The Natural Metaphysics of Computing Anticipatory Systems

Anticipation is a natural characteristic of any system. 'Natural' is difficult to define formally in a mathematical model. For a model is an artificial construct relying on reduced conditions and assumptions. A model gives rise to weak anticipation while strong anticipation requires us to raise our sights to metaphysics where naturality resides. A prime distinction is that metaphysics has a higher-order tense logic. Strong anticipation is no prisoner of time like weak anticipation. In general while adjointness has a logical ordering the operation of an environment C on a subobject A has a solution subobject B under Heyting inference A ⇒ B in the environment of C. This is represented as the expression C x A ⟶ B ┤ B^A ⟵ C, the adjunction of the natural metaphysical ordering which constitutes strong anticipation. The environment C may be more particularised as an adjunction between the induced monad and comonad functors. The uniqueness of the adjunction in natural metaphysics is examined in the context of the Beck-Chevalley test for computing the multiplicity of formal models possible for weak anticipation.