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Extensive Measurement Without an Order Relation

Published online by Cambridge University Press:  14 March 2022

Eric W. Holman
Eric W. Holman*
Affiliation:
University of California, Los Angeles
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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.

Type
Research Article
Information
Philosophy of Science , Volume 41 , Issue 4 , December 1974 , pp. 361 - 373
Copyright
Copyright © 1974 by The Philosophy of Science Association

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Footnotes

†

This work was supported by Grant GB-13588X from the National Science Foundation.

References

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