Everything that he says on this subject is so excellent that it is unnecessary to cover the ground again. Although the belief in the universality of natural law was, at the time of the renaissance, a bold faith going far in advance of the evidence, it has since been so successful that it is now[Pg 231] possible to defend it on inductive grounds. But there is some difficulty in deciding what we are to mean by it. I have dealt with this subject before,[51] and shall now consider it only briefly. The regularities which we first observe, and in which we first believe, are of the simple form: " is always accompanied (or preceded or succeeded) by ." But all such regularities are capable of having exceptions, and science soon seeks laws of a different kind. We arrive in the end (possibly not at the very end) at differential equations. I think that these are of two kinds, those expressing persistence, and those expressing accelerations (in a generalized sense). The former are concealed, more or less, by the assumption of permanent substance; but this is a topic which I shall consider in the next chapter. The latter are the ordinary differential equations of the second order which occur throughout mathematical physics. But in addition to these, in order to produce observed macroscopic results, there must be statistical laws governing quantum changes and radio-active disruptions of atoms. I want to inquire whether we are saying anything significant in assuming that there are laws governing the course of the physical world, or whether any set of percepts must be amenable to law by a sufficiently liberal use of hypothesis.