 The subscript “R” is used here because it seems appropriate to call this species of existential dependence of one object upon another rigid existential dependence. Why “rigid”? Because there is no flexibility here: the existence of a given x requires the existence of that very y. It could not be something a little bit like y, something falling roughly in the same category, for instance; it must be y. The definiens in (EDR) is equivalent to “Necessarily, if x exists, then y exists”, so that according to (EDR) the existential dependenceR of x upon y amounts to the strict implication of y’s existence by x’s existence. We have mentioned one example of rigid existential dependence, namely, sets ontologically depending on their members (more precisely, a set depends rigidly on the very members it has, i.e., any change in a set’s members will change the set itself). Another, although more controversial, example is a particular person depending for her existence on her parents, or, more precisely, on the particular sperm and egg that she originates from. This example is of course related to the essentiality of origin (as discussed in Kripke 1980).