Philosophy, over the last decade, has seen increasing interest in paraconsistent approaches to familiar paradox. One of the most popular approaches is also one of the best known: namely, the logic of paradox (LP)-based approach championed by Priest. This chapter highlights an important predecessor of LP, namely, the logic of antinomies (LA)-based approach championed first by Asenjo and Tamburino, and highlights the salient differences in the logics. The chapter argues that the differences in logic reflect a difference in both background philosophy of logic and background metaphysics. LA is motivated by a material approach to logical consequence combined with a metaphysical position involving antinomic predicates, while LP is compatible with both a formal and material approach to consequence and can be combined with a large host of metaphysical commitments (including few such commitments at all).