This paper explores the consequences of the two most prominent forms of contemporary structural realism for the notion of objecthood. Epistemic structuralists hold that we can know structural aspects of reality, but nothing about the natures of unobservable relata whose relations define structures. Ontic structuralists hold that we can know structural aspects of reality, and that there is nothing else to know—objects are useful heuristic posits, but are ultimately ontologically dispensable. I argue that structuralism does not succeed in ridding a (...) structuralist ontology of objects. (shrink)

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium in terms of Bose‐Einstein (...) statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London's model. (shrink)

This book argues that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it really is, and not on philosophers' a priori intuitions, common sense, or simplifications of science. In addition to showing how recent metaphysics has drifted away from connection with all other serious scholarly inquiry as a result of not heeding this restriction, this book demonstrates how to build a metaphysics compatible with current fundamental physics, which, when combined (...) with metaphysics of the special sciences, can be used to unify physics with the other sciences without reducing these sciences to physics itself. Taking science metaphysically seriously, this book argues, means that metaphysicians must abandon the picture of the world as composed of self-subsistent individual objects, and the paradigm of causation as the collision of such objects. The text assesses the role of information theory and complex systems theory in attempts to explain the relationship between the special sciences and physics, treading a middle road between the grand synthesis of thermodynamics and information, and eliminativism about information. The consequences of the books' metaphysical theory for central issues in the philosophy of science are explored, including the implications for the realism versus empiricism debate, the role of causation in scientific explanations, the nature of causation and laws, the status of abstract and virtual objects, and the objective reality of natural kinds. (shrink)

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least (...) as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

In the concluding chapter of Exceeding our Grasp Kyle Stanford outlines a positive response to the central issue raised brilliantly by his book, the problem of unconceived alternatives. This response, called "epistemic instrumentalism", relies on a distinction between instrumental and literal belief. We examine this distinction and with it the viability of Stanford's instrumentalism, which may well be another case of exceeding our grasp.

We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all (...) their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrodinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

This chapter contains sections titled: Introduction: Interpretation Bohr and Complementarity The Einstein‐Podolsky‐Rosen (EPR) Argument Bell's Theorem and Other No‐Go Results The Measurement Problem Future Directions: Interpreting QFT.

Hume famously warned us that the ‘[The] ultimate springs and principles are totally shut up from human curiosity and enquiry’. Or, again, Newton: ‘Hitherto I have not been able to discover the cause of these properties of gravity … and I frame no hypotheses.’ Aristotelian science was concerned with just such questions, the specification of occult qualities, the real essences that answer the question What is matter, etc?, the preoccupation with circular definitions such as dormative virtues, and so on. The (...) rise of modern science is usually seen as a break with the sterility of Aristotelianism, so what exactly is it that modern science does discover, if it is not the essential nature of matter, of force, of energy, of space and time? A famous answer was provided by Poincaré: ‘The true relations between these real objects are the only reality we can attain.’ This is often regarded as the manifesto of so-called structural realism, as espoused in recent years by John Worrall, for example ). In response to the arguments of Larry Laudan against convergent realism, Worrall points to the continuity in the formal relations between elements of reality expressed by mathematical equations, while the intrinsic nature of these elements of reality gets constantly revised. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

The practice of describing multiparticle quantum systems in terms of labeled particles indicates that we think of quantum entities as individuatable. The labels, together with particle indistinguishability, create the need for symmetrization or antisymmetrization (or, in principle, higher-order symmetries), which in turn results in “surplus formal structure” in the formalism, formal structure which corresponds to nothing in the real world. We argue that these facts show quanta to be unindividuatable entities, things in principle incapable of supporting labels, and so things (...) which support no factual difference_if two of them are thought of as being switched. When thinking of the metaphysics of quanta, we should eschew the misleading labels of the tensor product Hilbert space formalism and prefer the ontologically more faithful description of the Fock space formalism. This conception eliminates puzzles about the quantum statistics of bosons. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

Concentrating on genetics, this paper examines the strength of the links between our biological science -- our biology -- and the particular history which brought that science into being. Would quite different histories have produced roughly the same science? Or, on the contrary, would different histories have produced other, quite different biologies? One emphasis throughout is on the kinds of evidence that might be brought to bear from the actual past in order to assess claims about what might have been. (...) Another emphasis is on the implications for debates on realism and antirealism about genes. (shrink)

