Elements of a theory of inexact measurement

Philosophy of Science 32 (3/4):205-228 (1965)
Abstract
Modifications of current theories of ordinal, interval and extensive measurement are presented, which aim to accomodate the empirical fact that perfectly exact measurement is not possible (which is inconsistent with current theories). The modification consists in dropping the assumption that equality (in measure) is observable, but continuing to assume that inequality (greater or lesser) can be observed. The modifications are formulated mathematically, and the central problems of formal measurement theory--the existence and uniqueness of numerical measures consistent with data--are re-examined. Some results also are given on a problem which does not arise in current theories: namely that of determining limits of accuracy attainable on the basis of observations.
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DOI 10.1086/288044
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A Hundred Years of Numbers. An Historical Introduction to Measurement Theory 1887–1990.JoséA Díez - 1997 - Studies in History and Philosophy of Science Part A 28 (1):167-185.
Even-Chance Lotteries in Social Choice Theory.Peter C. Fishburn - 1972 - Theory and Decision 3 (1):18-40.
A Hundred Years of Numbers. An Historical Introduction to Measurement Theory 1887–1990.JoséA Díez - 1997 - Studies in History and Philosophy of Science Part A 28 (2):237-265.

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