Two Myths of Representational Measurement

Perspectives on Science 29 (6):701-741 (2021)
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Abstract

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.

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Eran Tal
McGill University

References found in this work

The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
Sense and reference.Gottlob Frege - 1948 - Philosophical Review 57 (3):209-230.
Calibration: Modelling the measurement process.Eran Tal - 2017 - Studies in History and Philosophy of Science Part A 65:33-45.
The metaphysics of quantity.Brent Mundy - 1987 - Philosophical Studies 51 (1):29 - 54.

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