for inferences would exhibit matter wholly in terms of sense-data, and
even, we may add, of the sense-data of a single person, since the
sense-data of others cannot be known without some element of
inference. This, however, must remain for the present an ideal, to be
approached as nearly as possible, but to be reached, if at all, only
after a long preliminary labour of which as yet we can only see the
very beginning. The inferences which are unavoidable can, however, be
subjected to certain guiding principles. In the first place they
should always be made perfectly explicit, and should be formulated in
the most general manner possible. In the second place the inferred
entities should, whenever this can be done, be similar to those whose
existence is given, rather than, like the Kantian _Ding an sich_,
something wholly remote from the data which nominally support the
inference. The inferred entities which I shall allow myself are of two
kinds: (_a_) the sense-data of other people, in favour of which there
is the evidence of testimony, resting ultimately upon the analogical
argument in favour of minds other than my own; (_b_) the "sensibilia"
which would appear from places where there happen to be no minds, and
which I suppose to be real although they are no one's data. Of these
two classes of inferred entities, the first will probably be allowed
to pass unchallenged. It would give me the greatest satisfaction to be
able to dispense with it, and thus establish physics upon a
solipsistic basis; but those--and I fear they are the majority--in
whom the human affections are stronger than the desire for logical
economy, will, no doubt, not share my desire to render solipsism
scientifically satisfactory. The second class of inferred entities
raises much more serious questions. It may be thought monstrous to
maintain that a thing can present any appearance at all in a place
where no sense organs and nervous structure exist through which it
could appear. I do not myself feel the monstrosity; nevertheless I
should regard these supposed appearances only in the light of a
hypothetical scaffolding, to be used while the edifice of physics is
being raised, though possibly capable of being removed as soon as the
edifice is completed. These "sensibilia" which are not data to anyone
are therefore to be taken rather as an illustrative hypothesis and as
an aid in preliminary statement than as a dogmatic part of the
philosophy of physics in its final form.


VII. PRIVATE SPACE AND THE SPACE OF PERSPECTIVES

We have now to explain the ambiguity in the word "place," and how it
comes that two places of different sorts are associated with every
sense-datum, namely the place _at_ which it is and the place _from_
which it is perceived. The theory to be advocated is closely analogous
to Leibniz's monadology, from which it differs chiefly in being less
smooth and tidy.

The first fact to notice is that, so far as can be discovered, no
sensibile is ever a datum to two people at once. The things seen by
two different people are often closely similar, so similar that the
same _words_ can be used to denote them, without which communication
with others concerning sensible objects would be impossible. But, in
spite of this similarity, it would seem that some difference always
arises from difference in the point of view. Thus each person, so far
as his sense-data are concerned, lives in a private world. This
private world contains its own space, or rather spaces, for it would
seem that only experience teaches us to correlate the space of sight
with the space of touch and with the various other spaces of other
senses. This multiplicity of private spaces, however, though
interesting to the psychologist, is of no great importance in regard
to our present problem, since a merely solipsistic experience enables
us to correlate them into the one private space which embraces all our
own sense-data. The place _at_ which a sense-datum is, is a place in
private space. This place therefore is different from any place in the
private space of another percipient. For if we assume, as logical
economy demands, that all position is relative, a place is only
definable by the things in or around it, and therefore the same place
cannot occur in two private worlds which have no common constituent.
The question, therefore, of combining what we call different
appearances of the same thing in the same place does not arise, and
the fact that a given object appears to different spectators to have
different shapes and colours affords no argument against the physical
reality of all these shapes and colours.

In addition to the private spaces belonging to the private worlds of
different percipients, there is, however, another space, in which one
whole private world counts as a point, or at least as a spatial unit.
This might be described as the space of points of view, since each
private world may be regarded as the appearance which the universe
presents from a certain point of view. I prefer, however, to speak of
it as the space of _perspectives_, in order to obviate the suggestion
that a private world is only real when someone views it. And for the
same reason, when I wish to speak of a private world without assuming
a percipient, I shall call it a "perspective. "

We have now to explain how the different perspectives are ordered in
one space. This is effected by means of the correlated "sensibilia"
which are regarded as the appearances, in different perspectives, of
one and the same thing. By moving, and by testimony, we discover that
two different perspectives, though they cannot both contain the same
"sensibilia," may nevertheless contain very similar ones; and the
spatial order of a certain group of "sensibilia" in a private space of
one perspective is found to be identical with, or very similar to, the
spatial order of the correlated "sensibilia" in the private space of
another perspective. In this way one "sensibile" in one perspective is
correlated with one "sensibile" in another. Such correlated
"sensibilia" will be called "appearances of one thing. " In Leibniz's
monadology, since each monad mirrored the whole universe, there was in
each perspective a "sensibile" which was an appearance of each thing.
In our system of perspectives, we make no such assumption of
completeness. A given thing will have appearances in some
perspectives, but presumably not in certain others. The "thing" being
defined as the class of its appearances, if ? is the class of
perspectives in which a certain thing ? appears, then ? is a member of
the multiplicative class of ? , ? being a class of mutually exclusive
classes of "sensibilia. " And similarly a perspective is a member of
the multiplicative class of the things which appear in it.

