ABSTRACT
This chapter examines a number of postulates, which state relationships between symbols at different hierarchical levels. It discusses a method, similar to that for deriving arguments, of generating more economical ways of stating values for certain higher-order symbols. By combining postulates, theorists can generate more precise, definitions for hierarchically superior symbols. The term theorem will be used to denote a formula that derives a set of values of a symbol from one or more postulates. The analysis progresses, it will be helpful to have a technique for proving theorems–deriving them from postulates–in recorded form. Even a small number of postulates can generate a considerable number of theorems. The process of proving theorems moves in the opposite direction from the process of deriving arguments. To derive an argument, theorists must move 'up' the ladder of generality, substituting hierarchically inferior symbols for superior ones, in order to ascertain a more general statement of the original argument.
