POINCARE AND THE PHILOSOPHY OF MATHEMATICS (Macmillan Studies in Contemporary Philosophy)

FOLINA Janet

Published by Palgrave Macmillan [&] Scots Philosophical Club, 1992

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From Rothwell & Dunworth (ABA, ILAB), Dulverton, United Kingdom Seller rating 5 out of 5 stars

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1st edn. 8vo. Original silver lettered black cloth (accession sticker at tail of spine - otherwise VG), no dustwrapper. Pp. xvii + 202 (ex academic library with usual stamps and markings). Seller Inventory # 184720

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Title: POINCARE AND THE PHILOSOPHY OF MATHEMATICS (...
Publisher: Palgrave Macmillan [&] Scots Philosophical Club, 1992
Binding: Hardcover
Edition: 1st Edition

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Poincar� and the Philosophy of Mathematics (MacMillan Studies in Contemporary Philosophy)

Folina, Janet M.

Published by Macmillan Press in association with the Scots Philosophical Club, 1992

ISBN 10: 0333558324 ISBN 13: 9780333558324

Used Hardcover First Edition

Seller: killarneybooks, Inagh, CLARE, Ireland

Seller rating 5 out of 5 stars

Hardcover. Condition: Very Good. No Jacket. 1st Edition. Hardcover, xvii + 202 pages, NOT ex-library. No dust jacket. Book is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Shelfworn ISBN sticker on the rear board. -- This book is a sympathetic reconstruction of Henri Poincar's anti-realist philosophy of mathematics. Although Poincar is recognized as the greatest mathematician of the late 19th century, his contribution to the philosophy of mathematics is not highly regarded. Many regard his remarks as idiosyncratic, and based upon a misunderstanding of logic and logicism. This book argues that Poincar's critiques are not based on misunderstanding; rather, they are grounded in a coherent and attractive foundation of neo-Kantian constructivism. -- Contents: Preface; Introduction; I. Kant and Mathematics, an Outline 1 Basic Distinctions 2 Synthetic a Priori 3 Synthetic a Priori Instantiated: Geometry 4 Synthetic a Priori Instantiated: Arithmetic 5 Foundation of the Theory of the Synthetic a Priori 6 Re-examination of How the Theory Works: A Precarious Analogy 7 Key to the Synthetic Aspect of Arithmetic: Induction; II. Introduction to Poincar�'s Theory of the Synthetic a Priori 1 Synthetic a Priori and Time 2 Synthetic a Priori and Space; III. Defending Mathematical Apriorism 1 Certainty and a Priori Knowledge 2 Definition of 'a Priori Warrant' and Some Counterexamples 3 Critique of Kitcher's Account 4 Alternative Ways to Look at the Relationship Between Apriority and Defeasibility 5 Defending Mathematical Apriorism by Defending the Traditional Account of a Priori Knowledge 6 Conclusion; IV. Logic and Intuition 1 Poincar�'s Conception of Logic: Is It a Mere Misconception? 2 Russell's Logicism Does Not Refute Kant 3 Intuitions and Poincar�'s Theory of 'Glossing Over'; V. The Attack on Logicism 1 Analysis of the Principle of Induction 2 Problem of Induction for the Logicists 3 Some Attempts to a Void the Circle 4 Second Order Principle 5 Non-inductive Arithmetic 6 Synthetic a Priori Nature of Arithmetic Intuition; VI. Set Theory and the Continuum 1 Poincar�'s Theory of Definitions 2 Axioms and Intuitions 3 Epistemology and the Characterisation Problem 4 Limits of the Arithmetisation of the Continuum 5 Sets as Contained Collections 6 Crucial Importance of Cantor's Result for Poincar�'s Theory of the Continuum 7 Argument for the Existence of Geometric Intuition [Argument That Continuity Is Foundational; Physical Discontinuity and Mathematical Continuity]; VII. Poincar�'s Theory of Predicativity 1 Poincar� and Platonism 2 Analysis of the Concept of Impredicativity 3 Emergence of the Concept [Poincar�'s Account; Russell's Account]; 4 Objection to Zermelo's Solution 5 Poincar�'s Diagnosis and Solution of the Paradoxes [Circles, Vicious Circles, and Two Types of Definitions; Poincar�'s Conception of Sets as Constructed Entities, and His 'True Solution']; VIII. Poincar�'s Theory of Meaning 1 Poincar�'s Criterion of Meaningfulness 2 How Poincar� Employs the Notion 3 A Generalised Version of the Criterion 4 Why Poincar�'s Theory of Meaning Is Not Intuitionistic 5 Potential Infinity and the Domain Argument Blocked 6 Why the Strict Finitist Objects to Potential Infinity 7 Poincar� Against the Finitist: the Metaphor of Construction; 9 Conclusion: Summary of Poincar�'s 'Middle Position' Between Intuitionism and Platonism; Bibliography; Author Index; Subject Index. Seller Inventory # 006844

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