| Description |
1 online resource |
| Series |
Nordic Wittgenstein studies ; volume 7 |
|
Nordic Wittgenstein studies ; v. 7.
|
| Contents |
Intro -- Preface -- Acknowledgments -- Contents -- Abbreviations -- Part I Overview -- 1 Introduction: The Context of the Annotations and Our Method of Approach -- 1.1 Foundations of Mathematics in the Tractatus -- 1.2 Wittgenstein's Middle Period, 1929-1933 -- The Blue and Brown Books 1933-1935 -- 1.3 The Emergence of Philosophical Investigations, 1937-1944 -- 1.4 Wittgenstein and Hardy -- 1.5 Structure of This Book -- 2 Wittgenstein's Non-Extensionalist Point of View -- Part II Analysis of the Annotations -- 3 Irrational Numbers: The Annotations on pp. 2-9, with Commentary |
|
3.1 Application is Essential, First Pass -- 3.2 Mathematics and Its Applications, Second Pass -- 3.3 ̀̀Unsinn''? -- 3.4 First Proof of the Irrationality of 2 -- 3.5 Second Proof of the Irrationality of 2 -- 3.6 A Strange Transformation of Hardy's Proof -- 3.7 ̀̀Everything Leans a Little'' -- 3.8 The ̀̀Phantasmagoric'' -- 4 The Law of the Excluded Middle: A Digression -- 4.1 Improper Pictures -- 4.2 The Status of the Law of Excluded Middle -- 4.3 Understanding in Mathematics -- 4.4 God and the Law of Excluded Middle? -- 5 The Continuum of Real Numbers: The Annotations on pp. 10-30, with Commentary |
|
6.4 Teaching One's Opponent -- 6.5 The Importance of Methods -- 6.6 Definition of a Limit -- Part III More on Wittgenstein and the Real Numbers -- 7 Wittgenstein on Cantor's Diagonal Method (Felix Mühlhölzer) -- 7.1 Introduction -- 7.2 Cantor's Diagonal Method -- 7.3 The Simplicity of Cantor's Idea -- 7.4 The Novelty of Cantor's Idea -- 7.5 Wittgenstein on Uncountability -- 7.6 The Concept of ̀̀Ordering in a Series'' and Its Negation -- 7.7 The Multiplicity and Openness of the Concept ̀̀Real Number'' -- 7.8 Résumé -- 8 The Generality of Cantor's Diagonal Procedure (Juliet Floyd) |
|
8.1 Introduction -- 8.2 Technique in Later Wittgenstein -- 8.3 Aspects vs. Techniques -- 8.4 Definability: Hobson -- 8.5 Turing on the Diagonal Process (1936-1937) -- 8.6 Rule-Following (1936-1937) -- 8.7 Notebooks 162a-162b -- 8.8 Wittgenstein's Diagonal Argument (1947) -- Part IV Wittgenstein's Annotations to Hardy -- 9 Images, Transcripts and Translations of the Annotations -- References -- Index |
| Summary |
This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy's classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein's remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy's textbook. They then go on to outline Wittgenstein's non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers (annotations on pages 2-9 of the 1941 edition of Hardy's book), the law of excluded middle in mathematics and the notion of an "improper picture," the continuum of real numbers (annotations on pages 10-30), and Wittgenstein's attitude toward functions and limits, which scrutinizes his annotations on pages 40-47 and 117-121 and examines their challenges and meaning in light of underlying manuscripts. Overall, the authors show that Wittgenstein's argumentation should not be taken to reject Dedekind cuts per se, but only a one-sided, reductive extensionalism that belies actual mathematical practice. They discuss and defend Wittgenstein's version of non-extensionalism and, in two final essays, debate the nature and contemporary relevance of this view |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from digital title page (viewed on October 16, 2020) |
| Subject |
Wittgenstein, Ludwig, 1889-1951 -- Knowledge and learning
|
|
Hardy, G. H. (Godfrey Harold), 1877-1947. Course of pure mathematics
|
| SUBJECT |
Wittgenstein, Ludwig, 1889-1951 fast |
| Subject |
Numbers, Real.
|
|
History of mathematics.
|
|
History of science.
|
|
Philosophy of mathematics.
|
|
Mathematics -- History & Philosophy.
|
|
Science -- History.
|
|
Learning and scholarship
|
|
Numbers, Real
|
| Form |
Electronic book
|
| Author |
Mühlhölzer, Felix, author
|
| ISBN |
9783030484811 |
|
3030484815 |
|
