Quantum Mechanics and Logical Type

The quasi-classical world of modern physics is a class of classical worlds superposed, literally a 'metaworld'. The measurement problem is itself evidence for the two different types of world, at the different levels of logical type. The enactment of linear dynamics in the classical worlds alters the class invariant, and thus induces physical collapse of the metaworld to a subclass. The complex formalism that seems deeply counterintuitive is class arithmetic. Measurement: set-selection of a subclass compatible with the observed outcome. Observable operators: partition of the class. Projection operators: set-selection of a subclass. Fourier transforms: switching set-selection. The uncertainty principle: incompatible set-selections. All the familiar structures of the formalism are transformed from postulates to inherent attributes of the class structure. The Born rule, unitary evolution, the complex structure of amplitudes, the probabilistic character of prediction, and the wave-mechanical form of the theory emerge as outputs of the ontology rather than independent axioms. The wavefunction is real. It is the ontological architecture of the metaworld and the reality of the quasi-classical world. The classical world, quantum mechanics and relativistic physics are unified in logical types.