This paper discusses the nature of consciousness' intrinsic intentionality from a transcendental-phenomenological viewpoint. In recent philosophy of mind the essentially intentional character of consciousness has become obscured because the latter is predominantly understood in terms of "qualia" or the "what-it-is-like-ness" of mental states and it is hard to see why such subjective "feels", of all things, could bestow states with objective reference. As the paper attempts to demonstrate, this is an inadequate understanding of consciousness, which should instead be defined in terms of presence. Consciousness essentially takes place as presence-of, i.e., consists in something coming to appearance. This presence-of is not only a fundamental, irreducible phenomenon, but also in a radical sense un-naturalisable. Naturalism only knows "nature", as the world of objects, and the question of intentionality then seems to be how certain inner-worldly objects can be "representations" of other inner-worldly objects. In fact, no object is ever intrinsically "about" anything. This is exclusively the nature of subjectivity qua consciousness, which is not an object alongside other objects but rather exists as the manifestation of objects.