Extensive measurement and ratio functions

Synthese 75 (1):1 - 23 (1988)
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Abstract

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This is interpreted as involving arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement.

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Citations of this work

Properties.Francesco Orilia & Michele Paolini Paoletti - 2020 - Stanford Encyclopedia of Philosophy.
Quantitative Properties.M. Eddon - 2013 - Philosophy Compass 8 (7):633-645.
The origins of the representational theory of measurement: Helmholtz, Hölder, and Russell.Joel Michell - 1993 - Studies in History and Philosophy of Science Part A 24 (2):185-206.

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References found in this work

The metaphysics of quantity.Brent Mundy - 1987 - Philosophical Studies 51 (1):29 - 54.
Abstract Measurement Theory.Louis Narens - 1988 - Synthese 76 (1):179-182.

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