What would it mean for humanity to have a united purpose?
Presumably, that, in addition to all their other goals, all, or almost all, humans would share at least one non-trivial, impersonal goal. The “almost all” qualification is intended to handle those incapable of holding rational goals – infants, lunatics, the senile, autistics, etc. The goal must be impersonal, because otherwise “I want to live,” (e.g.) would be the united purpose of humanity — which may be true, but is not what the Alephians mean.
