Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite. – Contents : – Preface; – 1. Objects and logic; – 2. Structuralism and nominalism; – 3. Modality and structuralism; – 4. A problem about sets; – 5. Intuition; – 6. Numbers as objects; – 7. Intuitive arithmetic and its limits; – 8. Mathematical induction; – 9. Reason.