An Aristotelian Realist Philosophy of Mathematics

Mathematics as the Science of Quantity and Structure
2014. Auflage 2014
ISBN: 978-1-137-40072-7
Verlag: Palgrave MacMillan UK

Buch, Englisch, 308 Seiten, Format (B × H): 147 mm x 223 mm, Gewicht: 5023 g

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Zielgruppe

Research

Autoren/Hrsg.

Franklin, J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie

Inhaltsverzeichnis

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

Über Autor(innen)

James Franklin is Professor of Mathematics at the University of New South Wales, Australia and founder of the 'Sydney School' in the philosophy of mathematics. His books include ; ; and .