The right way to deal with the problem of induction is to adopt what I call the nomological-explanatory solution (NES). This holds that when an inductive inference is rational, it can be shown to be so by breaking it down into two further steps of inference, neither of which is as such extrapolative. The first step is an inference to the best explanation of the hitherto exemplified regularity, where the regularity calls for explanation because it is too extensive to be deemed coincidental, and where the explanation offered is one which involves the postulation of some law or set of laws of nature, construed as forms of natural necessity. The second step is a deduction from this explanation that the regularity will continue to hold for the relevant unexamined case or cases, or will do so subject to the continued obtaining of certain standing conditions.
Keywords: explanation, induction, inference, laws of nature, natural necessity, NES, nomological