 (SUB-1) could be seen to follow the precedent of Aristotle, who—in the Categories—admitted only particulars as “primary” substances, while allowing some universals (the species and genera of primary substances) the status of “secondary” substances (see Aristotle, Categories: Ch. 2). However, (SUB-1), because it relies on  (EDR),  will be unsatisfactory for those who are convinced that the modal-existential analysis of ontological dependence is not sufficiently fine-grained; it will face the type of problems that we have discussed above in  §2.2.  We know already that it won’t do to replace the notion of existential dependence employed in (SUB-1) by appealing instead to the relation of essential existential dependence, as defined by  (EDE),  because the latter is neither an asymmetrical nor an antisymmetrical relation. Indeed, this is one lesson of the example of the sphere’s two hemispheres discussed immediately after the definition for (EDE) was given. For, whereas the whole sphere might well be taken to qualify as a substance, neither of its “halves” plausibly can, because they lack the requisite kind of ontological independence. But, while (SUB-1) reinterpreted in terms of (EDE) does indeed have the implication that neither of the hemispheres is a substance—because each dependsE for its existence on the other and hence on a particular distinct from itself—it also has the unwanted implication that the whole sphere is not a substance for the same reason, because it is arguably a part of the essence of the sphere as a whole that it exists only if each of its hemispheres exists. However, an obvious remedy is at hand. We can simply replace the appeal to any species of existential dependence in a definition on the pattern of (SUB-1) by an appeal to the relation of identity-dependence, as defined by  (ID),  to give: