Mathematical Thought and its Objects

Description

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.

Charles Parsons holds an AB (mathematics) and PhD (philosophy) from Harvard University and studied for a year at King's College, Cambridge. He was on the faculty at Harvard University from 1962-5 and 1989-2005 and at Columbia University from 1965-89. His publications are mainly in logic, philosophy of mathematics, and Kant. He was an editor of the posthumous works of Kurt Goedel (Collected Works, Volumes III-V).

'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