  The common-sense view of reality is expressed logically in Boolean subset
logic (each element is either definitely in or not in a subset, i.e., either
definitely has or does not have a property). But quantum mechanics does not
agree with this "properties all the way down" picture of micro-reality. Are
there other coherent alternative views of reality? A logic of partitions, dual
to the Boolean logic of subsets (partitions are dual to subsets), was recently
developed along with a logical version of information theory. In view of the
subset-partition duality, partition logic is the alternative to Boolean subset
logic and thus it abstractly describes the alternative dual view of
micro-reality. Perhaps QM is compatible with this dual view? Indeed, when the
mathematics of partitions using sets is "lifted" from sets to vector spaces,
then it yields the mathematics and relations of quantum mechanics. Thus the
vision of micro-reality abstractly characterized by partition logic matches
that described by quantum mechanics. The key concept explicated by partition
logic is the old idea of "objective indefiniteness" (emphasized by Shimony).
Thus partition logic, logical information theory, and the lifting program
provide the back story so that the old idea then yields the objective
indefiniteness interpretation of quantum mechanics.
