Thomas Aquinas’ Mathematical Realism

Jean W. Rioux is Professor and Chair of the Philosophy Department at Benedictine College, Atchison, USA. 

Chapter 1: Introduction.- Part 1: Mathematical Realism in Plato and Aristotle.- Chapter 2: Plato on Mathematics and the Mathematicals.- Chapter 3: Aristotle on the Objects of Mathematics.- Chapter 4: Aristotle on The Speculative and Middle Sciences. - Chapter 5: Aristotle on Abstraction and Intelligible Matter. Part 2: Mathematical Realism in Aquinas.- Chapter 6: The Objects of Mathematics, Mathematical Freedom, and the Art of Mathematics.- Chapter 7: To Be Virtually.- Chapter 8: Mathematics and the Liberal Arts.- Chapter 9: The Place of the Imagination in Mathematics.- Part 3: Aristotle, Aquinas, and Modern Philosophies of Mathematics.- Chapter 10: Subsequent Developments in Number Theory.- Chapter 11: Non-Euclidean Geometry.- Chapter 12: Cantor, Finitism, and the 20th-Century Controversies.- Chapter 13: Realism and Non-Realism in Mathematics.- Chapter 14: This account as compared to other modern Aristotelian-Thomistic accounts.- Chapter 15: Foundations Restored?

"Jean Rioux has written an admirable synthesis of the main debates in the philosophy of mathematics between those of a largely classical perspective ... . The book weaves together three main threads ... . The best quality of the book is precisely Rioux's interweaving of the threads of his investigation." (Timothy Kearns, Thomistica, thomistica.net, November 21, 2023)

“Jean Rioux has written an admirable synthesis of the main debates in the philosophy of mathematics between those of a largely classical perspective ... . The book weaves together three main threads … . The best quality of the book is precisely Rioux’s interweaving of the threads of his investigation.” (Timothy Kearns, Thomistica, thomistica.net, November 21, 2023)