Mathematical Thought and its Objects [Paperback]

In Mathematical Thought and its Objects, Charles Parsons examines the notion of object.In Mathematical Thought and Its Objects, 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.In Mathematical Thought and Its Objects, 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.In Mathematical Thought and Its Objects, 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.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.'This complete presentation of structuralism as a foundation programme in the philosophy of mathematics enriches significantly the debate and anyone interested in this area of studies will need to consider its relevance.' Minds & Machines