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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...

In this magisterial work, Roland Omnes takes us from the academies of ancient Greece to the laboratories of modern science as he seeks to do no less than rebuild the foundations of the philosophy of knowledge. One of the world's leading quantum physicists, Omnes reviews the history and recent development of mathematics, logic, and the physical sciences to show that current work in quantum theory offers new answers to questions that have puzzled philosophers for centuries: Is the world ultimately intelligible? Are all events caused? Do objects have definitive locations? Omnes addresses...

The interpretation of quantum mechanics has been controversial since the introduction of quantum theory in the 1920s. Although the Copenhagen interpretation is commonly accepted, its usual formulation suffers from some serious drawbacks. Based mainly on Bohr's concepts, the formulation assumes an independent and essential validity of classical concepts running in parallel with quantum ones, and leaves open the possibility of their ultimate conflict. In this book, Roland Omnes examines a number of recent advances, which, combined, lead to a consistent revision of the Copenhagen...

Here Roland Omnes offers a clear, up-to-date guide to the conceptual framework of quantum mechanics. In an area that has provoked much philosophical debate, Omnes has achieved high recognition for his Interpretation of Quantum Mechanics (Princeton 1994), a book for specialists. Now the author has transformed his own theory into a short and readable text that enables beginning students and experienced physicists, mathematicians, and philosophers to form a comprehensive picture of the field while learning about the most recent advances.

This new book presents a more...