It is quite natural to make P into a topological space with the convention that, if the point representing a system lies outside a certain closed set K of P (the set of catastrophe points), the qualitative nature of the state does not vary for a sufficiently small deformation of this state. Each type, each form of the process then corresponds to a connected component of P-K. If P also has a differentiable structure (e.g. Euclidean space Rm, or a differential manifold) the dynamical structure will be given by a vector field X on P. Existence and uniqueness theorems for solutions of differential equations with differentiable coefficients then give what is without doubt the typical paradigm for scientific determinism. The possibility of using a differential model is, to my mind, the final justification for the use of quantitative methods in science; of course, this needs some justification: the essence of the method to be described here consists in supposing a priori the existence of a differential model underlying the process to be studied and, without knowing explicitly what this model is, deducing from the single assumption of its existence conclusions relating to the nature of the singularities of the process. Thus postulating the existence of a model gives consequences of a local and qualitative nature; from quantitative assumptions but (almost always) without calculation, we obtain qualitative results. It is perhaps worthwhile to discuss this question in greater detail.