The arrangement of perspectives in a space is effected by means of the
differences between the appearances of a given thing in the various
perspectives. Suppose, say, that a certain penny appears in a number
of different perspectives; in some it looks larger and in some
smaller, in some it looks circular, in others it presents the
appearance of an ellipse of varying eccentricity. We may collect
together all those perspectives in which the appearance of the penny
is circular. These we will place on one straight line, ordering them
in a series by the variations in the apparent size of the penny. Those
perspectives in which the penny appears as a straight line of a
certain thickness will similarly be placed upon a plane (though in
this case there will be many different perspectives in which the penny
is of the same size; when one arrangement is completed these will form
a circle concentric with the penny), and ordered as before by the
apparent size of the penny. By such means, all those perspectives in
which the penny presents a visual appearance can be arranged in a
three-dimensional spatial order. Experience shows that the same
spatial order of perspectives would have resulted if, instead of the
penny, we had chosen any other thing which appeared in all the
perspectives in question, or any other method of utilising the
differences between the appearances of the same things in different
perspectives. It is this empirical fact which has made it possible to
construct the one all-embracing space of physics.

The space whose construction has just been explained, and whose
elements are whole perspectives, will be called "perspective-space. "


VIII. THE PLACING OF "THINGS" AND "SENSIBILIA" IN PERSPECTIVE SPACE

The world which we have so far constructed is a world of six
dimensions, since it is a three-dimensional series of perspectives,
each of which is itself three-dimensional. We have now to explain the
correlation between the perspective space and the various private
spaces contained within the various perspectives severally. It is by
means of this correlation that the one three-dimensional space of
physics is constructed; and it is because of the unconscious
performance of this correlation that the distinction between
perspective space and the percipient's private space has been blurred,
with disastrous results for the philosophy of physics. Let us revert
to our penny: the perspectives in which the penny appears larger are
regarded as being nearer to the penny than those in which it appears
smaller, but as far as experience goes the apparent size of the penny
will not grow beyond a certain limit, namely, that where (as we say)
the penny is so near the eye that if it were any nearer it could not
be seen. By touch we may prolong the series until the penny touches
the eye, but no further. If we have been travelling along a line of
perspectives in the previously defined sense, we may, however, by
imagining the penny removed, prolong the line of perspectives by
means, say, of another penny; and the same may be done with any other
line of perspectives defined by means of the penny. All these lines
meet in a certain place, that is, in a certain perspective. This
perspective will be defined as "the place where the penny is. "

It is now evident in what sense two places in constructed physical
space are associated with a given "sensibile. " There is first the
place which is the perspective of which the "sensibile" is a member.
This is the place _from_ which the "sensibile" appears. Secondly there
is the place where the thing is of which the "sensibile" is a member,
in other words an appearance; this is the place _at_ which the
"sensibile" appears. The "sensibile" which is a member of one
perspective is correlated with another perspective, namely, that which
is the place where the thing is of which the "sensibile" is an
appearance. To the psychologist the "place from which" is the more
interesting, and the "sensibile" accordingly appears to him subjective
and where the percipient is. To the physicist the "place at which" is
the more interesting, and the "sensibile" accordingly appears to him
physical and external. The causes, limits and partial justification of
each of these two apparently incompatible views are evident from the
above duplicity of places associated with a given "sensibile. "

We have seen that we can assign to a physical thing a place in the
perspective space. In this way different parts of our body acquire
positions in perspective space, and therefore there is a meaning
(whether true or false need not much concern us) in saying that the
perspective to which our sense-data belong is inside our head. Since
our mind is correlated with the perspective to which our sense-data
belong, we may regard this perspective as being the position of our
mind in perspective space. If, therefore, this perspective is, in the
above defined sense, inside our head, there is a good meaning for the
statement that the mind is in the head. We can now say of the various
appearances of a given thing that some of them are nearer to the thing
than others; those are nearer which belong to perspectives that are
nearer to "the place where the thing is. " We can thus find a meaning,
true or false, for the statement that more is to be learnt about a
thing by examining it close to than by viewing it from a distance. We
can also find a meaning for the phrase "the things which intervene
between the subject and a thing of which an appearance is a datum to
him. " One reason often alleged for the subjectivity of sense-data is
that the appearance of a thing may change when we find it hard to
suppose that the thing itself has changed--for example, when the
change is due to our shutting our eyes, or to our screwing them up so
as to make the thing look double. If the thing is defined as the class
of its appearances (which is the definition adopted above), there is
of course necessarily _some_ change in the thing whenever any one of
its appearances changes. Nevertheless there is a very important
distinction between two different ways in which the appearances may
change. If after looking at a thing I shut my eyes, the appearance of
my eyes changes in every perspective in which there is such an
appearance, whereas most of the appearances of the thing will remain
unchanged. We may say, as a matter of definition, that a thing changes
when, however near to the thing an appearance of it may be, there are
changes in appearances as near as, or still nearer to, the thing. On
the other hand we shall say that the change is in some other thing if
all appearances of the thing which are at not more than a certain
distance from the thing remain unchanged, while only comparatively
distant appearances of the thing are altered. From this consideration
we are naturally led to the consideration of _matter_, which must be
our next topic.


