This is the first of the artificial categories. It is an ideal
treatment of an associated group to facilitate a certain kind of
reasoning.
Reason--let me repeat--is the imaginary extension of experience
by comparison with more complete experience of a similar kind. By
reasoning in inherence we complete single objects; by inference in
association we complete groups. These two categories demonstrate that
a natural group consists of fragments of objects, and fragments of
other natural groups which are possible but not yet developed. A hill
is partly concealed by a house, the house partly concealed by a tree,
the tree by a stone fence, the fence by a growth of ivy. A river
disappears at a curve and is lost to view; we know from experience of
other rivers that under certain conditions we might perceive the river
further on as a feature in several more landscapes. As we gaze at an
association of objects these possible completions occur to us--not
fully or definitely but sufficiently to convince us that the group
might be developed into many other groups, and into a multitude of
objects of forms different from those we actually perceive. By our
hypothesis the observer has always been stationary, the objects have
moved to and fro but not from near to far. Their real dimensions have
remained unaltered, and nothing has occurred to suggest that they
ever appear of other dimensions. In short we are gazing on a piece of
stage-scenery.
But there is another element in perception. We and all other real
(mental) beings are part of the cosmic force. We are co-creators of
what we perceive--limited gods, not machine-men as the scientific
people would have us believe. But for our power of affecting each
other and our readiness to receive impressions from other minds, there
would be no perception--no material objects. We (that is, all
sentient beings) could, by unanimous resolution, annul the material
creation--blot out the universe of objective things in a moment.
United to and implied in this general power is the particular power
of modifying our world without destroying it. We can redistribute the
active and passive forces so as to produce other perceptual effects
than those present at a given moment. And we habitually do this to
some extent. Within a limited scope our world is plastic as dough,
and we knead it to any form we please. For example, we exert energy
to change our place, and immediately the group before us breaks up
and undergoes metamorphosis. Some objects disappear altogether, and
entirely new objects present themselves. Some become smaller, others
larger; some fractional forms fill out to completion, some integers
undergo curtailment, others separate into several distinct objects. In
a few minutes the first group has dissolved into a second, which may
merge into a third, and so on indefinitely.
In contemplating these phenomena we discern a third form of
completeness and incompleteness, distinct from those that enter into
inherence and association. Hence a new type of reasoning--another
category: the Perspective.
It will be convenient to suppose that the modifications to which it
refers are solely due to the observing mind, as the most conspicuous
and comprehensive really are, but some of the minor perspective
changes are due to the noumenon of the object.
We have first to get a criterion of perspective perfection. What this
shall be is to some extent a matter of convention. The standard I
shall adopt is, that an object of a nature to be perceptible to all
the senses would be most perfect if within reach of touch. If it can
be heard it is then heard at its loudest--this is correct enough for
our purpose,--if it can be seen it is then seen at its largest and
brightest. This is Perspective Completeness at the Tactual Range. It
means the closest contact of noumenon and subject, compatible with
clear definition in perception.
Now let us exert energy and disarrange a group. Those things that were
or might have been tangible in the former position, are no longer so,
but they may still be seen, heard, or even smelt. The bright colours
have however somewhat faded, the size has shrunk, some of the details
are lost. Here is a lapse from perspective completeness. It is
indicated, not as in the first two categories by mechanical cutting
away of mass and circumstance, but by deterioration all over the
object. We seem to be thrown out of focus in relation to it, and the
perspective degradation may increase until the object has dwindled to
a speck and finally disappears altogether.
The judgment in this category consists in observing the kind and
degree of degradation to which things are liable in perspection. In
addition to change in size, brightness, detail and loudness, which
have been already mentioned, occultation as in the second category
can be used as an indirect datum. An object which eclipses another is
invariably more perfect perspectively than the object eclipsed.
The motion of objects has also to be taken into account. As objects
degrade their movements slacken, and recover power as the objects are
restored.
By attending to all these indications and checking each by the rest,
we have the elements of a fairly accurate inference as to comparative
perspective condition. We have constant practice in this sort of
thought with frequent opportunities of verifying our conclusions;
penalties are annexed to failure and rewards to success. It is no
wonder then that in the course of years we become expert in judging of
perspective condition, so that when confronted with a natural group
we can estimate almost instantly the degree in which each object falls
short of perspective integrity.
The result of this practice is that on perceiving a natural group
of many objects, we graduate them according to the perspective
deterioration which each exhibits, and for greater precision we figure
the perspective difference as an interval between the objects--an
imaginary interval modelled on the true interval of association. The
object on a distant horizon is visually as near as the ground we can
touch by stooping, but in this imaginary group the former is placed
at the far end of the line and the latter at the near end, and between
them are ranged the other objects each at a point corresponding
to what we suppose to be its perspective distance. That is how a
landscape acquires depth. Space outwards is an ideal imitation of
real lateral interval. It is the measure and expression of perspective
defacement.
