There are two ways to challenge evidentialism. One is to argue (as in my previous post) that there can be 'practical' or non-epistemic reasons for belief. The other, which I want to explore presently, is to argue that there can be non-evidential epistemic reasons. There can be theoretical reasons for you to believe that p, which are not at the same time reasons for the truth of p.
How could this be? Well, the normative potency of evidence derives from taking truth as the normative standard against which to assess beliefs. We say "belief aims at truth", and then assess beliefs according to whether they achieve this goal. But there are other normative frameworks we might adopt instead. There is, for example, the standard of coherence, which assesses a set of beliefs for its internal coherence, rather than applying an external standard such as truth. Despite making no reference to truth, the standard of internal coherence is nevertheless clearly an epistemic standard, rather than a practical one.
So, I propose, we have epistemic reason to believe that p if doing so would yield a more coherent belief set. (There are shades of Michael Smith in this suggestion.)
Suppose that you believe that p, and believe that if p then q, and so on this basis you rationally form the belief that q. The two former beliefs provide you with a reason to adopt the latter belief. In doing so, you make your belief-set more coherent. This is epistemically rational.
So there we have a reason for believing. What about reasons for the thing believed, i.e. the proposition that q? If asked, you would likely point to the propositions that p, and that if p then q, as being your reasons for taking q to be true. However, let us suppose that your former beliefs are false: p is false, and if p then q is false. So while you took these to be reasons for the truth of q, in fact they are not. You were mistaken about whether there are reasons for the the truth of q. There are no such reasons in this case.
Thus we find that there can be (even epistemic) reasons for believing, which are not reasons for the truth of the thing believed. Musgrave's distinction is vindicated, even if his particular application of it is not.