 A second, more basic problem for structuralism starts again with the idea that all that matters about mathematical objects are their structural properties. With respect to non-eliminative structuralism, this is sometimes strengthened to the thesis that the positions in mathematical structures, as well as the abstract structures themselves, “only have structural properties”. But if not formulated more carefully, this leads to counterexamples (cf. Reck 2003). For instance, does the natural number structure not have the property that it is a favorite example in many debates about structuralism?  And isn’t it a property of the number 9 to have long been taken to be the number of planets in the Solar System? Both seem clearly non-structural properties.  Once again, structuralism appears incoherent or, at the very least, in need of further clarification.