Yet in several cases I was obliged to take a not too elementary example to support the point impressively enough. In fact, I felt that I should present also examples of historic interest, examples of real mathematical beauty, and examples illustrating the parallelism of the procedures in other sciences, or in everyday life. I should add that for many of the stories told the final form resulted from a sort of informal psychological experiment. Several passages incorporated in the following text have been suggested by the answers of my students, or my original version has been modified in some other manner by the reaction of my audience. In short, I tried to use all my experience in research and teaching to give an appropriate opportunity to the reader for intelligent imitation and for doing things by himself.
Some philosophers say Yes, most scientists think No.
In order to be discussed profitably, the question should be put differently. It should be treated differently, too, with less reliance on traditional verbalisms, or on newfangled formalisms, but in closer touch with the practice of scientists. Now, observe that inductive reasoning is a particular case of plausible reasoning. Then you may notice the possibility of obtaining some information about inductive reasoning by observing and comparing examples of plausible reasoning in mathematical matters. And so the door opens to investigating induction inductively.