 Perhaps the most avid supporter of isomorphism and embedding as the way to understand theory interpretation is van Fraassen. In a nutshell, if we distinguish (i) theoretical models, (ii) “empirical substructures” (van Fraassen 1980, 64, 1989, 227; alternatively: “surface models” 2008, 168), and (iii) “observable phenomena” (1989, 227, 2008, 168), then, van Fraassen argues, theory interpretation is a relation of isomorphism between observable phenomena and empirical substructures, which are themselves isomorphic with one or more theoretical models. Moreover, if a relation of isomorphism holds between \(X\) and a richer \(Y\), we say that we have embedded \(X\) in \(Y\). For instance, with respect to the seven-point geometry above (Figure 1), van Fraassen contends that isomorphism gives embeddability, and that the relation of isomorphism “is important because it is also the exact relation a phenomenon bears to some model or theory, if that theory is empirically adequate” (1989, 219–20; this kind of statement seems to be simultaneously descriptive and prescriptive about scientific representation, see Section 1.1 above). In The Scientific Image he is even clearer about fleshing out the empirical adequacy of a theory (with its theoretical models) in terms of isomorphism between “appearances” (i.e., “the structures which can be described in experimental and measurement reports,” 1980, 64, italics removed) and empirical substructures. Speaking metaphorically,