The Oxford Handbook of Philosophy of Mathematics and Logic

This Oxford Handbook covers the current state of the art in the philosophy of maths and logic in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 newly-commissioned chapters are by established experts in the field and contain both exposition and criticism as well as substantial development of their own positions. Select major positions are represented by two chapters - one supportive and one critical. The book includes a comprehensive bibliography.

Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.

The Oxford Handbook of the Philosophy of Mathematics and Logic is a very accessible, wide ranging work that serves not only to indicate the 'state of the art' in the given area, but, remarkably, also serves as a very fine introduction to the field. I recommend it highly, both to workers in the given field and, equally, to the 'general philosopher,' regardless of one's main area.

Autorentext
Stewart Shapiro is O'Donnell Professor of Philosophy at The Ohio State University and Professorial Fellow at the Arché Centre, University of St. Andrews.

Klappentext
Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general
philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last
decade has seen an explosion of scholarly work in these areas.
This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as
substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical.
The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the
discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Inhalt
1. Philosophy of Mathematics and Its Logic: Introductory Overview; 2. Philosophy of Mathematics in the Modern Period; 3. Later Empiricism and Logical Positivism; 4. The Logicism of Frege, Dedekind and Russell; 5. Logicism in the 21st Century; 6. Logicism Reconsidered; 7. Formalism; 8. Intuitionism; 9. Intuitionism and Mathematics; 10. Intuitionism Reconsidered; 11. Quine and the Web of Belief; 12. Three Forms of Naturalism; 13. Naturalism Reconsidered; 14. Nominalism; 15. Nominalism Reconsidered; 16. Structuralism; 17. Structuralism Reconsidered; 18. Predicativity; 19. Mathematics - Application and Applicability; 20. Logical Consequence, Proof Theory, and Model Theory; 21. Logical Consequence From a Constructivist Point of View; 22. Relevance in Reasoning; 23. No Requirement of Relevance; 24. Higher-order Logic; 25. Higher-order Logic Reconsidered

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