Measurement Across the Sciences: Developing a Shared Concept System for Measurement
Luca Mari (Università Cattaneo–LIUC), Mark Wilson (UC Berkeley) and Andrew Maul (UC Santa Barbara) — Springer Cham, Springer Series in Measurement Science and Technology, 2nd edition, 26 February 2023, xxxix + 307 pages, open access under CC BY 4.0. Eight chapters. The book asks a question none of the corpus’s other texts asks: what makes a procedure a measurement at all, and can one answer cover both a thermometer and a reading-comprehension test.
It is the first source in this spoke that is not mathematics. That is stated plainly here because the routing is arguable — see measurement-theory and open question 7 in synthesis.
The argument
The authors build a shared concept system: a set of conditions that any measurement satisfies, derived rather than stipulated, then checked against cases from both sides of the physical/psychosocial divide. Their four necessary conditions (ch. 2) are that measurement is an empirical process, designed on purpose, whose input is a property of an object, and whose output is information in the form of values of that property. They present these as uncontroversial. The rest of the book is the harder work of finding sufficient conditions, and that is where it takes positions.
Two examples run the whole length of the book and are chosen to be maximally far apart: the temperature of a body, and a person’s reading-comprehension ability. Chapter 1 does something deliberately provocative with the pair — it applies a psychosocial measurement method to a physical case, to test whether the asymmetry people assume between the two is real or inherited.
Model-dependent realism (ch. 4) is the book’s philosophical commitment. The chapter lays out three existing positions — naive realism, operationalism, representationalism — and takes something from each while rejecting their strong forms: models are unavoidable in measurement, and models are models of something, so the empirical apparatus exists to make the result carry information about the intended property. Two “stereotypes” fall out of the analysis: that measurement is quantification (which hides the empirical half of the process), and that measurement transmits a preexisting true value (which hides the modelling half).
Chapters 5 and 6 are an ontology and epistemology of properties: what a property is, whether individual properties exist, what a value of a property is, and — the part with the most reach — what scale types are and whether non-quantitative properties can be measured at all. The treatment of quantities is constructive: additivity, reference quantities, scale transformations, then the two cases that break additivity (temperature; reading comprehension).
Chapter 7 assembles the pieces into a general model of the measurement process, distinguishing direct from indirect measurement (an indirect measurement contains at least one direct one) and introducing the Hexagon Framework for measurand identification, new to this edition. Its quality criteria are two: object-relatedness (“objectivity”) and subject-independence (“intersubjectivity”). Chapter 8 closes with a semiotic reading — indication values are syntactic information, measurement results are semantic, and results plus context are pragmatic information for a decision.
The part that changes how the rest of this corpus reads
Chapter 3 separates two ways of accounting for imperfect measurement, and the second edition’s headline addition (per the publisher’s description) is a direct comparison of them:
- The error / true-value approach: there is a true value, and what you have differs from it by an error.
- The uncertainty approach: the result is a set of values compatible with the measurand plus the available information, and metrological traceability to conventionally defined units is what makes it mean the same thing to different people in different places.
The physical sciences went with uncertainty. The human sciences went instead to validity — early conceptions, construct validity, argument-based and causal accounts (ch. 4.3) — which asks not how far off the number is but whether the procedure measures the thing it claims to. The book’s claim is that these are two answers to one question, and that neither field has read the other’s.
That bears directly on mathematical-statistics. Everything in Larsen & Marx and herzog-understanding-statistics starts after a number exists: given data, infer the mechanism. This book is about how the datum came to be a number and what has to be true for it to mean anything. The two are stacked, not parallel — and the stack has a gap in it, because nothing in the statistics texts asks whether the measurand was well defined.
Standing and limits
T1 — a peer-reviewed Springer monograph in an established series, second edition, three authors with standing in measurement science and psychometrics, fully open access under CC BY 4.0. That licence is worth naming: it is the corpus’s first unrestricted open-access book, more open than herzog-understanding-statistics (CC BY-NC) and than keisler-elementary-calculus or trench-real-analysis (both NC-SA). The free-licence pattern this spoke tracks now has its strongest instance.
Two limits. It is not a textbook — there are no exercises, no worked technique, and a reader cannot learn to measure anything from it; it is a conceptual analysis aimed at researchers and specialists. And it is a position, not a settled consensus: model-dependent realism is the authors’ proposal, the publisher’s own copy calls the approach “provocative”, and the corpus holds nothing arguing the other side. Read it as the strongest single statement of one program in measurement science, not as the field’s agreed account.
Related
measurement-theory · mathematical-statistics · herzog-understanding-statistics · probability-theory · luca-mari · mark-wilson · andrew-maul · mathematics