Certain mathematical principles for the phenomenological description of data are introduced and applied to establish a new psychophysical function for the sensation of brightness. This function, which is the integral of the lognormal probability density function, has the psychophysical functions of Fechner and Stevens as limiting cases. The predictions of the new function are compared with experimental evidence on the discrimination of light intensity by the human eye, and an estimate of the total number of distinct steps of brightness discrimination is determined.