n
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.

Either a single approximate generalisation may be applied to an
individual instance, or several to the same instance. In the former
case, the proposition, as stating a general average, must be applied
only to average cases; it is, therefore, generally useless for guidance
in affairs which do not concern large numbers, and simply supplies, as
it were, the first term in a series of approximations. In the latter
case, when two or more approximations (not connected with each other)
are _separately_ applicable to the instance, it is said that two (or
more) _probabilities are joined by addition_, or, that there is a
_self-corroborative chain_ of evidence. Its type is: Most A