ONS IMPROPERLY SO CALLED.

Induction is the process by which what is true at certain times, or of
certain individuals, is inferred to be true in like circumstances at all
times, or of a whole class. There must be an inference from the known to
the unknown, and not merely from a less to a more general expression.
Consequently, there is no valid induction, 1, in those cases laid down
in the common works on Logic as the only perfect instances of induction,
viz. where what we affirm of the class has already been ascertained to
be true of each individual in it, and in which the seemingly general
proposition in the conclusion is simply a number of singular
propositions written in an abridged form; or, 2, when, as often in
mathematics, the conclusion, though really general, is a mere summing up
of the different propositions from which it is drawn (whether actually
ascertained, or, as in the case of the uncalculated terms of an
arithmetical series, when once its law is known, readily to be
understood); or, 3, when the several parts of a complex phenomenon,
which are only capable of being observed separately, have been pieced
together by one conception, and made, as it were, one fact represented
in a single proposition.

Dr. Whewell sets out this last operation, which he terms the
_colligation of facts_, as induction, and even as the type of induction
generally. But, though induction is always colligation, or (as we may,
with equal accuracy, characterise such a general expression obtained by
abstraction simply connecting observed facts by means of common
characters) _description_, colligation, or description, as such, though
a necessary preparation for induction, is not induction. Induction
explains and predicts (and, as an incident of these powers, describes).
Different explanations collected by real induction from supposed
parallel cases (e.g. the Newtonian and the _Impact_ doctrines as to the
motions of the heavenly bodies), or different predictions, i.e.
different determinations of the conditions under which similar facts may
be expected again to occur (e.g. the stating that the position of one
planet or satellite so as to overshadow another, and, on the other hand,
that the impending over mankind of some great calamity, is the condition
of an eclipse), cannot be true together. But, for a colligation to be
correct, it is enough that it enables the mind to represent to itself as
a whole all the separate facts ascertained a