Abstract

The existence of mathematical objects may be explained in terms of their occurrence in problems. Especially interesting problems arise at the overlap of domains, and the items that intervene in them are hybrids sharing the characteristics of both domains in an ambiguous way. Euclid's geometry, and Leibniz' work at the intersection of geometry, algebra and mechanics in the late seventeenth century, provide instructive examples of such problems and items. The complex and yet still formal unity of these items calls into question certain tenets of Resnik's structuralism, and of the reductive projects of the logicists.