Philosophy and Model Theory

Tim Button is a Senior Lecturer, and a Fellow of St John's College, at the University of Cambridge. His first book, The Limits of Realism (OUP 2013) explores the relationship between words and world; between semantics and scepticism. His main research interests lie in meta(meta)physics, logic, mathematics, and language. In 2014 he received a Philip Leverhulme Prize.

Sean Walsh is Associate Professor in the Department of Logic and Philosophy of Science at the University of California, Irvine. He did his graduate work in philosophy and mathematics at the University of Notre Dame, where he received a PhD in Logic and the Foundations of Mathematics, and subsequently worked for two years at Birkbeck, University of London.

A: Reference and realism
1. Logics and languages
2. Permutations and referential indeterminacy
3. Ramsey sentences and Newman's objection
4. Compactness, infinitesimals, and the reals
5. Sameness of structure and theory
B: Categoricity
6. Modelism and mathematical doxology
7. Categoricity and the natural numbers
8. Categoricity and the sets
9. Transcendental arguments
10. Internal categoricity and the natural numbers
11. Internal categoricity and the sets
12. Internal categoricity and truth
13. Boolean-valued structures
C: Indiscernibility and classification
14. Types and Stone spaces
15. Indiscernibility
16. Quantifiers
17. Classification and uncountable categoricity
D: Historical appendix
A short history of model theory, Wilfrid Hodges