IX. THE DEFINITION OF MATTER

We defined the "physical thing" as the class of its appearances, but
this can hardly be taken as a definition of matter. We want to be able
to express the fact that the appearance of a thing in a given
perspective is causally affected by the matter between the thing and
the perspective. We have found a meaning for "between a thing and a
perspective. " But we want matter to be something other than the whole
class of appearances of a thing, in order to state the influence of
matter on appearances.

We commonly assume that the information we get about a thing is more
accurate when the thing is nearer. Far off, we see it is a man; then
we see it is Jones; then we see he is smiling. Complete accuracy would
only be attainable as a limit: if the appearances of Jones as we
approach him tend towards a limit, that limit may be taken to be what
Jones really is. It is obvious that from the point of view of physics
the appearances of a thing close to "count" more than the appearances
far off. We may therefore set up the following tentative definition:

The _matter_ of a given thing is the limit of its appearances as their
distance from the thing diminishes.

It seems probable that there is something in this definition, but it
is not quite satisfactory, because empirically there is no such limit
to be obtained from sense-data. The definition will have to be eked
out by constructions and definitions. But probably it suggests the
right direction in which to look.

We are now in a position to understand in outline the reverse journey
from matter to sense-data which is performed by physics. The
appearance of a thing in a given perspective is a function of the
matter composing the thing and of the intervening matter. The
appearance of a thing is altered by intervening smoke or mist, by blue
spectacles or by alterations in the sense-organs or nerves of the
percipient (which also must be reckoned as part of the intervening
medium). The nearer we approach to the thing, the less its appearance
is affected by the intervening matter. As we travel further and
further from the thing, its appearances diverge more and more from
their initial character; and the causal laws of their divergence are
to be stated in terms of the matter which lies between them and the
thing. Since the appearances at very small distances are less affected
by causes other than the thing itself, we come to think that the limit
towards which these appearances tend as the distance diminishes is
what the thing "really is," as opposed to what it merely seems to be.
This, together with its necessity for the statement of causal laws,
seems to be the source of the entirely erroneous feeling that matter
is more "real" than sense-data.

Consider for example the infinite divisibility of matter. In looking
at a given thing and approaching it, one sense-datum will become
several, and each of these will again divide. Thus _one_ appearance
may represent _many_ things, and to this process there seems no end.
Hence in the limit, when we approach indefinitely near to the thing
there will be an indefinite number of units of matter corresponding to
what, at a finite distance, is only one appearance. This is how
infinite divisibility arises.

The whole causal efficacy of a thing resides in its matter. This is in
some sense an empirical fact, but it would be hard to state it
precisely, because "causal efficacy" is difficult to define.

What can be known empirically about the matter of a thing is only
approximate, because we cannot get to know the appearances of the
thing from very small distances, and cannot accurately infer the limit
of these appearances. But it _is_ inferred _approximately_ by means of
the appearances we can observe. It then turns out that these
appearances can be exhibited by physics as a function of the matter
in our immediate neighbourhood; e. g. the visual appearance of a
distant object is a function of the light-waves that reach the eyes.
This leads to confusions of thought, but offers no real difficulty.

One appearance, of a visible object for example, is not sufficient to
determine its other simultaneous appearances, although it goes a
certain distance towards determining them. The determination of the
hidden structure of a thing, so far as it is possible at all, can only
be effected by means of elaborate dynamical inferences.


X. TIME[30]

It seems that the one all-embracing time is a construction, like the
one all-embracing space. Physics itself has become conscious of this
fact through the discussions connected with relativity.

Between two perspectives which both belong to one person's experience,
there will be a direct time-relation of before and after. This
suggests a way of dividing history in the same sort of way as it is
divided by different experiences, but without introducing experience
or anything mental: we may define a "biography" as everything that is
(directly) earlier or later than, or simultaneous with, a given
"sensibile. " This will give a series of perspectives, which _might_
all form parts of one person's experience, though it is not necessary
that all or any of them should actually do so. By this means, the
history of the world is divided into a number of mutually exclusive
biographies.

