Fechner's conception of psychophysics included both “outer psychophysics” the relation between stimulus intensity and the response reflecting sensation strength, and “inner psychophysics” the relation between neurelectric responses and sensation strength. In his own time outer psychophysics focussed on the form of the psychophysical law, with Fechner espousing a logarithmic law, Delboeuf a variant of the logarithmic law incorporating a resting level of neural activity, and Plateau a power law. One of the issues on which the dispute was focussed concerned the (...) appearance of contrasts if the overall illumination was increased or decreased; another issue was the question of whether a sensation of a “just noticeable difference” established for one value of a sensory dimension appeared the same for a value elsewhere on the dimension. The development of “inner psychophysics” led through the works of Delboeuf, Solomons, Jastrow, and Thurstone to modern signal detection theory. A third line of research, devoted to the question of what was meant by the “measurement” of sensation strength, stemmed from the criticism of Fechner's work by von Kries (1882) and others. Although a valid body of science could be built up without the intervening variable called “sensation strength,” such a science might be a cumbersome representation of reality. When an optical contrast is set up, and its overall illumination is increased or decreased, subjective contrasts involving medium levels of lightness vary little as illumination varies (as a power law based on sensation ratios or a logarithmic law based on sensation differences predict), but subjective contrasts involving extreme levels of lightness might be subject to the effects of other variables. (shrink)

Attribute spaces are a type of conceptual spaces which Carnap introduced in his late basic system of inductive logic. This article shows how to extend Carnap's use of them into a full model of inductive reasoning with geometrically represented concepts, extending my earlier work. The proposed model draws on Bayesian non-parametric techniques in order to define a probability distribution over the attribute space and a way of updating it with data. The model is another example of conceptual and formal continuity (...) of Carnapian inductive logic with subsequent developments in statistics. (shrink)