Induction and Deduction

Abstract

As your correspondent invites discussion on this subject I hope you will allow me to repeat in a new form the views I expressed upon it in your columns some months ago. I quite agree with Mr. Russel in maintaining that “true induction is utterly unable to yield us any conclusion that is more than probable and approximate,” understanding by induction inference from one or more special cases to a more general rule. But on the other hand it appears to me that Miss Jones's criticism is quite destructive of Mr. Russel's interpretation of geometrical reasoning. The point which both have missed I believe to be this, that a proposition stated in given words, such as the enunciation of Euclid's pons asinorum does not always and to every one convey the same information; and if it is meant in one sense its degree of reliability, and the method by which it must be proved, will be quite different from what they would be if it were meant in another. There are at least three different kinds of interpretation which may thus be put upon the proposition. It may mean (1) the triangle used to illustrate this proposition has equal sides; therefore it has equal angles; or (2) I have conceived a triangle which has equal sides, therefore I have conceived one which has equal angles; or (3) the connotation ascribed by the adjective “isosceles” implies the connotation “having equal sides.”