  It is easier to think about circular objects than circular definitions.  Even so, it will be useful in reading this entry to keep circular definitions in mind.  The most conspicuous form of object circularity would be a set having itself as an element; even worse would be a set x such that x = {x}. For those with a background in standard set theory, such sets are ruled out by the axioms in the first place, and in the second it is not clear why one would want to change the axioms in order to admit them.  And if one does take the drastic step of altering the axioms of a well-established theory, what changes?  This entry is an extended discussion of this matter, and related ones.