Advertisement

Synthese

, Volume 175, Issue 2, pp 123–149 | Cite as

Outline of a general model of measurement

  • Aldo Frigerio
  • Alessandro Giordani
  • Luca Mari
Article

Abstract

Measurement is a process aimed at acquiring and codifying information about properties of empirical entities. In this paper we provide an interpretation of such a process comparing it with what is nowadays considered the standard measurement theory, i.e., representational theory of measurement. It is maintained here that this theory has its own merits but it is incomplete and too abstract, its main weakness being the scant attention reserved to the empirical side of measurement, i.e., to measurement systems and to the ways in which the interactions of such systems with the entities under measurement provide a structure to an empirical domain. In particular it is claimed that (1) it is on the ground of the interaction with a measurement system that a partition can be induced on the domain of entities under measurement and that relations among such entities can be established, and that (2) it is the usage of measurement systems that guarantees a degree of objectivity and intersubjectivity to measurement results. As modeled in this paper, measurement systems link the abstract theory of measuring, as developed in representational terms, and the practice of measuring, as coded in standard documents such as the International Vocabulary of Metrology.

Keywords

Measurement Representational measurement theory Measurement systems Objectivity Intersubjectivity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birkhoff, G. (1948). Lattice theory (American Mathematical Society colloquium series, Vol. 25).Google Scholar
  2. Bridgman P. (1927) The logic of modern physics. Macmillan, New YorkGoogle Scholar
  3. Carnap R. (1966) Philosophical foundations of physics. Basic Books, Inc., New York–LondonGoogle Scholar
  4. Finkelstein L. (2003) Widely, strongly and weakly defined measurement. Measurement 34: 39–48. doi: 10.1016/S0263-2241(03)00018-6 CrossRefGoogle Scholar
  5. Finkelstein L. (2005) Problems of measurement in soft systems. Measurement 38: 267–274. doi: 10.1016/j.measurement.2005.09.002 CrossRefGoogle Scholar
  6. Hempel C.G. (1952) Fundamentals in concepts formation in physical sciences. University of Chicago Press, ChicagoGoogle Scholar
  7. Hempel C.G. (1965) Aspects of scientific explanation and other essays in the philosophy of science. Free Press, GlencoeGoogle Scholar
  8. JCGM. (2008a). JCGM 200:2008, International vocabulary of metrology—basic and general concepts and associated terms (VIM, 3rd ed.). Downloadable from http://www.bipm.org.
  9. JCGM. (2008b). JCGM 100:2008, Evaluation of measurement data—guide to the expression of uncertainty in measurement (GUM, 1995 with minor corrections). Downloadable from http://www.bipm.org.
  10. Krantz D.H., Luce R.D., Suppes P., Tversky A. (1971) Foundations of measurement (Vol. I). Academic Press, New YorkGoogle Scholar
  11. Kuhn T.S. (1961) The function of measurement in modern physical sciences. Isis 52: 161–193. doi: 10.1086/349468 CrossRefGoogle Scholar
  12. IEC. (2008). IEC 60050 series, and Electropedia (also known as the “International Electrotechnical Vocabulary (IEV) Online”). Retrieved from http://www.electropedia.org.
  13. Luce, R. D. Krantz. D. H., Suppes, P. & Tversky, A. (1990). Foundations of measurement (Vol. III). San Diego: Academic PressGoogle Scholar
  14. Mari L. (2003) Epistemology of measurement. Measurement 34: 17–30. doi: 10.1016/S0263-2241(03)00016-2 CrossRefGoogle Scholar
  15. Mari, L. (2007). Measurability. In M. Boumans (Ed.), Measurement in economics (pp. 41-77). Amsterdam, Elsevier.Google Scholar
  16. Narens L. (1985) Abstract measurement theory. Mass MIT Press, CambridgeGoogle Scholar
  17. Narens L. (2002) Theories of meaningfulness. Mahwah, NJ, Lawrence Erlbaum AssociatesGoogle Scholar
  18. Niederée R. (1992) What do numbers measure? A new approach to fundamental measurement. Mathematical Social Sciences 24: 237–276. doi: 10.1016/0165-4896(92)90063-B CrossRefGoogle Scholar
  19. Pfanzagl, J. (1968). Theory of measurement (2nd ed.). New York: Wiley (Vienna: Physica, 1971).Google Scholar
  20. Roberts J. (1979) Measurement theory. Addison-Wesley, Reading, MassGoogle Scholar
  21. Scott D., Suppes P. (1958) Foundational aspects of theories of measurement. Journal of Symbolic Logic 23: 13–128. doi: 10.2307/2964453 CrossRefGoogle Scholar
  22. Stevens S. (1946) On the theory of scales of measurement. Science 103: 677–680. doi: 10.1126/science.103.2684.677 CrossRefGoogle Scholar
  23. Suppes P. (2006) Transitive indistinguishability and approximate measurement with standard finite ratio-scale representations. Journal of Mathematical Psychology 50: 329–336CrossRefGoogle Scholar
  24. Suppes P., Krantz D.H., Luce R.D., Tversky A. (1990) Foundations of measurement (Vol. II). Academic Press, New YorkGoogle Scholar
  25. Suppes, P., & Zinnes, J. L. (1963). Basic measurement theory. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.). Handbook of mathematical psychology (Vol. 1, pp. 1–76). New York, Wiley.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Università cattolicaMilanItaly
  2. 2.Università Carlo CattaneoCastellanza (Mi)Italy

Personalised recommendations