  This was von Wright’s proposed account of a continuous change in an ontology of intervals. The state \(\neg p\) changes continuously to \(p\) if there is a preceding interval which is \(\neg p\) throughout, then an interval with \(\neg p\) and \(p\) dense in each other, then a succeeding interval with p holding throughout. Von Wright described this as a kind of inconsistency. Unfortunately it is not clear from his written words whether he had in mind that the situation was inconsistent or only possibly inconsistent. His argument seems to be this. In an ontology of intervals we begin with descriptions like “It rained here yesterday” which means that it rained sometime here yesterday. The basic description is thus “\(p\) holds (somewhere) in the interval \(I\).” The special case where \(p\) holds throughout \(I\) is noted, where to hold throughout is for there to be no subinterval in which \(\neg p\) holds. Now \(p\)’s holding in \(I\) is of course compatible with \(\neg p\)’s holding in \(I\). But there is no contradiction here, as long as there is a partition of \(I\) into subintervals such that \(p\) holds throughout the subinterval or \(\neg p\) holds throughout the subinterval. Thus if we take in that a disjunction holds in an interval just in case there is a partition in which each of the disjuncts holds throughout its subintervals, we can say that if there is such a partition for \(p\), then the law of excluded middle \(p \vee \neg p\) holds throughout the interval. Von Wright introduced the modal operator \(Np\) for “Necessarily \(p\).” If we define “\(Np\) holds in \(I\)” to mean that \(p\) holds throughout \(I\), we can say that if there is no continuous change in the above sense, then Excluded Middle LEM holds necessarily, \(N(p \vee \neg p)\). However, defining the modal “Possibly” in the usual way as \(M =df \neg N\neg\) and assuming de Morgan’s Laws, Double Negation and Commutativity, we get the result that in an interval in which there is continuous change, \(M(p \amp \neg p)\) holds, i.e.. a contradiction is possible. Presumably it further follows that in a subinterval which has continuous change throughout, \(N(p \amp \neg p)\) holds. Needless to say this implies that a contradiction is true in that subinterval. We might note that the result that continuous change is a true contradiction follows without the detour through modal logic, since if LEM is false then \(\neg(p \vee \neg p)\) holds for some \(p\), and so by de Morgan and Double Negation, \(p \amp \neg p\) holds (throughout).