  Let us start with those who take realism to be prior to reason. To fix ideas consider the pluralist who accepts realism about the natural numbers but not about arbitrary subsets of natural numbers and then, on this basis, concludes that theoretical reasons can be offered in the case of new axioms in number theory but not in the case of analysis or set theory. When pressed on the source of this asymmetrical stance concerning realism in the two domains the pluralist usually responds by resorting to the intuition that the natural numbers are “clear” while the notion of an arbitrary subset of natural numbers is “inherently vague”. To this the non-pluralist might respond that the notion of clarity is not clear. Intuitions of clarity, like intuitions of self-evidence, are notoriously vague and subjective and hence a weak point upon which to rest one's case. 