Abstract

It has been explained how science, with the freedom which makes it an art, uses ideas of its own construction, and that they are verified by nature shows them to be, directly or indirectly, at differing degrees of remoteness, congenial to and so far inherent in the material which is the subject-matter of the science. Take, for an instance, velocity. It is expressed by the ratio of two integers which measure distance and time respectively. Now a ratio is a construction of the mind, and it does not exist in external things in the sense in which universals must be said to belong to them and have in one way or another been held to belong to them since the time of Socrates, or at least Plato. Even if we agree that the integers themselves are given to mind and not created by mind, their ratio implies the intervention of mind, and does not inhere in the integers themselves. But though velocity does not inhere in things, it corresponds to and stands for something which is found alike in all moving things and varies in the moving tram and the sea-plane in a Schneider race