The fourth dimension

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 unsubstantial 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 was 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.