  The positive operator (valued) measures (POMs) allow one to generalize the
notion of observable beyond the traditional one based on projection valued
measures (PVMs). Here, we argue that this generalized conception of observable
enables a consistent notion of unsharp reality and with it an adequate concept
of joint properties. A sharp or unsharp property manifests itself as an element
of sharp or unsharp reality by its tendency to become actual or to actualize a
specific measurement outcome. This actualization tendency - or potentiality -
of a property is quantified by the associated quantum probability. The
resulting single-case interpretation of probability as a degree of reality will
be explained in detail and its role in addressing the tensions between quantum
and classical accounts of the physical world will be elucidated. It will be
shown that potentiality can be viewed as a causal agency that evolves in a
well-defined way.
