Abstract

This paper presents a model for the structure of universal frameworks in logic, mathematics, and physics that are closed to logical conclusion by the mechanism of paradox across a dualism of elements. The prohibition takes different forms defined by the framework of observation inherent to the structure. Forms include either prohibition to conclusion on the logical relationship of internal elements or prohibition to conclusion based on the existence of an element not included in the framework of a first element. The model is applied to logical arguments in philosophy, mathematics, and physics and is initially a geometrical analysis of quantum theory and its application in experiment. Conclusion from the analysis is extended to give insight into the complexity of infinities above the two-dimensional boundary of the model.