Introduction 1. Five Puzzles in Search of an Explanation 2. Geometry and Mathematical Existence 3. The Van Inwagen Puzzle 4. Structuralism 5. Platonism 6. Minimal Anti-Nominalism 7. The Constructibility Theory 8. Constructible Structures 9. Applications 10. If-Thenism 11. Field's Account of Mathematics and Metalogic Appendix A: Some Doubts about Hellman's Views Appendix B: Balaguer's Fictionalism
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