When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes the condition that these mathematical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there are not enough qualitatively distinct (...) properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physicist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory provides tools to overcome this tension and to define physical properties. (shrink)

This paper is concerned with the problem of the validity of Leibniz's principle of the identity of indiscernibles in physics. After briefly surveying how the question is currently discussed in recent literature and which is the actual meaning of the principle for what concerns physics, we address the question of the physical validity of Leibniz's principle in terms of the existence of a sufficient number of naming predicates in the formal language of physics. This approach allows us to obtain in (...) a formal way the result that a principle of the identity of indiscernibles can be justified in the domain of classical physics, while this is not the case in the domain of quantum physics. (shrink)

he relationship between metaphysics and science has recently become the focus of increased attention. Ladyman and Ross, in particular, have accused even naturalistically inclined metaphysicians of pursuing little more than the philosophy of A-level chemistry and have suggested that analytic metaphysics should simply be discontinued. In contrast, we shall argue, first of all, that even metaphysics that is disengaged from modern science may offer a set of resources that can be appropriated by philosophers of physics in order to set physics (...) within an interpretational framework. Secondly, however, we shall urge that insofar as metaphysics is intended to be more than just a toolbox it needs to accommodate the implications of physics if many of its core claims are to be sustained. We shall illustrate this last point with a discussion of the nature of laws and modality in the context of modern physics. (shrink)

Structural realism first emerged as an epistemological thesis aimed to avoid the socalled pessimistic metainduction on the history of science. Some authors, however, have suggested that the preservation of structure across theory change is best explained by endorsing the metaphysical thesis that structure is all there is. Although the possibility of this latter, ‘ontic’ form of structural realism has been extensively debated, not much has been said concerning its justification. In this article, I distinguish between two arguments in favor of (...) ontic structural realism that can be reconstructed from the literature and find both of them wanting. (shrink)

Everything you always wanted to know about structural realism but were afraid to ask Content Type Journal Article Pages 227-276 DOI 10.1007/s13194-011-0025-7 Authors Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE UK Ioannis Votsis, Philosophisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Geb. 23.21/04.86, 40225 Düsseldorf, Germany Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are (...) false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles, and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity weaker than what we will call individuality : two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory. (shrink)

The paper spells out five different accounts of the relationship between objects and relations three of which are versions of ontic structural realism. We argue that the distinction between objects and properties, including relations, is merely a conceptual one by contrast to an ontological one: properties, including relations, are modes, that is the concrete, particular ways in which objects exist. We then set out moderate OSR as the view according to which irreducible relations are central ways in which the fundamental (...) physical objects exist. Physical structures thus consist in objects for whom it is essential that they are related in certain ways. There hence are objects, but they do not possess an intrinsic identity. This view can also admit intrinsic properties as ways in which objects exist provided that these do not amount to identity conditions for the objects. Finally, we indicate how this view can take objective modality into account. (shrink)

It is shown that Lewis’ ontological doctrine of Humean supervenience incorporates at its foundation the so-called separability principle of classical physics. In view of the systematic violation of the latter within quantum mechanics, the claim that contemporary physical science may posit non-supervenient relations beyond the spatiotemporal ones is reinforced on a foundational basis concerning constraints on the state representation of physical systems. Depending on the mode of assignment of states to quantum systems — unit state vectors versus statistical density operators (...) — we distinguish between strongly and weakly non-Humean, non-supervenient relations. It is demonstrated that in either case, the relations of quantum entanglement constitute prototypical examples of irreducible physical relations that do not supervene upon a spatiotemporal arrangement of Humean qualities, weakening, thereby, the thesis of Humean supervenience. In this respect, the status of Lewis’ recombination principle is examined, whereas his conception of lawhood is critically investigated. It is concluded that the assumption of ontological reductionism, as expressed in Lewis’ Humean doctrine, cannot be regarded as a reliable code of the nature of the physical world and its contents. It is proposed instead that due to the undeniable existence of non-supervenient relations, a metaphysic of relations of a moderate kind ought to be acknowledged as an indispensable part of our understanding of the natural world at a fundamental level. (shrink)

After decades of neglect philosophers of physics have discovered gauge theories--arguably the paradigm of modern field physics--as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism--in the eyes of its proponents the best suited realist position towards modern physics--has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories--in particular (...) U(1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov-Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed. (shrink)

The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.

