Mathematical Models in Theoretical Psychophysics: A Historical Perspective

According to Robert Cummins, the primary explananda of psychology are mental capacities. One fundamental capacity—studied in psychophysics—is the ability to perceive aspects of the physical world. Traditionally, psychophysicists employ behavioral techniques to uncover lawful relationships between physical stimuli and their corresponding responses. However, we argue that theoretical progress in psychophysics has primarily resulted from the development of theories that specify the non-observables underlying these empirical laws. For instance, while Gustav Theodor Fechner utilized discrimination tasks to assess the functional relation between stimulus magnitude and perceived intensity, it was not until the advent of Signal Detection Theory and related Thurstonian models that the underlying mechanisms were theoretically specified. We contend that mathematical models play a crucial role in theoretical psychophysics, as the deductive power of mathematics enables us to generate logically valid and precise predictions from theoretical core assumptions. We illustrate this point by outlining the historical development of mathematical models of stimulus discrimination. Furthermore, we note that theoretical psychophysics in the Thurstonian tradition reflects central meta-theoretical convictions introduced into psychology by Hermann von Helmholtz, and discuss the potential of this approach for cognitive psychology.Keywords: history of science; philosophy of science; psychophysics; theoretical psychology; scientific laws; mathematical models