Mathematical Thought and its Objects

In Mathematical Thought and its Objects, Charles Parsons examines the notion of object.

Charles Parsons (Author)

9780521119115, Cambridge University Press

Paperback, published 17 September 2009

400 pages
23 x 15.3 x 2.5 cm, 0.61 kg

'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

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.

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.

Subject Areas: Philosophy of science [PDA], Mathematics [PB], Philosophy [HP]