Sensory scaling and the psychophysical law

Sensory scaling is analysed as a sensori-motor task for which two relations must be determined, the first, S = f(I), being the relation between I, the stimulus intensity, and S, a measure of the neural effect of the stimulus, and the second being the relation between the subject's response, R, and S. It is shown that for any scaling procedure the relation between R and S can be arbitrarily specified, and according to the choice made S = f(I) will be found to be either a power function or a logarithmic function; these two “psycho- physical laws” do not reflect empirical differences between scaling procedures but conventional differences in the assumptions made when interpreting these procedures. A model is then elaborated in which S = f(I) is fixed and the relation between R and S depends on the demands of the psychophysical task and the effects of previous learning. With this more complex model the empirical implications of the power function and log function differ; it is shown that if the latter is accepted explanations can be given for two major problems in scaling theory, the disparity between the functions given by category scaling and the direct methods, and the difference between prothetic and metathetic continua.