We have now to correlate the times in the different biographies. The
natural thing would be to say that the appearances of a given
(momentary) thing in two different perspectives belonging to different
biographies are to be taken as simultaneous; but this is not
convenient. Suppose _A_ shouts to _B_, and _B_ replies as soon as he
hears _A's_ shout. Then between _A's_ hearing of his own shout and his
hearing of _B's_ there is an interval; thus if we made _A's_ and _B's_
hearing of the same shout exactly simultaneous with each other, we
should have events exactly simultaneous with a given event but not
with each other. To obviate this, we assume a "velocity of sound. "
That is, we assume that the time when _B_ hears _A's_ shout is
half-way between the time when _A_ hears his own shout and the time
when he hears _B's_. In this way the correlation is effected.

What has been said about sound applies of course equally to light. The
general principle is that the appearances, in different perspectives,
which are to be grouped together as constituting what a certain thing
is at a certain moment, are not to be all regarded as being at that
moment. On the contrary they spread outward from the thing with
various velocities according to the nature of the appearances. Since
no _direct_ means exist of correlating the time in one biography with
the time in another, this temporal grouping of the appearances
belonging to a given thing at a given moment is in part conventional.
Its motive is partly to secure the verification of such maxims as that
events which are exactly simultaneous with the same event are exactly
simultaneous with one another, partly to secure convenience in the
formulation of causal laws.


XI. THE PERSISTENCE OF THINGS AND MATTER

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 a single space;
2. the construction of a single time;
3. the construction of permanent things or matter.

We have already considered the first and second of these problems; it
remains to consider the third.

We have seen how correlated appearances in different perspectives are
combined to form one "thing" at one moment in the all-embracing time
of physics. We have now to consider how appearances at different times
are combined as belonging to one "thing," and how we arrive at the
persistent "matter" of physics. The assumption of permanent substance,
which technically underlies the procedure of physics, cannot of course
be regarded as metaphysically legitimate: just as the one thing
simultaneously seen by many people is a construction, so the one thing
seen at different times by the same or different people must be a
construction, being in fact nothing but a certain grouping of certain
"sensibilia. "

We have seen that the momentary state of a "thing" is an assemblage of
"sensibilia," in different perspectives, not all simultaneous in the
one constructed time, but spreading out from "the place where the
thing is" with velocities depending upon the nature of the
"sensibilia. " The time _at_ which the "thing" is in this state is the
lower limit of the times at which these appearances occur. We have now
to consider what leads us to speak of another set of appearances as
belonging to the same "thing" at a different time.

For this purpose, we may, at least to begin with, confine ourselves
within a single biography. If we can always say when two "sensibilia"
in a given biography are appearances of one thing, then, since we have
seen how to connect "sensibilia" in different biographies as
appearances of the same momentary state of a thing, we shall have all
that is necessary for the complete construction of the history of a
thing.

It is to be observed, to begin with, that the identity of a thing for
common sense is not always correlated with the identity of matter for
physics. A human body is one persisting thing for common sense, but
for physics its matter is constantly changing. We may say, broadly,
that the common-sense conception is based upon continuity in
appearances at the ordinary distances of sense-data, while the
physical conception is based upon the continuity of appearances at
very small distances from the thing. It is probable that the
common-sense conception is not capable of complete precision. Let us
therefore concentrate our attention upon the conception of the
persistence of matter in physics.

The first characteristic of two appearances of the same piece of
matter at different times is _continuity_. The two appearances must be
connected by a series of intermediaries, which, if time and space form
compact series, must themselves form a compact series. The colour of
the leaves is different in autumn from what it is in summer; but we
believe that the change occurs gradually, and that, if the colours are
different at two given times, there are intermediate times at which
the colours are intermediate between those at the given times.

But there are two considerations that are important as regards
continuity.

First, it is largely hypothetical. We do not observe any one thing
continuously, and it is merely a hypothesis to assume that, while we
are not observing it, it passes through conditions intermediate
between those in which it is perceived. During uninterrupted
observation, it is true, continuity is nearly verified; but even here,
when motions are very rapid, as in the case of explosions, the
continuity is not actually capable of direct verification. Thus we can
only say that the sense-data are found to _permit_ a hypothetical
complement of "sensibilia" such as will preserve continuity, and that
therefore there _may_ be such a complement. Since, however, we have
already made such use of hypothetical "sensibilia," we will let this
point pass, and admit such "sensibilia" as are required to preserve
continuity.

