Extensive measurement without an order relation

Philosophy of Science 41 (4):361-373 (1974)

Abstract

This paper states two sets of axioms sufficient for extensive measurement. The first set, like previously published axioms, requires that each of the objects measured must be classifiable as either greater than, or less than, or indifferent to each other object. The second set, however, requires only that any two objects be classifiable as either indifferent or different, and does not need any information about which object is greater. Each set of axioms produces an extensive scale with the usual properties of additivity and uniqueness except for unit. Moreover, the axioms imply Weber's Law: whether two objects are indifferent depends only upon the ratio of their scale values

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References found in this work

A Set of Independent Axioms for Extensive Quantities.Patrick Suppes - 1951 - Portugaliae Mathematica 10 (4):163-172.
Extensive Measurement in Semiorders.David H. Krantz - 1967 - Philosophy of Science 34 (4):348-362.

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