Generalize does need to be more specific in order to make sense. In current ML work, generalizability means something else than what it typically used to mean in AI work.

One way to look at what generalizability is would be like this: problem domains typically come with sets of axioms. Generalizability is the ability for a solution approach to work across different domains that don't have 100% axiom overlap. The wider the difference between axiom sets for a domain, the more difficult / impressive the generalization.

Solving two problems within the same domain, necessarily sharing a 100% overlapping axiom set, is not generalization at all.

The reason the axioms supporting the domain matter is that they (in part) guide which heuristics work, and how they should be applied. And that's the sort of generalizability that is missing from current work: some solutions can make some pre-programmed choices about applying different heuristics depending on the problem set (driverless cars are doing this now). This is the "bag of tricks" approach. But they don't typically morph in how they are applied, or the end that they're trying to accomplish when they're applied.