ver C Since the probability calculus on the left-side of the table is a non-commutative version of the old Laplace-Boole logical finite probability theory [3], the correspondence with the right-side of the table gives precision to the thesis that the mathematics of QM is a type of logical probability calculus complexified in Hilbert spaces. For instance, the equiprobability or indifference principle of that classical logical finite probability calculus-that is, the equality of all non-zero coeffi cients in a vector over Z2-generalizes to the QM probability calculus using the coeffi cients of vectors over C, and the Born Rule applies to orthogonal decompositions in both cases. Crossing the sets-vector-space bridge the other way, we have seen that the classical logical probability calculus (in its non-commutative version) is a type of quantum mechanics over sets. 5.14 Whence von Neumann's Type 1 and Type 2 processes? When some particularly mysterious process like measurement can be clearly and distinctly modeled in QM/sets, then it casts some sense-making light back on full QM. A good example is von Neumann's distinction between Type 1 measurement-like processes and Type 2 processes of unitary evolution [42]. In QM/sets, we have seen that measurement is a distinction-making process described by the partition join operation. In terms of the lattice of set partitions, such a "Type 1" process moves up in the lattice to more refined partitions.25 This means in QM/sets that a "Type 2" evolution would be a distinction-preserving process that, as it were, moves horizontally in the lattice of partitions. 25The usual notion of refinement of partitions, i.e., π = {B} is more (or equally) refined than σ = {C}, denoted σ  π, if for each B ∈ π, there is a C ∈ σ such that B ⊆ C, is just the inclusion relation on distinctions, i.e., σ  π iff dit (σ) ⊆ dit (π), so moving up in the ordering means making more distinctions. 24 Figure 8: "Type 1" distinction-making and "Type 2" distinction-preserving processes in Q