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Converging Realities : Toward a Common Philosophy of Physics and Mathematics - Roland Omnes

Converging Realities

Toward a Common Philosophy of Physics and Mathematics

Hardcover Published: 19th December 2004
ISBN: 9780691115306
Number Of Pages: 288

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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.

"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 Omnes] comes forward with a new idea, which he proposes to call 'physism.' ... I hope Omnes'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 Omnes 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

Prefacep. vii
Preliminaries
Beginningsp. 3
Brain and Realityp. 12
Mathematics and Classical Realityp. 22
Reality and the Quantum World
First Encounter with the Quantum Worldp. 51
Quantity and Realityp. 65
More about Physical Quantitiesp. 76
On the Extent of the "Lingua Mathematica"p. 86
Virtual Processesp. 95
Back to Classical Realityp. 105
Decoherencep. 114
Did You Say "Paradox"?p. 126
The Character of Physical Laws
The Character of Fundamental Lawsp. 141
The Character of Classical Realityp. 164
Physism
The Philosophy of Mathematicsp. 179
Physism: The Thesisp. 199
Physism and the Philosophy of Mathematicsp. 216
Physism: A Discussionp. 231
Ontologyp. 243
Bibliographyp. 253
Indexp. 261
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691115306
ISBN-10: 0691115303
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 288
Published: 19th December 2004
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 2.54
Weight (kg): 0.54