Converging Realities: Toward a Common Philosophy of Physics and Mathematics

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Princeton University Press, 2005 - Mathematics - 264 pages
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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 Omn s) have now reconciled the foundations of physics with objectivity and common sense. In Converging Realities, Roland Omn s is among the first scholars to consider the connection of natural laws with mathematics.

 

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User Review  - fpagan - LibraryThing

"Physism": the contention that the foundations of math belong to the laws of nature. Much of the book talks about quantum theory, but the not-so-clear writing can't be entirely ascribed to that. I ... Read full review

Contents

Beginnings
3
Brain and Reality
12
Mathematics and Classical Reality
22
REALITY AND THE QUANTUM WORLD
49
First Encounter with the Quantum World
51
Quantity and Reality
65
More about Physical Quantities
76
On the Extent of the Lingua Mathematica
86
THE CHARACTER OF PHYSICAL LAWS
135
The Character of Fundamental Laws
141
The Character of Classical Reality
164
PHYSISM
175
The Philosophy of Mathematics
179
Physism The Thesis
199
Physism and the Philosophy of Mathematics
216
Physism A Discussion
231

Virtual Processes
95
Back to Classical Reality
105
Decoherence
114
Did You Say Paradox?
126
Ontology
243
BIBLIOGRAPHY
253
INDEX
261
Copyright

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About the author (2005)

Roland Omnes is Professor of Physics at the University of Paris XI.

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