Roger Jones asks what Newtonian realists should be realists about, given that there are four empirically equivalent formulations of Newtonian mechanics which have different ontological commitments and explanatory mechanisms. A realist answer is sketched: Newtonians should be realists about what the best metaphysical considerations dictate, where the best metaphysical considerations are those which have yielded the best physics. Metaphysical considerations are required within physics, just as they are required to eliminate idealist and surrealist theories which are empirically equivalent to realist (...) ones. Realists must reject the positivist assumption that empirically equivalent theories are explanatory and evidential equivalents, too. (shrink)

Roger Jones asks what Newtonian realists should be realists about, given that there are four empirically equivalent formulations of Newtonian mechanics which have different ontological commitments and explanatory mechanisms. A realist answer is sketched: Newtonians should be realists about what the best metaphysical considerations dictate, where the best metaphysical considerations are those which have yielded the best physics. Metaphysical considerations are required within physics, just as they are required to eliminate idealist and surrealist theories which are empirically equivalent to realist (...) ones. Realists must reject the positivist assumption that empirically equivalent theories are explanatory and evidential equivalents, too. (shrink)

The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the (...) theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. -/- The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. (shrink)

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, (...) the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. (shrink)

The identity and diversity of individual objects may be grounded or ungrounded, and intrinsic or contextual. Intrinsic individuation can be grounded in haecceities, or absolute discernibility. Contextual individuation can be grounded in relations, but this is compatible with absolute, relative or weak discernibility. Contextual individuation is compatible with the denial of haecceitism, and this is more harmonious with science. Structuralism implies contextual individuation. In mathematics contextual individuation is in general primitive. In physics contextual individuation may be grounded in relations via (...) weak discernibility. (shrink)

This paper explores varieties of scientific structuralism. Central to our investigation is the notion of `shared structure'. We begin with a description of mathematical structuralism and use this to point out analogies and disanalogies with scientific structuralism. Our particular focus is the semantic structuralist's attempt to use the notion of shared structure to account for the theory-world connection, this use being crucially important to both the contemporary structural empiricist and realist. We show why minimal scientific structuralism is, at the very (...) least, a powerful methodological standpoint. Our investigation also makes explicit what more must be added to this minimal structuralist position in order to address the theory-world connection, namely, an account of representation. (shrink)

Preanalytically, we are all scientific realists. But both philosophers and scientists become uncomfortable when forced into analysis. In the case of scientists, this discomfort often arises from practical difficulties in setting out a carefully described set of objects which adequately account for the phenomena with which they are concerned. This paper offers a set of representative examples of these difficulties for contemporary physicists. These examples challenge the traditional realist vision of mature scientific activity as struggling toward an ontologically well-defined world (...) picture. They challenge antirealist alternatives as well. (shrink)

The author begins by distinguishing six fundamental issues on the metaphysics of individuality.

-/- Although much of its history has been neglected or misunderstood, a structuralist ‘tendency’ has re-emerged within the philosophy of science. Broadly speaking, it consists of two fundamental strands: on the one hand, there is the identification of structural commonalities between theories; on the other, there is the metaphysical decomposition of objects in structural terms. Both have been pressed into service for the realist cause: the former has been identified primarily with Worrall's ‘epistemic’ structural realism; the latter with Ladyman's ‘ontic’ (...) form. And both raise important issues of general interest within the philosophy of science and metaphysics, respectively. The former invites questions regarding the identification and appropriate representation of these commonalities; the latter touches on different views regarding the nature of objects, the constitutive role of properties and the seat of causal powers. Both strands have recently come under critical fire. It is my intention to present a unified account of the 'structuralist tendency’ which emphasizes the dual roles of structure as representational and constitutive, and to indicate how the more acute critical remarks can be dealt with. (shrink)

Although Eddington's philosophy of physics has been subjected to critical re-evaluation in recent years, neither the exact nature of his structuralist views nor his response to criticism by the likes of Braithwaite have been made clear. In this paper I trace, in particular, the incorporation into Eddington's structuralism of the non-classical indistinguishability of quantum objects. His metaphysical view of such objects as the product of group-theoretical analysis is crucial for understanding his response to Braithwaite's criticisms of the whole structuralist endeavor. (...) These criticisms closely resemble more recent attacks on structural realism in the philosophy of science. I conclude with a brief comparison between these more modern forms of structuralism and Eddington's. (shrink)

