S. Austin Allibone, comp. Prose Quotations from Socrates to Macaulay. 1880.
Induction is the counter-process in scientific method to deduction. Induction implies the raising of individuals into generals, and these into still higher generalities. Deduction is the bringing down of universals to lower genera, or to individuals. Every deduction, therefore, to be valid, must rest on a prior induction, which, in order that we may obtain logical certainty, must be a complete induction,that is to say, must include all the individuals which constitute the genus.
The principle of deduction is, that things which agree with the same thing agree with one another. The principle of induction is, that in the same circumstances and in the same substances, from the same causes the same effects will follow. The mathematical and metaphysical sciences are founded on deduction; the physical sciences rest on induction.
When by comparing a number of cases agreeing in some circumstances, but differing in others, and all attended with the same result, a philosopher connects, as a general law of nature, the event with its physical cause, he is said to proceed according to the method of induction.
The logic of induction consists in stating the facts and the inference in such a manner that the evidence of the inference is manifest; just as the logic of deduction consists in stating the premises and the conclusion in such a manner that the evidence of the conclusion is manifest.