Since we're talking about induction as the basis of science, I'm surprised the concept of "falsification" wasn't mentioned, which has been the "workhorse" of most science during the past two hundred years. See https://en.wikipedia.org/wiki/Falsifiability
Specifically in the context of classical statistics methods (frequentist statistics), the idea of using p-values for scientific discovery only makes sense as part of repeated studies (induction over multiple tests of a theory). It's easy for any one study to observe some pattern by chance (one black raven), but if repeated studies all show this pattern exists, then we kind of start to believe the pattern might be true.
Bayesian statisticians don't use the falsification paradigm directly, but instead focus on estimation, and combining the evidence from multiple experiments to obtain "tighter bounds" on the estimated quantities of interest. The conceptual machinery is very different, but the idea of induction is still kind of present in the form of "more data reduces uncertainty".