Joel David Hamkins.
Lectures on the Philosophy of Mathematics.
MIT Press. 2020
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 such topics as platonism, realism, logicism, structuralism, formalism, infinity,
and intuitionism in mathematical contexts.
He organizes the book by mathematical themes—numbers, rigor, geometry, proof,
computability, incompleteness, and set theory—that give rise again and again
to philosophical considerations.
Throughout, Hamkins offers a clear and engaging exposition
that is both accessible and sophisticated, intended for readers whose mathematical backgrounds range
from novice to expert.