other. It might be described in the language of ancient philosophy, as
'the Not-being' of objects. It is a negative idea which in the course
of ages has become positive. It is originally derived from the
contemplation of the world without us--the boundless earth or sea, the
vacant heaven, and is therefore acquired chiefly through the sense of
sight: to the blind the conception of space is feeble and inadequate,
derived for the most part from touch or from the descriptions of others.
At first it appears to be continuous; afterwards we perceive it to be
capable of division by lines or points, real or imaginary. By the
help of mathematics we form another idea of space, which is altogether
independent of experience. Geometry teaches us that the innumerable
lines and figures by which space is or may be intersected are absolutely
true in all their combinations and consequences. New and unchangeable
properties of space are thus developed, which are proved to us in a
thousand ways by mathematical reasoning as well as by common experience.
Through quantity and measure we are conducted to our simplest and purest
notion of matter, which is to the cube or solid what space is to
the square or surface. And all our applications of mathematics are
applications of our ideas of space to matter. No wonder then that they
seem to have a necessary existence to us. Being the simplest of our
ideas, space is also the one of which we have the most difficulty in
ridding ourselves. Neither can we set a limit to it, for wherever we
fix a limit, space is springing up beyond. Neither can we conceive a
smallest or indivisible portion of it; for within the smallest there
is a smaller still; and even these inconceivable qualities of space,
whether the infinite or the infinitesimal, may be made the subject of
reasoning and have a certain truth to us.

Whether space exists in the mind or out of it, is a question which has
no meaning. We should rather say that without it the mind is incapable
of conceiving the body, and therefore of conceiving itself. The mind may
be indeed imagined to contain the body, in the same way that Aristotle
(partly following Plato) supposes God to be the outer heaven or circle
of the universe. But how can the individual mind carry about the
universe of space packed up within, or how can separate minds have
either a universe of their own or a common universe? In such conceptions
there seems to be a confusion of the individual and t