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-orwrong alternatives but dual or complementary logics. Linear logic is an incomplete realization of this duality. While its completion is not essential 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. 1 A Postcard from the Edge ∗This work was supported by ONR under grant number N00014-92-J-1974