Speakable in quantum mechanics: babbling on

This paper consists of a short version of the derivation of the intuitionistic quantum logic L_QM (which was originally introduced by Caspers, Heunen, Landsman and Spitters). The elaboration consists of extending this logic to a classical logic CL_QM. Some first steps are then taken towards setting up a probabilistic framework based on CL_QM in terms of Rényi's conditional probability spaces. Comparisons are then made with the traditional framework for quantum probabilities.