Secondly, continuity is not a sufficient criterion of material
identity. It is true that in many cases, such as rocks, mountains,
tables, chairs, etc. , where the appearances change slowly, continuity
is sufficient, but in other cases, such as the parts of an
approximately homogeneous fluid, it fails us utterly. We can travel by
sensibly continuous gradations from any one drop of the sea at any one
time to any other drop at any other time. We infer the motions of
sea-water from the effects of the current, but they cannot be inferred
from direct sensible observation together with the assumption of
continuity.

The characteristic required in addition to continuity is conformity
with the laws of dynamics. Starting from what common sense regards as
persistent things, and making only such modifications as from time to
time seem reasonable, we arrive at assemblages of "sensibilia" which
are found to obey certain simple laws, namely those of dynamics.
By
regarding "sensibilia" at different times as belonging to the same
piece of matter, we are able to define _motion_, which presupposes the
assumption or construction of something persisting throughout the
time of the motion. The motions which are regarded as occurring,
during a period in which all the "sensibilia" and the times of their
appearance are given, will be different according to the manner in
which we combine "sensibilia" at different times as belonging to the
same piece of matter. Thus even when the whole history of the world is
given in every particular, the question what motions take place is
still to a certain extent arbitrary even after the assumption of
continuity. Experience shows that it is possible to determine motions
in such a way as to satisfy the laws of dynamics, and that this
determination, roughly and on the whole, is fairly in agreement with
the common-sense opinions about persistent things. This determination,
therefore, is adopted, and leads to a criterion by which we can
determine, sometimes practically, sometimes only theoretically,
whether two appearances at different times are to be regarded as
belonging to the same piece of matter. The persistence of all matter
throughout all time can, I imagine, be secured by definition.

To recommend this conclusion, 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 when a
sufficient collection of "sensibilia" is given. 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. Thus we may lay down the following
definition: _Physical things are those series of appearances whose
matter obeys the laws of physics_. That such series exist is an
empirical fact, which constitutes the verifiability of physics.


XII. ILLUSIONS, HALLUCINATIONS, AND DREAMS

It remains to ask how, in our system, we are to find a place for
sense-data which apparently fail to have the usual connection with the
world of physics. Such sense-data are of various kinds, requiring
somewhat different treatment. But all are of the sort that would be
called "unreal," and therefore, before embarking upon the discussion,
certain logical remarks must be made upon the conceptions of reality
and unreality.

Mr. A. Wolf[31] says:

"The conception of mind as a system of transparent activities is,
I think, also untenable because of its failure to account for the
very possibility of dreams and hallucinations. It seems impossible
to realise how a bare, transparent activity can be directed to
what is not there, to apprehend what is not given. "

This statement is one which, probably, most people would endorse. But
it is open to two objections. First it is difficult to see how an
activity, however un-"transparent," can be directed towards a nothing:
a term of a relation cannot be a mere nonentity. Secondly, no reason
is given, and I am convinced that none can be given, for the assertion
that dream-objects are not "there" and not "given. " Let us take the
second point first.

(1) The belief that dream-objects are not given comes, I think, from
failure to distinguish, as regards waking life, between the
sense-datum and the corresponding "thing. " In dreams, there is no such
corresponding "thing" as the dreamer supposes; if, therefore, the
"thing" were given in waking life, as e. g. Meinong maintains,[32] then
there would be a difference in respect of givenness between dreams and
waking life. But if, as we have maintained, what is given is never the
thing, but merely one of the "sensibilia" which compose the thing,
then what we apprehend in a dream is just as much given as what we
apprehend in waking life.

Exactly the same argument applies as to the dream-objects being
"there. " They have their position in the private space of the
perspective of the dreamer; where they fail is in their correlation
with other private spaces and therefore with perspective space. But in
the only sense in which "there" can be a datum, they are "there" just
as truly as any of the sense-data of waking life.

(2) The conception of "illusion" or "unreality," and the correlative
conception of "reality," are generally used in a way which embodies
profound logical confusions. Words that go in pairs, such as "real"
and "unreal," "existent" and "non-existent," "valid" and "invalid,"
etc. , are all derived from the one fundamental pair, "true" and
"false. " Now "true" and "false" are applicable only--except in
derivative significations--to _propositions_. Thus wherever the above
pairs can be significantly applied, we must be dealing either with
propositions or with such incomplete phrases as only acquire meaning
when put into a context which, with them, forms a proposition. Thus
such pairs of words can be applied to _descriptions_,[33] but not to
proper names: in other words, they have no application whatever to
data, but only to entities or non-entities described in terms of data.

