D. Dieks has proposed a semantical rule which he claims yields a realistic interpretation of the formalism of quantum mechanics without the projection postulate. I argue that his proposal is unacceptable because it violates a natural requirement of psychophysical parallelism. His "semantical rule" is not an acceptable interpretive rule because it does not identify structures in the theory with structures in our experience, but postulates a merely probabilistic relationship between the two. Dieks' interpretation is contrasted with Everett's relative state interpretation, which attempts the same task but respects psychophysical parallelism.
This is an attempt to apply Nagel's distinction between internal and external statements to the interpretation of quantum mechanics. I propose that this distinction resolves the contradiction between unitary evolution and the projection postulate. I also propose a more empirically realistic version of the projection postulate. The result is a version of Everett's relative-state interpretation, including a proposal for how probabilities are to be understood. Based on a talk given at the 9th UK Foundations of Physics meeting in Birmingham on 12 September 2000.