The Process of Induction may be resolved into three steps; the Selection of the Idea, the Construction of the Conception, and the Determination of the Magnitudes.
Aphorism XXXV.
These three steps correspond to the determination of the Independent Variable, the Formula, and the Coefficients, in mathematical investigations; or to the Argument, the Law, and the Numerical Data, in a Table of an astronomical or other Inequality.
Aphorism XXXVI.
The Selection of the Idea depends mainly upon inventive sagacity: which operates by suggesting and trying various hypotheses. Some inquirers try erroneous hypotheses; and thus, exhausting the forms of errour, form the Prelude to Discovery.
Aphorism XXXVII.
The following Rules may be given, in order to the selection of the Idea for purposes of Induction:—the Idea and the Facts must be homogeneous; and the Rule must be tested by the Facts.
Sect. I.—The Three Steps of Induction.
1. WHEN facts have been decomposed and phenomena measured, the philosopher endeavours to combine them into general laws, by the aid of 187 Ideas and Conceptions; these being illustrated and regulated by such means as we have spoken of in the last two chapters. In this task, of gathering laws of nature from observed facts, as we have already said[24], the natural sagacity of gifted minds is the power by which the greater part of the successful results have been obtained; and this power will probably always be more efficacious than any Method can be. Still there are certain methods of procedure which may, in such investigations, give us no inconsiderable aid, and these I shall endeavour to expound.