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Quantity and Quality: Some Aspects of Measurement

Published online by Cambridge University Press:  28 February 2022

Arnold Koslow
Arnold Koslow*
Affiliation:
The Graduate School, C.U.N.Y., and Brooklyn College
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Extract

We shall not belabor the importance of having a clear idea of the difference between classificatory, comparative, and quantitative terms. Even though some of the goals that were set for theories of measurement of empirical attributes no longer seem viable, and some do not seem generally applicable, there is every reason to believe that suitable general goals for such theories will rely upon a distinction between quantitative and qualitative terms. The distinction seems also to have an intrinsic interest, even though some of the claims originally made for it, no longer seem historically accurate, or philosophically defensible. The subject, then, is quantitative terms in theories of the measurement of empirical attributes like length, mass, charge, and utility. We shall consider two problems.

Type
Part V. Measurement, Verisimilitude and Decision
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1982 , Issue 1: Volume One: Contributed Papers 1982 , 1982 , pp. 183 - 198
Copyright
Copyright © Philosophy of Science Association 1982

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Footnotes

1

This is part of a monograph. Quantity and Quality (Koslow 1982). Some of these results were prepared for a contribution to the Festschrift for Richard Bevan Braithwaite (Mellor 1980). Unfortunately, the paper reached the press a little too late for inclusion. This is but a small token of my gratitude and affection. I would also like to thank J.Barshay, H.Kyburg Jr.,D.T.Langendoen, D.Rosenthal, and R.Schwartz for some very helpful comments and discussions on earlier versions of this study. Although I cannot claim full credit for what is right in it, I do take full credit for any residual errors and shortcomings that still dog its pages.

References

Adams, E.W. et al. (1965). “A Theory of Appropriate Statistics.“ Psychometrika 30: 99–127.CrossRefGoogle ScholarPubMed
Adams, E.H. (1974). “Model-theoretic Aspects of Fundamental Measurement Theory.” In Proceedings of the Tarski Symposium. (Proceedings of Symposia in Pure Mathematics, Volume XXV.) Edited by Henkin, L., et al. Providence: American Mathematical Society. Pages 437–416.CrossRefGoogle Scholar
Campbell, N. (1921). What is Science. London: Methuen.Google Scholar
Carnap, R. (1926). Physikalische Begriffsbildung. Karlsruhe: Braun.Google Scholar
Carnap, R. (1950). Logical Foundations of Probability. London: Routledge and Kegan Paul.Google Scholar
Carnap, R. (1966). Philosophical Foundations of Physics. (ed.) Gardner, M., New York: Basic Books.Google Scholar
Cohen, R.S. and Elkana, I. (eds.). (1977). Hermann von Helmholtz: Epistemological Writings. (Boston Studies in the Philosophy of Science, Volume XXXVII.) Dordrecht: D. Reidel.Google Scholar
Helmholtz, H. von. (1887). “Zahlen und Messen Erkenntnistheoretisch Betrachtet.” In Philosophische Aufsätze, Eduard Zeller zu seinem fünfziglährigen Doctor-Jubiläum gewidmet. Leipzig: Fues’ Verlag. Pages 17–52. (As translated and reprinted as “Numbers and Measuring from an Epistemological Viewpoint.” In Cohen and Elkan. (1977). Pages 72-103.)Google Scholar
Hempel, C.G. and Oppenheim, P. (1936). Der Typusbegriff Im Lichte der Neuen Logik. Leiden: A.W. Sijthoff.Google Scholar
Hempel, C.G. and Oppenheim, P. (1952). Fundamentals of Concept Formation in Empirical Science. (International Encyclopedia of Unified Science, Volume II, Number 7.) Chicago: University of Chicago Press.Google Scholar
Hempel, C.G. and Oppenheim, P. (1958). “The Theoretician's Dilemma.” In Concepts, Theories, and the Mind-Body Problem. (Minnesota Studies in the Philosophy of Science. Volume II.) Edited by Feigl, H., et al. Minneapolis: University of Minnesota Press. Pages 37–98. (As reprinted in Aspects of Sclentifio Explanation. New York: The Free Press, 1965. Pages 173-226.)Google Scholar
Hempel, C.G. and Oppenheim, P. (1970). “On the ‘Standard Conception’ of Scientific Theories.” In Analyses of Theories and Methods of Physics and Psychology. (Minnesota Studies in the Philosophy of Science. Volume IV.) Edited by Radnor, M. and Winokur, S.. Minneapolis: University of Minnesota Press. Pages 142–163.Google Scholar
Hertz, P. (1977). “Notes and Comments.” In Cohen and Elkan. (1977). Pages 103–114.Google Scholar
Johnson, W.E. (1921). Logic, Demonstrative Inference; Deductive and Inductive. Part I. Cambridge: Cambridge University Press. (As reprinted New York: Dover, 1964.)Google Scholar
Koslow, A. (1965). Changes in the Concept of Mass, from Newton to Einstein. Unpublished Ph.D. Dissertation, Columbia University. Xerox University Microfilms Publication Number 65-9164.Google Scholar
Koslow, A. (1982). Quantity and Quality. (Unpublished manuscript).Google Scholar
Krantz, D. et al. (1971). Foundations of Measurement. Volume I. New York: Academic Press.Google Scholar
Kyburg, H.E. Jr., (1979). “Direct Measurement.” American Philosophical Quarterly 16: 259–272.Google Scholar
Luce, R.D. (1978). “Dimensionally Invariant Numerical Laws Correspond to Meaningful Qualitative Relations.” Philosophy of Science 45: 1–16.CrossRefGoogle Scholar
Maclaurin, C. (1748). An Account of Sir Isaac Newton's Philosophical Discoveries. London: Patrick Murdoch.Google Scholar
Mellor, D.H. (ed.). (1980). Science, Belief, and Behaviour: Festschrift for R.B. Braithwaite. Cambridge: Cambridge University Press.Google Scholar
Menger, K. (1959). “Mensuration and other Mathematical Connections of Observable Material.” In Measurement: Definitions and Theories. Edited by Churchman, C.W. and Ratoosh, P.. New York: Wiley. Pages 97–128.Google Scholar
Narens, L. (1981). “A General Theory of Ratio Scalability with Remarks about the Measurement-Theoretic Concept of Meaningfulness.” Theory and Decision 13: 1–70.CrossRefGoogle Scholar
Newton, Isaac. (1709-1713). The Correspondence of Isaac Newton Volume V: 1709-1713. (eds.) Hall, A.R. and Trilling, L.. Cambridge: Cambridge University Press, 1975.Google Scholar
Putnam, H. (1962). “What Theories are not.” In Logic, Methodology and Philosophy of Science. Edited by Nagel, E., et al. Stanford: Stanford University Press. Pages 240–251. (As reprinted in Mathematics. Matter, and Method, Volume I. New York: Cambridge University Press, 1975. Pages 215-217.)Google Scholar
Roberts, F.S. (1979). Measurement Theory, with Applications to Decision-Making, Utility, and the Social Sciences. Reading, Mass.: Addison-Wesley.Google Scholar
Roberts, F.S. (1980). “On Luce's Theory of Meaningfulness. “ Philosophy of Science 47: 424–433.CrossRefGoogle Scholar
Scott, D. and Suppes, P. (1958). “Foundational Aspects of Theories of Measurement.” The Journal of Symbolic Logic 23: 113–128. (As reprinted in Suppes (1969). Pages 46-64.)CrossRefGoogle Scholar
Suppes, P. (1951). “A Set of Independent Axioms for Extensive Quantities.” Portugaliae Mathematica 10: 163–172. (As reprinted in Suppes (1969). Pages 36-45)Google Scholar
Suppes, P. (1956). “The Role of Subjective Probability and Utility in Decision-Making.” In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954-1955. Pages 61-73. (As reprinted in Suppes (1969). Pages 87-104.)Google Scholar
Suppes, P. (1959). “Measurement, Empirical Meaningfulness, and Three-Valued Logic.” In Measurement: Definitions and Theories. Edited by Churchmann, C.W. and Ratoosh, P.. New York: Wiley. Pages 129–143. (As reprinted in Suppes (1969). Pages 65-80.)Google Scholar
Suppes, P. (1969). Studies in the Methodology and Foundations of Science. Selected Writings from 1951 to 1969. Dordrecht: Reidel.Google Scholar
Suppes, P. and Zinnes, J.L. (1963). “Basic Measurement Theory.” In Handbook of Mathematical Psychology Volume I. New York: Wiley. Pages 1–76.Google Scholar
von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. (As reprinted as Mathematical Foundations of Quantum Mechanics, (trans.) Beyer, R.T.. Princeton: Princeton University Press, 1955.)Google Scholar