Open Access

The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective: (Invited Article)

Batitsky, V. (1998). Empiricism and the myth of fundamental measurement. Synthese, 116, 51-73.10.1023/A:1005016725551Search in Google Scholar

Batitsky, V. (2002). Some measurement-theoretic concerns about Hale's "Reals by Abstraction". Philosophia Mathematica, 10 (3), 286-303.10.1093/philmat/10.3.286Search in Google Scholar

Batitsky, V., Domotor, Z. (2007). When good theories make bad predictions. Synthese, 157, 79-103.10.1007/s11229-006-9033-0Search in Google Scholar

Beltramenti, E. G., Cassinelli, G. (1981). The Logic of Quantum Mechanics. Reading, Massachusetts: Addison-Wesley.Search in Google Scholar

Benatti, F., Cappellini, V. (2005). Continuous limit of discrete sawtooth maps and its algebraic framework. Journal of Mathematical Physics, 46, 062702, 1-26.10.1063/1.1917283Search in Google Scholar

Bratelli, O., Robinson, D. W. (1987). Operator Albebras and Quantum Statistical Mechanics: Volume 1. New York: Springer.10.1007/978-3-662-02520-8Search in Google Scholar

Campbell, N. R. (1920). Physics: The Elements. Cambridge: Cambridge University Press.Search in Google Scholar

Carnap, R. (1966). Philosophical Foundations of Physics. New York: Basic Books.Search in Google Scholar

de Groote, H. F. (2005). Observables. arXiv:math-ph/0507.019.Search in Google Scholar

Domotor, Z., Stelzer, J. (1971). Representation of finitely additive semiordered qualitative probability structures. Journal of Mathematical Psychology, 8, 145-158.10.1016/0022-2496(71)90010-1Search in Google Scholar

Döring, A. (2005). Observables as functions: Antonymous functions. arXiv:math-ph/0510.102.Search in Google Scholar

Döring, A., Isham, C. J. (2008). A topos foundation for theories of physics: I. Formal languages for physics. Journal of Mathematical Physics, 49, 0053515, 1-25.10.1063/1.2883740Search in Google Scholar

Gelfand, I. M. (1939). On normed rings. Doklady Akademii Nauk U. S. S. R, 23, 430-432.Search in Google Scholar

González, J. A. N., de Salas J. B. S. (2003). C∞-Differentiable Spaces. Lecture Notes in Mathematics, No. 1824. New York: Springer.10.1007/b13465Search in Google Scholar

von Helmholtz, H. (1887). Zählen und Messen erkenntnistheoretisch Betrachtet. In Philosophische Aufsätze Eduard Zeller gewidmet. Leibzig: Fuess.Search in Google Scholar

Hilbert, D. (1899). Grundlagen der Geometrie. In Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen. Leibzig: Teubner, 1-92.Search in Google Scholar

Hölder, O. (1901). Die Axiome der Quantität und die Lehre vom Mass. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig: Mathematisch-Physische Klasse, 53, 1-64.Search in Google Scholar

Krantz, D. H. (1968). A survey of measurement theory. In Danzig, G. B., Veinott, A. F. (eds.) Mathematics of the Decision Sciences: Part 2. Providence, RI: American Mathematical Society, 314-350.Search in Google Scholar

Krantz, D. H., Luce, D., Suppes, P., Tversky, A. (1971). Foundations of Measurement: Volume 1. New York: Academic Press.Search in Google Scholar

Kyburg, H. E. (1997). Quantities, magnitudes and numbers. Philosophy of Science, 64, 377-411.10.1086/392558Search in Google Scholar

Larsen, R. (1973). Banach Algebras. An Introduction. New York: Dekker.Search in Google Scholar

Luce, D., Marley, A. A. J. (1969). Extensive measurement when concatenation is restricted and maximal elements may exist. In Morgenbesser, S., Suppes, P., White, M. (eds.) Philosophy, Science, and Method: Essays in Honor of Ernest Nagel. New York: St. Martin Press, 235-249.Search in Google Scholar

Luce, D., Narens L. (1994). Fifteen problems concerning the representational theory of measurement. In Humphreys, P. (ed.) Patrick Suppes: Scientific Philosopher. Volume 2. Kluwer Academic Publishers, 219-249.10.1007/978-94-011-0776-1_9Search in Google Scholar

Luce, D., Suppes P. (2002). Representational measurement theory. In Wixted, J., Pashler, H. (eds.) Stevens' Handbook of Experimental Psychology: Volume 4. New York: Wiley, 1-41.10.1002/0471214426.pas0401Search in Google Scholar

Mari, L. (2000). Beyond the representational viewpoint: A new formalization of measurement. Measurement, 27, 71-84.10.1016/S0263-2241(99)00055-XSearch in Google Scholar

Mundy, B. (1987). Faithful representation, physical extensive measurement theory and Archimedean axioms. Synthese, 70, 373-400.10.1007/BF00414156Search in Google Scholar

Narens, L. (1985). Abstract Measurement Theory. Cambridge: MIT Press.Search in Google Scholar

Nassopoulos, G. F. (1999). On a comparison of real with complex involutive complete algebras. Journal of Mathematical Sciences, 36, 3755-3765.10.1007/BF02172669Search in Google Scholar

Stevens, S. S. (1951). Mathematics, measurement and psychophysics. In Stevens, S. S. (ed.) Handbook of Experimental Psychology. New York: Wiley, 1-49.Search in Google Scholar

Pfanzagl, J. (1968). Theory of Measurement. New York: Wiley.Search in Google Scholar

Sontag, E. D. (1990). Mathematical Control Theory. New York: Springer.10.1007/978-1-4684-0374-9Search in Google Scholar

Suppes, P. (1969). Studies in the Methodology and Foundations of Science. Boston: D. Reidel.10.1007/978-94-017-3173-7Search in Google Scholar

Suppes, P. (1969a). A set of independent axioms for extensive quantities. In Suppes (1969).10.1007/978-94-017-3173-7_3Search in Google Scholar

Suppes, P., Zinnes, J. (1963). Basic measurement theory. In Luce, R. D. et al. (eds.) Handbook of Mathematical Psychology: Volume 1. New York: Wiley, 3-76.Search in Google Scholar

Suppes, P., Krantz, D. H., Luce, D., Tversky, A. (1989). Foundations of Measurement: Volume 2. New York: Academic Press.Search in Google Scholar

van Fraassen, B. (1980). The Scientific Image. New York: Oxford University Press.10.1093/0198244274.001.0001Search in Google Scholar

eISSN:
1335-8871
Language:
English
Publication timeframe:
6 times per year
Journal Subjects:
Engineering, Electrical Engineering, Control Engineering, Metrology and Testing