Paul Busch argued that the positive operator (valued) measure, a generalization of the standard quantum observable, enables a consistent notion of unsharp reality based on a quantifiable degree of reality whereby systems can possess generalized properties jointly, whereas related sharp properties cannot be so possessed (Busch and Jaeger in Found Phys 40:1341, 2010). Here, the work leading up to the formalization of this notion to which he made great contributions is reviewed and explicated in relation to Heisenberg's notions of potentiality and actuality. The notion of unsharp reality is then extended further by the introduction of a distinction between actual and actualizable elements of reality based on these mathematical innovations.
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