Those who contend that there is a kind of argument called Inductive
different from the Deductive, illustrate their view by some such
example as the following:--'This, that, and the other magnet' [that
is, all the magnets we know] 'attract iron; therefore all possible
magnets attract iron.' They say there is an irresistible compulsion
in the mind to draw such a conclusion from information of the kind
exemplified, and they contrast that type of thought with a deductive
argument like--'All magnets attract iron; this object is a magnet;
therefore it attracts iron.' They figure the former as a progress
upwards, the latter as a regress downwards.
That is Induction as understood by J. S. Mill and Sir William
Hamilton; on this point these philosophers happen to agree.
The first of those arguments is a deduction with the precedent
omitted. Expressed in full it amounts to this--'Any relation
observed several times to subsist between two classes of objects, and
concerning which no exception has ever been observed, may be taken as
universal; there is such a relation between known magnets and known
iron; therefore it may be regarded as universal.' The precedent is not
a mental compulsion, but a result of experience. Induction as above
defined is therefore only a species of deductive conclusions.
Most logicians take the word Induction in its etymological sense, as
meaning systematic observation carried on with a view to obtaining
a general idea of some class of objects; or of establishing a
categorical relation between one object or class and another, by
eliminating all the alternative correlatives. In neither operation
would Induction be argument.
In science a 'perfect induction' is one in which all existing objects
of a class, or all objects related in a certain manner, have been
perceived, so that there is no other object concerning which a
conclusion can be drawn. In such cases, says Mill, there is no
induction--only a summary of experience. He evidently regarded the
conclusion with respect to unknown cases as the essence of induction,
whereas in the scientific sense the induction is the positive content
of the idea, or the abstract relation--the unknown cases are ignored,
or there may be none. In scientific writings induction sometimes means
the _method_ of observation rather than the result--the method of
correcting inferences by perception, wherever possible.