Charles Parsons

Mathematical Thought and its Objects (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 24. Dezember 2007
• Englisch
• ISBN-13: 9780511372582
• Artikelnr.: 38211892

Autorenporträt

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 Gödel (Collected Works, Volumes III-V).

Inhaltsangabe

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.