INDUCTIONS 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 at a given time, so that
successive tentative descriptions of a phenomenon, got by guessing till
a guess is found which tallies with the facts, may, though conflicting
(e.g. the theories respecting the motions of the heavenly bodies), be
_all_ correct _so far as they go_. Induction is proof, the inferring
something unobserved from something observed; and to provide a proper
test of proof is the special purpose of inductive logic. But colligation
simply sums up the facts observed, as seen under a new point of view.
Dr. Whewell contends that, besides the sum of the facts, colligation
introduces, as a principle of connection, a conception of the mind not
existing in the facts. But, in fact, it is only because this conception
is a copy of something in the facts, although our senses are too weak to
recognise it directly, that the facts are rightly classed under the
conception. The conception is often even got by abstraction from the
facts which it colligates; but also when it is a hypothesis, borrowed
from strange phenomena, it still is accepted as true only because found
actually, and as a fact, whatever the origin of the knowledge of the
fact, to fit and to describe as a whole the separate observations. Thus,
though Kepler's consequent inference that, _because_ the orbit of a
planet is an ellipse, the planet would _continue_ to revolve in that
same ellipse, was an induction, his previous application of the
conception of an ellipse, abstracted from other phenomena, to sum up his
direct observations of the successive positions occupied by the
different planets, and thus to describe their orbits, was no induction.
It altered only the _predicate_, changing--The successive places of,
e.g. Mars, are A, B, C, and so forth, into--The successive places of,
e.g. Mars, are points in an ellipse: whereas induction always widens the
_subject_.