The Oxford Handbook of Philosophy of Mathematics and Logic
This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the book begins with a historical section, consisting of a chapter on the modern period, Kant and his intellectual predecessors, a chapter on later...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
New York
Oxford University Press
03.03.2005
Oxford University Press, Incorporated |
| Vydání: | 1 |
| Edice: | Oxford Handbooks in Philosophy |
| Témata: | |
| ISBN: | 0195148770, 9780195148770 |
| On-line přístup: | Získat plný text |
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| Abstract | This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the book begins with a historical section, consisting of a chapter on the modern period, Kant and his intellectual predecessors, a chapter on later empiricism, including Mill and logical positivism, and a chapter on Wittgenstein. The next section of the volume consists of seven chapters on the views that dominated the philosophy and foundations of mathematics in the early decades of the 20th century: logicism, formalism, and intuitionism. They approach their subjects from a variety of historical and philosophical perspectives. The next section of the volume deals with views that dominated in the later twentieth century and beyond: Quine and indispensability, naturalism, nominalism, and structuralism. The next chapter in the volume is a detailed and sympathetic treatment of a predicative approach to both the philosophy and the foundations of mathematics, which is followed by an extensive treatment of the application of mathematics to the sciences. The last six chapters focus on logical matters: two chapters are devoted to the central notion of logical consequence, one on model theory and the other on proof theory; two chapters deal with the so-called paradoxes of relevance, one pro and one contra; and the final two chapters concern second-order logic (or higher-order logic), again one pro and one contra. |
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| AbstractList | This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the book begins with a historical section, consisting of a chapter on the modern period, Kant and his intellectual predecessors, a chapter on later empiricism, including Mill and logical positivism, and a chapter on Wittgenstein. The next section of the volume consists of seven chapters on the views that dominated the philosophy and foundations of mathematics in the early decades of the 20th century: logicism, formalism, and intuitionism. They approach their subjects from a variety of historical and philosophical perspectives. The next section of the volume deals with views that dominated in the later twentieth century and beyond: Quine and indispensability, naturalism, nominalism, and structuralism. The next chapter in the volume is a detailed and sympathetic treatment of a predicative approach to both the philosophy and the foundations of mathematics, which is followed by an extensive treatment of the application of mathematics to the sciences. The last six chapters focus on logical matters: two chapters are devoted to the central notion of logical consequence, one on model theory and the other on proof theory; two chapters deal with the so-called paradoxes of relevance, one pro and one contra; and the final two chapters concern second-order logic (or higher-order logic), again one pro and one contra. 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 generalphilosophical 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 lastdecade 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 assubstantial 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 thediscipline, from advanced undergraduates to professional philosophers, mathematicians, and historians. |
| Author | Shapiro, Stewart |
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| Keywords | nominalism higher-order logic formalism logical consequence mathematics logical positivism logicism naturalism structuralism paradoxes of relevance Wittgenstein Quine empiricism John Stuart Mill intuitionism indispensability second-order logic Immanuel Kant logic predicativity |
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| Snippet | This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the... 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... |
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| SubjectTerms | 20th-Century Philosophy Logic Logic, Symbolic and mathematical Mathematics Philosophy Philosophy of Mathematics and Logic |
| TableOfContents | Intro -- 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 |
| Title | The Oxford Handbook of Philosophy of Mathematics and Logic |
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