An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Struct

Preface PART I: THE SCIENCE OF QUANTITY AND STRUCTURE 1. The Aristotelian Realist Point of View 2. Uninstantiated Universals and 'Semi-Platonist' Aristotelianism 3. Elementary Mathematics: Quantity and Number 4. Higher Mathematics: Science of the Purely Structural 5. Necessary Truths about Reality 6. The Formal Sciences Discover the Philosophers' Stone 7. Comparisons and Objections 8. Infinity 9. Geometry: Mathematics or Empirical Science? PART II: KNOWING MATHEMATICAL REALITY 10. Knowing Mathematics: Pattern Recognition and Perception of Quantity and Structure 11. Knowing Mathematics: Visualization 12. Knowing Mathematics: Understanding and Proof 13. Explanation in Mathematics 14. Idealization: An Aristotelian View 15. Non-Deductive Logic in Mathematics Epilogue: Mathematics, Last Bastion of Reason Notes Select Bibliography Index