The Conventionality of Real Valued Quantities

The original architects of the representational theory of measurement interpreted their formalism operationally and explicitly acknowledged that some aspects of their representations are conventional. In this paper we argue that the conventional elements of the representations afforded by the theory require careful scrutiny as one moves toward a more metaphysically robust interpretation by showing that there is a sense in which the very number system one uses to represent a physical quantity such as mass or length is conventional. This result undermines inferences which impute structure from the numerical representational structure to the quantity it is used to represent.