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Knowledge as knowledge of facts is based on the appearance of time as fundamental difference between past and future. Taking asymmetry in time as precondition of experience, the time symmetry of the basic laws of physics has to be explained. We give an explanation founded on the abstraction leading from semigroups to groups and the essential role of the concept of groups to define stationary states and observables. We then present a short outline of the construction of an abstract quantum theory as theory of knowledge based on the asymmetry between facts and possibilities. It is well known that the second law of thermodynamics cannot be derived from theH-theorem without a further hypothesis. We show that the application of the concept of probability to the past yields inconsistency of theH-theorem and a derivation of the second law via a Boltzmann-type hypothesis. The question remains whether the distinction of facts and possibilities as precondition of a theory of knowledge is rooted in a theory of cognition itself.