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.
CHAPTER XXIII.
APPROXIMATE GENERALISATIONS, AND PROBABLE EVIDENCE.
The inferences called _probable_ rest on approximate generalisations.
Such generalisations, besides the inferior assurance with which they
can be applied to individual cases, are _generally_ almost useless as
premisses in a deduction; and therefore in _Science_ they are valuable
chiefly as steps towards universal truths, the discovery of which is its
proper end. But in _practice_ we are forced to use them--1, when we have
no others, in consequence of not knowing what general property
distinguishes the portion of the class which have the attribute
predicated, from the portion which have it not (though it is true that
we can, in such a case, usually obtain a collection of exactly true
propositions by subdividing the class into smaller classes); and, 2,
when we _do_ know this, but cannot examine whether that general property
is present or not in the individual case; that is, when (as usually in
_moral_ inquiries) we could get universal majors, but not minors to
correspond to them. In any case an approximate generalisation can never
be more than an empirical law. Its authority, however, is less when it
composes the whole of our knowledge of the subject, than when it is
merely the most available form of our knowledge for practical guidance,
and the causes, or some certain mark of the attribute predicated, being
known to us as well as the effects, the proposition can be tested by our
trying to deduce it from the causes or mark. Thus, our belief that most
Scotchmen can read, rests on our knowledge, not merely that most
Scotchmen that we have known about could read, but also that most have
been at efficient schools.