Lectures on the Philosophy of Mathematics

In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice.

He treats philosophical issues as they arise organically in mathematics, discussing topics such as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts.

The book is organized by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that repeatedly give rise to philosophical considerations.