 It is not quite straight-forward to define essential dependence, although a formal definition will be given below. Before that, we ought to get a better picture of what it means to say that an object depends upon something for its identity, that is, we should clarify the relation of identity-dependence. Note that the notion of “identity” at play here is not the one symbolized with the “equals” sign, i.e., “=”. Rather, we mean “identity” in the sense of what a thing is, or which thing of a certain kind a thing is (compare this with Aristotle’s to ti esti, “the what it is”, see §7 of the separate entry on  Aristotle’s metaphysics).  Informally speaking, to say that the identity of x depends on the identity of y—or, more briefly, that x depends for its identity upon y—is to say that which thing of its kind y is fixes (or at least helps to fix) which thing of its kind x is. By “fixes” in this context is meant metaphysically determines. For instance, then, the identity of a set is fixed by the identities of its members, as was hinted already in  §1.  Likewise, the identity of an assassination is (at least partially) fixed by the identity of the person assassinated. These relationships of identity-dependence are direct consequences of the identity-criteria governing the kinds of which the items thus related are instances. (For further discussion on identity-criteria and identity-dependence, see Lowe 1989, 2009: Ch. 2, and 2012.)