In 2009, we wrote the paper 'Keep ‘hoping’ for rationality: a solution to the backward induction paradox', based on a new formalization of a concept we introduced, namely the notion of dynamic rationality. The notion of dynamic rationality that we work with, changes its meaning after every act of learning, and it may become true after players learn it is false. By using the dynamic nature of our concept of rationality we explain this this paper why our conditions avoid the apparent circularity of the 'backward induction paradox'. The paper address both the work of R. Aumann and R. Stalnaker on the problem.