The Philosophical Significance of the Representational Theory of Measurement —RTM as Semantic Foundations
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Abstract
The Representational Theory of Measurement (RTM), especially the canonical three volume Foundations of Measurement by Krantz et al., is a landmark accomplishment in our understanding of measurement. Despite this, it has been far from easy to pinpoint what exactly we can learn about measurement from RTM, and who the target audience for RTM’s formal results should be. In what sense does RTM provide foundations of measurement, and what is the philosophical significance of such foundations? I argue that RTM provides semantic foundations of measurement, and that their philosophical significance lies in a shift towards structural representation.
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Wolff, J. (2023). The Philosophical Significance of the Representational Theory of Measurement —RTM as Semantic Foundations. Crítica. Revista Hispanoamericana De Filosofía, 55(163), 81–107. https://doi.org/10.22201/iifs.18704905e.2023.1409
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References
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Wigner, Eugene, 1960, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, Communications in Pure and Applied Mathematics, vol. 13, no. 1, p. 9.
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https://doi.org/10.1016/j.shpsa.2018.12.002.
Benacerraf, Paul, 1965, “What Numbers Could Not Be”, The Philosophical Review, vol. 74, no. 1, pp. 47–73.
Berka, Karel, and Augustin Riska, 1983, Measurement: Its Concepts, Theories and Problems, D. Reidel Publishing Company, Dordrecht, Holland.
Brandom, Robert B., 1998, Making It Explicit: Reasoning, Representing, and Discursive Commitment, Harvard University Press, Cambridge, MA.
Campbell, Norman Robert, 1920, Physics: The Elements, Cambridge University Press, Cambridge.
Carnap, Rudolf, 1966, Philosophical Foundations of Physics, edited by Martin Gardner, Basic Books, New York.
Chang, Hasok, 2004, Inventing Temperature: Measurement and Scientific Progress, Oxford University Press, Oxford/New York.
Cliff, Norman, 1992, “Abstract Measurement Theory and the Revolution That Never Happened”, Psychological Science, vol. 3, no. 3, pp. 186-190.
Díez, José A., 1997a, “A Hundred Years of Numbers. An Historical Introduction to Measurement Theory 1887–1990: Part I: The Formation Period. Two Lines of Research: Axiomatics and Real Morphisms, Scales and Invariance”, Studies in History and Philosophy of Science Part A, vol. 28, no. 1, pp. 167–185.
Díez, José A., 1997b, “A Hundred Years of Numbers. An Historical Introduction to Measurement Theory 1887–1990: Part II: Suppes and the Mature Theory. Representation and Uniqueness”, Studies in History and Philosophy of Science Part A, vol. 28, no. 2, pp. 237–265.
Forrest, Peter, and David M. Armstrong, 1987, “The Nature of Number”, Philosophical Papers, vol. 16, no. 3, pp. 165–186.
https://doi.org/10.1080/05568648709506275.
French, Steven, 2014, The Structure of the World: Metaphysics and Representation, Oxford University Press, Oxford.
Frigerio, Aldo, Alessandro Giordani, and Luca Mari, 2010, “Outline of a General Model of Measurement”, Synthese, vol. 175, no. 2, pp. 123–149.
https://doi.org/10.1007/s11229-009-9466-3.
Goodman, Nelson, 1976, Languages of Art: An Approach to a Theory of Symbols, Hackett, Indianapolis.
Heilmann, Conrad, 2015, “A New Interpretation of the Representational Theory of Measurement”, Philosophy of Science, vol. 82, no. 5, pp. 787-797.
Isaac, Alistair M.C., 2013, “Objective Similarity and Mental Representation”, Australasian Journal of Philosophy, vol. 91, no. 4, pp. 683–704.
https://doi.org/10.1080/00048402.2012.728233.
Krantz, David H., R. Duncan Luce, Patrick Suppes, and Amos Tversky [1971] 2007, Foundations of Measurement I: Additive and Polynomial Representations, vol. 1, Mineola, New York/Dover.
Krantz, David H., R. Duncan Luce, Patrick Suppes, and Amos Tversky, 1971, Foundations of Measurement, Academic Press, New York.
Kyburg Jr., and E. Henry, 1990, Science and Reason, Oxford University Press, New York.
Ladyman, James, 1998, “What Is Structural Realism?”, Studies in History and Philosophy of Science, vol. 29, no. 3, pp. 409–424.
Luce, R. Duncan, David H. Krantz, Patrick Suppes, and Amos Tversky [1990] 2007, Foundations of Measurement 3: Representation, Axiomatization, and Invariance, vol. 3, Mineola, New York/Dover.
Maxwell, Grover, 1971, “Structural Realism and the Meaning of Theoretical Terms”, Minnesota Studies in Philosophy of Science, vol. 4, pp. 181-192.
Michell, Joel, 1999, Measurement in Psychology – Critical History of a Methodological Concept, Cambridge University Press, Cambridge, UK.
Narens, Louis [2002] 2012, Theories of Meaningfulness, Psychology Press, Taylor & Francis Group, New York.
Redhead, Michael, 2003, “The Interpretation of Gauge Symmetry”, in Katherine Brading and Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections, Cambridge University Press, Cambridge.
Savage, C. Wade, and Philip Ehrlich (eds.), 1992, Philosophical and Foundational Issues in Measurement Theory, Lawrence Erlbaum Associates Inc., Hillsdale, New Jersey.
Shapiro, Stewart, 2000, Thinking about Mathematics, Oxford University Press, Oxford/New York.
Shapiro, Stewart, 1997, Philosophy of Mathematics: Structure and Ontology, Oxford University Press, Oxford/New York.
Sider, Theodore, 2011, Writing the Book of the World, Oxford University Press, Oxford.
Stevens, Stanley Smith, 1946, “On the Theory of Scales of Measurement”, Science, vol. 103, no. 2684, pp. 677–680.
Suárez, Mauricio, 2004, “An Inferential Conception of Scientific Representation”, Philosophy of Science, vol. 71, no. 5, pp. 767–779.
Suárez, Mauricio, 2003, “Scientific Representation: Against Similarity and Isomorphism”, International Studies in the Philosophy of Science, vol. 17, no. 3, pp. 225–244.
https://doi.org/10.1080/0269859032000169442.
Suppes, Patrick, 2002, Representation and Invariance of Scientific Structures, CSLI Publications, Stanford.
Suppes, Patrick, 1969, “Models of Data”, in Studies in the Methodology and Foundations of Science, Springer, pp. 251–261.
Suppes, Patrick, David H. Krantz, R. Duncan Luce, and Amos Tversky [1989] 2007, Foundations of Measurement 2: Geometrical, Threshold, and Probabilistic Representations, vol. II, Mineola, New York/Dover.
Tal, Eran, 2021, “Two Myths of Representational Measurement”, Perspectives on Science, vol. 29, no. 6, pp. 701–741.
van Fraassen, Bas C., 2008, Scientific Representation: Paradoxes of Perspective, Oxford University Press, Oxford/New York.
Wigner, Eugene, 1960, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, Communications in Pure and Applied Mathematics, vol. 13, no. 1, p. 9.
Wolff, J.E., 2020, The Metaphysics of Quantities, Oxford University Press, Oxford.
Wolff, J.E., 2019, “Representationalism in Measurement Theory. Structuralism or Perspectivalism?”, in Understanding Perspectivism, Routledge, New York/London.
Worrall, John, 1989, “Structural Realism: The Best of Both Worlds?”, Dialectica, vol. 43, no. 1–2, pp. 99–124.
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