On the Fourfold Root of the Principle of Sufficient Reason, and On the Will in Nature: Two Essays (revised edition)
Schopenhauer · en
refer it, and all its outlines will contract in similar proportion.
From this ensues the fundamental law of all perspective; for, as
objects and the intervals between them must necessarily diminish in
constant proportion to their distance from us, all their outlines
thereby contracting, the result will be, that with increasing distance,
what is above us will descend, what is below us will ascend, and all
that lies at our sides will come nearer together. This progressive
convergence, this linear perspective, no doubt enables us to estimate
distances, so far as we have before us an uninterrupted succession of
visibly connected objects; but we are not able to do this by means of
the visual angle alone, for here the help of another datum is required
by the Understanding, to act, in a sense, as commentary to the visual
angle, by indicating more precisely the share we are to attribute to
distance in that angle. Now there are four principal data of this kind,
which I am about to specify. Thanks to these data, even where there
is no linear perspective to guide us, if a man standing at a distance
of 200 feet appears to me subtending a visual angle twenty-four times
smaller than if he were only 2 feet off, I can nevertheless in most
cases estimate his size correctly. All this proves once more that
perception is not only a thing of the senses, but of the intellect
also.--I will here add the following special and interesting fact in
corroboration of what I have said about the basis of linear perspective
as well as about the intellectual nature of all perception. When I have
looked steadily at a coloured object with sharply defined outlines--say
a red cross--long enough for the physiological image to form in my
eye as a green cross, the further the surface on to which I project
it, the larger it will appear to me: and _vice versa_. For the image
itself occupies an unvarying portion of my retina, _i.e._ the portion
originally affected by the red cross; therefore when referred outwards,
or, in other words, recognised as the effect of an external object,
it forms an unchanging visual angle, say of 2°. Now if, in this case,
where all commentary to the visual angle is wanting, I remove it to
a distant surface, with which I necessarily identify it as belonging
to its effect, the cross will occupy 2° of a distant and therefore
larger sphere, and is consequently large. If, on the other hand, I
project the image on to a nearer object, it will occupy 2° of a smaller
sphere, and is therefore small. The resulting perception is in both
cases completely objective, quite like that of an external object;
and as it proceeds from an entirely subjective reason (from the image
having been excited in quite a different way), it thus confirms the
intellectual character of all objective perception.--This phenomenon
(which I distinctly remember to have been the first to notice, in 1815)
forms the theme of an essay by Séguin, published in the "_Comptes