Mathematics and Its Logics: Philosophical Essays

ISBN-13: 9781108714006 / Angielski / Miękka / 2022 / 294 str.

Geoffrey (University of Minnesota) Hellman

Opis

The essays in this volume present a sustained case for a healthy pluralism in mathematics and its logics.

Spis treści

Introduction; Part I. Structuralism, Extendability, and Nominalism: 1. Structuralism without Structures?; 2. What Is Categorical Structuralism?; 3. On the Significance of the Burali-Forti Paradox; 4. Extending the Iterative Conception of Set: A Height-Potentialist Perspective; 5. On Nominalism; 6. Maoist Mathematics? Critical Study of John Burgess and Gideon Rosen, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics (Oxford, 1997); Part II. Predicative Mathematics and Beyond: 7. Predicative Foundations of Arithmetic (with Solomon Feferman); 8. Challenges to Predicative Foundations of Arithmetic (with Solomon Feferman); 9. Predicativism as a Philosophical Position; 10. On the Gödel-Friedman Program; Part III. Logics of Mathematics: 11. Logical Truth by Linguistic Convention; 12. Never Say 'Never'! On the Communication Problem between Intuitionism and Classicism; 13. Constructive Mathematics and Quantum Mechanics: Unbounded Operators and the Spectral Theorem; 14. If 'If-Then' Then What?; 15. Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis.