Faithful representation, physical extensive measurement theory and archimedean axioms

Synthese 70 (3):373 - 400 (1987)
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Abstract

The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong extensive measurement, in the sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom.

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Citations of this work

Survey article. Listening to fictions: A study of fieldian nominalism.Fraser MacBride - 1999 - British Journal for the Philosophy of Science 50 (3):431-455.
On the possibility of science without numbers.Chris Mortensen - 1998 - Australasian Journal of Philosophy 76 (2):182 – 197.

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Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
The scientific image.C. Van Fraassen Bas - 1980 - New York: Oxford University Press.
The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.
Physics: The Elements.N. R. Campbell - 1921 - Mind 30 (118):207-214.

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