Introduction to Symbolic Logic and Its Applications

This book is one of the clearest, most comprehensive and rigorous introductions to modern symbolic logic available in any language. Professor Carnap, a world authority on symbolic logic, dvelops the subject from elementary concepts and simple exercises through the construction and analysis of a number of relatively complex logical languages. He then considers, in great detail, the application of symbolic logic to the clarification and axiomatization of various theories in mathematics, physics and biology. Such topics as the nature and use of constants and variables, predicates, sentential connectives, truth-tables, universal and existential sentences, definitions, identity, isomorphism, syntactical and semantical systems and the relation between them, the system of types, varieties of relations, linear order, special operators, structures and cardinal numbers, descriptions, finite and infinite concepts, continuity, thing languages, coordinate languages, axiom systems for set theory, arithmetic, geometry, space-time topology, biological concepts, and many others, are covered in detail. The logic of relations is given a particularly extensive treatment. Hundreds of problems, examples and exercises are included to give the student practice in the techniques of symbolic logic and familiarize him with its use.