Inasmuch as mathematical platonism can be clearly matched with the radical realism, there exists a possibility to point out an approach, promoted by a French physicist, Roland Omnes, that is equivalent to the Aristotelian position of moderate realism. This standpoint denies the existence of an independent universum of mathematical entities and claims that mathematics is encoded in the laws of physics. In analogy to logicism, where mathematics is considered to be reducible to logic, Omnes' position is called by him 'physism' to stress the reducibility of mathematics to the laws of physics. The goal of Roland Omnes is to construct a common philosophy of mathematics and physics where the realities of these two disciplines converge. The first part of the analysis aims at the description and critical evaluation of physism from the point of view of the adequacy of the consistent histories interpretation of quantum mechanics to provide physical basis of the abstraction of the mathematical structures from the physical reality.
Inasmuch as mathematical platonism can be clearly matched with the radical realism, there exists a possibility to point out an approach, promoted by a French physicist, Roland Omnes, that is equivalent to the Aristotelian position of moderate realism. This standpoint denies the existence of an independent universum of mathematical entities and claims that mathematics is encoded in the laws of physics. In analogy to logicism, where mathematics is considered to be reducible to logic, Omnes' position is called by him 'physism' to stress the reducibility of mathematics to the laws of physics. The goal of Roland Omnes is to construct a common philosophy of mathematics and physics where the realities of these two disciplines converge. The first part of the analysis aims at the description and critical evaluation of physism from the point of view of the adequacy of the consistent histories interpretation of quantum mechanics to provide physical basis of the abstraction of the mathematical structures from the physical reality.
Inasmuch as mathematical platonism can be clearly matched with the radical realism, there exists a possibility to point out an approach, promoted by a French physicist, Roland Omnés, that is equivalent to the Aristotelian position of moderate realism. This standpoint denies the existence of an independent universum of mathematical entities and claims that mathematics is encoded in the laws of physics. In analogy to logicism, where mathematics is considered to be reducible to logic, Omnés' position is called by him 'physism' to stress the reducibility of mathematics to the laws of physics. The goal of Roland Omnés is to construct a common philosophy of mathematics and physics where the realities of these two disciplines converge. The first part of the analysis aims at the description and critical evaluation of physism from the point of view of the adequacy of the consistent histories interpretation of quantum mechanics to provide physical basis of the abstraction of the mathematical structures from the physical reality.
In this magisterial work, Roland Omnès 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, Omnès 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? Omnès addresses these profound questions with vigorous arguments and clear, colorful writing, aiming not just to advance scholarship but to enlighten readers with no background in science or philosophy. The book opens with an insightful and sweeping account of the main developments in science and the philosophy of knowledge from the pre-Socratic era to the nineteenth century. Omnès then traces the emergence in modern thought of a fracture between our intuitive, commonsense views of the world and the abstract and--for most people--incomprehensible world portrayed by advanced physics, math, and logic. He argues that the fracture appeared because the insights of Einstein and Bohr, the logical advances of Frege, Russell, and Gödel, and the necessary mathematics of infinity of Cantor and Hilbert cannot be fully expressed by words or images only. Quantum mechanics played an important role in this development, as it seemed to undermine intuitive notions of intelligibility, locality, and causality. However, Omnès argues that common sense and quantum mechanics are not as incompatible as many have thought. In fact, he makes the provocative argument that the "consistent-histories" approach to quantum mechanics, developed over the past fifteen years, places common sense (slightly reappraised and circumscribed) on a firm scientific and philosophical footing for the first time. In doing so, it provides what philosophers have sought through the ages: a sure foundation for human knowledge. Quantum Philosophy is a profound work of contemporary science and philosophy and an eloquent history of the long struggle to understand the nature of the world and of knowledge itself.
