Interpretation of Quantum Theory: the quantum "grue-bleen" problem

DeWitt described the many-worlds interpretation by stating that "The mathematical formalism of the quantum theory is capable of yielding its own interpretation." Can this be true? We introduce a general framework applicable to many kinds of dynamical theories, asking whether a system's state and time evolution alone can support non-trivial interpretational statements. For many theories, including both quantum mechanics and classical Hamiltonian mechanics, the answer is no. Wallace and others have noted the need for an additional "frame" structure to support even a many-worlds interpretation of quantum mechanics. We argue that such structure cannot (for example) have its origin in the dynamics of the system.