The Continuum: A Critical Examination of the Foundation of Analysis (Dover Books on Mathematics)

"The hard won power ... to assess correctly the continuum of the natural numbers grew out of titanic struggles in the realm of mathematical logic in which Hermann Weyl took a leading part." — John Archibald WheelerHermann Weyl (1885–1955) ranks among the most important mathematicians and physicists of this century. Though Weyl was not primarily a philosopher, his wide-ranging philosophical reflections on the formal and empirical sciences remain extremely valuable. Besides indicating clearly which results of classical analysis are invalidated by an important family of "non-circular" (predicative) theories, The Continuum wrestles with the problem of applying constructive mathematical models to cases of concrete physical and perceptual continuity. This new English edition features a personal reminiscence of Weyl written by John Archibald Wheeler.Originally published in German in 1918, the book consists of two chapters. Chapter One, entitled Set and Function, deals with property, relation and existence, the principles of the combination of judgments, logical inference, natural numbers, iteration of the mathematical process, and other topics. The main ideas are developed in this chapter in such a way that it forms a self-contained whole.In Chapter Two, The Concept of Numbers & The Continuum, Weyl systematically begins the construction of analysis and carries through its initial stages, taking up such matters as natural numbers and cardinalities, fractions and rational numbers, real numbers, continuous functions, curves and surfaces, and more.Written with Weyl's characteristic passion, lucidity, and wisdom, this advanced-level volume is a mathematical and philosophical landmark that will be welcomed by mathematicians, physicists, philosophers, and anyone interested in foundational analysis.