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This book is for any person interested in very different, thought provoking, off the beaten track views on the foundations of science, but also on how to consider very differently our being in the world in general. A great amount of highly unusual positions is suggested throughout the entire book. As a whole, it represents no less than a new theory of knowledge called multi-objective relativism which is a new theory of truth and a new theory of cognition. The ambition of science is to see knowledge as a mirror of nature. In philosophy this has always led to paradoxes like the contradiction between free will and determinism. No theory has until now succeeded in preserving the intelligibility of the totality of what is in the world without running into paradoxical problems. This book presents an original approach which solves these problems by use of different real infinities in the world and of an adapted system of cognitive treatment which is the open brain that works not by pure representation but, faced with these infinity-based incommensurabilities of the open world, uses its own infinity-based completions for generating adapted comprehensions.