Preface -- Contents -- PART ONE: PROBLEMS AND POSITIONS -- 1. Introduction -- 2. What is Mathematical Realism? -- 1. To Characterize Realism... -- 2. Immanent Truth -- 3. Realism and Immanent Truth -- 4. Some Concluding Remarks -- 3. The Case for Mathematical Realism -- 1. The Prima Facie Case for Realism -- 2. The Quine-Putnam View of Applied Mathematics -- 3. Indispensability Arguments for Mathematical Realism -- 4. Indispensability and Fictionalism about Science -- 5. Conclusion -- 4. Recent Attempts at Blunting the Indispensability Thesis -- 1. Synthetic Science: Field -- 2. Saving the Mathematical Formalism while Changing its Interpretation: Chihara and Kitcher -- 3. An Intermediate Approach: Hellman's Modal-Structuralism -- 4. What Has Introducing Modalities Gained? -- 5. Conclusion -- 5. Doubts about Realism -- 1. How Can We Know Mathematical Objects? -- 2. How Can We Refer to Mathematical Objects? -- 3. The Incompleteness of Mathematical Objects -- 4. Some Morals for Realists -- 5. An Aside: Penelope Maddy's Perceivable Sets -- PART TWO: NEUTRAL EPISTEMOLOGY -- Introduction to Part Two -- 6. The Elusive Distinction between Mathematics and Natural Science -- 1. How Physics Blurs the Mathematical/Physical Distinction -- 2. Some Other Attempts to Distinguish Mathematical from Physical Objects -- 3. Our Epistemic Access to Space-Time Points -- 4. Morals for the Epistemology of Mathematics -- 7. Holism: Evidence in Science and Mathematics -- 1. The Initial Case for Holism -- 2. Objections to Holism -- 3. Testing Scientific and Mathematical Models -- 4. Global and Local Theories -- 5. Revising Logic and Mathematics -- 8. The Local Conception of Mathematical Evidence: Proof, Computation, and Logic -- 1. Some Norms of Mathematical Practice -- 2. Computation and Mathematical Empiricism -- 3. Mathematical Proof, Logical Deduction and Apriority.

4. Summary -- 9. Positing Mathematical Objects -- 1. Introduction -- 2. A Quasi-Historical Account -- 3. Mathematical Positing Naturalized? -- 4. Positing and Knowledge -- 5. Postulational Epistemologies and Realism -- PART THREE: MATHEMATICS AS A SCIENCE OF PATTERNS -- Introduction to Part Three -- 10. Mathematical Objects as Positions in Patterns -- 1. Introduction -- 2. Patterns and their Relationships -- 3. Patterns and Positions: Entity and Identity -- 4. Composite and Unified Mathematical Objects -- 5. Mathematical Reductions -- 6. Reference to Positions in Patterns -- 7. Concluding Remarks on Reference and Reduction -- 11. Patterns and Mathematical Knowledge -- 1. Introduction -- 2. From Templates to Patterns -- 3. From Proofs to Truth -- 4. From Old Patterns to New Patterns -- 12. What is Structuralism? And Other Questions -- 1. Introduction -- 2. On 'Facts of the Matter' -- 3. Patterns as Mathematical Objects -- 4. Structural Relativity -- 5. Structuralist Formulations of Mathematical Theories? -- 6. The Status of Structuralism -- 7. Structuralism, Realism, and Disquotationalism -- 8. Epistemic vs. Ontic Structuralism: Structuralism All the Way Down -- 9. A Concluding Summary -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.