[The function of analogies in natural sciences, also in contrast to metaphors and models].

This introduction surveys the various functions of analogies in science, medicine and technology. The focus is on their heuristic importance. The productiveness of analogies is linked to the systematic depth and breadth of the established connections. Various examples are presented from different periods in the history of science, most notably Galileo; such late-Victorian Maxwellians as George Francis FitzGerald and Oliver Lodge; and Heinrich HERTZ and Niels BOHR. These examples are examined in terms of the specific differing temporal ranges of their claimed validities. They serve as evidence or counterevidence for various systematic analyses of analogies as put forward by various philosophers of science, most notably Francis Bacon, John Stuart Mill, Ernst Mach, Harald Høffding, Ernest Nagel, Mary Hesse and Peter Achinstein. The analytic framework for analogies supported here is what the cognitive scientist Dedre Gentner has termed structure-mapping.