The Oxford Handbook of Philosophy of Mathematics and Logic (Oxford Handbooks in Philosophy)

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. 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. Philosophy Of Mathematics And Its Logic : Introduction / Stewart Shapiro -- Apriority And Application : Philosophy Of Mathematics In The Modern Period / Lisa Shabel -- Later Empiricism And Logical Positivism / John Skorupski -- Wittgenstein On Philosophy Of Logic And Mathematics / Juliet Floyd -- The Logicism Of Frege, Dedekind, And Russell / William Demopoulos, Peter Clark -- Logicism In The Twenty-first Century / Bob Hale, Crispin Wright -- Logicism Reconsidered / Agustín Rayo -- Formalism / Michael Detlefsen -- Intuitionism And Philosophy / Carl Posy -- Intuitionism In Mathematics / C.c. Mccarty -- Intuitionism Reconsidered / Roy Cook -- Quine And The Web Of Belief / Michael D. Resnik -- Three Forms Of Naturalism / Penelope Maddy -- Naturalism Reconsidered / Alan Weir -- Nominalism / Charles Chihara -- Nominalism Reconsidered / Gideon Rosen, John P. Burgess -- Structuralism / Geoffrey Hellman -- Structuralism Reconsidered / Fraser Macbride -- Predicativity / Solomon Feferman -- Mathematics - Application And Applicability / Mark Steiner -- Logical Consequence, Proof Theory, And Model Theory / Stewart Shapiro -- Logical Consequence From A Constructivist Point Of View / Dag Prawitz -- Relevance In Reasoning / Neil Tennant -- No Requirement Of Relevance / John P. Burgess -- Higher-order Logic / Stewart Shapiro -- Higher-order Logic Reconsidered / Ignacio Jané. Edited By Stewart Shapiro. Includes Bibliographical References And Index. Contents Notes on the Contributors 1. Philosophy of Mathematics and Its Logic: Introduction 2. Apriority and Application: Philosophy of Mathematics in the Modern Period 3. Later Empiricism and Logical Positivism 4. Wittgenstein on Philosophy of Logic and Mathematics 5. The Logicism of Frege, Dedekind, and Russell 6. Logicism in the Twenty-first Century 7. Logicism Reconsidered 8. Formalism 9. Intuitionism and Philosophy 10. Intuitionism in Mathematics 11. Intuitionism Reconsidered 12. Quine and the Web of Belief 13. Three Forms of Naturalism 14. Naturalism Reconsidered 15. Nominalism 16. Nominalism Reconsidered 17. Structuralism 18. Structuralism Reconsidered 19. Predicativity 20. Mathematics—Application and Applicability 21. Logical Consequence, Proof Theory, and Model Theory 22. Logical Consequence From a Constructivist Point of View 23. Relevance in Reasoning 24. No Requirement of Relevance 25. Higher-order Logic 26. Higher-order Logic Reconsidered Index A B C D E F G H I J K L M N O P Q R S T U V W Y Z "The Oxford Handbook of Philosophy of Mathematics and Logic is a groundbreaking reference like no other in its field. It is a central resource for those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and for those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians."--Jacket FROM the beginning, Western philosophy has had a fascination with mathematics.