Abstract
Given a qualitative scientific structure, a structure preserving mapping into a numerical, vectorial, or geometric structure is called a representation of it. Within such numerical, vectorial or geometric structures other concepts can always be defined. Some of these correspond to a qualitative property of the underlying system, and they are called ‘meaningful’ concepts. And others do not correspond to a qualitative property; and they are called ‘meaningless’. The article investigates precise meanings of ‘meaningfulness’ and ‘meaninglessness’ and their relation to several notions of invariance, some of which are widely used in science.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Aczél, J., and F.S. Roberts. 1989. On the possible merging functions. Mathematical Social Sciences 17: 205–243.
Aczél, J., F.S. Roberts, and Z. Rosenbaum. 1986. On scientific laws without dimensional constants. Journal of Mathematical Analysis and Applications 119: 389–416.
Falmagne, J.-C. 1985. Elements of psychophysical theory. New York: Cambridge University Press.
Falmagne, J.-C. 2004. Meaningfulness and order-invariance: Two fundamental principles for scientific laws. Foundations of Physics 34: 1341–1348.
Falmagne, J.-C., and L. Narens. 1983. Scales and meaningfulness of quantitative laws. Synthese 55: 287–325.
Klein, F. 1872. Vergleichende Betrachtungen iiber neuere geometrische Vorschungen: Programm zu Eintritt in die philosophische Facultät und den Senat der Universität zu Erlangen. Erlangen: Deichert.
Krantz, D.H., R.D. Luce, P. Suppes, and A. Tversky. 1971. Foundations of measurement. Vol. 1. New York: Academic Press.
Luce, R.D. 1959. On the possible psychophysical laws. Psychological Review 66 (2): 81–95.
Luce, R.D. 1964. A generalization of a theorem of dimensional analysis. Journal of Mathematical Psychology 1: 278–284.
Luce, R.D. 1978. Dimensionally invariant numerical laws correspond to meaningful qualitative relations. Philosophy of Science 45: 1–16.
Luce, R.D., D.H. Krantz, P. Suppes, and A. Tversky. 1990. Foundations of measurement. Vol. 3. New York: Academic.
Narens, L. 1981. A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision 13: 1–70.
Narens, L. 1985. Abstract measurement theory. Cambridge, MA: MIT Press.
Narens, L. 2002. Theories of meaningfulness. Mahwah: Lawrence Erlbaum and Associates.
Narens, L. 2007. Introduction to the theories of measurement and meaningfulness and the role of invariance in science. Mahwah: Lawrence Erlbaum and Associates.
Narens, L., and R.D. Luce. 1983. How we may have been misled into believing in the interpersonal comparability of utility. Theory and Decision 15: 247–260.
Pfanzagl, J. 1968. Theory of measurement. New York: Wiley. 2nd ed. Vienna: Physica, 1971.
Pickering, J.F., J.A. Harrison, and C.D. Cohen. 1973. Identification and measurement of consumer confidence: Methodology and some preliminary results. Journal of the Royal Statistical Society Series A 136: 43–63.
Roberts, F.S. 1980. On Luce’s theory of meaningfulness. Philosophy of Science 47: 424–433.
Roberts, F.S. 1985. Applications of the theory of meaningfulness to psychology. Journal of Mathematical Psychology 229: 311–332.
Roberts, F.S., and C.H. Franke. 1976. On the theory of uniqueness in measurement. Journal of Mathematical Psychology 14: 211–218.
Stevens, S.S. 1946. On the theory of scales of measurement. Science 103: 677–680.
Stevens, S.S. 1951. Mathematics, measurement and psychophysics. In Handbook of experimental psychology, ed. S.S. Stevens. New York: Wiley.
Suppes, P., and J.L. Zinnes. 1963. Basic measurement theory. In Handbook of mathematical psychology, ed. R.D. Luce, R.R. Bush, and E. Galanter, vol. 1. New York: Wiley.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Narens, L., Luce, R.D. (2018). Meaningfulness and Invariance. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_826
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_826
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences