Personal Structures: I. a Basis for Personal Structures
Personal structures were defined as structures pairing judgments and sets of environmental states. It was shown how either the judgments or environmental sets of these structures could be treated both as Boolean algebras and as Boolean rings. It was shown that a basis for the personal structures always existed, and this basis made it possible uniquely to construct the remainder of the personal structure. Some discussion was presented concerning the usefulness of the concepts of personal structure and a basis for a personal structure. These discussions were, however, very preliminary, and the real usefulness of this approach rests upon developments in future papers, in particular the further development of the concept of uncertain judgment. It may be that this concept of an uncertain judgment will have to “absorb” much of the variability usually found in psychological experiments. In this connection it is to be noted that we have thus far not limited the concept of judgment to a single instant in time, nor even to a continuous interval in time, thus permitting the concept of uncertain judgment to include as factors, judgments made over a series of trials.