ETA 2: this tile reads as if it is justifying induction as a principle, rather than when it is justifying induction in particular. Insifar as it is not addressing the problem o induction, it is on-point. I just don't think that point is terribly interesting, as it basically says "what counts as evidence depends on what we want to prove." My original comment follows, and applies if this was supposed to be about the problem of induction. I think you fundamentally misunderstand the problem of induction. The very concept of causation and updating on evidence rests on the assumption induction is possible. Without induction, there is no Bayes's theorem, because the very concept of evidence presupposes induction.

The problem of induction is, in short, how do we know that the future will be like the past? How do we know that our current observations at truly evidence of what the future will be like? The only evidence we have is that the future has always been like the past. Thus, the only evidence to justify induction presumes induction is possible.

This post does not appear to have anything to do with that. You can't use Bayesian evidence for induction, because the very concept of Bayesian evidence presupposes induction to be valid. ETA: stating that Bayes theorem presupposes induction may have been a bit strong. The point is that the thing that feeds into Bayes' presumes induction. Without induction, you cannot update on evidence, because "evidence" is a hollow concept. Bayes may not technically depend on induction; it's just that any actual application of it to the real world does.