Phenomenological models versus deductive models: The stochastic limit of quantum theory

After discussing in general the advantages, for the applications to physics, of deductive models with respect to phenomenological ones, we concentrate on open systems and describe the main ideas of the stochastic limit approach to open systems. We discuss the various levels of the stochastic limit (in increasing order of complexity of the interaction Hamiltonian) describing the new features that emerge at each level and their applications to different branches of physics. We illustrate some examples which highlight how, using the stochastic limit approach, one can answer long-standing questions on various physical behaviors of the composite system solving problems that cannot even be formulated in the reduced evolution (master equation) scheme. In the second part of the paper, we outline the main ideas of the proofs of some of the new features described in the first part. For lack of space, we focus our attention on Level 1 and we have to omit most physical applications. These topics will be the object of a future publication.