ABSTRACT
This chapter is devoted to discussion and investigation of an open problem in the psychophysical theory ofintensity perceptionas formulated by R. D. Luce in a series of papers (Luce, 2002,2004,2005; see also Steingrimsson &Luce, 2005a, 2005b, 2006, 2007). Luce's theory follows the classical model for measurements of physical attributes like mass, with a behavioral adaptation to psychophysical intensity attributes like loudness. The material presented here includes a compact outline of part of this theory, derived from lectures by Professor Luce in 2005 (at the joint Summer Meeting of the Canadian Mathematical Society and the Canadian Society for History and Philosophy of Mathematics, June 4-6) and 2007 (at the University of Waterloo, June 14), in which he derived some representation theorems on loudness, and stated the problem to be considered here—it is to characterize the precise mathematical form that a certain psychophysical function takes.
