The main objectives of this book are to critically evaluate the problem of scientificity in Edmund Husserl’s phenomenology, to argue that his phenomenological reflection further awakens possibilities for the rational sciences and finally, to question the standard narratives of his theory of reason in order to revitalize his intuitions in light of the present day. The contributions gathered in this volume seek to gain a better understanding of the theoretical complexity of the interconnections between Husserl and other prominent critics of the theoretical sciences, such as David Hilbert, Oskar Becker, Ludwig Wittgenstein, Marc Richir, Herrman Weyl, Dag Prawitz and Arend Heyting. This collection is innovative in arguing that the phenomenological reflection inspired by the revolutionary spirit of Husserl's doctrine is indispensable for explaining central concepts underlying scientific theories and higher-order objective structures. This text contains fourteen seminal essays by a team of international scholars that orchestrate a dialogue between Husserl’s idea of phenomenology of ‘awakened reason’ and the foundations, methodologies, and limits of scientific theories, logic, and mathematics. The key audience for this title are students and researchers of phenomenology working in theoretical philosophy, continental philosophy, epistemology, philosophy of science, and philosophy of mathematics.