Model Theory and the Philosophy of Mathematical Practice: Formalization without Foundationalism

By: John T. Baldwin

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Synopsis: 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 motivation.