When psychologists apply mathematical machinery to psychological ideas, that machinery imposes certain requirements in the linkage of numbers and notions. These impose choices driven by the mathematics and not the psychology. These decisions, forced by the mathematics, induce theoretical issues in the psychology. Attempting a theory-neutral approach to research in psychology, where commitments in response to the options are made unknowingly, thus becomes instead a theory-by-default psychology. This paper begins to catalogue some of these mathematical choices to make them explicit, in order to allow psychologists the opportunity to make explicit theoretical commitments.
Aitken, A.C. (1952). Statistical mathematics. Edinburgh: Oliver & Boyd.
2.
Anastasi, A. , & Urbina, S. (1997). Psychological testing (7th ed.). Upper Saddle River, NJ: Prentice Hall.
3.
Benlap, N.D., Jr. , & Steele, T.B., Jr. (1976). The logic of questions and answers. New Haven, CT: Yale University Press.
4.
Child, D. (1990). The essentials of factor analysis (2nd ed.). New York: Holt, Rinehart & Winston.
5.
Clark, R.W. (1971). Einstein: The life and times. New York: World Publishing Co.
6.
Danziger, K. (1990). Constructing the subject: Historical origins of psychological research. Cambridge: Cambridge University Press.
7.
Davison, M. (1995). Spatial and deterministic limits on randomness. Unpublished doctoral dissertation, University of Western Ontario, London, Canada.
8.
Esch, R. (1974). Functional approximation. In C.E. Pearson (Ed.), Handbook of applied mathematics (pp. 942-999). New York: Van Nostrand Reinhold.
9.
Essex, C. , Lookman, T., & Nerenberg, M.A.H. (1987). The climate attractor over short timescales. Nature, 326, 64-66.
10.
Falmagne, J.-C. (1992). Measurement theory and the research psychologist. Psycho-logical Science, 3, 88-93.
11.
Feynman, R. (1985). Cargo cult science. In R. Feynman, R. Leighton, & E. Hutchings (Eds.), Surely you are joking Mr. Feynman! (pp. 308-317). New York: Norton.
12.
Gigerenzer, G. , Swijtink, Z., Porter, T., Daston, L., Beatty, J., & Kruger, L. (1989). The empire of chance: How probability changed science and everyday life. Cambridge: Cambridge University Press.
13.
Green, C.D. (1992). Of immortal mythological beasts: Operationism in psychology. Theory & Psychology, 2, 291-320.
14.
Green, D.M. , & Swets, J.A. (1966). Signal detection theory and psychophysics. New York: Wiley.
15.
Hamming, R.W. (1980). The unreasonable effectiveness of mathematics. American Mathematical Monthly, 87, 81-90.
16.
Harwitt, M. (1973). Astrophysical concepts. New York: Wiley.
17.
Hentschel, H.G.E. , & Proccacia, I. (1983). The infinite number of generalized dimensions. Physica, 8D, 435-444.
18.
Holton, G. (1968). Mach, Einstein, and the search for reality. Daedalus, 97, 636-673.
19.
Krantz, D.H. , Luce, R.D., Suppes, P., & Tversky, A. (1971). Foundations of measurement: Vol. I. Additive and polynomial representations. New York: Academic Press.
20.
Leahey, T.H. (1980). The myth of operationsim. Journal of Mind and Behavior, 1, 127-143.
21.
Lockhart, R.S. , & Murdock, B.B., Jr. (1970). Memory and the theory of signal detection. Psychological Bulletin, 74, 100-109.
22.
Luce, R.D. , Krantz, D.H., Suppes, P., & Tversky, A. (1990). Foundations of measurement: Vol. III. Representation, axiomatization, and invariance. San Diego, CA: Academic Press.
23.
Maraun, M.D. (1998). Measurement as a normative practice: Implications of Wittgenstein's philosophy for measurement in psychology. Theory & Psychology, 8, 435-461.
24.
Neisser, U. , Boodoo, G., Bouchard, T.J., Jr., Boykin, A.W., Brody, N., Cesi, S.J., Halpem, D.F., Loehlin, J.C., Perloff, R., Sternberg, R.J., & Urbina. S. (1996). Intelligence: Knowns and unknowns. American Psychologist, 51, 77-101.
25.
Ott, E. , Withers, W.D., & Yorke, J.A. (1984). Is the dimension of chaotic attractors invariant under coordinate changes?Journal of Statistical Physics, 36, 687-697.
26.
Rogers, T.B. (1989). Operationism in psychology: A discussion of the contextual antecedents and an historical interpretation of its longevity. Journal of the History of the Behavioral Sciences, 15, 139-153.
27.
Rubin, H.J. , & Rubin, I.S. (1995). Qualitative interviewing: The art of hearing data. Thousand Oaks, CA: Sage.
28.
Salamon, P. , & Berry, R.S. (1983). Thermodynamic length and dissipated availability. Physical Review Letters, 51, 1127-1130.
29.
Scheinerman, E.R. (1996). Invitation to dynamical systems. Upper Saddle River, NJ: Prentice Hall.
30.
Shepard, R.N. (1964). Attention and the metric structure of the stimulus space. Journal of Mathematical Psychology, 1, 54-87.
31.
Shepard, R.N. (1982). Geometrical approximations to the structure of musical pitch. Psychological Review, 89, 305-333.
32.
Shepard, R.N. (1984). Ecological constraints on internal representation: Resonant kinematics of perceiving, imagining, thinking, and dreaming. Psychological Review, 91, 417-447.
33.
Suppes, P. , Krantz, D.H., Luce, R.D., & Tversky (1989). Foundations of measurement: Vol. IL. Geometrical, threshold, and probabilistic representations. San Diego, CA: Academic Press.
34.
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.
35.
Tolman, C.W. (Ed.). (1992). Positivism in psychology: Historical and contemporary problems. New York: Springer.
36.
Tolman, R.C. (1938). The principles of statistical mechanics. Oxford: Oxford University Press.
37.
Weron, A. , & Weron, R. (1995). Computer simulation of ox-stable variables and processes. Lecture Notes in Physics, 457, 379-392.
38.
Whittaker, E.T. , & Robinson, G. (1929). Calculus of observation. London: Blackie & Sons.
