OF THE IDEA OF SPACE.
1. BY speaking of space as an Idea, I intend to imply, as
has already been stated, that the apprehension of objects as
existing in space, and of the relations of position, &c.,
prevailing among them, is not a consequence of experience,
but a result of a peculiar constitution and activity of the
mind, which is independent of all experience in its origin,
though constantly combined with experience in its exercise.
That the idea of space is thus independent of experience,
has already been pointed out in speaking of ideas in
general: but it may be useful to illustrate the doctrine
further in this particular case.
I assert, then, that space is not a notion obtained by
experience. Experience gives us information concerning
things without us: but our apprehending them _as_ without
us, takes for granted their existence in space. Experience
acquaints us what are the form, position, magnitude of
particular objects: but that they have form, position,
magnitude, presupposes that they are in space. We cannot
derive from appearances, by the way of observation, the
habit of representing things to ourselves as in space; for
no single act of observation is possible any otherwise than
by beginning with such a representation, and conceiving
objects as already existing in space.
2. That our mode of representing space to ourselves is not
derived from experience, is clear also from this: that
through this mode of representation we arrive at
propositions which are rigorously universal and necessary.
Propositions of such a kind could not possibly be obtained
from experience; for experience can {92} only teach us by a
limited number of examples, and therefore can never securely
establish a universal proposition: and again, experience can
only inform us that anything is so, and can never prove that
it must be so. That two sides of a triangle are greater than
the third is a universal and necessary geometrical truth: it
is true of all triangles; it is true in such a way that the
contrary cannot be conceived. Experience could not prove
such a proposition. And experience has not proved it; for
perhaps no man ever made the trial as a means of removing
doubts: and no trial could, in fact, add in the smallest
degree to the certainty of this truth. To seek for proof of
geometrical propositions by an appeal to observation proves
nothing in reality, except that the person who has recourse
to such grounds has no due apprehension of the nature of
geometrical demonstration. We have heard of persons who
convinced themselves by measurement that the geometrical
rule respecting the squares on the sides of a right-angled
triangle was true: but these were persons whose minds had
been engrossed by practical habits, and in whom the
speculative development of the idea of space had been
stifled by other employments. The practical trial of the
rule may illustrate, but cannot prove it. The rule will of
course be confirmed by such trial, because what is true in
general is true in particular: but the rule cannot be proved
from any number of trials, for no accumulation of particular
cases makes up a universal case. To all persons who can see
the force of any proof, the geometrical rule above referred
to is as evident, and its evidence as independent of
experience, as the assertion that sixteen and nine make
twenty-five. At the same time, the truth of the geometrical
rule is quite independent of numerical truths, and results
from the relations of space alone. This could not be if our
apprehension of the relations of space were the fruit of
experience: for experience has no element from which such
truth and such proof could arise.
3. Thus the existence of necessary truths, such as those of
geometry, proves that the idea of space from {93} which they
flow is not derived from experience. Such truths are
inconceivable on the supposition of their being collected
from observation; for the impressions of sense include no
evidence of necessity. But we can readily understand the
necessary character of such truths, if we conceive that
there are certain necessary conditions under which alone the
mind receives the impressions of sense. Since these
conditions reside in the constitution of the mind, and apply
to every perception of an object to which the mind can
attain, we easily see that their rules must include, not
only all that has been, but all that can be, matter of
experience. Our sensations can each convey no information
except about itself; each can contain no trace of another
additional sensation; and thus no relation and connexion
between two sensations can be given by the sensations
themselves. But the mode in which the mind perceives these
impressions as objects, may and will introduce necessary
relations among them: and thus by conceiving the idea of
space to be a condition of perception in the mind, we can
conceive the existence of necessary truths, which apply to
all perceived objects.
4. If we consider the impressions of sense as the mere
materials of our experience, such materials may be
accumulated in any quantity and in any order. But if we
suppose that this matter has a certain form given it, in the
act of being accepted by the mind, we can understand how it
is that these materials are subject to inevitable
rules;--how nothing can be perceived exempt from the
relations which belong to such a form. And since there are
such truths applicable to our experience, and arising from
the nature of space, we may thus consider space as a _form_
which the materials given by experience necessarily assume
in the mind; as an arrangement derived from the perceiving
mind, and not from the sensations alone.
5. Thus this phrase,--that space is a _form_ belonging to
our perceptive power,--may be employed to express that we
cannot perceive objects as in space, without an operation of
the mind as well as of the senses--without active as well as
passive faculties. This phrase, however, {94} is not
necessary to the exposition of our doctrines. Whether we
call the conception of space a Condition of perception, a
Form of perception, or an Idea, or by any other term, it is
something originally inherent in the mind perceiving, and
not in the objects perceived. And it is because the
apprehension of all objects is thus subjected to certain
mental conditions, forms or ideas, that our knowledge
involves certain inviolable relations and necessary truths.
The principles of such truths, so far as they regard space,
are derived from the idea of space, and we must endeavour to
exhibit such principles in their general form. But before we
do this, we may notice some of the conditions which belong,
not to our Ideas in general, but to this Idea of Space in
particular.
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