OF SOME PECULIARITIES OF THE IDEA OF SPACE.
1. SOME of the Ideas which we shall have to examine involve
conceptions of certain relations of objects, as the idea of
Cause and of Likeness; and may appear to be suggested by
experience, enabling us to _abstract_ this general relation
from particular cases. But it will be seen that Space is not
such a general conception of a relation. For we do not speak
of _Spaces_ as we speak of Causes and Likenesses, but of
Space. And when we speak of _spaces_, we understand by the
expression, parts of one and the same identical
everywhere-extended Space. We conceive a universal Space;
which is not made up of these partial spaces as its
component parts, for it would remain if these were taken
away; and these cannot be conceived without presupposing
absolute space. Absolute Space is essentially one; and the
complication which exists in it, and the conception of
various spaces, depends merely upon boundaries. Space must,
therefore, be, as we have said, not a general conception
abstracted from particulars, but a universal mode of
representation, altogether independent of experience.
2. Space is infinite. We represent it to ourselves as an
infinitely great magnitude. Such an idea as that of Likeness
or Cause, is, no doubt, found in an infinite number of
particular cases, and so far includes these cases. But these
ideas do not include an infinite number of cases as parts of
an infinite whole. When we say that all bodies and partial
spaces exist _in_ infinite space, we use an expression which
is not applied in the same sense to any cases except those
of Space and Time. {96}
3. What is here said may appear to be a denial of the real
existence of space. It must be observed, however, that we do
not deny, but distinctly assert, the existence of space as a
real and necessary condition of all objects perceived; and
that we not only allow that objects are seen external to us,
but we found upon the fact of their being so seen, our view
of the nature of space. If, however, it be said that we deny
the reality of space as an object or thing, this is true.
Nor does it appear easy to maintain that space exists as a
thing, when it is considered that this thing is infinite in
all its dimensions; and, moreover, that it is a thing,
which, being nothing in itself, exists only that other
things may exist in it. And those who maintain the real
existence of space, must also maintain the real existence of
time in the same sense. Now two infinite things, thus really
existing, and yet existing only as other things exist in
them, are notions so extravagant that we are driven to some
other mode of explaining the state of the matter.
4. Thus space is not an object of which we perceive the
properties, but a form of our perception; not a thing which
affects our senses, but an idea to which we conform the
impressions of sense. And its peculiarities appear to depend
upon this, that it is not only a form of sensation, but of
_intuition_; that in reference to space, we not only
perceive but _contemplate_ objects. We see objects in space,
side by side, exterior to each other; space, and objects in
so far as they occupy space, have parts exterior to other
parts; and have the whole thus made up by the juxtaposition
of parts. This mode of apprehension belongs only to the
ideas of space and time. Space and Time are made up of
parts, but Cause and Likeness are not apprehended as made up
of parts. And the term _intuition_ (in its rigorous sense)
is applicable only to that mode of contemplation in which we
thus look at objects as made up of parts, and apprehend the
relations of those parts at the same time and by the same
act by which we apprehend the objects themselves.
5. As we have said, space limited by _boundaries_ {97} gives
rise to various conceptions which we have often to consider.
Thus limited, space assumes _form_ or _figure_; and the
variety of conceptions thus brought under our notice is
infinite. We have every possible form of line, straight
line, and curve; and of curves an endless number;--circles,
parabolas, hyperbolas, spirals, helices. We have plane
surfaces of various shapes,--parallelograms, polygons,
ellipses; and we have solid figures,--cubes, cones,
cylinders, spheres, spheroids, and so on. All these have
their various properties, depending on the relations of
their boundaries; and the investigation of their properties
forms the business of the science of Geometry.
6. Space has three dimensions, or directions in which it may
be measured; it cannot have more or fewer. The simplest
measurement is that of a straight line, which has length
alone. A surface has both length and breadth: and solid
space has length, breadth, and thickness or depth. The
origin of such a difference of dimensions will be seen if we
reflect that each portion of space has a boundary, and is
extended both _in_ the direction in which its boundary
extends, and also in a direction _from_ its boundary; for
otherwise it would not be a boundary. A point has no
dimensions. A line has but one dimension,--the distance from
its boundary, or its _length_. A plane, bounded by a
straight line, has the dimension which belongs to this line,
and also has another dimension arising from the distance of
its parts from this boundary line; and this may be called
_breadth_. A solid, bounded by a plane, has the dimensions
which this plane has; and has also a third dimension, which
we may call _height_ or _depth_, as we consider the solid
extended above or below the plane; or _thickness_, if we
omit all consideration of up and down. And no space can have
any dimensions which are not resoluble into these three.
We may now proceed to consider the mode in which the idea of
space is employed in the formation of Geometry.
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