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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.

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