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 _infimae 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 i