The mysterious beauty, harmony, and consistency of mathematics once caused philosopher Hilary Putnam to term its existence a "miracle." Now, advances in the understanding of physics suggest that the foundations of mathematics are encompassed by the laws of nature, an idea that sheds new light on both mathematics and physics. The philosophical relationship between mathematics and the natural sciences is the subject of Converging Realities, the latest work by one of the leading thinkers on the subject. Based on a simple but powerful idea, it shows that the axioms needed for the mathematics used in physics can also generate practically every field of contemporary pure mathematics. It also provides a foundation for current investigations in string theory and other areas of physics. This approach to the nature of mathematics is not really new, but it became overshadowed by formalism near the end of nineteenth century. The debate turned eventually into an exclusive dialogue between mathematicians and philosophers, as if physics and nature did not exist. This unsatisfactory situation was enforced by the uncertain standing of physical reality in quantum mechanics.
The recent advances in the interpretation of quantum mechanics (as described in Quantum Philosophy, also by Omnes) have now reconciled the foundations of physics with objectivity and common sense. In Converging Realities, Roland Omnes is among the first scholars to consider the connection of natural laws with mathematics.
Roland Omnes is Professor Emeritus of Theoretical Physics at the Universite de Paris-Sud. Having made a career in particle physics and astrophysics, he contributed significantly to the modern renewal in the foundations and interpretation of quantum mechanics.
PREFACE vii PART ONE - PRELIMINARIES CHAPTER ONE: Beginnings 3 CHAPTER TWO: Brain and Reality 12 CHAPTER THREE: Mathematics and Classical Reality 22 PART TWO - REALITY AND THE QUANTUM WORLD CHAPTER FOUR: First Encounter with the Quantum World 51 CHAPTER FIVE: Quantity and Reality 65 CHAPTER SIX: More about Physical Quantities 76 CHAPTER SEVEN: On the Extent of the "Lingua Mathematica" 86 CHAPTER EIGHT: Virtual Processes 95 CHAPTER NINE: Back to Classical Reality 105 CHAPTER TEN: Decoherence 114 CHAPTER ELEVEN: Did You Say "Paradox"? 126 PART THREE - THE CHARACTER OF PHYSICAL LAWS CHAPTER TWLEVE: The Character of Fundamental Laws 141 CHAPTER THIRTEEN: The Character of Classical Reality 164 PART FOUR - PHYSISM CHAPTER FOURTEEN: The Philosophy of Mathematics 179 CHAPTER FIFTEEN: Physism: The Thesis 199 CHAPTER SIXTEEN: Physism and the Philosophy of Mathematics 216 CHAPTER SEVENTEEN: Physism: A Discussion 231 CHAPTER EIGHTEEN: Ontology 243 BIBLIOGRAPHY 253 INDEX 261