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An Alternative “Fundamental” Axiomatization of Multiplicative Power Relations Among Three Variables

Published online by Cambridge University Press:  14 March 2022

A. A. J. Marley
A. A. J. Marley*
Affiliation:
University of Alberta, Edmonton
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Abstract

Suppose that the axioms of conjoint measurement hold for quantities having two independent components and that the axioms of extensive measurement hold for each of these components separately. In a recent paper, Luce shows that if a certain axiom relates the two measurement systems, then the conjoint measure on each component is a power function of the extensive measure on that component. Luce supposes that each component set contains all “rational fractions” of each element in that set; in this note we present an alternative form of the axiom relating the measurement systems that enables us to prove Luce's result without requiring that such “rational fractions” exist.

Type
Research Article
Information
Philosophy of Science , Volume 35 , Issue 2 , June 1968 , pp. 185 - 186
Copyright
Copyright © 1968 The Philosophy of Science Association

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Footnotes

1

This research was performed while the author was a Fellow of the Miller Institute for Basic Research in Science, University of California, Berkeley.

References

[1] Luce, R. D., ‘A “fundamental” axiomatization of multiplicative power relations among three variables,‘ Philosophy of Science, vol. 32, 1965, pp. 301–309.10.1086/288054CrossRefGoogle Scholar
[2] Luce, R. D. and Tukey, J. W., ‘Simultaneous conjoint measurement: a new type of fundamental measurement,‘ Journal of Mathematical Psychology, vol. 1, 1964, pp. 1–27.CrossRefGoogle Scholar
[3] Suppes, P., ‘A set of independent axioms for extensive quantities.‘ Portugaliae Mathematica, vol. 10, 1951, pp. 163–172.Google Scholar