  This ingenious construction has its problems. It is certainly dangerous to assume De Morgan’s Laws and Double Negation when the logic of intervals is the case in point. They both fail for open set logic, which is to say intuitionism, just as they both fail for its topological dual, closed set logic. On the other hand, what is one to say if the world is structured as intervals, non-punctate, and if there are subintervals in which propositions and their negations are dense in each other, interspersed with intervals where one of the propositions holds throughout? The latter are clearly periods of non-change, and the former are reasonably described as intervals of change. And yet it would seem that the best one can do is to say that \(p \amp \neg p\) holds in the transition periods: there appears to be no consistent way of describing what is happening in the situation which adheres to intervals and eschews points.