Philosophers have conjectured that human cognitive limitations might preclude our ever resolving the hard problem of consciousness. Few, however, have offered suggestions as to what it might be about our conceptual apparatus that poses the problem. I do so in this essay, arguing that our central difficulties lie with two conceptual categories that pervade philosophical discussion of the hard problem. They are compositional concepts -- part/whole, constituents/constitution, and the like – and instantiational concepts: properties/objects, universals/particulars, and the like. I look (...) at the uses of these two conceptual categories in four contexts in which the hard problem is considered: multiple realizability, zombies, mental causation, and panpsychism. I show that the two conceptual categories run into the same kinds of obstacles in each case, which suggests that they might be key to the cognitive limitations about which some have speculated. (shrink)