Periodicity in the Operator Hierarchy

All the dual closures introduced so far, from quarks to molecules and from cells to multi-cellular organisms and neuronmemons, lead to a hierarchy of increasingly complex types of operators. The basic first-order logic of the hierarchy is the result of the dual closure theorem. This first-order hierarchy is summarised in Table 5.1. This hierarchy is consistent in its use of dual closure and in its inclusion of only operators, and can be used as a basis for extrapolations leading to predictions.