Hinton - The Fourth Dimension.pdf

38
THE FOURTH DIMENSION
which it separates, so the plane is inconceivable without
the solids which it limits on either hand. And so space
itself cannot be positively defined. It is the negation
of the possibility of movement in more than three
dimensions. The conception of space demands that of
a higher space. As a surface is thin and mathematical
without the substance of which it is the surface, so matter
itself is thin without the higher matter.
Just as Aristotle invented that algebraical method of
representing unknown quantities by mere symbols, not by
lines necessarily determinate in length as what the habit
of the Greek geometers, and so struck out the path
towards those objectifications of thought which, like
independent machines for reasoning, supply the mathematician
with his analytical weapons, so in the formulation
of the doctrine of matter and form, of potentiality and
actuality, of the relativity of substance, he produced
another kind of objectification of mind—a definition
which had a vital force and an activity of its own.
In none of his writings, as far as we know, did he carry it
to its legitimate conclusion on the side of matter, but in
the direction of the formal qualities he was led to his
limiting conception of that existence of pure form which
lies beyond all known determination of matter. The
unmoved mover of all things is Aristotle’s highest
principle. Towards it, to partake of its perfection all
things move. The universe, according to Aristotle, is an
active process—he does not adopt the illogical conception
that it was once set in motion and has kept on ever since.
There is room for activity, will, self-determination, in
Aristotle’s system, and for the contingent and accidental
as well. We do not follow him, because we are accustomed
to find in nature infinite series, and do not feel
obliged to pass on to a belief in the ultimate limits to
which they seem to point.