The disjunction problem and the distality problem each presents a challenge that any theory of mental content must address. Here we consider their bearing on purely probabilistic causal theories. In addition to considering these problems separately, we consider a third challenge—that a theory must solve both. We call this “the hard problem.” We consider 8 basic ppc theories along with 240 hybrids of them, and show that some can handle the disjunction problem and some can handle the distality problem, but (...) none can handle the hard problem. This is our main result. We then discuss three possible responses to that result, and argue that though the first two fail, the third has some promise. (shrink)