As a matter of fact, naturalism is unable to justify the problem of induction. The appeal is circular. You can only justify the uniformity and stability of natural laws if, in fact, the future resembles the past. But the past can hardly count as evidence for the future unless natural laws are uniform and stable. Conversely, evidence that natural laws are uniform and stable depends on whether you can project the past into the future. Not to mention that our knowledge of the past is quite piecemeal. Indeed, we reconstruct the past based on interpolations that take for granted the uniformity of nature! That's how we plug the gaps. So there seems to be no way to justify his extrapolation from inside the circle of empirical observation itself. (Unjustifiable naturalism)
I am somewhat suspicious of the UoNP as a justifier for induction. Is nature really uniform? What does that really mean? I say some parts of nature are uniform, and some aren't. The egg-production process for any given species operates uniformly enough. But what about the occasional freak of nature? Sometimes you get bad eggs. Or no eggs. Biological processes are generally 'uniform', because lifeforms reproduce after their own kind. There are natural processes that are chaotic (ultimately unpredictable) too, some involving life, some involving only nonliving interactions, like weather.