The title¹ "Classical and quantum descriptions' is a technical version of the problem of a semantical interpretation of quantum theory. The question is: what does quantum theory mean? Hence the task is not to improve quantum theory by new additions, but to understand it. Its mathematical structure is not disputed. On the existing interpretation — usually called the Copenhagen interpretation — there have been decades of discussion. They have their origin in the fact that we can only accept this interpretation if we take some rather fundamental philosophical decisions. In this paper I do not try to argue for these decisions except for an attempt to contribute to a clarification of their meaning. I take a particular approach in starting from the idea of a quantum logic. This is in my view not a peculiar "empirical" logic, but a specification of a general logic of temporal statements, that is of statements on facts and possibilities. Statements on facts are "classical descriptions", statements on possibilities are embodied in the quantum state vectors.