Constructivism constitutes a distinctive thesis about the nature of normative facts. Roughly, what is distinctive about it is the claim that the facts about what we ought to do, what is wrong, or what is just, are grounded in facts about what we would believe or accept if we were to reflect appropriately. This is a metaphysical thesis. Constructivists often advertise their view as one which enjoys certain epistemological benefits. It has been said that only constructivism explains why moral beliefs survive evolutionary debunking, or can be retained in the face of disagreement, among other things. This paper asks the question of whether the Constructivist metaphysics supports these epistemological claims. I first consider two arguments for an affirmative answer to this question, which I call the Closure and Constitution Arguments. Given a natural set of assumptions, both arguments fail. Then I close by exploring whether the Closure and Constitution arguments might be supplemented with additional assumptions to yield a non-trivial case that knowledge of the normative is possible according to Constructivism.