Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T00:13:42.624Z Has data issue: false hasContentIssue false
  • English
  • Français

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 [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

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

References

Berka, Karel. Measurement: Its Concepts, Theories and Problems. Reidel, Dordrecht, 1983.10.1007/978-94-009-7828-7_2CrossRefGoogle Scholar
Birkhoff, Garrett. Hydrodynamics: a Study in Logic, Fact, and Similitude. Princeton University Press, Princeton, 1960.Google Scholar
Bridgman, Percy W. Dimensional Analysis. Yale University Press, New Haven, 1963.Google Scholar
Campbell, Norman R. An Account of the Principles of Measurement and Calculation. Longmans, New York, 1928.Google Scholar
Carnap, Rudolf. The Logical Foundations of Probability. University of Chicago Press, Chicago, 1950.Google Scholar
Carnap, Rudolf. Philosophical Foundations of Physics. Basic Books, New York, 1966.Google Scholar
Causey, Robert L. Derived measurement and the foundations of dimensional analysis. Technical report, University of Oregon, Eugene Oregon, 1967.Google Scholar
Ellis, Brian. Basic Concepts of Measurement. Cambridge University Press, Cambridge, 1968.Google Scholar
Helmholtz, H. Von. Numbering and measuring from an epistemological viewpoint. In Cohen and Elkana (eds.), Epistemological Writings. Reidel, Dordrecht, 1977.10.1007/978-94-010-1115-0CrossRefGoogle Scholar
Hempel, Carl G. Fundamentals of Concept Formation in Empirical Science. University of Chicago Press, Chicago, 1952.Google Scholar
Hempel, Carl G. Philosophy of Natural Science. Prentice-Hall; Englewood Cliffs, N.J. 1966.Google Scholar
Krantz, David H., Luce, R. Duncan, Suppes, Patrick, and Tversky, Amos. Foundations of Measurement, vol I. Academic Press, New York and London, 1971.Google Scholar
Kyburg, Henry E., Jr, . Theory and Measurement. Cambridge University Press, Cambridge, 1984.Google Scholar
Kyburg, Henry E., Jr, . Theories as mere conventions. In Wade Savage (ed.), Scientific Theories, volume XIV, pp. 158–174. University of Minnesota Press, Minneapolis, 1990.Google Scholar
Luce, R. Duncan, Krantz, David H., Suppes, Patrick, and Tversky, Amos. Foundations of Measurement, vol HI. Academic Press, New York and London, 1990.Google Scholar
Margenau, Henry and Murphy, George. The Mathematics of Physics and Chemistry. Van Nostrand, Princeton, 1956.Google Scholar
Massey, B. S. Measures in Science and Engineering. Ellis Horwood, Chichester, 1986.Google Scholar
Mayo, Deborah. Error and the Growth of Experimental Knowledge. University of Chicago Press, Chicago, 1996.10.7208/chicago/9780226511993.001.0001CrossRefGoogle Scholar
Nagel, Ernest. Measurement. In Arthur Danto and Sidney Morgenbesser (eds.), Philosophy of Science, pp. 121–140. Meridian Books, New York, 1960.Google Scholar
Palacios, J. Dimensional Analysis. Macmillan, London, 1964.Google Scholar
Roberts, Fred S. Measurement Theory. Addison-Wesley, Reading, 1979.Google Scholar
Sedov, L. I. Similarity and Dimensional Methods in Mechanics. Academic Press, New York, 1959.Google Scholar
Stevens, S. S. On the theory of scales of measurement. Science Science: 103–677, 1946.Google Scholar
Stevens, S. S. Mathematics, measurement, and psychophysics. in Stevens, S. S. (ed.), Handbook of Experimental Psychology, pp. 1–49. John Wiley, New York, 1951.Google Scholar
Suppes, Patrick, Krantz, David H., Luce, R. Duncan, and Tversky, Amos. Foundations of Measurement, vol II. Academic Press, New York and London, 1989.Google Scholar
Whitney, H. The mathematics of physical quantities. part i: Mathematical models for measurement. part ii: Quantity structures and dimensional analysis. American Mathematical Monthly 75, 1968.Google Scholar