Our modelist might do better to focus on definitional equivalence instead of isomorphism (see Button & Walsh 2018: § §5.1-5.2); but this would not change the dialectic. 6 Button & Walsh (2018: ch.6) coined the term, and go into more detail. 7 The remainder of this section presents the central problem I extract from Putnam's (1980) invocation of the Löwenheim-Skolem Theorem. (Admittedly, Putnam raised the issue in a more "objectual" than "conceptual" key; but see footnote 1, above.) Dummett (1963: 192) raised a similar problem, focussing on Gödelian incompleteness. For more, see Button & Walsh (2018: ch.7). 45 Cf. Button (2013, 217). 46 Cf. Meadows (2013, 539-40). 47 Putnam (1980. 48 At this point, the modelist might start to say things like: maybe I don't even understand (at all) the worry that I am "trapped" in M! At that point, I feel we have earned the right to walk away from the modelist. Of course, there is more to say about such ineffable scepticism; but for more, see Button & Walsh (2018: ch.9, §11.6). 49 Cf. Button & Walsh (2018: §11.6) on "indefinite extensibility" in this context.