 In the larger family of paradoxes of self-reference beyond the semantic, dialetheism affords a treatment of the set-theoretic paradoxes. These paradoxes arise in set theories based on an unrestricted ‘comprehension schema’ for sets: for any condition or property, including paradoxical ones like non-self-membership, there exists a corresponding set. In particular, inconsistent sets like Russell’s are admitted; analogously to the Liar, the Russell set is and is not a member of itself. As with the truth schema, the set comprehension principle seems very natural and intuitive, and such contradictions do not give rise to triviality due to the paraconsistent logic underlying the formal theories. Though the issue is too technical to be addressed here, and more appropriately dealt with in the entries on  paraconsistent logic  and  inconsistent mathematics,  the reader can consult Routley 1979, Brady 1989, for inconsistent set theories, and Weber 2012. See also Mortensen 1995. For different approaches to dialetheic set theory, see Restall 1992 and Ripley 2015b.