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Propositions such as are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore's paradox. Sydney Shoemaker has recently argued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker's own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account is the claim that conscious beliefs are always partly about themselves; it will be shown to follow from this that conscious beliefs in Moorean propositions are self-contradictory.