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Model Theory and the Philosophy of Mathematical Practice

Model Theory and the Philosophy of Mathematical Practice
Formalization without Foundationalism

  • Date Published: January 2018
  • availability: Available
  • format: Hardback
  • isbn: 9781107189218


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About the Authors
  • Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.

    • Explains the philosophical significance of the transformation in model theory and its impact on traditional mathematics
    • The technical logic is grounded in historical and philosophical contexts, making the subject accessible to philosophers as well as mathematicians
    • Includes source materials from model theorists discussing their methods and motivations
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    Product details

    • Date Published: January 2018
    • format: Hardback
    • isbn: 9781107189218
    • length: 362 pages
    • dimensions: 254 x 178 x 23 mm
    • weight: 0.78kg
    • contains: 8 b/w illus.
    • availability: Available
  • Table of Contents

    Part I. Refining the Notion of Categoricity:
    1. Formalization
    2. The context of formalization
    3. Categoricity
    Part II. The Paradigm Shift:
    4. What was model theory about?
    5. What is contemporary model theory about?
    6. Isolating tame mathematics
    7. Infinitary logic
    8. Model theory and set theory
    Part III. Geometry:
    9. Axiomatization of geometry
    10. π, area, and circumference of circles
    11. Complete: the word for all seasons
    Part IV. Methodology:
    12. Formalization and purity in geometry
    13. On the nature of definition: model theory
    14. Formalism-freeness
    15. Summation.

  • Author

    John T. Baldwin, University of Illinois, Chicago
    John T. Baldwin is Professor Emeritus in the Department of Mathematics, Statistics and Computer Science at the University of Illinois, Chicago. He has published widely on mathematics and philosophy, and he is the author of books including Fundamentals of Stability Theory (1988) and Categoricity (2009).

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