Interpretation of quantum theory: the quantum "grue-bleen" problem

We present a critique of the many-world interpretation of quantum mechanics, based on different ``pictures'' that describe the time evolution of an isolated quantum system. Without an externally imposed frame to restrict these possible pictures, the theory cannot yield non-trivial interpretational statements. This is analogous to Goodman's famous ``grue-bleen'' problem of language and induction. Using a general framework applicable to many kinds of dynamical theories, we try to identify the kind of additional structure (if any) required for the meaningful interpretation of a theory. We find that the ``grue-bleen'' problem is not restricted to quantum mechanics, but also affects other theories including classical Hamiltonian mechanics. For all such theories, absent external frame information, an isolated system has no interpretation.