| Abstract: | The probability-distance hypothesis states that the probability with which one stimulus is discriminated from another is a function of some subjective distance between these stimuli. The analysis of this hypothesis within the framework of multidimensional Fechnerian scaling yields the following results. If the hypothetical subjective metric is internal (which means, roughly, that the distance between two stimuli equals the infimum of the lengths of all paths connecting them), then the underlying assumptions of Fechnerian scaling are satisfied and the metric in question coincides with the Fechnerian metric. Under the probability-distance hypothesis, the Fechnerian metric exists (i.e., the underlying assumptions of Fechnerian scaling are satisfied) if and only if the hypothetical subjective metric is internalizable, which means, roughly, that by a certain transformation it can be made to coincide in the small with an internal metric; and then this internal metric is the Fechnerian metric. The specialization of these results to unidimensional stimulus continua is closely related to the so-called Fechner problem proposed in 1960's as a substitute for Fechner's original theory. |
