Chapter 34

THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES.

Derivative laws are inferior to ultimate laws, both in the extent of the propositions, and in their degree of certainty within that extent. In particular, the uniformities of coexistence and sequence which obtain between effects depending on different primæval causes, vary along with any variation in the collocation of these causes. Even when the derivative uniformity is between different effects of the same cause, it cannot be trusted to, since one or more of the effects may be producible by another cause also. The effects, even, of derivative laws of _causation_ (resulting, i.e. the laws, from the combination of several causes) are not independent of collocations; for, though laws of causation, whether ultimate or derivative, are themselves universal, being fulfilled even when counteracted, the peculiar probability of the latter kind of laws of causation being counteracted (as compared with ultimate laws, which are liable to frustration only from one set of counteracting causes) is fatal to the universality of the derivative uniformities made up of the sequences or coexistences of their effects; and, therefore, such derivative uniformities as the latter are to be relied on only when the collocations are known not to have changed.

Derivative laws, not causative, may certainly be extended beyond the limits of observation, but only to cases _adjacent_ in time. Thus, we may not predict that the sun will rise this day 20,000 years, but we can predict that it will rise to-morrow, on the ground that it has risen every day for the last 5,000 years. The latter prediction is lawful, _because_, while we know the causes on which its rising depends, we know, also, that there has existed hitherto no perceptible cause to counteract them; and that it is opposed to experience that a cause imperceptible for so long should start into immensity in a day. If the uniformity is empirical only, that is, if we do not know the causes, and if we infer that they remain uncounteracted from their effects alone, we still can extend the law to adjacent cases, but only to cases still more closely adjacent in time; since we can know neither whether changes in these unknown causes may not have occurred, nor whether there may not exist now an adverse cause capable after a time of counteracting them.

An empirical law cannot generally be extended, in reference to _Place_, even to adjacent cases (since there is no uniformity in the collocations of primæval causes). Such an extension is lawful only if the new cases are _presumably_ within the influence of the same individual causes, even though unknown. When, however, the causes are known, and the conjunction of the effects is deducible from laws of the causes, the derivative uniformity may be extended over a wider space, and with less abatement for the chance of counteracting causes.