 The strongest versions of all these composition principles are obtained by asserting them as axiom schemas holding for every condition ψ, i.e., effectively, by foregoing any reference to ψ altogether. Formally this amounts in each case to dropping the second conjunct of the antecedent, i.e., to asserting the schema expressed by the relevant consequent with the only proviso that there are some φ-ers. In particular, the following schema is the unrestricted version of (P.15ψ,i), to the effect that every specifiable non-empty set of entities has a sumi: 