  The question of pluralism in its most general formulation is the question of whether there is a correct path through the hierarchy of interpretability or whether instead a multitude of mutually incompatible theories must be admitted as equally legitimate from the point of view of theoretical reason and mathematical truth. There are really two problems that must be addressed. The first is the question of how far the hierarchy of interpretability extends, that is, which degrees are non-trivial in that the theories within them are consistent. This is the problem of consistency (or non-triviality). The second is the question of whether, for a given (non-trivial) degree of interpretability, there are theoretical reasons that can be given for one theory over another. This is the problem of selection. If one managed to solve both problems—determining the extent of the non-trivial degrees and locating the correct path through them—then one would have completely solved the problem of mathematical truth. There are, however, two important things to stress about this. First, because of the incompleteness theorems, any such solution would have to be “schematic” concerning the first part (vertical independence). Second, the solution to the full problem of selection even for the degree of ZFC is a very difficult one since it involves resolving CH and a multitude of other independent statements that arise already at this level. 