There Is More to Measurement than Just Measurement: Measurement Theory, Symmetry, and Substantive Theorizing. Review of Foundations of Measurement. Vol. 3: Representation, Axiomatization, and Invariance, by R. Duncan Luce, David H. Krantz, Patrick Suppes, and Amos Tversky

Abstract

R. Duncan Luce is Distinguished Professor of Cognitive Sciences and Economics, and Director of the Institute for Mathematical Behavioral Sciences at the University of California, Irvine; Victor S. Thomas Professor of Psychology Emeritus at Harvard University; and recipient of the American Psychological Association's (APA's) Distinguished Scientific Contribution Award: his most recent book is Sound and Hearing: A Conceptual Introduction. David H. Krantz is Professor of Psychology at Columbia University with one major research interest being measurement issues in vision. Patrick Suppes is Professor of Philosophy, Statistics, Education, and Psychology at Stanford University; Past President of Computer Curriculum Corporation, and recipient of the APA's Distinguished Scientific Contribution Award. His most recent book is Models and Methods in the Philosophy of Science: Selected Essays. Amos Tversky is Davis-Brack Professor of Behavioral Science at Stanford University and a Permanent Fellow of the Sackler Institute for Advanced Study at Tel Aviv University: a recipient of the APA's Distinguished Scientific Contribution Award and of the McArthur prize; and he is a coeditor, with Daniel Kahneman and Paul Slovic of Judgment Under Uncertainty: Heuristics and Biases. Reinhard Niederée is wissenschaftlicher Assistent at the Institut für Psychology at the University of Kiel. He received his Ph.D. in logic at the University of Bonn in 1990. His research interests include measurement theory, visual perception, and philosphy of mind and of science. Centered around a review of Volume 3 of the Foundations of Measurement series, the present paper discusses a number of basic issues, problems, and recent developments in the axiomatic-representational theory of measurement. These topics include measurement theory as a tool for the development and qualitative analysis of substantive theories; the role of "higher order axioms" such as Archimedeaness or symmetry assumptions in this connection; Narens' and Alper's qualitative characterization of scale types; nonadditive representations; measurement-theoretic concepts of "meaningfulness" (including meaningfulness issues in inferential statistics); axiomatizability issues; testability and empirical content of measurement-theoretic concepts of "meaningfulness" (including meaningfulness issues in inferential statistics); axiomatizability issues; testability and empirical content of measurement-theoretic axioms and the error problem; the construction of scales, measurement procedures, and the role of numbers as values of measurement. The paper attempts to provide a unifying coherent perspective that takes into account important aspects of the criticism found in the non-representational literature on measurement, and it strives for a clarification of some controversial issues, notably in the context of "meaningfulness."