 A more general issue concerns the modal implications of each notion. In particular, is there a form of ontological dependence that is both necessary and sufficient for grounding? This seems unlikely (as argued in Rydéhn forthcoming). While there are some instances of grounding which are clearly rigid in the same sense as rigid existential dependence, it is also clear that this connection is not necessary and sufficient. Take for instance the fact [f] and assume that it is fully grounded in [g]. This entails that [f] cannot be grounded except by [g]. An example would be the case of the set of singleton Socrates, whose existence is rigidly grounded in the fact that Socrates exists. In such cases, [f] rigidly existentially depends upon [g], and it is also plausible that [f] depends for its identity upon [g]. However, other instances of grounding do not require that the grounded fact rigidly depends upon its grounds. For example, suppose that [f] is the fact that a particular subject is feeling pain, and that [f] is fully grounded in a particular neural fact about this subject, [g]. It seems possible that this subject could have been in pain, so [f] could have obtained, even if [g] did not obtain. This would be the case if [f] had been grounded in a different neural fact, [h]. In this case, [f] cannot depend for its identity upon [g], since [f] is not rigidly dependent upon [g]. This rules out some simple options for linking grounding and rigid ontological dependence, but there are arguably also problems for linking it with generic varieties of ontological dependence (for a more detailed discussion, see Rydéhn forthcoming).