Joel D. Hamkins.Lectures on the Philosophy of Mathematics.

"Joel D. Hamkins.Lectures on the Philosophy of Mathematics" is an introductory textbook written by a prominent set theorist. The book covers both mathematical and philosophical material, combining interesting mathematical material with discussions of philosophical issues. While the book may cover too much mathematical material for some readers, it could be of great interest to students studying a combination of math and philosophy. The book is divided into chapters on Number, Rigor, Infinity, Geometry, Proof, Computability, Incompleteness, and Set theory, with the chapters on Number and Set theory being the longest. The author often adopts a lecturing attitude, introducing key ideas but leaving the issues open for further exploration. The book also discusses the ontological controversy between the universe and multiverse views in set theory, with the author presenting arguments for the multiverse view. Overall, the book provides a wide and ambitious coverage of the philosophy of mathematics, although some readers may find certain topics could have been presented in a different light or more carefully. [Extracted from the article]