The Foundations of Mathematics

Name: The Foundations of Mathematics | A Study in the Philosophy of Science
Brand: Elsevier
Price: 215.0 EUR
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A Study in the Philosophy of Science

Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

781 Seiten

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978-0-08-095745-6 (ISBN)

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Inhalt

Front Cover
The Foundations of Mathematics: A Study in the Philosophy of Science
Copyright Page
Summary Table of Contents
Preface
Remarks on Terminology and Notation-Instructions for Use
Part I: The Historical Background of Research into the Foundations of Mathematics
Chapter 1. The Prehistory of Research into Foundations (Sections 1-10)
Chapter 2. Aristotle's Theory of Science (Sections 11-21)
Chapter 3. Historical Development of Symbolic Logic and Formalised Axiomatics (Sections 22-29)
Part II: Elementary Axiomatics
Chapter 4. Introduction (Sections 30-35)
Chapter 5. Extension of the System of Natural Numbers (Sections 36-42)
Chapter 6. The Theory of Natural Numbers (Sections 43-53)
Chapter 7. Axiomatics of Fundamental Theories of Modern Mathematics (Sections 54-58)
Part III: Formalised Axiomatics
Chapter 8. Introduction (Sections 59-71)
Chapter 9. Survey of Symbolic Logic (Sections 72-80)
Chapter 10. Finitary Theory of Proof (Sections 81-85)
Part IV: Non-Elementary Metamathematics
Chapter 11. Syntax (Sections 86-97)
Chapter 12. Semantics (Sections 98-104)
Part V: The Existence of Mathematical Entities
Chapter 13. Logicism (Sections 105-110)
Chapter 14. Cantorism (Sections 111-130)
Chapter 15. Intuitionism (Sections 131-145)
Chapter 16. Nominalism (Sections 146-153)
Part VI: The Paradoxes
Chapter 17. The Paradoxes of Logic and Set Theory and Their Solution (Sections 154-180)
Part VII: Applications of Set Theory and Topology in Metamathematics
Chapter 18. Completeness Theorems for Logical Systems (Sections 181-186)
Chapter 19. The Calculus of Systems and Models (Sections 187-196)
Chapter 20. Further Applications of Topological Methods (Sections 197-210)
Part VIII: Recursive Functions, Sets, and Predicates
Chapter 21. The Theory of Recursive Functions and the Negative Results Concerning the Decision Problem (Sections 211-221)
Part IX: Concluding Remarks
Chapter 22. Metamathematics, Philosophy of Mathematics, and General Philosophy (Sections 222-232)
Exercises I-LXXXVIII
Bibliography
Index of Authors
Index of Subjects
Table of Contents
Harper Torchbooks

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