ABSTRACT
Mathematical relations, in their fundamental character, are indifferently spatial or numerical; so that space can have no adverse effect on the accuracy of the mathematical knowledge. This chapter explains that Descartes's qualms concerning the certainty of physics are justified by his own theory of verification; that the difficulties of certain knowledge do in fact increase as inquiry passes from the more general to the more specific; that, none the less, the certainty of the method is not in principle impaired; and that the basic vision of the uniformity of nature is more firmly established than ever. From the moment that Descartes offers his definition of extension without reference to motion, the issue is already settled. Descartes puts the matter as clearly as possible when he says that the difference between a live body and a dead body is the same as that between a watch wound up and a watch run down.
