AN ANCIENT PARADOX FOR DISCRIMINATION JUDGEMENTS
According to the pairwise-comparison version of the ancient sorites 'paradox', a stimulus space may contain sequences of stimuli in which any two successive stimuli are not discriminable while the first and the last one are. This hypothesis, often described as an empirical fact, motivates such well-known theoretical constructs as semiorders and interval orders. A rigorous analysis of the notion of (in)discriminability, however, shows that the hypothesis has no empirical justification. Moreover, the pairwise-comparison version of sorites is ruled out by the laws of Regular Minimality (for same-different judgments) and Regular Mediality (for greater-less judgments) proposed by the author as governing principles for comparisons of stimuli belonging to two fixed observation areas (e.g., right-left, or first-second). To deal with all possible forms of perceptual sorites, however, a generalization of Regular Minimality / Mediality is presented which involves multiple observation areas (e.g, mutiple spatial locations).