John P. McCaskey’s Key to Induction shows what scientific induction is all about:
“[Scientists] want to know not only what is generally true but what is universally so, what is true without any possible exception. Below are three cases in which scientists were able to begin with general statements and progress to exceptionless universal ones. In each of the cases, scientists’ definitions evolved from being merely descriptive to identifying causes. That transition was crucial.”
He goes on to detail what happened with the science of cholera, electrical resistance, and tides, in which generalizations led to inductions. More famous examples would be the passage from the generalizations of Ptolemy and Kepler to the inductions of Galileo and Newton, or from the ad hoc transformations of Lorentz to Einstein’s principles.
As McCaskey puts it in Induction Without the Uniformity Principle, “The whole project of mature abstract thought is to identify similarities and differences, uniformities and changes, and to classify accordingly. And that—to Aristotle and followers such as Bacon and Whewell—is what induction is.”
Science progresses from data collection, to generalizations, to universals, to deductive hypotheses, and then new data collection to repeat the cycle. Sometimes “induction” is considered generalization (or testing) and universals are guessed by “abduction” (cf., C.S. Peirce) but the process of developing universals is the key element of induction.
In the series of posts on space and time, I have tried to show how approximate generalizations in transportation are exact inductions in physics.