  The debate between the pluralist and the non-pluralist is really a hierarchy of debates. At the one extreme there is pluralism with regard to all of mathematics and at the other extreme there is non-pluralism with regard to all of mathematics. The intermediate positions (which are much more common) involve embracing non-pluralism for certain domains (say first-order arithmetic), while advocating pluralism with regard to others (say those where the notion of the full powerset enters the picture). Fortunately, the mathematical systems that arise in practice can be arranged in a well-founded hierarchy—ranging from weak systems like Robinson's arithmetic Q, up through Peano arithmetic PA, the subsystems of second-order arithmetic, the subsystems of set theory, and the hierarchy of large cardinal axioms. One can thus arrange the hybrid non-pluralist/pluralist positions and the corresponding debates in a well-founded hierarchy, where along the way one embraces more and more non-pluralism. The challenge for those with non-pluralist tendencies is to make the case that non-pluralism extends further and further into the upper reaches of higher mathematics. The challenge for those with pluralist tendencies is to draw the line in a principled manner and make the case that no argument for non-pluralism will succeed for the domains of mathematics beyond that line. 