Linear Logic complements Classical Logic

Classical logic enforces the separation of individuals and predicates, linear logic draws them together via interaction; these are not right-or- wrong alternatives but dual or complementary logics. Linear logic is an incomplete realization of this duality. While its completion is not essen- tial for the development and maintenance of logic, it is crucial for its application. We outline the "four-square" program for completing the connection, whose corners are set, function, number, and arithmetic, and define ordinal Set, a bicomplete equational topos, meaning its canonical isomorphisms are identities, including associativity of product.