One important criterion for an acceptable physical theory is that its ontology and its epistemology be consonant: Namely, any concept defined within the theory as a physical observable should be accompanied by a prescription for its ideal measurement; and any limitations on the co-definability of a pair of such observables should be consistent with similar limitations on their co-measurability. Examples will be given from quantum mechanics, quantum electrodynamics, general relativity, and the search for quantum gravity.