CHAPTER XXII.
UNIFORMITIES OF COEXISTENCE NOT DEPENDENT ON CAUSATION.
Besides uniformities of succession, which always depend on causation, there are uniformities of coexistence. These also, whenever the coexisting phenomena are effects of causes, whether of one common cause or of several different causes, depend on the laws of their cause or causes; and, till resolved into these laws, are mere empirical laws. But there are some uniformities of coexistence, viz. those between the ultimate properties of kinds, which do not depend on causation, and therefore seem entitled to be classed as a peculiar sort of laws of nature. As, however, the presumption always is (except in the case of those kinds which are called simple substances or elementary natural agents), that a thing's properties really depend on causes though not traced, and we never can be certain that they do not; we cannot safely claim (though it may be an ultimate truth) higher certainty than that of an empirical law for any generalisation about coexistence, that is to say (since kinds are known to us only by their properties, and, consequently, all assertions about them are assertions about the coexistence of something with those properties), about the properties of kinds.
Besides, no rigorous inductive system can be applied to the uniformities of coexistence, since there is no general axiom related to them, as is the law of causation to those of succession, to serve as a basis for such a system. Thus, Bacon's practical applications of his method failed, from his supposing that we can have previous certainty that a property must have an invariable coexistent (as it must have an invariable antecedent), which he called its form. He ought to have seen that his great logical instrument, elimination, is inapplicable to coexistences, since things, which agree in having certain apparently ultimate properties, often agree in nothing else; even the properties which (e.g. Hotness) are effects of causes, generally being not connected with the ultimate resemblances or diversities in the objects, but depending on some outward circumstance.
Our only substitute for an universal law of coexistence is the ancients' induction per enumerationem simplicem ubi non reperitur instantia contradictoria, that is, the improbability that an exception, if any existed, could have hitherto remained unobserved. But the certainty thus arrived at can be only that of an empirical law, true within the limits of the observations. For the coexistent property must be either a property of the kind, or an accident, that is, something due to an extrinsic cause, and not to the kind (whose own indigenous properties are always the same). And the ancients' class of induction can only prove that within given limits, either (in the latter case) one common, though unknown, cause has always been operating, or (in the former case) that no new kind of the object has as yet or by us been discovered.
The evidence is, of course (with respect both to the derivative and the ultimate uniformities of coexistence), stronger in proportion as the law is more general; for the greater the amount of experience from which it is derived, the more probable is it that counteracting causes, or that exceptions, if any, would have presented themselves. Consequently, it needs more evidence to establish an exception to a very general, than to a special, empirical law. And common usage agrees with this principle. Still, even the greater generalisations, when not based on connection by causation, are delusive, unless grounded on a separate examination of each of the included infimæ species, though certainly there is a probability (no more) that a sort of parallelism will be found in the properties of different kinds; and that their degree of unlikeness in one respect bears some proportion to their unlikeness in others.