Cover -- Half Title -- Title -- Copyright -- Contents -- Acknowledgements -- Preface -- 1. Infinity -- 1. Introduction -- 2. Zeno's paradoxes -- 3. Potential versus actual infinity -- 4. The ordinal notion of infinity -- 5. The cardinal notion of infinity -- 6. Summary -- 2. Mathematical Platonism and realism -- 1. Introduction -- 2. Historical origins -- 3. Realism in general -- 4. Kurt Gödel -- 5. Penelope Maddy -- 6. General problems with set-theoretic realism -- 7. Conclusion -- 8. Summary -- 3. Logicism -- 1. Introduction -- 2. Frege's logicism: technical accomplishments -- 3. Frege's logicism: philosophical accomplishments -- 4. Problems with Frege's logicism -- 5. Whitehead and Russell's logicism -- 6. Philosophically, what is wrong with Whitehead and Russell's type theory? -- 7. Other attempts at logicism -- 8. Conclusion -- 9. Summary -- 4. Structuralism -- 1. Introduction -- 2. The motivation for structuralism: Benacerraf's puzzle -- 3. The philosophy of structuralism: Hellman -- 4. The philosophy of structuralism: Resnik and Shapiro -- 5. Critique -- 6. Summary -- 5. Constructivism -- 1. Introduction -- 2. Intuitionist logic -- 3. Prima facie motivations for constructivism -- 4. Deeper motivations for constructivism -- 5. The semantics of intuitionist logic: Dummett -- 6. Problems with constructivism -- 7. Summary -- 6. A pot-pourri of philosophies of mathematics -- 1. Introduction -- 2. Empiricism and naturalism -- 3. Fictionalism -- 4. Psychologism -- 5. Husserl -- 6. Formalism -- 7. Hubert -- 8. Meinongian Philosophy of Mathematics -- 9. Lakatos -- Appendix: Proof: ex falso quod libet -- Glossary -- Notes -- Guide to further reading -- Bibliography -- Index.