Presents a unique study of Integrative Problem-Solving (IPS). The consideration of 'Decadence' is essential in the scientific study of environmental and other problems and their rigorous solution, because the broad context within which the problems emerge can affect their solution. Stochastic reasoning underlines the conceptual and methodological framework of IPS, and its formulation has a mathematical life of its own that accounts for the multidisciplinarity of real world problems, the multisourced uncertainties characterizing their solution, and the different thinking modes of the people involved. Only by interpolating between the full range of disciplines (including stochastic mathematics, physical science, neuropsychology, philosophy, and sociology) and the associated thinking modes can scientists arrive at a satisfactory account of problem-solving, and be able to distinguish between a technically complete problem-solution, and a solution that has social impact.