Suppose we have any axiom of the form: (2) For every Tweedledee there is a Tweedledum R-related to it. Axioms of the form (2) cut two ways. They can be construed as putting a limit on the Tweedledees: only those exist for which there is an R-related Tweedledum. On the other hand, they can be seen as postulating the existence of a rich collection of Tweedledums. There are so many of them that there is at least one R-related to every single Tweedledee.