From what has been said it follows that the near objects will be
relatively large, clear, and lively in motion, while the far will
be small, dull, and slow, but this rule is liable to many exceptions
which can only be learnt by experience.
On the analogy of the other forms of inference--which consist in
completing imperfect things by reference to others more perfect--the
essence of an argument in perspection is the power to imagine an
object which is perspectively defective, brought up to the tactual
range and displaying all the qualities it would possess in that
position. This is done by comparing it with the idea of the same or
a similar object experienced at the tactual range; and is done for an
ulterior purpose, like all other intellectual operations. A great part
of our material happiness consists in the exercise of the short senses
(taste, touch and smell), and the chief use of perspective reasoning
is to enable us to judge of the energy required to bring a distant
object near for close perception. We have therefore to observe our
energic fluctuations in conjunction with perspective change, if we
would extract the utmost practical benefit from this category. The
perspective inferences are none the less useful after we discover that
they are not intuitions, and that the completeness we imaginatively
assign to distant objects has no existence until we exert the
corresponding energy.
A landscape being rendered perspective we can determine the
perspective state of any new object that may enter it, by reference to
the objects adjoining it, and this though the object be of a species
quite unknown to us and which therefore, by itself, would afford no
clue to its perspective distance.
The imaginary interval we place between objects of different
perspective effacement, can be expressed in terms of exact lateral
measurement. This is done by developing and measuring the associative
groups represented in the perspective group. Supposing we wish to
get an exact definition of the perspective condition of a mountain
relative to a certain station, we can, from that station, develop
all the natural groups up to the mountain (walk over the ground)
and measure the lateral intervals and masses disclosed. The total
measurements will be a definition of the mountain's perspective
distance in terms of true associative distance. That is what we mean
by saying a mountain is ten miles off. It is not _really_ ten miles
off--it is not an inch off. But to render it tactually perfect we
should have to expend an amount of energy equal to 17,600 times the
energy required to move from one associative object to another a
yard apart from it laterally. If we practise the mileage scale in
conjunction with the perspective indications, we may acquire the art
of expressing in miles, though not measured, the distance of objects
estimated from purely perspective data, but few can do this with any
near approach to exactness[14].
The realistic three-dimensioned space is a combination of the true
interval of association and the false interval of perspection. This
generates an idea resembling the capacity or vacancy in a room
or vessel, and thus it is supposed that objects occupy a sort of
universal room without walls, floor, or ceiling. It is however the
enclosing objects which make a room, and when they are abstracted
there remains nothing. The universal room is therefore nothing--a
myth. It is a useful working theory for common purposes, but in
philosophy it is superfluous and obstructive.
In the definitions of geometry no difference is made between the depth
of a landscape and the 'third dimension' of any small cubic object.
They are both called 'third dimension' or 'cubic dimension.' Yet
they are inferences of different categories, and neither is real.
The former, as we have just seen, is the imagined redintegration of
objects perspectively shrunk and defaced. The latter is the imaginary
completion of a thing having many surfaces or facets, only one of
which can be shown at a time.
_Sky Perspection._ The effect produced on our mind by the observation
of celestial objects, reveals at once the artificiality of cubic
space. Clouds in their form and movements are somewhat like earthly
things--vapour or mountains,--and so we conceive them partially
graduated in distance and floating in a concavity. But whether they
are a mile off, or twenty miles off, few of us can tell.
When we contemplate the sun, moon and stars, our realism is completely
at fault. These we cannot modify at will, and they move too slowly and
present too uniform an aspect to cause the perspective effect. Since
we have never seen them at the tactual range we know not to what
degree they are perspectively incomplete; hence they appear without
relative distance--distance being simply a metaphor of perspective
effacement. If 'cubic space' is real, let the realists tell us why we
do not see it in the sky--why we do not arrange the stars behind
each other according to their calculated distances. This question
is unanswerable realistically, but idealistically it presents no
difficulty. The sky is not spaced, because the conditions are wanting
under which the illusion of terrestrial space is formed in the
intellect.
By close instrumental attention to the moon and planets a slight
parallax is observable, and on the analogy of terrestrial parallax
astronomers are able to calculate what they call the distance of these
bodies. Perhaps their calculations are right, but the magnitudes are
not conceivable as associative distance, being so much greater than we
have any experience of. We take them to mean that the heavenly bodies
are extremely degraded, perspectively speaking. Their noumena are in
contact with our minds, for this is essential to perception, but
if astronomical calculations are correct the contact is infinitely
slight, compared with what it would be, supposing--to speak
realistically--we could go to the stars or they could be brought to
us.
Berkeley's _Theory of Vision_ and _Dialogues_ are occupied with the
analysis of perspection. The arguments he uses to show that distance
outwards is not real are in the main those given in this section.