| In this lecture we would like to analyse the concepts of determinism, predictability and complexity, considering the role of deterministic Chaos and singular limits. The precise definition of these concepts is blurry and a debate is going on since the famous words of Laplace. Historically determinism has been improperly associated with reductionism. Thus to bring the analysis on firm basis, it is useful to consider the more general philosophical notions of reductionism and emergence. In this framework, the deterministic chaos appears to play an important role. The existence of Chaos distinguishes clearly determinism from predictability, because of the sensitive dependence on initial conditions. Furthermore, the details of the time evolution of dynamical systems are hidden in initial conditions, which are almost all algorithmically complex. This leads to the necessity of a probabilistic approach which reveals one more instance of singular limits. New statistical laws emerge in this singular limit, showing that chaotic macroscopic phenomena cannot be reduced to deterministic mechanistic laws. |