Perceptual matching and sorites: experimental study of an ancient Greek paradox

Loosely derived from the sorites "paradox" attributed to the 4th century BCE Greek philosopher Eubulides, comparative soritical sequence of stimuli is defined as an enumeration of several stimuli, x 1, x 2, …, x n , such that, when these stimuli are presented pairwise, any two of them with consecutive numbers appear "identical, " whereas the first and the last ones do not. There is a widespread belief that stimuli of virtually any kind can be arranged in soritical sequences. This belief, often presented as a "well-known" empirical fact, is in fact based on the following piece of persuasive reasoning: an observer "obviously" should not be able to distinguish physically very similar stimuli, whereas sufficient number of very small differences eventually add up to an arbitrarily large and clearly discernible one. However, this view overlooks the well-known empirical fact that discrimination judgments are fundamentally probabilistic. One and the same pair of stimuli, including two physically identical ones, will sometimes be judged the same and sometimes different. Therefore, in order for the truth or falsity of the relation "stimulus x is perceptually matched by stimulus y" to be uniquely determined by x and y, this relation should be computed from probability distributions rather than directly observed. We show that if one uses conventional psychophysical computations of matching stimuli, soritical sequences need not exist, and that in fact there is no empirical evidence they do. In particular, we develop a mathematical theory for a procedure in which stimuli are repeatedly adjusted to match each other, and we present negative results of an experimental investigation aimed at detecting soritical sequences.