Alan Musgrave, in 'How Popper [Might Have] Solved the Problem of Induction', distinguishes between (i) reasons for the thing believed, i.e. evidence that it is true; and (ii) reasons for (the act of) believing it. It seems at least possible to have non-truth-indicative reasons for believing something. Perhaps there could be moral or prudential reasons why having a particular belief would be a good thing, independently of whether it is true.
Now, Musgrave employs this distinction in support of the Popperian programme, i.e. 'appeasing' the inductive skeptic. He grants that there are no inductive reasons, no evidence which provides (even defeasible) reasons to think that something is true. But he argues that this doesn't require full-blown irrationalism. We can be justified in believing because the absence of type-(i) reasons does not entail the absence of type-(ii) reasons, and it is the latter that matter.
I'm suspicious. Actually, I think strong inductive skepticism is absurd. But I won't pursue that here. Further, I'm dubious of the sharp distinction Popperians draw between confirmation and falsification. It's fine to prefer the latter on pragmatic methodological grounds. But I'm not sure that the distinction is entirely clear cut, at least in principle. For one thing, while experimental results 'confirming' a hypothesis never guarantee that the hypothesis is true, neither do apparently 'disconfirming' results guarantee for certain that the hypothesis is false. It is always possible to discard some auxiliary hypothesis instead, say by claiming that the observation was in error - whether due to human error or malfunctioning equipment. (Many of my high-school chemistry lab experiments didn't get the expected results. But that didn't lead us to throw out the textbook. We concluded from the incongruent results that it was our experiments that didn't work, not the theories.)
Perhaps more importantly for present purposes, a lack of falsification (despite one's best attempts) can itself provide a form of inductive confirmation -- as used in my recent argument on the raven paradox. Indeed, if the lack of falsification was not evidence for the truth of a hypothesis, why should we believe it?
It isn't enough for Musgrave to merely point to the believed-believing distinction. If there are reasons for believing something, we want to know what sorts of reasons they are. Most of the time we take them to be truth-indicative reasons, i.e. reasons for the thing believed. But Popperians don't think there are any such reasons. So what's left? Presumably they don't think we have moral (etc.) reasons for believing scientific theories. And while it might be pragmatically useful (and thus prudential) to believe them, my reasons for thinking this are surely inductive in themselves. (Science has proven useful in the past. Therefore it will probably continue to be useful in future.) So it doesn't seem that these reasons are available to the inductive skeptic. And besides, presumably the reason why science is useful is that it is within some approximation of the truth. It's useful to believe true things. Our best scientific theories are (roughly) true, thus we have prudential reasons to believe them. Clearly the Popperian cannot accept that argument either, since he denies that we have any reason to think that our best theories are true. So it's left a mystery just what sorts of reasons for believing Musgrave takes us to have.