Here Roland Omnès offers a clear, up-to-date guide to the conceptual framework of quantum mechanics. In an area that has provoked much philosophical debate, Omnès 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 streamlined version of the Copenhagen interpretation, showing its logical consistency and completeness. The problem of measurement is a major area of inquiry, with the author surveying its history from Planck to Heisenberg before describing the consistent-histories interpretation. He draws upon the most recent research on the decoherence effect (related to the modern resolution of the famous Schrödinger’s cat problem) and an exact formulation of the correspondence between quantum and particle physics (implying a derivation of classical determinism from quantum probabilism). Interpretation is organized with the help of a universal and sound language using so-called consistent histories. As a language and a method, it can now be shown to be free of ambiguity and it makes interpretation much clearer and closer to common sense.
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 interpretation. His aim is to show how this interpretation can fit all present experiments, to weed out unnecessary or questionable assumptions, and to assess the domain of validity where the older statements apply. The text offers a self-contained treatment of interpretation (in nonrelativistic physics) in a manner accessible to both physicists and students. Although some hard results are included, the concepts and mathematical developments are maintained at an undergraduate level. This book enables readers to check every step, apply the techniques to new problems and make sure that no paradox or obscurity
Decoherentism, as being developed by many outstanding contemporary physicists, and elaborated in a systematic form by French physicist Roland Omnčs, eliminates eventually the long-lasting quantum-classical dualism in physics. It proves that in consequence of decoherence effect, the laws of quantum mechanics (with their probabilistic character) turn into the deterministic laws of classical physics; it describes therewith a real process through which the phenomenal world as given immediately to our sensory perception arises from quantum fundamentals; accordingly, classical determinism is a direct and controlled consequence of quantum mechanics.At the same time, decoherentism elaborated quantum logic (which is based on Griffiths' notion of consistent histories and corresponds to quantum mechanics) and proves that when decoherence acts, classical logic becomes a special kind of quantum logic. Since classical logic is essentially a learned version of common sense, the decoherentistic approach shows that the validity of common sense has its foundation in the rules of quantum mechanics. Thus, decoherentism eliminates the conflicts between quantum theory and common sense (in doing so, it proves that the famous paradoxes of Schrödinger's cat and the wave function reduction as well as the EPR paradox came from the mistake of having no account of decoherence effect).Nevertheless, decoherentism admits that the logic of common sense and as well as determinism itself have some probability of error which can be estimated in principle. These probabilities are most often extremely small and the corresponding errors have no practical consequence.Contrary to both classical and pre-decoherentistic quantum dynamics, decoherentism implies that the logical structure of quantum mechanics must select a definite direction of time, which necessarily coincides with the one occurring in thermodynamics; this means that the 2. law of thermodynamics (together with the irreversibility of time finds its basis in the decoherentistic interpretation of quantum mechanics.Hence it follows that decoherentism is truly a scientific revolution because the former principles (such as the principle of quantum-classical correspondence) turns in its frame into ordinary laws whic are derived from more fundamental principles.Considering the fact that classical determinism is a necessary presupposition for all scientific experiments, decoherentism's ability to derive determinism from newly interpreted quantum mechanics enables us to characterise it with the metaphor of "serpent gnawing his own tail." This means that quantum mechanics (in its decoherentistic interpretation) is able to explain even its own basic presuppositions; or, in other words, the results of the development of physical science turns back in order to explain its starting point. This important advancement makes physics structurally analogous to Adam Smith's economics (and to its metaphysical transcriptions in Hegel's Logic), to evolutionary biology and other sciences dealing with spontaneous order and self-organisation.
Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered from the point of view of philosophical idealism. Some of the ways in which infinitary mathematics arises in modern mathematical physics are discussed. Empirical science has led to the mathematics of quantum theory. This in turn can be taken to suggest a picture of reality involving possible minds and the physical laws which determine their probabilities. In this picture, finitary and infinitary mathematics play separate roles. It is argued that mind, language, and finitary mathematics have similar prerequisites, in that each depends on the possibility of possibilities. The infinite, on the other hand, can be described but never experienced, and yet it seems that sets of possibilities and the physical laws which define their probabilities can be described most simply in terms of infinitary mathematics.