Heterodox economics has, since its inception, stressed the extreme importance of financial crises to understand the nature of finance. Heterodox modelling and heterodox economics were in line with their objective: a critical posture of the neoclassical finance arising from orthodox financial theory. Two distinct research programmes were established in financial modelling to tackle the leptokurtic issue: the first Mandelbrot programme based on stable Levy processes and the alternative non-stable Levy processes approach based on Merton's view. This chapter argues that some of the key differences between the competitive representations of financial uncertainty can be illuminated by reference to a familiar debate in philosophy over the principle of continuity. It also argues on the contrary that the divergent positions about the mind-set behind the price changes implicate entirely different views of what is important to capture and how to model it.