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Quantities, Magnitudes, and Numbers

Published online by Cambridge University Press:  01 April 2022

Henry E. Kyburg Jr.
Henry E. Kyburg Jr.*
Affiliation:
Departments of Philosophy and Computer Science, University of Rochester
*
†Send reprint requests to the author, Computer Science and Philosophy, University of Rochester, Rochester, NY 14627; e-mail kyburg@cs.rochester.edu
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Abstract

Quantities are naturally viewed as functions, whose arguments may be construed as situations, events, objects, etc. We explore the question of the range of these functions: should it be construed as the real numbers (or some subset thereof)? This is Carnap's view. It has attractive features, specifically, what Carnap views as ontological economy. Or should the range of a quantity be a set of magnitudes? This may have been Helmholtz's view, and it, too, has attractive features. It reveals the close connection between measurement and natural law, it makes dimensional analysis intelligible, and explains the concern of scientists and engineers with units in equations. It leaves the philosophical problem of the relation between the structure of magnitudes and the structure of the reals. What explains it? And is it always the same? We will argue that on the whole, construing the values of quantities as magnitudes has some advantages, and that (as Helmholtz seems to suggest in “Numbering and Measuring from an Epistemological Viewpoint”) the relation between magnitudes and real numbers can be based on foundational similarities of structure.

Type
Research Article
Information
Philosophy of Science , Volume 64 , Issue 3 , September 1997 , pp. 377 - 410
Copyright
Copyright © Philosophy of Science Association 1997

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Footnotes

‡

Some of this research was done with the support of grant IRI-9411267 from the National Science Foundation.

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