 However, that belief that p is neither necessary nor sufficient for intuition that p is suggested by conflicts between a person’s beliefs and their intuitions. One plausible characterization of a paradox holds that it is a set of a propositions, each of which is intuitive, but not all of which could be true. If one has reasoned one’s way to a satisfactory resolution of a paradox and identified the false proposition, one often still has the intuition that the rejected proposition is true. Hence, supposing that in such a case one’s beliefs are not contradictory, one can have an intuition that p while one does not believe p and one can have a belief that p without having an intuition that p. Indeed, even before such reasoning, one might suspend belief about the contradictory set while each remained intuitive. More generally, it seems that one may believe something—that some theory is true, that some mathematical or logical proposition is a theorem, that one is hungry, or that a person is now speaking—without having any intuition that p and so belief that p is not sufficient for intuition that p.