  A basic derivation in this set theory is that the Russell set exists, and is both a member of itself and not a member of itself. The paradoxes, in other words, are proofs, and the resulting contradictions are theorems (1979b, 302). Sylvan sketches the further work needed to show that elementary principles such as the Zermelo-Fraenkel axioms and their immediate consequences can be derived. And he speculates, much more ambitiously, that the Axiom of Choice and the Continuum Hypothesis could be decided as well; see Weber (2012). Priest 2006, chapter 18 is a discussion of paraconsistent set theory in this tradition.