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.
XXV—CONCRETION
If we take a cricket-ball in the hand and turn it round we shall perceive a series of discs. Only one of these can be seen at a time, but if we perceive and remember the whole series we shall be able to infer all from the perception of one in a similar object. The same occurs with other cubical or solid objects. This is a form of ideal construction different from any we have yet considered. It differs from inherence in that the object which we conceptually put together is never objectively perceived as a whole. It is an imaginary whole constructed in the intellect out of fragmentary experience. It differs from association on the same grounds; the latter can be all perceived at once in forming the judgment. It differs from perspection in that the imperfection of experience is due to curtailment, not to general deterioration. What we actually see may be perspectively perfect. It differs also from the next category in that the series of perceptions can occur in various orders of succession.
The 'backs' of Things. We talk of the back of a thing, but nobody has ever seen a back. Things have no backs in the popular sense of the word. When we turn round a back to perceive it, it is then a front. Everything is a flat upright surface, and its appearance of solidity can be imitated on a surface known to be flat, and with nearly the same illusive completeness as in the original object. In turning things round we merely change the surface; we are exercising our power to alter primary consciousness.
When two persons perceive the 'same' object from contrary directions, the sameness means that the two objects proceed from the same cause, or can be reduced to the same general idea. But the objects are numerically distinct. By a similar turn of speech we say that A and a are the same letter, but they are evidently distinct and dissimilar objects. If we hold a thing before a mirror and see what is termed its back, we produce a new object resembling the first in some respects but without its resistance.