Philosophy of Mathematics: Selected Readings

Philosophy of Mathematics: Selected Readings is a collection of essays edited by Paul Benacerraf and Hilary Putnam that spans major developments in mathematical philosophy from the early 20th century through the 1960s. The anthology features writings from influential thinkers including Gottlob Frege, Bertrand Russell, Kurt Gödel, and others who shaped modern perspectives on mathematical foundations. The book is structured into sections that address core questions in the field: the nature of mathematical truth, the existence of mathematical objects, and the relationship between mathematics and logic. Each reading is preceded by editorial commentary that provides context and connections between the works. The essays examine topics such as logicism, formalism, and intuitionism - competing views on what mathematics fundamentally is and how we can know mathematical truths. Technical discussions of set theory, infinity, and mathematical proof methods are balanced with broader philosophical investigations. This collection represents a pivotal moment in the development of mathematical philosophy, capturing the transition from classical views to modern analytical approaches. The included works continue to influence contemporary debates about the foundations and nature of mathematical knowledge.

Readers describe this as a comprehensive collection of important papers in mathematical philosophy, frequently used in graduate-level courses. The anthology contains works from both historical figures and contemporary mathematicians. Likes: - Clear organization of papers by topic - Includes both foundational texts and modern perspectives - Helpful introductions before each section - Contains seminal papers like Benacerraf's "What Numbers Could Not Be" Dislikes: - Some papers are technically dense for beginners - Price is high for a paperback - Second edition omits some papers from first edition - No coverage of more recent developments post-1980s Ratings: Goodreads: 4.2/5 (21 ratings) Amazon: 4.5/5 (12 reviews) One graduate student reviewer noted: "The selections strike a good balance between accessibility and rigor." Another reader commented: "Missing some key voices in mathematical structuralism, but remains the standard introduction to philosophy of math."

The Foundations of Mathematics by Stewart Shapiro This text examines mathematical realism, structuralism, and the philosophical implications of different approaches to mathematical foundations.

Logic and Structure by Dirk van Dalen The book connects mathematical logic to set theory, model theory, and the foundations of mathematics through formal proofs and systematic development.

Philosophy of Set Theory by Mary Tiles This work explores the philosophical questions arising from set theory and its role as a foundation for mathematics.

Thinking about Mathematics by Stewart Shapiro The text presents the major philosophical views on the nature of mathematics from Plato to modern debates about mathematical truth and reality.

The Mathematical Experience by Philip J. Davis This book examines mathematics from multiple perspectives including its foundations, methods, and relationship to human thought and culture.

🔰 This influential anthology, first published in 1964, helped establish philosophy of mathematics as a distinct subfield within analytic philosophy 📚 The book includes landmark essays by Kurt Gödel, Willard Van Orman Quine, and other prominent mathematicians and philosophers who shaped 20th-century mathematical thought 🎓 Co-editor Paul Benacerraf's essay "What Numbers Could Not Be" (included in the collection) revolutionized discussions about the nature of mathematical objects and remains widely debated today 💡 The second edition (1983) added crucial new material reflecting developments in mathematical structuralism and the foundations of mathematics debate 🤝 Co-editors Benacerraf and Putnam were both students of logical positivist Hans Reichenbach, though they later developed opposing views on mathematical truth and reality