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Viser: Philosophy and Model Theory

Philosophy and Model Theory

Philosophy and Model Theory

Tim Button og Sean Walsh
(2018)
Sprog: Engelsk
Oxford University Press, Incorporated
1.510,00 kr.
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Detaljer om varen

  • Hardback: 544 sider
  • Udgiver: Oxford University Press, Incorporated (Maj 2018)
  • Forfattere: Tim Button og Sean Walsh
  • ISBN: 9780198790396
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.
A: Reference and realism1. Logics and languages2. Permutations and referential indeterminacy3. Ramsey sentences and Newman's objection4. Compactness, infinitesimals, and the reals5. Sameness of structure and theoryB: Categoricity6. Modelism and mathematical doxology7. Categoricity and the natural numbers8. Categoricity and the sets9. Transcendental arguments10. Internal categoricity and the natural numbers11. Internal categoricity and the sets12. Internal categoricity and truth13. Boolean-valued structuresC: Indiscernibility and classification14. Types and Stone spaces15. Indiscernibility16. Quantifiers17. Classification and uncountable categoricityD: Historical appendixA short history of model theory, Wilfrid Hodges
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