Foundations Of Cognitive Science

Mathematical Model

A mathematical model is one of the types of models that one finds used in psychology or cognitive science (Dawson, 2004). In general, it is an attempt to use a mathematical expression to express a psychological law, assuming that such laws can be expressed as mathematical or quantitative relationships between psychological variables. The purpose of such laws are to capture generalities. From the first efforts toward psychological measurement, investigators have had in mind the goal of making progress toward generality in psychological theory by developing quantities analogous to mass, charge, and the like in physics and showing that laws and principals formulated in terms of these derive quantities would have greater generality than those formulated in terms of observables” (Estes, 1975). Mathematical models are generally derived from existing data, and are judged in terms of their goodness-to-fit to this data, but they are also used to generate novel predictions which can then be evaluated later via experimentation. Classic examples of mathematical models can be found in the study of animal learning (Rescorla & Wagner, 1972), choice behavior (Luce, 1959) and response latencies (Luce, 1986).


  1. Dawson, M. R. W. (2004). Minds And Machines : Connectionism And Psychological Modeling. Malden, MA: Blackwell Pub.
  2. Estes, W. K. (1975). Some targets for mathematical psychology. Journal of Mathematical Psychology, 12, 263-282.
  3. Luce, R. D. (1959). Individual Choice Behavior. New York,: Wiley.
  4. Luce, R. D. (1986). Response Times: Their Role In Infeering Elementary Mental Organization. Oxford: Oxford University Press
  5. Rescorla, R. A., & Wagner, A. R. (1972). A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement. In A. H. Black & W. F. Prokasy (Eds.), Classical Conditioning II: Current Research And Theory (pp. 64-99). New York, NY: Appleton-Century-Crofts.

(Added March 2010)