constituent and which therefore is mental. The sense-datum, on the
other hand, stands over against the subject as that external object of
which in sensation the subject is aware. It is true that the
sense-datum is in many cases in the subject's body, but the subject's
body is as distinct from the subject as tables and chairs are, and is
in fact merely a part of the material world. So soon, therefore, as
sense-data are clearly distinguished from sensations, and as their
subjectivity is recognised to be physiological not psychical, the
chief obstacles in the way of regarding them as physical are removed.
V. "SENSIBILIA" AND "THINGS"
But if "sensibilia" are to be recognised as the ultimate constituents
of the physical world, a long and difficult journey is to be performed
before we can arrive either at the "thing" of common sense or at the
"matter" of physics. The supposed impossibility of combining the
different sense-data which are regarded as appearances of the same
"thing" to different people has made it seem as though these
"sensibilia" must be regarded as mere subjective phantasms. A given
table will present to one man a rectangular appearance, while to
another it appears to have two acute angles and two obtuse angles; to
one man it appears brown, while to another, towards whom it reflects
the light, it appears white and shiny. It is said, not wholly without
plausibility, that these different shapes and different colours cannot
co-exist simultaneously in the same place, and cannot therefore both
be constituents of the physical world. This argument I must confess
appeared to me until recently to be irrefutable. The contrary opinion
has, however, been ably maintained by Dr. T.P. Nunn in an article
entitled: "Are Secondary Qualities Independent of Perception?"[29] The
supposed impossibility derives its apparent force from the phrase:
"_in the same place_," and it is precisely in this phrase that its
weakness lies. The conception of space is too often treated in
philosophy--even by those who on reflection would not defend such
treatment--as though it were as given, simple, and unambiguous as
Kant, in his psychological innocence, supposed. It is the unperceived
ambiguity of the word "place" which, as we shall shortly see, has
caused the difficulties to realists and given an undeserved advantage
to their opponents. Two "places" of different kinds are involved in
every sense-datum, namely the place _at_ which it appears and the
place _from_ which it appears. These belong to different spaces,
although, as we shall see, it is possible, with certain limitations,
to establish a correlation between them. What we call the different
appearances of the same thing to different observers are each in a
space private to the observer concerned. No place in the private world
of one observer is identical with a place in the private world of
another observer. There is therefore no question of combining the
different appearances in the one place; and the fact that they cannot
all exist in one place affords accordingly no ground whatever for
questioning their physical reality. The "thing" of common sense may in
fact be identified with the whole class of its appearances--where,
however, we must include among appearances not only those which are
actual sense-data, but also those "sensibilia," if any, which, on
grounds of continuity and resemblance, are to be regarded as belonging
to the same system of appearances, although there happen to be no
observers to whom they are data.
An example may make this clearer. Suppose there are a number of people
in a room, all seeing, as they say, the same tables and chairs, walls
and pictures. 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 κ is the class of
perspectives in which a certain thing θ appears, then θ
is a member of
the multiplicative class of κ, κ 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 commo