Metrological legitimacy and the human sciences

When is it scientifically permissible to represent the outcome of an experiment numerically, such that algebraic manipulations of that representation are meaningful? This is the question of quantification. This article defends a particular answer to this question, namely: quantitative representation is permissible when numerical assignments uniquely specify invariant relationships between the outcomes of a contingent, well-defined procedure. I call this criterion metrological legitimacy as it answers the question of quantification by appealing to structural features of a measurement procedure, rather than the theoretical context in which it is embedded. This account builds on a long tradition of taking invariance to be the key criterion for the meaningfulness of scientific representations, drawing specific inspiration from the Representational Theory of Measurement. Nevertheless, it is novel insofar as it appeals to invariance over permissible alterations to a measurement procedure, rather than invariance over mathematical abstractions, models, or theories. It contributes to our understanding of the epistemic authority of measurement by showing how the structural features of a measurement procedure ensure its epistemic value, giving it a privileged position in the complex negotiation to cohere measurement and theory. The practical value of this criterion is illustrated by applying it to two contentious examples: magnitude estimation of loudness and early factor analytic measurements of intelligence.