  The first sort of puzzle relates to the intuition that a boundary separates two entities (or two parts of the same entity), which are then said to be continuous with each other. Imagine ourselves traveling from Maryland to Pennsylvania. What happens as we cross the Mason-Dixon line? Do we pass through a last point p in Maryland and a first point q in Pennsylvania? Clearly not, given the density of the continuum; for then we should have to admit an infinite number of further points between p and q that would be in neither State. But, equally clearly, we can hardly acknowledge the existence of just one of p and q, as is dictated by the standard mathematical treatment of the continuum, for either choice would amount to a peculiar privileging of one State over the other. And we cannot identify p with q, either, for we are speaking of two adjacent States, so their territories cannot have any parts in common. So, where is the Mason-Dixon line, and how does it relate to the two adjacent entities it separates?