The following definitions and explanations are decisions formulated arbitrarily in a sense. However, the underlying assumptions serving as a guide to their formulation are found in both pragmatism and logical positivism. Yet there has been some confusion of the difference between definitions, axioms, postulates, etc., and as a result there is a confusion of certain phases of formal and factual knowledge. For example, one notices in C. I. Lewis' works that all formal statements are thought of as “definitive.” A more effective word, I believe, is “prescriptive.” Axioms are prescriptive, yet, as will be seen below, they are not definitions, and no one in practice conceives of them as such, as can be seen in mathematical works. Axioms prescribe the logical relationship between two or more concepts or words. If interpreted, the factual referents of the words, whose logical relations have been prescribed in axioms, are different. This is not the case with definitions.