The article discusses the features of mathematical psychology in the beginning of 19th century, discusses on three questions: 1) what kind of difficulties the representatives of mathematical psychology encountered in the 19th century while transferring the data of empirical psychology to the quantitative perspective, 2) some of methodological issues related to the application of mathematics to psychology, 3) analyzes specific application of “negligibly decreasing value” examples in order to describe “thresholds of consciousness”. J. F. Herbart’s conclusions of mathematical psychology are compared to some of the statements of contemporary mathematical psychology.