 While their stance towards operationalism and conventionalism is largely critical, realists are more charitable in their assessment of mathematical theories of measurement. Brent Mundy (1987) and Chris Swoyer (1987) both accept the axiomatic treatment of measurement scales, but object to the empiricist interpretation given to the axioms by prominent measurement theorists like Campbell (1920) and Ernest Nagel (1931; Cohen and Nagel 1934: Ch. 15). Rather than interpreting the axioms as pertaining to concrete objects or to observable relations among such objects, Mundy and Swoyer reinterpret the axioms as pertaining to universal magnitudes, e.g., to the universal property of being 5 meter long rather than to the concrete instantiations of that property. This construal preserves the intuition that statements like “the size of x is twice the size of y” are first and foremost about two sizes, and only derivatively about the objects x and y themselves (Mundy 1987:  34).[15]  Mundy and Swoyer argue that their interpretation is more general, because it logically entails all the first-order consequences of the empiricist interpretation along with additional, second-order claims about universal magnitudes. Moreover, under their interpretation measurement theory becomes a genuine scientific theory, with explanatory hypotheses and testable predictions. Building on this work, Jo Wolff (2020a) has recently proposed a novel realist account of quantities that relies on the Representational Theory of Measurement. According to Wolff’s structuralist theory of quantity, quantitative attributes are relational structures. Specifically, an attribute is quantitative if its structure has translations that form an Archimedean ordered group. Wolff’s focus on translations, rather than on specific relations such as concatenation and ordering, means that quantitativeness can be realized in multiple ways and is not restricted to extensive structures. It also means that being a quantity does not have anything special to do with numbers, as both numerical and non-numerical structures can be quantitative.