Stevens vs Fechner: A plea for dismissal of the case

Fechner's Law is based on the assumption that jnd's can be concatenated in order to get a measure of sensation. Stevens contended this assumption; he argued that measurement of sensation by measuring jnd's is ‘indirect’. His ‘direct’ methods, however, appear to be much less direct than originally assumed. Especially Stevens' (implicit) assumption that subjects use numbers on an absolute scale appears to be unwarranted. Ratio scaling is therefore nothing more than cross-modality matching between the number scale and another modality. This view has two consequences. Firstly, it is quite natural to find power functions by cross-modality matching, even when Fechner's Law holds for both modalities. Secondly, if Stevens' power law is true, there will be an overestimation of all exponents by a factor 2.5. All typical power functions will be concave downward after correction for this effect. The discussion boils down to a discrimination between two quite similar curve families: log functions and power functions with an exponent below 0.6. The practical significance of this discussion is doubted.