In this book the author pledges for the generalization of the Lupasco-Nicolescu’s Law of Included Middle [A, nonA, and a third value T which resolves their contradiction at another level of reality] to the Law of Included Multiple-Middle [A, antiA, and neutA, where neutA is split into a multitude of neutralities between A and antiA, such as neut1A, neut2A, etc.]. The neutA value (i.e. neutrality or indeterminacy related to A) actually comprises the included middle value. Further, similarly to the extension from dialectics to neutrosophy, the author extends the Principle of Dynamic Opposition [opposition between A and antiA] to the Principle of Dynamic Neutrosophic Opposition [which means oppositions among A, antiA, and neutA]. Explanation: The following dialogues are a compilation of different dialogues I had – during the years – on neutrosophy and related topics with academic colleagues, mostly by email. As they were non-protocol dialogues, initially not intended for publication, I invented a fictional character (somehow resurrected from Plato’s dialogues), Filokratos, and put in his mouth opinions, ideas, questions, comments expressed by academic fellows, in a collective spirit. Many thanks to all friends and dialogue partners who paid attention to neutrosophy and connected areas.