Mathematical measurement, i.e. the concept of a measurable function, and hence, the concept of probability, are not empirical issues. The measurement issue in empirical sciences is empirical, as it matters with theory and the world as far as we can name it, or with experience if one does not want to engage in metaphysical ontology. It follows that one cannot consistently claim that the mathematical meaning of the word “measurement” suffices to enable one to juge whether empirical measurement has been achieved in a given area of observables; as what is needed is empirical testing, not only definitions. Use at least one testable theory of measurement before claiming that measurement has been achived in a certain psychological area. (See here for an example of a testable theory of measurement, and my comment on Stevens’ approach to measurement here).