  Correlation does not imply anything about the inner nature of the corresponding items. Contrast this with correspondence as isomorphism, which requires the corresponding items to have the same, or sufficiently similar, constituent structure. This aspect of correspondence, which is more prominent (and more notorious) than the previous one, is also much more difficult to make precise. Let us say, roughly, that a correspondence theorist may want to add a claim to her theory committing her to something like the following: