  Axioms of set theory have arisen in part out of our understanding of the paradoxes. The most striking feature of the paradoxes is something vulgarly called “self-reference”, and ideas about how to deal with it have been a useful constraint on our invention of axioms for set theory. The search for a spell to ward off the evils attendant upon self-reference has fed into the axiomatisation of set theory in two ways, corresponding to the two ways in which self-reference has been (mis)-understood. Is it circularity in the specification of sets that is to be eschewed? Or do we locate the problem in circularity in the membership relation between sets? At all events, we have to be careful to keep to a minimum the number of sinews we cut, for there are important theorems (Gödel’s Incompleteness theorem among others) whose proofs rely on the same “self-reference” that we find in the paradoxes but which we are loath to abandon.