A Combinatorial Model of Perceptual Categorization Unifying the Stevens and Weber–Fechner Laws

Classical psychophysics describes the relation between physical stimulus intensityand subjective sensation using either logarithmic (Weber–Fechner) or power functions(Stevens). However, these empirical laws lack a unifying mathematical foundationgrounded in discrete cognitive processes. Here, we propose a combinatorial model ofperceptual categorization based on set partitions and equivalence relations. By treatingperception as a process of grouping stimuli into equivalence classes of indistinguishability,we show that the expected number of perceptual categories m grows with thenumber of stimuli n according to a sigmoidal law. Asymptotically, this model recoversboth Stevens’ power law and Fechner’s logarithmic law as limiting cases, revealing aformal combinatorial basis for classical psychophysical scaling.