Passing on to Aristotle, we will touch on the points which most immediately concern our enquiry.
Just as a scientific man of the present day in reviewing the speculations of the ancient world would treat them with a curiosity half amused but wholly respectful, asking of each and all wherein lay their relation to fact, so Aristotle, in discussing the philosophy of Greece as he found it, asks, above all other things: “Does this represent the world? In this system is there an adequate presentation of what is?”
He finds them all defective, some for the very reasons which we esteem them most highly, as when he criticises the Atomic theory for its reduction of all change to motion. But in the lofty march of his reason he never loses sight of the whole; and that wherein our views differ from his lies not so much in a superiority of our point of view, as in the fact which he himself enunciates—that it is impossible for one principle to be valid in all branches of enquiry. The conceptions of one method of investigation are not those of another; and our divergence lies in our exclusive attention to the conceptions useful in one way of apprehending nature rather than in any possibility we find in our theories of giving a view of the whole transcending that of Aristotle.
He takes account of everything; he does not separate matter and the manifestation of matter; he fires all together in a conception of a vast world process in which everything takes part—the motion of a grain of dust, the unfolding of a leaf, the ordered motion of the spheres in heaven—all are parts of one whole which he will not separate into dead matter and adventitious modifications.
And just as our theories, as representative of actuality, fall before his unequalled grasp of fact, so the doctrine of ideas fell. It is not an adequate account of existence, as Plato himself shows in his “Parmenides”; it only explains things by putting their doubles beside them.
For his own part Aristotle invented a great marching definition which, with a kind of power of its own, cleaves its way through phenomena to limiting conceptions on either hand, towards whose existence all experience points.
In Aristotle’s definition of matter and form as the constituent of reality, as in Plato’s mystical vision of the kingdom of ideas, the existence of the higher dimensionality is implicitly involved.
Substance according to Aristotle is relative, not absolute. In everything that is there is the matter of which it is composed, the form which it exhibits; but these are indissolubly connected, and neither can be thought without the other.
The blocks of stone out of which a house is built are the material for the builder; but, as regards the quarrymen, they are the matter of the rocks with the form he has imposed on them. Words are the final product of the grammarian, but the mere matter of the orator or poet. The atom is, with us, that out of which chemical substances are built up, but looked at from another point of view is the result of complex processes.
Nowhere do we find finality. The matter in one sphere is the matter, plus form, of another sphere of thought. Making an obvious application to geometry, plane figures exist as the limitation of different portions of the plane by one another. In the bounding lines the separated matter of the plane shows its determination into form. And as the plane is the matter relatively to determinations in the plane, so the plane itself exists in virtue of the determination of space. A plane is that wherein formless space has form superimposed on it, and gives an actuality of real relations. We cannot refuse to carry this process of reasoning a step farther back, and say that space itself is that which gives form to higher space. As a line is the determination of a plane, and a plane of a solid, so solid space itself is the determination of a higher space.