Matter and Mathematics: An Essentialist Account of Laws of Nature

To borrow a phrase from Galileo: What does it mean that the story of the creation is "written in the language of mathematics?" This book is an attempt to understand the natural world, its consistency, and the ontology of what we call laws of nature, with a special focus on their mathematical expression. It does this by arguing in favor of the Essentialist interpretation over that of the Humean and Anti-Humean accounts. It re-examines and critiques Descartes' notion of laws of nature following from God's activity in the world as mover of extended bodies, as well as Hume's arguments against causality and induction. It then presents an Aristotelian-Thomistic account of laws of nature based on mathematical abstraction, necessity, and teleology, finally offering a definition for laws of nature within this framework. Contents Acknowledgments Foreword by Michael J. Dodds, OP Introduction Essentialism, Nominalism, and Platonism Mathematical Laws of Natureand Essentialism The Peripatetic Axiom versus A Priori Knowledge Apologia Chapter 1. Descartes, Modern Science, and Scholasticism Descartes’s Methodversus Scholastic Abstraction Body as Extension Aloneversus Body as Matter and Form Laws of Nature and Occasionalismversus a Creator God of Active Substances Chapter 2. Causation and the Problem of Induction The Problem of Induction Critique of Humean Skepticism The Aristotelian Picture Conclusion Chapter 3. Quantum Mechanics, Act, and Potency Potency and Quantum Mechanics Wave Functions as Mathematical Expressions of Potentiality The Act of Measurement and the Actualization of the Particle Conclusion Chapter 4. Mathematical Abstraction Metaphysics XIII.3: Mathematicals as True Abstractions Metaphysics I.9 and XIV.5: How Forms, Including Mathematicals, Cannot Be Causes Metaphysics XIV.6: Coincidences and Analogies Conclusion Chapter 5. Necessity and Teleology Senses of Necessity Physics II.9 Matter: Necessary or Contingent? Or: Necessity: Material or Immaterial? Conclusion: Mathematical Necessity Chapter 6. Defining the Laws of Nature Mathematical Constraint and Formal Causality Abstraction and Necessity Defining the Laws of Nature Conclusion: Is “Law” Talk Useful Conclusion Appendix: Laws and the Lawgiver A Creator God Necessity and Aseity Divine Ideas and Laws of Nature Bibliography Index "This book is an attempt to understand the natural world, its consistency, and the ontology of what we call laws of nature, with a special focus on their mathematical expression. It does this by arguing in favor of the Essentialist interpretation over that of the Humean and Anti-Humean accounts. It re-examines and critiques Descartes' notion of laws of nature following from God's activity in the world as mover of extended bodies, as well as Hume's arguments against causality and induction. It then presents an Aristotelian-Thomistic account of laws of nature based on mathematical abstraction, necessity, and teleology, finally offering a definition for laws of nature within this framework"-- Provided by publisher What is ‘A Law of Nature’? It's a question that's vexed philosophers and scientists ever since Descartes first coined the term. Andrew Younan explores it in this insightful book. After carefully reviewing the positions of Humeans and Anti-Humeans, he employs the philosophy of Aristotle and Aquinas to argue for an essentialist understanding.