Tweedle-dum

noun

a) A fictional little fat man who is the twin brother of Tweedle-dee and appears in multiple artistic works, including certain nursery rhymes and Lewis Carrolls .

Some ſay, compar’d to Bononcini, / That Mynheer Handel’s but a Ninny; / Others aver, that he to Handel / Is ſcarcely fit to hold a Candle: / Strange all this Difference ſhould be, / ’Twixt Tweedle-dum and Tweedle-dee!

b) One of a pair (the other of the pair being Tweedle-dee) of nominally different (often: but practically identical) things.

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.