11. INDUCTION BY SIMPLE ENUMERATION.
As its name implies this type of inductive research consists in observing many instances which may exemplify the particular uniformity under consideration. The process is quantitative rather than qualitative, the certitude of the generalization depending on the mass of facts collected rather than on any striking resemblance or any detailed analysis. The aim is to observe, accurately if not scientifically, instance after instance until all doubt is removed. The outcome of such observation may be three fold. (1) The enumeration may be complete. This gives the so-called “perfect induction” which will receive attention later. (2) The enumeration may be incomplete and without exceptions; generalizing in this way from uncontradicted experience gives what are termed “empirical” truths. (3) The enumeration may be incomplete with exceptions. It is obvious that this type of induction could give no valid generalization; but the result may be put in the form of a ratio between the uniformities and the exceptions. Such a procedure is a mere “calculation of chances” and the result simply an expressed probability.
THE THREE KINDS OF SIMPLE ENUMERATION ILLUSTRATED.
The subject to receive investigation is a school examination.
(1) Complete enumeration. Every paper is read and marked; this leads to the generalization, “All the class have passed.”
(2) Incomplete enumeration with no exceptions. Representative papers are read and marked in which no failures are found. Generalization, “Probably all of the class have passed.”
(3) Incomplete enumeration with exceptions. Representative papers are read and marked in which there are 20 failures out of the hundred papers examined. Generalization, “Probably about 80% of the class have passed.”
Briefly, simple enumeration may take the form of (1) a perfect induction, (2) a probable induction, (3) a mere calculation of chances. The first necessitates completed experience, the second uncontradicted experience and the third contradicted experience.