The Unactualized Certainty-Actuality Correspondence

Abstract

This paper investigates the correspondence between unactualized certainties, interpreted ontologically, and actualities. It does this first through the lens of a recently proposed enrichment of axiomatic probability which makes it possible to distinguish between actualities and unactualized possibilities, including those which are certain. Two kinds of unactualized certainties are considered: those due to the sample space being a singleton, and those involving a sample space with more than one element. After comparing standard axiomatic probability with the enrichment in regards to how they represent the distinction, attention is then focused on quantum mechanics. There, the correspondence will be examined through the lens of a recently proposed modification of the standard formalism, the Heisenberg Interpretation which, unlike the standard quantum formalism but like the enrichment of probability, also permits distinctions between unactualized possibilities and actualities. Two situations are found to exemplify the correspondence there: one involving partially measured entangled systems and the other involving the Born rule. Finally, it will be shown how the correspondence clarifies the very concept of an unactualized possibility.