Philosophy and Model Theory
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Product details:
- Publisher OUP Oxford
- Date of Publication 15 March 2018
- ISBN 9780198790396
- Binding Hardback
- No. of pages544 pages
- Size 241x162x37 mm
- Weight 940 g
- Language English 0
Categories
Short description:
Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike.
MoreLong description:
Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics.
But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers.
The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures.
Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.
The book provides a masterly overview of many central stakes in philosophy of mathematics where model theory is involved, either as a source or as a tool. Anyone interested in mathematical structures, in categoricity, or in internalization of semantics, especially in the cases of arithmetic and set theory, will find everything she is looking for, and more.
Table of Contents:
A: Reference and realism
Logics and languages
Permutations and referential indeterminacy
Ramsey sentences and Newman's objection
Compactness, infinitesimals, and the reals
Sameness of structure and theory
B: Categoricity
Modelism and mathematical doxology
Categoricity and the natural numbers
Categoricity and the sets
Transcendental arguments
Internal categoricity and the natural numbers
Internal categoricity and the sets
Internal categoricity and truth
Boolean-valued structures
C: Indiscernibility and classification
Types and Stone spaces
Indiscernibility
Quantifiers
Classification and uncountable categoricity
D: Historical appendix
A short history of model theory
