The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.

Applying the rules and systems of mathematics and logic to instance ontology, this work argues for the validity and problem-solving capacities of instance ontology, and associates it with a version of the realist position which is named by the author as moderate realism.

From reviews of the hardback edition: a deep study of 20th century field ... of the conceptual origins and development of twentieth century field theories, ...

The intuition of the naı¨ve realist, miracle arguments notwithstanding, is countered forcefully by a host of considerations, including the possibility of underdetermination, and criticisms of abductive inferences to explanatory hypotheses. Some have suggested that an induction may be performed, from the perspective of present theories, on their predecessors. Past theories are thought to be false, strictly speaking; it is thus likely that present-day theories are also false, and will be taken as such at an appropriate future time.

The book is drawn from the Tarner lectures, delivered in Cambridge in 1993. It is concerned with the ultimate nature of reality, and how this is revealed by modern physical theories such as relativity and quantum theory. The objectivity and rationality of science are defended against the views of relativists and social constructionists. It is claimed that modern physics gives us a tentative and fallible, but nevertheless rational, approach to the nature of physical reality. The role of subjectivity in science (...) is examined in the fields of relativity theory, statistical mechanics and quantum theory, and recent claims of an essential role for human consciousness in physics is rejected. Prospects for a 'Theory of Everything' are considered, and the related question of how to assess scientific progress is carefully examined. (shrink)

In this paper a constructive empiricist account of scientific change is put forward. Based on da Costa's and French's partial structures approach, two notions of empirical adequacy are initially advanced (with particular emphasis on the introduction of degrees of empirical adequacy). Using these notions, it is shown how both the informativeness and the empirical adequacy requirements of an empiricist theory of scientific change can then be met. Finally, some philosophical consequences with regard to the role of structures in this context (...) are drawn.Now, we daily see what science is doing for us. This could not be unless it taught us something about reality; the aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relations between things; outside those relations there is no reality knowable. (shrink)

Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.

A draft version of Chapter 11 of the edited volume 'Interpreting Bodies. Classical and Quantum Objects in Modern Physics',. The Chapter is devoted to illustrating the group-theoretic approach to the issue of physical objects. In particular, the Chapter discusses the group-theoretic constitution of classical and quantum particles in the nonrelativistic case.

D. W. Mertz provides a "new" competitor in the universals debate by reviving, developing, and defending the medieval doctrine of Moderate Realism. This book is a substantial contribution to ontology and logic, combining interesting new arguments for polyadic relations and unit attributes, careful and thorough historical studies, and a logic that could solve many old problems.

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

Some recent work in the philosophy of quantum mechanics has suggested that quantum systems can be thought of as non-separable and therefore non-individual, in some sense, in Bell and E.P.R. type situations. This suggestion is set in the context of previous work regarding the individuality of quantal particles and it is argued that such entities can be considered as individuals if their non-classical statistical correlations are understood in terms of non-supervenient relations holding between them. We conclude that such relations are (...) strongly non-supervenient in Cleland's sense and note a possible connection between this idea and the realist quantum logic programme. (shrink)

The book is drawn from the Tarner lectures, delivered in Cambridge in 1993. It is concerned with the ultimate nature of reality, and how this is revealed by modern physical theories such as relativity and quantum theory. The objectivity and rationality of science are defended against the views of relativists and social constructionists. It is claimed that modern physics gives us a tentative and fallible, but nevertheless rational, approach to the nature of physical reality. The role of subjectivity in science (...) is examined in the fields of relativity theory, statistical mechanics and quantum theory, and recent claims of an essential role for human consciousness in physics are rejected. Prospects for a 'Theory of Everything' are considered, and the related question of how to assess scientific progress is carefully examined. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

We outline Ladyman's 'metaphysical' or 'ontic' form of structuralrealism and defend it against various objections. Cao, in particular, has questioned theview of ontology presupposed by this approach and we argue that by reconceptualisingobjects in structural terms it offers the best hope for the realist in thecontext of modern physics.