Let us illustrate by the terms "existence" and "non-existence. " Given
any datum _x_, it is meaningless either to assert or to deny that _x_
"exists. " We might be tempted to say: "Of course _x_ exists, for
otherwise it could not be a datum. " But such a statement is really
meaningless, although it is significant and true to say "My present
sense-datum exists," and it may also be true that "_x_ is my present
sense-datum. " The inference from these two propositions to "_x_
exists" is one which seems irresistible to people unaccustomed to
logic; yet the apparent proposition inferred is not merely false, but
strictly meaningless. To say "My present sense-datum exists" is to say
(roughly): "There is an object of which 'my present sense-datum' is a
description. " But we cannot say: "There is an object of which '_x_' is
a description," because '_x_' is (in the case we are supposing) a
name, not a description. Dr. Whitehead and I have explained this point
fully elsewhere (_loc. cit. _) with the help of symbols, without which
it is hard to understand; I shall not therefore here repeat the
demonstration of the above propositions, but shall proceed with their
application to our present problem.

The fact that "existence" is only applicable to descriptions is
concealed by the use of what are grammatically proper names in a way
which really transforms them into descriptions. It is, for example, a
legitimate question whether Homer existed; but here "Homer" means
"the author of the Homeric poems," and is a description. Similarly we
may ask whether God exists; but then "God" means "the Supreme Being"
or "the _ens realissimum_" or whatever other description we may
prefer. If "God" were a proper name, God would have to be a datum; and
then no question could arise as to His existence. The distinction
between existence and other predicates, which Kant obscurely felt, is
brought to light by the theory of descriptions, and is seen to remove
"existence" altogether from the fundamental notions of metaphysics.

What has been said about "existence" applies equally to "reality,"
which may, in fact, be taken as synonymous with "existence. "
Concerning the immediate objects in illusions, hallucinations, and
dreams, it is meaningless to ask whether they "exist" or are "real. "
There they are, and that ends the matter. But we may legitimately
inquire as to the existence or reality of "things" or other
"sensibilia" inferred from such objects. It is the unreality of these
"things" and other "sensibilia," together with a failure to notice
that they are not data, which has led to the view that the objects of
dreams are unreal.

We may now apply these considerations in detail to the stock arguments
against realism, though what is to be said will be mainly a repetition
of what others have said before.

(1) We have first the variety of normal appearances, supposed to be
incompatible. This is the case of the different shapes and colours
which a given thing presents to different spectators. Locke's water
which seems both hot and cold belongs to this class of cases. Our
system of different perspectives fully accounts for these cases, and
shows that they afford no argument against realism.

(2) We have cases where the correlation between different senses is
unusual. The bent stick in water belongs here. People say it looks
bent but is straight: this only means that it is straight to the
touch, though bent to sight. There is no "illusion," but only a false
inference, if we think that the stick would feel bent to the touch.
The stick would look just as bent in a photograph, and, as Mr.
Gladstone used to say, "the photograph cannot lie. "[34] The case of
seeing double also belongs here, though in this case the cause of the
unusual correlation is physiological, and would therefore not operate
in a photograph. It is a mistake to ask whether the "thing" is
duplicated when we see it double. The "thing" is a whole system of
"sensibilia," and it is only those visual "sensibilia" which are data
to the percipient that are duplicated. The phenomenon has a purely
physiological explanation; indeed, in view of our having two eyes, it
is in less need of explanation than the single visual sense-datum
which we normally obtain from the things on which we focus.

(3) We come now to cases like dreams, which may, at the moment of
dreaming, contain nothing to arouse suspicion, but are condemned on the
ground of their supposed incompatibility with earlier and later data. Of
course it often happens that dream-objects fail to behave in the
accustomed manner: heavy objects fly, solid objects melt, babies turn
into pigs or undergo even greater changes. But none of these unusual
occurrences _need_ happen in a dream, and it is not on account of such
occurrences that dream-objects are called "unreal. " It is their lack of
continuity with the dreamer's past and future that makes him, when he
wakes, condemn them; and it is their lack of correlation with other
private worlds that makes others condemn them. Omitting the latter
ground, our reason for condemning them is that the "things" which we
infer from them cannot be combined according to the laws of physics with
the "things" inferred from waking sense-data. This might be used to
condemn the "things" inferred from the data of dreams. Dream-data are no
doubt appearances of "things," but not of such "things" as the dreamer
supposes. I have no wish to combat psychological theories of dreams,
such as those of the psycho-analysts. But there certainly are cases
where (whatever psychological causes may contribute) the presence of
physical causes also is very evident. For instance, a door banging may
produce a dream of a naval engagement, with images of battleships and
sea and smoke. The whole dream will be an appearance of the door
banging, but owing to the peculiar condition of the body (especially the
brain) during sleep, this appearance is not that expected to be produced
by a door banging, and thus the dreamer is led to entertain false
beliefs. But his sense-data are still physical, and are such as a
completed physics would include and calculate.

