The Foundations of Mathematics in the Theory of Sets [Hardcover]

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.This unified approach to the foundations of mathematics in the theory of sets covers both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of natural number and set . The book contains an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, and the analysis of proof by induction and definition by recursion. The book should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.Preface; Part I. Preliminaries: 1. The idea of foundations of mathematics; 2. Simple arithmetic; Part II. Basic Set ThlƒH