Converging Realities: Toward a Common Philosophy of Physics and Mathematics

Converging Realities: Toward a Common Philosophy of Physics and Mathematics

by Roland Omnes
     
 

ISBN-10: 0691115303

ISBN-13: 9780691115306

Pub. Date: 11/29/2004

Publisher: Princeton University Press

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

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Overview

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 Omnès) have now reconciled the foundations of physics with objectivity and common sense. In Converging Realities, Roland Omnès is among the first scholars to consider the connection of natural laws with mathematics.

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Product Details

ISBN-13:
9780691115306
Publisher:
Princeton University Press
Publication date:
11/29/2004
Pages:
264
Product dimensions:
6.42(w) x 9.44(h) x 0.92(d)

Table of Contents

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

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