The two ways to interpret a superposition
This paper sketches the development of the logic of partitions (dual to the usual Boolean logic of subsets) and logical information theory with the duality between “elements of a subset” and “distinctions of a partition” playing a central role. Meta-physically, this duality between existence (“elements”) and information (“distinctions”) then leads to two quite different notions of reality: (1) the notion of reality always fully definite (“all the way down”) where the concepts of Boolean logic and classical physics apply, and (2) the notion of an objectively indefinite reality where the concepts of partition logic and quantum physics apply. In this manner, the “killer application” of the duality between existence and information is the objective indefiniteness interpretation of quantum mechanics.