 The important feature of single-abstraction identity principles of the kind on which we are focusing is that they are free of ontological commitment. Theories that postulate or prove them need to be supplemented with specific further ontologically committal postulates before incurring commitment to the sort of entities whose broad logical behavior is captured by a single-abstraction identity principle. For example, the set-abstraction principle above merely places constraints on how sets, membership (‘∈’) and set-defining conditions F interrelate. It logically implies both extensionality and the conversion schemata (“If u is a member of the set of all and only Fs, then u is an F”, and “If u is an F, and the set of all and only Fs exists, then u is a member of it”), but does not guarantee the existence of any sets—not even that of the empty set. 