 Inconsistent Mathematics began historically with foundational considerations. Frege and Russell proposed to found their mathematics on the naive principle of set theory: to every predicate is a set. But the naive principle leads rapidly to a proof of the existence of the Russell set, the set of all sets not members of themselves, which both is and is not a member of itself. This and other set-theoretic paradoxes noted by Russell and others led to attempts to produce consistent set theories as a foundation for mathematics. Perhaps the best known of these was Zermelo-Fraenkel set theory ZF. But ZF and others such as NBG and the like were in various ways ad hoc, having to include multiple independent principles instead of a single simple comprehension axiom. Hence, a number of people including da Costa (1974), Brady (1971, 1989), Priest, Routley, &amp; Norman (1989, pp. 152, 498), considered it preferable to retain the full power of the natural comprehension principle, and tolerate a degree of inconsistency in set theory. Brady, in particular, has extended, streamlined and simplified these results on naive set theory in his book (2006). For a clear account see also Restall’s review (2007).