Quantum Sets, Assemblies and Plexi

Set theory may be used as a language to talk about things in some mathematical or nonmathematical domain of discourse, representing things by sets. When our knowledge of these things is complete and unchanging, it is convenient to represent one thing by one point, providing a 1-1 or complete description of the domain of discourse. When our knowledge is incomplete at the time the Inaguage is being formulated, it is customary to represent one thing by many points, in a 1-to-many or incomplete description, later reducing this multiplicity on the basis of later information. The multiplicity representing a thing in such an incomplete description is called the space of the thing, and is generally provided with further structure. The phase space of classical mechanics, the phase space of thermodynamics, the sample space of statistics and the vector space of quantum mechanics are examples of such spaces and incomplete descriptions, often of the same thing. In all these examples but the quantum it is supposed that the incomplete description finally completed, or at least may be, by choosing one point of the space on the basis of later information. In the quantum case, the space is used to record a process of production or preparation, and a dual space records the subsequent process of absorption or detection.