Structuralism and the Notion of Dependence

The notion of dependence figures prominently in recent discussions of non-eliminative mathematical structuralism. Structuralists often argue that mathematical objects from one and the same structure depend on one another and on the structure to which they belong. Their opponents often argue that there cannot be any such dependence. I first show that the structuralists' claims about dependence are more important to their view than is generally recognized. Then I defend a compromise view concerning the dependence relations between mathematical objects, according to which the structuralists are right about some mathematical objects but wrong about others. I end with some remarks about the crucial notion of dependence.