Mathematical Thought and Its Objects

Erscheinungsjahr 2009
ISBN: 978-0-521-11911-5
Verlag: Cambridge University Press

Buch, Englisch, 400 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 647 g

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.

Autoren/Hrsg.

Parsons, Charles

Fachgebiete

• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie

Inhaltsverzeichnis

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.

Über Autor(innen)

Parsons, Charles
Charles Parsons is Edgar Pierce Professor of Philosophy, Emeritus, at Harvard University. He held appointments at Columbia (1965-1989) and Harvard (1989-2005). He is author of Mathematics in Philosophy (1983) and Mathematical Thought and its Objects (2008) and editor, with Solomon Feferman and others, of the posthumous works of Kurt Gödel (Collected Works, Vols. III-V, 1995, 2003). He is a former President of the Association for Symbolic Logic.