Converging Realities: Toward a Common Philosophy of Physics and Mathematics

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9780691115306: Converging Realities: Toward a Common Philosophy of Physics and Mathematics

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.

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Recensione:

"It is refreshing to find a physicist joining today's ongoing public conversation about the nature of mathematics. . . . As a physicist who loves mathematics, in Converging Realities [Roland Omnès] comes forward with a new idea, which he proposes to call 'physism.' . . . I hope Omnès's daring proposal is taken seriously by those interested in these matters and receives the analysis and critique it deserves." --Reuben Hersh, American Scientit

"Roland Omnès provides a systematic development of mathematics and classical reality and then the quantum world, with specific notes on the associated mathematical structures and historical developments. He argues persuasively, with many examples, how the realm of the possible (mathematics) and the realm of the actual (physics) are converging yet distinct realities." --Choice

Contenuti:

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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Descrizione libro Princeton University Press, United States, 2004. Hardback. Condizione libro: New. 236 x 158 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAH9780691115306

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Descrizione libro Princeton University Press, United States, 2004. Hardback. Condizione libro: New. 236 x 158 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAH9780691115306

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Descrizione libro PRINCETON UNIVERSITY PRESS, LAWRENCEVILLE, NJ, 2005. Encuadernacion original. Condizione libro: NUEVO / NEW. OMNES, R. CONVERGING REALITIES. TOWARD A COMMON PHILOSOPHY OF PHYSICS AND MATHEMATICS. LAWRENCEVILLE, NJ, 2005, xvii 264 p. figuras Encuadernacion original. Nuevo. Codice libro della libreria 362892

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