Anticipation as Prediction in the Predication of Data Types

Every object in existence has its type. Every subject in language has its predicate. Every intention in logic has its extension. Each therefore has two levels but with the fundamental problem of the relationship between the two. The formalism of set theory cannot guarantee the two are co-extensive. That has to be imposed by the axiom of extensibility, which is inadequate for types as shown by Bertrand Russell's ramified type theory, for language as by Henri Poincare's impredication and for intention unless satisfying Port Royal's definitive concept. An anticipatory system is usually defined to contain its own future state. What is its type? What is its predicate? What is its extension? Set theory can well represent formally the weak anticipatory system, that is in a model of itself. However we have previously shown that the metaphysics of process category theory is needed to represent strong anticipation. Time belongs to extension not intention. The apparent prediction of strong anticipation is really in the structure of its predication. The typing of anticipation arises from a combination of c5 and μ - respectively (co) multiplication of the ( co )monad induced by adjointness of the system's own process. As a property of Cartesian closed categories this predication has significance for all typing in general systems theory including even in the definition of time itself.