1. Philosophy of Mathematics and Its Logic: Introductory Overview ; 2. Philosophy of Mathematics in the Modern Period ; 3. Later Empiricism and Logical Positivism ; 4. The Logicism of Frege, Dedekind and Russell ; 5. Logicism in the 21st Century ; 6. Logicism Reconsidered ; 7. Formalism ; 8. Intuitionism ; 9. Intuitionism and Mathematics ; 10. Intuitionism Reconsidered ; 11. Quine and the Web of Belief ; 12. Three Forms of Naturalism ; 13. Naturalism Reconsidered ; 14. Nominalism ; 15. Nominalism Reconsidered ; 16. Structuralism ; 17. Structuralism Reconsidered ; 18. Predicativity ; 19. Mathematics - Application and Applicability ; 20. Logical Consequence, Proof Theory, and Model Theory ; 21. Logical Consequence From a Constructivist Point of View ; 22. Relevance in Reasoning ; 23. No Requirement of Relevance ; 24. Higher-order Logic ; 25. Higher-order Logic Reconsidered