The uniformity of the course of nature is a complex fact made up of all the separate uniformities in respect to single phenomena. Each of these separate uniformities, if it be not a mere case of and result from others, is a law of nature; for, though law is used for any general proposition expressing a uniformity, law of nature is restricted to cases where it has been thought that a separate act of creative will is necessary to account for the uniformity. Laws of nature, in the aggregate, are the fewest general propositions from which all the uniformities in the universe might be deducted. Science is ever tending to resolve one law into a higher. Thus, Kepler's three propositions, since having been resolved by Newton into, and shown to be cases of the three laws of motion, may be indeed called laws, but not laws of nature.

Since every correct inductive generalisation is either a law of nature, or a result from one, the problem of inductive logic is to unravel the web of nature, tracing each thread separately, with the view, 1, of ascertaining what are the several laws of nature, and, 2, of following them into their results. But it is impossible to frame a scientific method of induction, or test of inductions, unless, unlike Descartes, we start with the hypothesis that some trustworthy inductions have been already ascertained by man's involuntary observation. These spontaneous generalisations must be revised; and the same principle which common sense has employed to revise them, correcting the narrower by the wider (for, in the end, experience must be its own test), serves also, only made more precise, as the real type of scientific induction. As preliminary to the employment of this test, nature must be surveyed, that we may discover which are respectively the invariable and the variable inductions at which man has already arrived unscientifically. Then, by connecting these different ascertained inductions with one another through ratiocination, they become mutually confirmative, the strongest being made still stronger when bound up with the weaker, and the weakest at least as strong as the weakest of those from which they are deduced (as in the case of the Torricellian experiment) while those leading deductively to incompatible consequences become each other's test, showing that one must be given up (e.g. the old farmers' bad induction that seed never throve if not sown during the increase of the moon). It is because a survey of the uniformities ascertained to exist in nature makes it clear that there are certain and universal uniformities serving as premisses whence crowds of lower inductions may be deduced, and so be raised to the same degree of certainty, that a logic of induction is possible.