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.
Tweedledum’s chum stood with his hand resting lightly on the back of her arm, as if to turn her away from some potentially corrupting sight. I stood my ground, smiled, and introduced myself. I'm looking for Timothy Butler. That must be you. I calmed down enough to notice that Timothy Butler was clenching and unclenching his right hand in an effort at self-control. Tweedledum noticed it too. She rushed to his defense.