In this category we widen the attention so as to include several
objects in one act of perception.
The first result of this diffusion of attention is to lessen the
brilliancy of objects. Our attention is a light which is intensified
when narrowed and concentrated--enfeebled when dispersed over several
objects. The observation of a group amounts practically to observing
the objects in rapid succession. At a given moment we perceive only
one thing well, or it may be only a small part of a thing, but we have
a dull sense of other things adjacent, which we have just seen and
may immediately see again in any order we please. That is all that is
meant by perception of a group.
To distinguish this category properly from the next we must consider
the group of objects as divested of depth or distance outwards. It
is to be regarded as a flat surface standing a few feet from us, the
objects in it having absolutely the dimensions they appear to
have. This is in fact their _real_ magnitude, for the supposed real
magnitude is a matter of theory, and means the perceptual magnitude
taken under certain conditions of observation. The real magnitude is
constantly changing, so for practical convenience in determining size,
etc., we refer all objects to one condition of observation--that in
which they can be touched as well as seen.
In metaphysic we are not obliged to recognise this convention. If an
object a mile off appears to be an inch high, it is an inch high
as really as if it were in a photograph or picture and materially
represented of that height. The mystery of the change of size in
objects is not explained or reasoned away by any device for overcoming
some of its practical inconveniences. It depends on the degree of
energy with which minds affect each other.
A group has properties which an object has not; or, if this be not
strictly the case, we may say that the properties we look for in a
group are not those we distinguish in a single object. The special
properties of a group are _positions_. It is unnecessary to say
'relative' positions, for position cannot be otherwise than relative.
Position cannot be defined by reference to anything more simple. What
is meant is intuitively known to everybody. But let us take a concrete
example--a man with a horse and cart standing on a bridge. Each object
in this group has a position towards the other objects. The bridge is
_over_ the river and _under_ the cart; the cart is _upon_ the bridge
and _behind_ the horse; the man is _in_ the cart; the horse is
_before_ and _outside_ of the cart, it is _near_ one end of the
bridge, _far_ from the other, and _between_ the two extremities. These
are the principal positions in a natural group or association,
by which is meant the objects we can see (or are supposed to see)
simultaneously, and whose mutual positions we are considering.
The use of observing positions is the same as that which moves us to
all rational study, namely, its value in prediction. We can reason
from one object to another in a group just as we reason from one
property to another in an object.
Suppose our perception of a landscape is interrupted for a moment,
and when we next endeavour to perceive it we find we only perceive a
portion of it, the rest being 'hidden' by an intervening object. As
far as we are concerned the hidden part has been annihilated. We only
remember what was there. But this recollection is also a preconception
of what we may be able to cause to appear again, either by removing
the obstructing object, by waiting till it has been removed, or by
walking round and standing between it and the landscape.
If this be too close to mere recollection, we have pure reasoning
when from the general appearance of a group we imagine generally some
concealed part of it not before seen. A procession of people dressed
in mourning is usually accompanied by a hearse: from perceiving the
people only on a certain occasion we predict the hearse. The sound of
a steam-whistle enables us to imagine a train in a certain locality,
though fog or other obstruction may prevent our seeing it. The scent
of flowers prepares us for finding them somewhere near us. From smoke
we predict the nearness of a chimney. The trail of an animal is a clue
to his position.
The judgment in this category is therefore a consciousness of
position, such as those mentioned above. The argument is a completion
of one association by comparison with another--the expectation of
similarity in groups.
_Movement._ All judgments as to _change_ of position in objects come
under this category. It takes at least two things arranged in a group
to produce the perception of movement. If there were but one thing in
our field of observation we could not say whether it moved or not, for
there would be nothing which it would pass, or leave, or approach. It
would appear to stand still. There is, however, more in movement than
depends on mere perception.
All movement is due to energy either in the observer or in the other
mind acting upon his. Energy is not a generalisation of moving things,
nor a property, nor a relation, though all these may be signs of
energy. The most abstract idea of movement is _Motion_. It may be
defined as a series of positions.
_Number._ If we treat a group as a large loose object we shall
perceive in it certain properties not strictly positional. Number is
one of these.
A group of three coins has not the same practical value as a group
of six or sixty, and we are thus obliged to notice the difference and
distinguish degrees of this property by names--hence Arithmetic.
_Flat Space_ or space of two dimensions is another property of a
group. Grouped objects have frequently intervals between them.
Such intervals are negations of perception--interruptions or
discontinuities of experience. But by abstraction we can reduce the
objects bounding an interval to a geometrical line, and so give a sort
of positive existence to the interval. Thus we talk of a hole or of
darkness as if they were true objects, and measure them by standards
of length.
If we abstract the boundary lines from a space we get the idea
'intervalness,' which is the right name for two-dimensioned space.
This abstract idea is nearly the same as abstract size. Space is
interval without bounds--size is object without contents. Space and
size are equally _nothing_ intrinsically or in their own right,
but they have been reached by different modes of refining away the
positive qualities associated with them, and this difference of origin
is slightly suggested by their names. Spaces have a use in perception
similar to _rests_ in music--they relieve the attention and give
contrast and vigour to the next positive object.