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 [kappa] is the class of
perspectives in which a certain thing [theta] appears, then [theta] is
a member of the multiplicative class of [kappa], [kappa] 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.