(4) The last class of illusions are those which cannot be discovered
within one person's experience, except through the discovery of
discrepancies with the experiences of others. Dreams might conceivably
belong to this class, if they were jointed sufficiently neatly into
waking life; but the chief instances are recurrent sensory
hallucinations of the kind that lead to insanity. What makes the
patient, in such cases, become what others call insane is the fact
that, within his own experience, there is nothing to show that the
hallucinatory sense-data do not have the usual kind of connection with
"sensibilia" in other perspectives. Of course he may learn this
through testimony, but he probably finds it simpler to suppose that
the testimony is untrue and that he is being wilfully deceived. There
is, so far as I can see, no theoretical criterion by which the patient
can decide, in such a case, between the two equally satisfactory
hypotheses of his madness and of his friends' mendacity.

From the above instances it would appear that abnormal sense-data, of
the kind which we regard as deceptive, have intrinsically just the
same status as any others, but differ as regards their correlations or
causal connections with other "sensibilia" and with "things. " Since
the usual correlations and connections become part of our unreflective
expectations, and even seem, except to the psychologist, to form part
of our data, it comes to be thought, mistakenly, that in such cases
the data are unreal, whereas they are merely the causes of false
inferences. The fact that correlations and connections of unusual
kinds occur adds to the difficulty of inferring things from sense and
of expressing physics in terms of sense-data. But the unusualness
would seem to be always physically or physiologically explicable, and
therefore raises only a complication, not a philosophical objection.

I conclude, therefore, that no valid objection exists to the view
which regards sense-data as part of the actual substance of the
physical world, and that, on the other hand, this view is the only one
which accounts for the empirical verifiability of physics. In the
present paper, I have given only a rough preliminary sketch. In
particular, the part played by _time_ in the construction of the
physical world is, I think, more fundamental than would appear from
the above account. I should hope that, with further elaboration, the
part played by unperceived "sensibilia" could be indefinitely
diminished, probably by invoking the history of a "thing" to eke out
the inferences derivable from its momentary appearance.

FOOTNOTES:

[29] _Proc. Arist. Soc. _, 1909-1910, pp. 191-218.

[30] On this subject, compare _A Theory of Time and Space_, by Mr.
A. A. Robb (Camb. Univ. Press), which first suggested to me the views
advocated here, though I have, for present purposes, omitted what is
most interesting and novel in his theory. Mr. Robb has given a sketch
of his theory in a pamphlet with the same title (Heffer and Sons,
Cambridge, 1913).

[31] "Natural Realism and Present Tendencies in Philosophy," _Proc.
Arist. Soc. _, 1908-1909, p. 165.

[32] _Die Erfahrungsgrundlagen unseres Wissens_, p. 28.

[33] Cf. _Principia Mathematica_, Vol. I, * 14, and Introduction,
Chap. III. For the definition of _existence_, cf. * 14. 02.

[34] Cf. Edwin B. Holt, _The Place of Illusory Experience in a
Realistic World. _ "The New Realism," p. 303, both on this point and as
regards _seeing double_.




IX

ON THE NOTION OF CAUSE


In the following paper I wish, first, to maintain that the word
"cause" is so inextricably bound up with misleading associations as to
make its complete extrusion from the philosophical vocabulary
desirable; secondly, to inquire what principle, if any, is employed in
science in place of the supposed "law of causality" which philosophers
imagine to be employed; thirdly, to exhibit certain confusions,
especially in regard to teleology and determinism, which appear to me
to be connected with erroneous notions as to causality.

All philosophers, of every school, imagine that causation is one of
the fundamental axioms or postulates of science, yet, oddly enough, in
advanced sciences such as gravitational astronomy, the word "cause"
never occurs. Dr. James Ward, in his _Naturalism and Agnosticism_,
makes this a ground of complaint against physics: the business of
those who wish to ascertain the ultimate truth about the world, he
apparently thinks, should be the discovery of causes, yet physics
never even seeks them. To me it seems that philosophy ought not to
assume such legislative functions, and that the reason why physics has
ceased to look for causes is that, in fact, there are no such things.
The law of causality, I believe, like much that passes muster among
philosophers, is a relic of a bygone age, surviving, like the
monarchy, only because it is erroneously supposed to do no harm. In
order to find out what philosophers commonly understand by "cause," I
consulted Baldwin's _Dictionary_, and was rewarded beyond my
expectations, for I found the following three mutually incompatible
definitions:--

"CAUSALITY. (1) The necessary connection of events in the
time-series. . . .

"CAUSE (notion of). Whatever may be included in the thought or
perception of a process as taking place in consequence of
another process. . . .

