Axiomatic measurement theories are commonly interpreted as claiming that, in order to quantify an empirical domain, the qualitative structure of data about that domain must be mapped to a numerical structure. Such mapping is supposed to be established independently, i.e., without presupposing that the domain can be quantified. This interpretation is based on two myths: that it is possible to independently infer the qualitative structure of objects from empirical data, and that the adequacy of numerical representations can only be justified (...) by mapping such qualitative structures to numerical ones. I dispel the myths and show that axiomatic measurement theories provide an inadequate characterization of the kind of evidence required to detect quantities. (shrink)

The development of nineteenth-century geodetic measurement challenges the dominant coherentist account of measurement success. Coherentists argue that measurements of a quantity are epistemically successful if their numerical outcomes converge across varying contextual constraints. Aiming at numerical convergence, in turn, offers an operational aim for scientists to solve problems of coordination. Geodesists faced such a problem of coordination between two indicators of the earth’s ellipticity, which were both based on imperfect ellipsoid models. While not achieving numerical convergence, their measurements produced novel (...) data that grounded valuable theoretical hypotheses. Consequently, they ought to be regarded as epistemically successful. This insight warrants a dynamic revision of coherentism, allowing to judge the success of a metric based on both its coherence and fruitfulness. On that view, scientific measurement aims to coordinate theoretical definitions and produce novel data and theoretical insights. (shrink)

There is a widely held view on measurement inferences, that goes back to Stevens’s ([1946]) theory of measurement scales and ‘permissible statistics’. This view defends the following prohibition: you should not make inferences from averages taken with ordinal scales (versus quantitative scales: interval or ratio). This prohibition is general—it applies to all ordinal scales—and it is sometimes endorsed without qualification. Adhering to it dramatically limits the research that the social and biomedical sciences can conduct. I provide a Bayesian analysis of (...) this inferential problem, determining when measurements from ordinal scales can be used to confirm hypotheses about relative group averages. The prohibition, I conclude, cannot be upheld, even in a qualified sense. The beliefs needed to make average comparisons are less demanding than those appropriate for quantitative scales. I illustrate with the alleged paradigm ordinal scale, Mohs’ scale of mineral hardness, arguing that the literature has mischaracterized it. (shrink)