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On Luce's Theory of Meaningfulness

Published online by Cambridge University Press:  01 April 2022

Fred S. Roberts
Fred S. Roberts*
Affiliation:
Rutgers University
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Abstract

This paper studies the theory of uniqueness of scales of measurement, and in particular, the theory of meaningfulness of statements using scales. The paper comments on the general theory of meaningfulness adopted by Luce in connection with his work on dimensionally invariant numerical laws. It comments on Luce's generalization of the concept of meaningfulness of a statement involving scales to a concept of meaningfulness of an arbitrary relation relative to the defining relations in a relational structure. It is argued that in studying the concept of meaningfulness, it is necessary to consider invariance under endomorphisms, not just automorphisms. The difference between the endomorphism and automorphism concepts of meaningfulness is studied. Luce's primary result, that automorphism meaningfulness is preserved under isomorphism, is extended to the result that endomorphism meaningfulness is preserved under homomorphism.

Type
Research Article
Information
Philosophy of Science , Volume 47 , Issue 3 , September 1980 , pp. 424 - 433
Copyright
Copyright © 1980 by Philosophy of Science Association

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Footnotes

†

The author thanks Carl Bredlau for his helpful comments.

References

Adams, E. W., Fagot, R. F., and Robinson, R. E. (1965), “A Theory of Appropriate Statistics,” Psychometrika 30: 99–127.CrossRefGoogle ScholarPubMed
Hays, W. L. (1973), Statistics for the Social Sciences. New York: Holt, Rinehart, Winston.Google Scholar
Luce, R. D. (1956), “Semiorders and a Theory of Utility Discrimination,” Econometrica 24: 178–191.CrossRefGoogle Scholar
Luce, R. D. (1967), “Remarks on the Theory of Measurement and its Relation to Psychology,” in Les Modèles et la Formalisation du Comportement, Paris: Editions du Centre National de la Recherche Scientifique.Google Scholar
Luce, R. D. (1978), “Dimensionally Invariant Numerical Laws Correspond to Meaningful Qualitative Relations,” Philosophy of Science 45: 1–16.CrossRefGoogle Scholar
Pfanzagl, J. (1968), Theory of Measurement. New York: Wiley.Google Scholar
Roberts, F. S. (1979a), Measurement Theory, with Applications to Decision-making, Utility, and the Social Sciences. Reading, Mass.: Addison-Wesley.Google Scholar
Roberts, F. S. (1979b), “Structural Modeling and Measurement Theory,” Technol. Forecast. Soc. Change 14: 353–365.CrossRefGoogle Scholar
Roberts, F. S., and Franke, C. H. (1976), “On the Theory of Uniqueness in Measurement,” J. Math. Psychol. 14: 211–218.CrossRefGoogle Scholar
Robinson, R. E. (1963), A Set-theoretical Approach to Empirical Meaningfulness of Empirical Statements. Tech. Rept. 55, Institute for Mathematical Studies in the Social Sciences, Stanford, California: Stanford University.Google Scholar
Scott, D., and Suppes, P. (1958), “Foundational Aspects of Theories of Measurement,” J. Symbolic Logic 23: 113–128.CrossRefGoogle Scholar
Stevens, S. S. (1968), “Measurement, Statistics, and the Schemapiric View,” Science 161: 849–856.CrossRefGoogle ScholarPubMed
Suppes, P. (1959), “Measurement, Empirical Meaningfulness, and Three-valued Logic,” in Churchman, C. W. and Ratoosh, P. (eds.), Measurement: Definitions and Theories, New York: Wiley, 129–143.Google Scholar
Suppes, P., and Zinnes, J. L. (1963), “Basic Measurement Theory,” in Luce, R. D., Bush, R. R., and Galanter, E. (eds.), Handbook of Mathematical Psychology, Vol. I, New York: Wiley, 1–76.Google Scholar