I observe some ravens, and they are all black. This gives me good reason to think all ravens are black. This is an inductive inference within a natural kind. One might have this picture of the inductive inference here: observing the ravens, we learn something about the appropriate-level universal raven that they fall under. One might then think that all inductive inference is like this: We observe instances of a genuine, non-gerrymandered natural kind K, and conclude that the kind is such-and-such.
But I don't think this is all that happens. Here are a few other kinds of cases.
- From the fact that octopi behave in some ways like we do, we infer that they are conscious. But there is no biological taxon K that contains both octopi and humans such that we have good reason to think that all Ks are conscious. The lowest level taxon containing octopi and humans is the subregnum Bilateria and we have little reason to think all Bilateria are conscious. We might seek for a natural kind that isn't a taxon, like critters that exhibit apparently intelligent behavior. But that's a gerrymandered kind. We might try for a non-gerrymandered kind, like critters that exhibit intelligent behavior, but then we would have to have reason to think that octopi exhibit intelligent behavior rather than merely apparently intelligent behavior, and our problem would return.
- We have good reason to think that all life on earth descends from a single ancestor. But organism on earth isn't a natural kind.
- We can do induction within artificial kinds. That all the pens that I have observed have ink in them gives me reason to think all pens have ink. But pen isn't a natural kind.
Does this matter? Maybe. (I think a theist may have a better explanation of why induction not-within-a-kind works than a naturalist. But the thoughts here are inchoate.)