An alternative "fundamental" axiomatization of multiplicative power relations among three variables

Philosophy of Science 35 (2):185-186 (1968)
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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



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A set of independent axioms for extensive quantities.Patrick Suppes - 1951 - Portugaliae Mathematica 10 (4):163-172.

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