Functional relations and causality in Fechner and Mach

In the foundations of Fechner's psychophysics, the concept of "functional relation'' plays a highly relevant role in three different respects: (1) in respect to the principles of measurement, (2) in respect to the mind-body problem, and (3) in respect to the concept of a law of nature. In all three cases, it is important to explain the difference between a functional dependency of a variable upon another and a causal relationship between two (or more) variables. In all three respects, Ernst Mach developed Fechner's ideas further and tried to extend the lessons he had learned from using the concept of a functional relation in psychophysics to the whole of science. For all three cases, I explain why they are still relevant for psychophysics and philosophy today.