(1) Aristotle, Dignāga, Descartes, Arnauld, Locke, Brentano, Sartre and many others are right about the nature of conscious awareness: all such awareness comports—somehow carries within itself—awareness of itself . (2) This is a necessary condition of awareness being awareness at all: no "higher-order' account of what makes conscious states conscious can be correct. (3) But (2) is very paradoxical: it seems to require that awareness be somehow already present, in such a way as to be available to itself as object of awareness, in order to be constituted as awareness in the first place. (4) Can anything relate to itself in this way? Can there be a relation that is (i) necessarily one-term, (ii) reflexive, (iii) non-logical (non-trivial), (iv) concretely realizable, (v) dynamically real, (vi) such that its holding is a necessary condition of the existence of the thing it holds of? It helps to consider the thought this very thought is puzzling. (5) Many accept the reality of the kind of awareness of awareness posited in (1) and (2), and think it must be not only "pre-reflective' and "non-positional', but also irrelational or non-intentional. But perhaps such awareness of awareness can be fully relational and fully intentional, and can be legitimately said to be its own object or content, even while being pre-reflective and non-positional.