Model Theory and the Philosophy of Mathematical Practice
Formalization without Foundationalism
- Author: John T. Baldwin, University of Illinois, Chicago
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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.Read more
- 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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- Date Published: February 2018
- format: Adobe eBook Reader
- isbn: 9781108103015
- contains: 8 b/w illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Part I. Refining the Notion of Categoricity:
2. The context of formalization
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
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