simple parts, and everywhere in it there exists nothing simple.” Here, as before, the proofs of both thesis and antithesis are open to criticism, but for the purpose of vindicating physics and the world of sense it is enough to find a fallacy in one of the proofs. We will choose for this purpose the proof of the antithesis, which begins as follows:
“Assume that a complex thing (as substance) consists of simple parts. Since all external relation, and therefore all composition out of substances, is only possible in space, the space occupied by a complex thing must consist of as many parts as the thing consists of. Now space does not consist of simple parts, but of spaces.”
The rest of his argument need not concern us, for the nerve of the proof lies in the one statement: “Space does not consist of simple parts, but of spaces.” This is like Bergson’s objection to “the absurd proposition that motion is made up of immobilities.” Kant does not tell us why he holds that a space must consist of spaces rather than of simple parts. Geometry regards space as made up of points, which are simple; and although, as we have seen, this view is not scientifically or logically necessary, it remains prima facie possible, and its mere possibility is enough to vitiate Kant’s argument. For, if his proof of the thesis of the antinomy were valid, and if the antithesis could only be avoided by assuming points, then the antinomy itself would afford a conclusive reason in favour of points. Why, then, did Kant think it impossible that space should be composed of points?
I think two considerations probably influenced him. In the first place, the essential thing about space is spatial order, and mere points, by themselves, will not account for spatial order. It is obvious that his argument
