Abstract

Noonan’s book comprises, along with a substantial introduction, chapters on Frege’s logic, his philosophy of arithmetic, his philosophical logic and his theory of meaning, among them covering all his principal contributions to philosophy. The exposition, while remaining throughout accessible to any nonspecialist reader with a reasonable background in analytical philosophy, is sympathetic but at the same time searching and critical, aimed both at deepening our understanding of the reasons that led Frege to his most important doctrines and of the connections between them, and at bringing out clearly the difficulties to which they give rise. After a brief but engaging account of Frege’s life and career, Noonan’s introductory chapter provides a helpful sketch of the origins and development of his leading ideas in their philosophical and mathematical context—Kant’s thesis that mathematics, while a priori, must be synthetic and his associated insistence on the role of intuition; the emergence of non-Euclidean geometries; and the drive for rigor and the arithmetization of analysis by Augustine Cauchy, Karl Weierstrass, and others—followed by a concise overview of Frege’s main contributions which serves as a useful background to their more detailed discussion in the chapters that follow.