The Logical Foundations of Mathematics
eBook - PDF

The Logical Foundations of Mathematics

Foundations and Philosophy of Science and Technology Series

  1. 330 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

The Logical Foundations of Mathematics

Foundations and Philosophy of Science and Technology Series

Book details
Table of contents
Citations

About This Book

The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.

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Yes, you can access The Logical Foundations of Mathematics by William S. Hatcher, Mario Bunge in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics Reference. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Pergamon
Year
2014
ISBN
9781483189635
Topic
Mathematics
Subtopic
Mathematics Reference
Index
Mathematics

Table of contents

  1. Front Cover
  2. The Logical Foundations of Mathematics
  3. Copyright Page
  4. Table of Contents
  5. Dedication
  6. Preface
  7. Chapter 1. First-order Logic
  8. Chapter 2. The Origin of Modern Foundational Studies
  9. Chapter 3. Frege's System and the Paradoxes
  10. Chapter 4. The Theory of Types
  11. Chapter 5. Zermelo-Fraenkel Set Theory
  12. Chapter 6. Hilbert's Program and Godel's Incompleteness Theorems
  13. Chapter 7. The Foundational Systems of W. V. Quine
  14. Chapter 8. Categorical Algebra
  15. Selected Bibliography
  16. Index