{"product_id":"philosophy-of-mathematics-isbn-9781405189910","title":"Philosophy of Mathematics","description":"\u003cp\u003e\u003cb\u003e\u003ci\u003ePhilosophy of Mathematics: An Introduction\u003c\/i\u003e provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eOffers beginning readers a critical appraisal of philosophical viewpoints throughout history\u003c\/li\u003e \u003cli\u003eGives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism\u003c\/li\u003e \u003cli\u003eProvides readers with a non-partisan discussion until the final chapter, which gives the author's personal opinion on where the truth lies\u003c\/li\u003e \u003cli\u003eDesigned to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals\u003c\/li\u003e \u003c\/ul\u003e  Introduction. \u003cp\u003e\u003cb\u003ePart I: Plato versus Aristotle:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e\u003cu\u003eA. Plato\u003c\/u\u003e.\u003c\/p\u003e \u003cp\u003e1. The Socratic Background.\u003c\/p\u003e \u003cp\u003e2. The Theory of Recollection.\u003c\/p\u003e \u003cp\u003e3. Platonism in Mathematics.\u003c\/p\u003e \u003cp\u003e4. Retractions: the Divided Line in Republic VI (509d−511e).\u003c\/p\u003e \u003cp\u003e\u003cu\u003eB. Aristotle\u003c\/u\u003e.\u003c\/p\u003e \u003cp\u003e5. The Overall Position.\u003c\/p\u003e \u003cp\u003e6. Idealizations.\u003c\/p\u003e \u003cp\u003e7. Complications.\u003c\/p\u003e \u003cp\u003e8. Problems with Infinity.\u003c\/p\u003e \u003cp\u003e\u003cu\u003eC. Prospects\u003c\/u\u003e.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II: From Aristotle to Kant:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Medieval Times.\u003c\/p\u003e \u003cp\u003e2. Descartes.\u003c\/p\u003e \u003cp\u003e3. Locke, Berkeley, Hume.\u003c\/p\u003e \u003cp\u003e4. A Remark on Conceptualism.\u003c\/p\u003e \u003cp\u003e5. Kant: the Problem.\u003c\/p\u003e \u003cp\u003e6. Kant: the Solution.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III: Reactions to Kant:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Mill on Geometry.\u003c\/p\u003e \u003cp\u003e2. Mill versus Frege on Arithmetic.\u003c\/p\u003e \u003cp\u003e3. Analytic Truths.\u003c\/p\u003e \u003cp\u003e4. Concluding Remarks.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV: Mathematics and its Foundations:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Geometry.\u003c\/p\u003e \u003cp\u003e2. Different Kinds of Number.\u003c\/p\u003e \u003cp\u003e3. The Calculus.\u003c\/p\u003e \u003cp\u003e4. Return to Foundations.\u003c\/p\u003e \u003cp\u003e5. Infinite Numbers.\u003c\/p\u003e \u003cp\u003e6. Foundations Again.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V: Logicism:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Frege.\u003c\/p\u003e \u003cp\u003e2. Russell.\u003c\/p\u003e \u003cp\u003e3. Borkowski\/Bostock.\u003c\/p\u003e \u003cp\u003e4. Set Theory.\u003c\/p\u003e \u003cp\u003e5. Logic.\u003c\/p\u003e \u003cp\u003e6. Definition.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI: Formalism:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Hilbert.\u003c\/p\u003e \u003cp\u003e2. Gödel.\u003c\/p\u003e \u003cp\u003e3. Pure Formalism.\u003c\/p\u003e \u003cp\u003e4. Structuralism.\u003c\/p\u003e \u003cp\u003e5. Some Comments.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VII: Intuitionism:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Brouwer.\u003c\/p\u003e \u003cp\u003e2. Intuitionist Logic.\u003c\/p\u003e \u003cp\u003e3. The Irrelevance of Ontology.\u003c\/p\u003e \u003cp\u003e4. The Attack on Classical Logic.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VIII: Predicativism:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e1. Russell and the VCP.\u003c\/p\u003e \u003cp\u003e2. Russell’s Ramified Theory and the Axiom of Reducibility.\u003c\/p\u003e \u003cp\u003e3. Predicative Theories after Russell.\u003c\/p\u003e \u003cp\u003e4. Concluding Remarks.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IX: Realism versus Nominalism:\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e\u003cu\u003eA. Realism\u003c\/u\u003e.\u003c\/p\u003e \u003cp\u003e1. Gödel.\u003c\/p\u003e \u003cp\u003e2. Neo-Fregeans.\u003c\/p\u003e \u003cp\u003e3. Quine and Putnam.\u003c\/p\u003e \u003cp\u003e\u003cu\u003eB. Nominalism\u003c\/u\u003e.\u003c\/p\u003e \u003cp\u003e4. Reductive Nominalism.\u003c\/p\u003e \u003cp\u003e5. Fictionalism.