Format:
Online-Ressource (XXV, 1062 S, digital)
ISBN:
9783540694441
Series Statement:
SpringerLink
Content:
Introduction -- Hilbert's Lectures on Principles of Mathematics from 1917-18 -- Hilbert's Lectures on the Logical Calculus from 1920 -- Chapter 3: Hilbert's Lectures on Problems of Mathematical Logic from 1920 -- Hilbert's Lectures on Foundations of Mathematics from 1921-22 -- Hilbert's Lectures on Logical Foundations of Mathematics from 1922-23 -- Hilbert's Lectures on the Infinite from 1924-25 -- Hilbert's Typescript on the Foundations of Thought from c. 1925 -- Hilbert's Lecture on Infinity from 1933 -- Miscellanea -- Appendix A: Bernays's Habilitation Thesis from 1918 -- Appendix B: First Edition of Hilbert and Ackermann, 1928.
Content:
The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.
Note:
Description based upon print version of record
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Preface; Contents; 1. Presentation of the Documents; 2. Rules for the Constitution of Hilbert's Annotations; 3. Rules for the Constitution of Texts Prepared by Hilbert's Collaborators; 4. General Procedure; The Layout; Footnotes, Marginal Remarks and Larger Pieces of Text; Spelling and Punctuation; Omissions and Repetitions; Additions, Deletions and Substitutions; Text Obscured by Pasting; Textual Symbols; The Editing and Reproduction of the Texts; Introduction; 1. 1899-1917: Towards Mathematical Logic; 2. 1917-1920: Logic and Metamathematics; 3. 1920-1922: From Logic Towards Proof Theory
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4. 1922-1925: Finitist Proof Theory5. 1925-1931: An Elementary Finiteness Theorem?; 6. Material Omitted from this Volume; Chapter 1 Lectures on the Principles of Mathematics; Introduction; 1. Intellectual Context; 2. Broad Overview; 3. Logical Calculi and Existential Axiomatics; 4. Metalogical Issues; 4.1 Decidability; 4.2. Independence and Consistency; 4.3. Completeness; 5. Higher-Order Logic and the Development of Arithmetic; 6. Some Historical Issues; 6.1. Russellian Connections; 6.2. Relationship to the Textbook Hilbert and Ackermann 1928; 6.3. Collaboration with Bernays
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6.4 Working methods and 'nostrification'6.5 The Text of the Lectures; Prinzipien der Mathematik; A. Axiomatische Methode; I. Axiome der Verknüpfung; II. Axiome der Anordnung; III. Axiome der Kongruenz; IV. Parallelen-Axiom; V. Axiome der Stetigkeit; B Mathematische Logik; Textual Notes; Description of the Text; Appendix:The Bernays Habilitation Thesis of 1918; Introduction to Paul Bernays: 'Beiträge zur axiomatischen Behandlung des Logik-Kalküls' (Göttingen Habilitationsschrift, 1918); 1. Formal Systems.; 2. Completeness, Consistency and Decidability; 3. Independence
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4. Axioms and Rules of Inference5. The Puzzle of Completeness; Beiträge zur axiomatischen Behandlung des Logik-Kalküls; Eingereicht Göttingen 1918; Textual Notes; Description of the Text; Chapter 2 Lectures on Logic; Introduction to the 1920 Lectures; 1. Logical Calculus; 2. Strict Finitist Number Theory; 3. Interlude: Brouwer and Weyl; 4. The Summer Semester Lectures; 4.1. Constructive Restrictions; 4.2. Zermelo's Set Theory; 4.3. The Axiom of Reducibility; 5. Direct Consistency Proofs; 6. Note on the Texts; Logik-Kalkül; Textual Notes; Description of the Text
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Probleme der mathematischen LogikTextual Notes; Description of the Text; Introduction to the Undated Draft; 1. Background; 2. Correctness proof, attempted; 3. Correctness proof, repaired; 4. Consistency proof and extensions; 5. Historical and methodological remarks; 6. Note on the Text; (Undated Draft); Textual Notes; Description of the Text; Chapter 3 Lectures on Proof Theory; Introduction; 1. Direct Proofs; 2. Finitist Proof Theory: Sentential Logic; 3. Finitist Proof Theory: Quantifiers; Grundlagen der Mathematik (1921/22); Inhalts-Übersicht
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I. Bisherige Beweismethoden für Widerspruchsfreiheit
Additional Edition:
ISBN 9783540205784
Additional Edition:
Erscheint auch als Druck-Ausgabe Hilbert, David, 1862 - 1943 David Hilbert's lectures on the foundations of mathematics and physics ; 3: David Hilbert's lectures on the foundations of arithmetic and logic Berlin : Springer, 2013 ISBN 3540205780
Additional Edition:
ISBN 9783540205784
Language:
German
Subjects:
Mathematics
DOI:
10.1007/978-3-540-69444-1
Author information:
Ewald, William Bragg 1925-
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