Model Theory and the Philosophy of Mathematical Practice: Formalization without Foundationalism
Cambridge University Press, 1/9/2020
EAN 9781316638835, ISBN10: 1316638839
Paperback, 366 pages, 24.4 x 17 x 2.1 cm
Language: English
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.
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. À, 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.