This paper concerns the question of whether Pauli's Exclusion Principle (EP) vindicates the contingent truth of Leibniz's Principle of the Identity of Indiscernibles (PII) for fermions as H. Weyl first suggested with the nomenclature ‘Pauli–Leibniz principle’. This claim has been challenged by a time-honoured argument, originally due to H. Margenau and further articulated and champione by other authors. According to this argument, the Exclusion Principle—far from vindicating Leibniz's principle—would refute it, since the same reduced state, viz. an improper mixture, can (...) be assigned as a separate state to each fermion of a composite system in antisymmetric state. As a result, the two fermions do have the same monadic state-dependent properties and hence are indiscernibles. PII would then be refuted in its strong version (viz. for monadic properties). I shall argue that a misleading assumption underlies Margenau's argument: in the case of two fermions in antisymmetric state, no separate states should be invoked since the states of the two particles are entangled and the improper mixture—assigned to each fermion by reduction—cannot be taken as an ontologically separate state nor consequently as encoding monadic properties. I shall then conclude that the notion of monadic properties together with the strong version of PII are inapplicable to fermions in antisymmetric state and this undercuts Margenau's argument. (shrink)

There has been considerable recent philosophical debate over the implications of many particle quantum mechanics for the metaphysics of individuality (cf. Huggett [1997]). In this paper I look at things from a rather different perspective: by investigating the significance of permutation symmetry. I consider how various philosophical positions link up to the physical postulate of the indistinguishability of permuted states-permutation invariance-and how this postulate is used to explain quantum statistics. I offer an explanation of the statistics that relies on the (...) neglected parallel between permutations and covariant spatial transformation. And I explore the parallel, showing that a further kind of symmetry explains why permutations are invariant when spatial symmetries are not. (shrink)

Sir Arthur Eddington, the celebrated astrophysicist, made great strides towards his own 'theory of everything'in his last two books published in 1936 and 1946. Unlike his earlier lucid and authoritative works, these are strangely tentative and obscure - as if he were nervous of the significant advances that he might be making. This volume examines both how Eddington came to write these uncharacteristic books - in the context of the physics and history of the day - and what value they (...) have to modern physics. The result is an illuminating description of the development of theoretical physics, in the first half of the twentieth century, from a unique point of view: how it affected Eddington's thought. This will provide fascinating reading for scholars in the philosophy of science, theoretical physics, applied mathematics and the history of science. (shrink)

The ArgumentRecent archival research has brought about a new understanding of the import of Einstein's puzzling remarks (1916) attributing a physical meaning to general covariance. Debates over the scope and meaning of general covariance still persist, even within physics. But already in 1921 Cassirer identified the significance of general covariance as a novel stage in the development of the criterion of objectivity within physics; an account of this development, and its implications, is the primary task undertaken in his monograph of (...) “epistemological considerations” on the theory of relativity. Cassirer's assessment is correct: general covariance, understood as an injunction against dynamical theories with background elements, is a “limiting heuristic principle” guiding Einstein's fundamental conception of a “complete field theory”; as such, it underlies a “separation principle” built into the conceptual framework of the EPR criticism of quantum mechanics. In conclusion, a further parallel is noted: mutual recognition that the principle of general covariance is but a form of “anthropomorphism.”. (shrink)

Ernst Cassirer: Scientific Knowledge and the Concept of Man by Seymour W. Itzkoff is currently one of the few books available in the English language that discusses the philosophy of twentieth-century German philosopher Ernst Cassirer. Itzkoff's study brings Cassirer's perspective directly into the contemporary debate over the evolution of human thought and its relationship to animal life. Further, Itzkoff places Cassirer directly in the context of recent philosophical thought, arguing for the importance of his Kantian perspective, a significance that is (...) amply vindicated by the current interest in Cassirer's ideas. For this second edition, Seymour has written a new introduction and has added a new retrospective essay. (shrink)