The axioms of quantity and the theory of measurement: Translated from part I of Otto Hölder's German text "die axiome der quantität und die lehre vom mass"

Journal of Mathematical Psychology

Volumn 40, Issue 3, 1996, Pages 235-252

  Michell, Joel ^a   Ernst, Catherine ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030243574     PISSN: 00222496     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmps.1996.0023     Document Type: Article

References (37)

1. Bunge, M. (1973). On confusing "measure" with "measurement" in the methodology of behavioral science. In M. Bunge (Ed.), The methodological Unity of science (pp. 105-122). Dordrecht, Holland: Reidel.
2. Campbell, N. R. (1920). Physics, the elements. London: Cambridge Univ. Press.
3. Caygill, H. (1995). A Kant dictionary. Oxford: Blackwell.
4. Dorian, A. F. (1970). Dictionary of science and technology. German-English. Amsterdam: Elsevier.
5. Editor. (1891-92). What does Anschauung mean? The Monist 2, 527-532.
6. Ferguson, A., Myers, C. S., Bartlett, R. J., Banister, H., Bartlett, F. C., Brown, W., Campbell, N. R., Craik, K. J. W., Drever, J., Guild, J., Houstoun, R. A., Irwin, J.O., Kaye, G. W. C., Philpott, S. J. F., Richardson, L. F., Shaxby, J. H., Smith, T., Thouless, R. H., & Tucker, W. S. (1940). Quantitative estimates of sensory events. Advancement of Science, 2, 331-349.
7. Frege, G. (1903). Grundgesetze der Arithmetik: Vol. 2. Hildescheim: Olms.
8. Helmholtz, H. von (1887-1971). An epistemological analysis of counting and measurement. In R. Kahl (Ed.), Selected writings of Hermann von Helmholtz. Connecticut: Wesleyan Univ. Press.
9. Herland, L. (1951). Dictionary of mathematical sciences: Vol. 1. German-English. London: Hafner.
10. Hölder, E. (1972). Hölder, Otto Ludwig. In C. C. Gillispie (Ed.), Dictionary of scientific biography, Vol. V (pp. 472-474). New York: Scribners.
11. Hölder, O. (1900). Anschaung und Denken in der Geometrie. Leipzig: Teubner.
12. Hölder, O. (1924). Die mathematische Methode. Logisch-erkenntnistheoretische Untersuchungen im Gebiet der Mathematik, Mechanik and Physik. Berlin.
13. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement, Vol. 1. New York: Academic Press.
14. Luce, R. D. (1986). Uniqueness and homogeneity of ordered relational structures. Journal of Mathematical Psychology, 30, 391-415.
15. Luce, R. D. (1987). Measurement structures with Archimedean ordered translation groups. Order, 4, 165-189.
16. Luce, R. D. (1994). The ongoing dialog between empirical science and measurement theory. Unpublished address delivered at Kiel conference on Foundations of Measurement: The Theory of Representability and the Nature of Numbers.
17. Luce, R. D., Krantz, D. H., Suppes, P., & Tversky, A. (1990). Foundations of Measurement, Vol. 3. San Diego: Academic Press.
18. Michell, J. (1990). An introduction to the logic of psychological measurement Hillsdale N.J., Erlbaum.
19. Michell, J. (1993). The origins of the representational theory of measurement: Helmholtz, Hölder, and Russell. Studies in History and Philosophy of Science, 24, 185-206.
20. Michell, J (1994). Numbers as quantitative relations and the traditional theory of measurement. British Journal for the Philosophy of Science, 45, 389-406.
21. Mundy, B. (1987). The metaphysics of quantity. Philosophical Studies, 51, 29-54.
22. Nagel, E. (1932). Measurement. Erkenntnis, 2, 313-333.
23. Narens, L. (1985). Abstract measurement theory. Cambridge, MA: MIT Press.
24. Niederée, R. (1987). On the reference to real numbers in fundamental measurement: a model-theoretic approach. In E. Roskam & R. Suck (Eds.), Progress in mathematical psychology. Amsterdam: North-Holland.
25. Niederée, R. (1992). What do numbers measure? A new approach to fundamental measurement. Mathematical Social Sciences, 24, 237-276.
26. Russell, B. (1903). Principles of mathematics. Cambridge: Cambridge Univ. Press.
27. Savage, C. W., & Ehrlich, P. (1992). A brief introduction to measurement theory and to the essays. In C. W. Savage & P. Ehrlich (Eds.), Philosophical and foundational issues in measurement theory (pp. 1-14). Hillsdale, NJ, Erlbaum.
28. Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677-680.
29. Stevens, S. S. (1951). Mathematics, measurement, and psychophysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1-49). New York: Wiley.
30. Suppes, P. (1951). A set of independent axioms for extensive quantities. Portugaliae Mathematica, 10, 163-172.
31. Suppes, P., & Zinnes, J. (1963). Basic measurement theory. In R. D. Luce, R. R. Bush, & E. H. Galanter (Eds.), Handbook of mathematical psychology (pp. 1-76). New York: Wiley.
32. Swoyer, C. (1987). The metaphysics of measurement. In J. Forge (Ed.), Measurement, realism and objectivity (pp. 235-290). Dordrecht: Reidel.
33. Whitehead, A. N., & Russell, B. (1913). Principia mathematica: Vol. 3. Cambridge: Cambridge Univ. Press.
34. Whiteside, D. T. (1967). The mathematical works of Isaac Newton: Vol. 2. New York: Johnson Reprint Corp.
35. Wiener, N. (1914). A contribution to the theory of relative position. Proceedings of the Cambridge Philosophical Society, 17, 441-449.
36. Wiener, N. (1915). Studies in synthetic logic. Proceedings of the Cambridge Philosophical Society, 18, 14-28.
37. Wiener, N. (1921). A new theory of measurement: A study in the logic of mathematics. Proceedings of the London Mathematical Society, 19, 181-205.