"CAUSE AND EFFECT. (1) Cause and effect . . . are correlative terms
denoting any two distinguishable things, phases, or aspects of
reality, which are so related to each other that whenever the
first ceases to exist the second comes into existence
immediately after, and whenever the second comes into existence
the first has ceased to exist immediately before. "

Let us consider these three definitions in turn. The first, obviously,
is unintelligible without a definition of "necessary. " Under this
head, Baldwin's _Dictionary_ gives the following:--

"NECESSARY. That is necessary which not only is true, but would
be true under all circumstances. Something more than brute
compulsion is, therefore, involved in the conception; there is
a general law under which the thing takes place. "

The notion of cause is so intimately connected with that of necessity
that it will be no digression to linger over the above definition,
with a view to discovering, if possible, _some_ meaning of which it is
capable; for, as it stands, it is very far from having any definite
signification.

The first point to notice is that, if any meaning is to be given to
the phrase "would be true under all circumstances," the subject of it
must be a propositional function, not a proposition. [35] A
proposition is simply true or false, and that ends the matter: there
can be no question of "circumstances. " "Charles I's head was cut off"
is just as true in summer as in winter, on Sundays as on Mondays. Thus
when it is worth saying that something "would be true under all
circumstances," the something in question must be a propositional
function, i. e. an expression containing a variable, and becoming a
proposition when a value is assigned to the variable; the varying
"circumstances" alluded to are then the different values of which the
variable is capable. Thus if "necessary" means "what is true under all
circumstances," then "if _x_ is a man, _x_ is mortal" is necessary,
because it is true for any possible value of _x_. Thus we should be
led to the following definition:--

"NECESSARY is a predicate of a propositional function, meaning
that it is true for all possible values of its argument or
arguments. "

Unfortunately, however, the definition in Baldwin's _Dictionary_ says
that what is necessary is not only "true under all circumstances" but
is also "true. " Now these two are incompatible. Only propositions can
be "true," and only propositional functions can be "true under all
circumstances. " Hence the definition as it stands is nonsense. What is
meant seems to be this: "A proposition is necessary when it is a value
of a propositional function which is true under all circumstances,
i. e. for all values of its argument or arguments. " But if we adopt
this definition, the same proposition will be necessary or contingent
according as we choose one or other of its terms as the argument to
our propositional function. For example, "if Socrates is a man,
Socrates is mortal," is necessary if Socrates is chosen as argument,
but not if _man_ or _mortal_ is chosen. Again, "if Socrates is a man,
Plato is mortal," will be necessary if either Socrates or _man_ is
chosen as argument, but not if Plato or _mortal_ is chosen. However,
this difficulty can be overcome by specifying the constituent which is
to be regarded as argument, and we thus arrive at the following
definition:

"A proposition is _necessary_ with respect to a given constituent if
it remains true when that constituent is altered in any way compatible
with the proposition remaining significant. "

We may now apply this definition to the definition of causality quoted
above. It is obvious that the argument must be the time at which the
earlier event occurs. Thus an instance of causality will be such as:
"If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will
be followed by the event [Math: e_{2}]. " This proposition is intended
to be necessary with respect to [Math: t_{1}], i. e. to remain true
however [Math: t_{1}] may be varied. Causality, as a universal law,
will then be the following: "Given any event [Math: t_{1}], there is
an event [Math: e_{2}] such that, whenever [Math: t_{1}] occurs,
[Math: e_{2}] occurs later. " But before this can be considered
precise, we must specify how much later [Math: e_{2}] is to occur.
Thus the principle becomes:--

"Given any event [Math: e_{1}], there is an event [Math: e_{2}] and a
time-interval ? such that, whenever [Math: e_{1}] occurs, [Math:
e_{2}] follows after an interval ? . "

I am not concerned as yet to consider whether this law is true or
false. For the present, I am merely concerned to discover what the law
of causality is supposed to be. I pass, therefore, to the other
definitions quoted above.

The second definition need not detain us long, for two reasons. First,
because it is psychological: not the "thought or perception" of a
process, but the process itself, must be what concerns us in
considering causality. Secondly, because it is circular: in speaking
of a process as "taking place in consequence of" another process, it
introduces the very notion of cause which was to be defined.

The third definition is by far the most precise; indeed as regards
clearness it leaves nothing to be desired. But a great difficulty is
caused by the temporal contiguity of cause and effect which the
definition asserts. No two instants are contiguous, since the
time-series is compact; hence either the cause or the effect or both
must, if the definition is correct, endure for a finite time; indeed,
by the wording of the definition it is plain that both are assumed to
endure for a finite time. But then we are faced with a dilemma: if the
cause is a process involving change within itself, we shall require
(if causality is universal) causal relations between its earlier and
later parts; moreover, it would seem that only the later parts can be
relevant to the effect, since the earlier parts are not contiguous to
the effect, and therefore (by the definition) cannot influence the
effect. Thus we shall be led to diminish the duration of the cause
without limit, and however much we may diminish it, there will still
remain an earlier part which might be altered without altering the
effect, so that the true cause, as defined, will not have been
reached, for it will be observed that the definition excludes
plurality of causes.