This book, written by the outstanding Russian philosopher A. A. Zinoviev, examines a number of interesting philosophical problems related to the emergence and development of many-valued logic. Brief remarks about two-valued logic and the notation system are given, the conditions for the emergence of the first multi-valued logical systems and the features of these systems are considered. Philosophical questions of multi-valued propositional calculus are explored; a separate chapter is devoted to predicate calculus. The book is intended for a wide range of philosophers and logicians interested in the philosophical and logical problems of modern science.