\u003c\/p\u003e \u003cp\u003e6. Concluding Remarks.\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex\u003c\/p\u003e  \u003cp\u003e“Given this caveat, Bostock’s new book is highly recommendable as a text for undergraduate seminars in the philosophy of mathematics and also for individual study. It covers all the essentials and more. It should appeal not only to students who have already developed a preference for the general approach and style of contemporary analytic philosophy, but also to a broader audience of students and to people with a non-professional interest in philosophy and mathematics.”  (\u003ci\u003eErkenn\u003c\/i\u003e, 2011)\u003c\/p\u003e \"This is a concise as well as comprehensive presentation of core topics in the philosophy of mathematics, written in a clear and engaged manner, hence well readable.\" (Zentralblatt MATH, 2011)  \u003cp\u003e\"This book is an undergraduate introduction to the basic ideas on the nature of mathematics that have played a significant role in the development of philosophy from Antiquity to contemporary debates . . . throughout the book the emphasis is on the basic ideas as well as their current variations, leading up to recent debates between realists and nominalists.\" (Mathematical Reviews, 2011) \u003c\/p\u003e \u003cb\u003eDavid Bostock\u003c\/b\u003e has been a Fellow and Tutor in Philosophy at \u003cst1:placename w:st=\"on\"\u003eMerton\u003c\/st1:placename\u003e \u003cst1:placetype w:st=\"on\"\u003eCollege\u003c\/st1:placetype\u003e, and Lecturer in Philosophy at the \u003cst1:place w:st=\"on\"\u003e\u003cst1:placetype w:st=\"on\"\u003eUniversity\u003c\/st1:placetype\u003e of \u003cst1:placename w:st=\"on\"\u003eOxford\u003c\/st1:placename\u003e\u003c\/st1:place\u003e. His recent publications include \u003ci\u003eIntermediate Logic\u003c\/i\u003e (1997)\u003ci\u003e, Aristotle’s Ethics\u003c\/i\u003e (2000)\u003ci\u003e,\u003c\/i\u003e and \u003ci\u003eSpace, Time, Matter, and\u003c\/i\u003e \u003ci\u003eForm: Essays on Aristotle's Physics (2006)\u003c\/i\u003e.  In this new introduction to the philosophy of mathematics, David Bostock guides the reader through the basic ideas on the nature of mathematics that have played a major part in the development of philosophy from antiquity to the present.  \u003cp\u003eThe chapters proceed historically, beginning with the earliest serious views on the interpretation of mathematics, due to Plato and Aristotle. They then move quickly through the middle ages and the early moderns, but continue with extended discussions of Kant, Mill, and Frege. Later chapters explore the main schools of thought at the start of the twentieth century, i.e. the movements known as logicism, formalism, intuitionism, and what may be called predicativism. These chapters also discuss more modern variations on the same basic themes. Finally the book concludes with a discussion of the most recent debates between realists and nominalists. The emphasis throughout is not simply to describe, but to offer a critical appraisal of, the views discussed. The result is an engaging, clear, and remarkably comprehensive panorama of the major issues in the field.\u003c\/p\u003e \u003cp\u003eThe book assumes no prior knowledge of mathematics, beyond what is commonly taught in schools, and only a minimal exposure to standard philosophical terminology. It is aimed at undergraduates in philosophy and mathematics, but will also provide an important new perspective on the subject for more experienced readers.\u003c\/p\u003e  \"The best textbook on the philosophy of mathematics bar none\" –\u003ci\u003eAlexander Paseau, University of Oxford\u003c\/i\u003e  \u003cp\u003e\"Bostock's 'Philosophy of Mathematics' is remarkably comprehensive compared to other surveys of philosophy of mathematics. The writing is engaging and clear, and it treats a wide range of issues in considerable depth, including issues that are often ignored or downplayed in more general discussions.\" –\u003ci\u003eAlan Baker, Swarthmore College\u003c\/i\u003e\u003c\/p\u003e","brand":"Wiley-Blackwell","offers":[{"title":"Default Title","offer_id":47989780807909,"sku":"NP9781405189910","price":37.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781405189910.jpg?v=1761785441","url":"https:\/\/k12savings.com\/products\/philosophy-of-mathematics-isbn-9781405189910","provider":"K12savings","version":"1.0","type":"link"}