Although much of its history has been neglected or misunderstood, a structuralist 'tendency' has re-emerged within the philosophy of science. Broadly speaking, it consists of two fundamental strands: on the one hand, there is the identification of structural commonalities between theories; on the other, there is the metaphysical decomposition of objects in structural terms. Both have been pressed into service for the realist cause: the former has been identified primarily with Worrall's 'epistemic' structural realism; the latter with Ladyman's 'ontic' form. (...) And both raise important issues of general interest within the philosophy of science and metaphysics, respectively. The former invites questions regarding the identification and appropriate representation of these commonalities; the latter touches on different views regarding the nature of objects, the constitutive role of properties and the seat of causal powers. Both strands have recently come under critical fire. It is my intention to present a unified account of the 'structuralist tendency' which emphasizes the dual roles of structure as representational and constitutive, and to indicate how the more acute critical remarks can be dealt with. (shrink)

Steven French and Decio Krause examine the metaphysical foundations of quantum physics. They draw together historical, logical, and philosophical perspectives on the fundamental nature of quantum particles and offer new insights on a range of important issues. Focusing on the concepts of identity and individuality, the authors explore two alternative metaphysical views; according to one, quantum particles are no different from books, tables, and people in this respect; according to the other, they most certainly are. Each view comes with certain (...) costs attached and after describing their origins in the history of quantum theory, the authors carefully consider whether these costs are worth bearing. Recent contributions to these discussions are analyzed in detail and the authors present their own original perspective on the issues. The final chapter suggests how this perspective can be taken forward in the context of quantum field theory. (shrink)

We are used to talking about the “structure” posited by a given theory of physics, such as the spacetime structure of relativity. What is “structure”? What does the mathematical structure used to formulate a theory tell us about the physical world according to the theory? What if there are different mathematical formulations of a given theory? Do different formulations posit different structures, or are they merely notational variants? I consider the case of Lagrangian and Hamiltonian classical mechanics. I argue that, (...) contrary to standard wisdom, these are not genuinely equivalent theories: they differ in statespace structure. I suggest that we should be realists about statespace structure. (shrink)

In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what is (...) needed to overcome the stalemate. The main thesis of this paper is that, whatever the interpretative difficulties of generally covariant spacetime physics are, they do not support or suggest structural realism. In particular, I hope to show that there is in fact no analogy that supports a similar interpretation of the metaphysics of spacetime points and of quantum particles. (shrink)

This chapter is concerned with the representation of time and change in classical (i.e., non-quantum) physical theories. One of the main goals of the chapter is to attempt to clarify the nature and scope of the so-called problem of time: a knot of technical and interpretative problems that appear to stand in the way of attempts to quantize general relativity, and which have their roots in the general covariance of that theory. The most natural approach to these questions is via (...) a consideration of more clear cases. So much of the chapter is given over to a discussion of the representation of time and change in other, better understood theories, starting with the most straightforward cases and proceeding through a consideration of cases that lead up to the features of general relativity that are responsible for the problem of time. (shrink)

We have now celebrated the centenary of J. J. Thomson’s famous paper (1897) on the electron and have examined one hundred years of the history of our first fundamental particle. What should philosophers of science learn from this history? To some, the fundamental moral is already suggested by the rapid pace of this history. Thomson’s concern in 1897 was to demonstrate that cathode rays are electrified particles and not aetherial vibrations, the latter being the “almost unanimous opinion of German physicists” (...) (p. 293) But were these German physicists so easily vanquished? De Broglie proposed in 1923 that electrons are a wave phenomenon after all and his proposal was soon multiply vindicated, even by the detection of the diffraction of the electron waves. Should we not learn from such a reversal? Should we not dispense with the simple-minded idea that Thomson discovered our first fundamental particle and admit that the very notion of discovery might well be ill-suited to science? (shrink)

In the debate over scientific realism, attention has been given recently to a realist position referred to as structural realism. In this essay, I offer a version of this position and indicate how it addresses two standard forms of underdetermination argument posed by the anti-realist.