 A nice feature of  Division  is that it automatically validates the pseudometric space axioms (i)–(iii) above. (By contrast, if we measured the degree of similarity of \(x\) and \(y\) by summing the degrees of naturalness of the properties shared by \(x\) and \(y\), we would have to allow some objects—namely, those that instantiate many natural properties—to be more similar to themselves than others.) But the approach also faces several problems: