Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the metaphysical nature of its objects. Taking mathematics at face value seems to favour the Platonist view according to which mathematics concerns causally inert objects existing outside space‐time, but this view seems to preclude any account of how we acquire mathematical knowledge without using some mysterious intellectual intuition. In this book, I defend a version of mathematical realism, motivated ... More

Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the metaphysical nature of its objects. Taking mathematics at face value seems to favour the Platonist view according to which mathematics concerns causally inert objects existing outside space‐time, but this view seems to preclude any account of how we acquire mathematical knowledge without using some mysterious intellectual intuition. In this book, I defend a version of mathematical realism, motivated by the indispensability of mathematics in science, according to which (1) mathematical objects exist independently of us and our constructions, (2) much of contemporary mathematics is true, and (3) mathematical truths obtain independently of our beliefs, theories, and proofs.