Karl Popper and the Accountability of Scientific Models

Karl Popper has written extensively on the methodology of scientific research. In his “Postscript to the Logic of Scientific Discovery” he formulates the principle of scientific accountability: “Scientific determinism requires the ability to predict every event with any desired degree of precision, provided we are given sufficiently precise intitial conditions. Our theory will have to account for the imprecision of the prediction: given the degree of precision which we require of the prediction, the theory will have to enable us to calculate the degree of precision which we require of the prediction, the theory will have to enable us to calculate the degree of precision in the initial conditions. For systems that exhibit sensitive dependence on initial conditions, this demand is nearly impossible to meet. This paper focuses on the potential consequences of insisting on accountability in the development of mathatical models of chaotic systems.