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.

Relationism holds that objects entirely depend on relations or that they must be eliminated in favour of the latter. In this article, I raise a problem for relationism. I argue that relationism cannot account for the order in which non-symmetrical relations apply to their relata. In Section 1, I introduce some concepts in the ontology of relations and define relationism. In Section 2, I present the Problem of Order for non-symmetrical relations, after distinguishing it from the Problem of Differential Application. (...) I also examine four main existing strategies to solve it. In Section 3, I develop my argument. The first step consists in arguing that—among those strategies—relationism can only accept directionalism. The second step consists in arguing that directionalism is affected by a serious problem: the Problem of Converses. I also show that relationists who embrace directionalism cannot solve this problem. In Section 4, I introduce and rebut several strategies on behalf of relationists to cope with my argument. In Section 5, I briefly draw some conclusions. (shrink)

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)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: [email protected] , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected] . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, based on (...) a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. (shrink)

This article aims to clarify how aspects of current chemical understanding relate to some important contemporary problems of philosophy. The first section points out that the long-running philosophical debates concerning how properties stay together in substances have neglected the important topic of structure-determining closure. The second part describes several chemically-important types of closure and the third part shows how such closures ground the properties of chemical substances. The fourth section introduces current discussions of structural realism (SR) and contextual emergence: the (...) final sections reconsider the coherence of the properties of substances and concludes that recognition that structures qualify as determinants of specific outcomes—as ‘causes’ as that designation is used in Standard English—clarifies how properties stay together in chemical entities, and by analogy, how characteristics cohere in ordinary items. (shrink)

Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we effectively provide a coherent picture of the puzzling entangled correlations among spatially separated systems. We further argue that the generalized phenomenon of quantum nonseparability implies contextuality for the production of well-defined events in the quantum domain, whereas contextuality entails in turn a structural-relational conception of quantal objects, viewed as (...) carriers of dispositional properties. It is finally suggested that contextuality, if considered as a conditionalization preparation procedure of the object to be measured, naturally leads to a separable concept of reality whose elements are experienced as distinct, well-localized objects having determinate properties. In this connection, we find it necessary to distinguish the meaning of the term reality from the criterion of reality for us. The implications of the latter considerations for the notion of objectivity in quantum mechanics are also discussed. (shrink)

The present paper argues that the typical structuralist claims according to which invariances, symmetries and the like are fundamental – especially in physics – should not be understood in terms of physical relations being fundamental. Rather, they should be understood in terms of ‘metaphysical coherentism’ - the idea that object-like parts of reality exhibit symmetric relations of ontological dependence. The view is developed in some detail, in particular by showing that i) symmetric ontological dependence does not necessarily lead to uninformative (...) metaphysical explanations, and ii) metaphysical coherentism strikes the best balance between the requirements of naturalism and those of theoretical consistency – especially in view of the difficulties that structuralists seem to have in accounting for all state-independent properties of particles in relational terms. On this basis, the coherentist picture is applied to the interpretation of the quantum domain, and contrasted with extant varieties of structuralism, of both the eliminative and the non-eliminative sort, and holism. (shrink)

Quasi-set theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as a non-classical logic (a non-reflexive logic). In this paper we revise and correct some aspects of quasi-set theory as presented in [12], so as to avoid some misunderstandings and possible misinterpretations about the results achieved by the theory. Some further ideas with regard to quantum field theory are also (...) advanced in this paper. (shrink)

We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations (...) to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively. (shrink)

Modern particle physics suggests an intriguing vision of physical reality: we are to imagine the symmetries of the world as fundamental, whereas the material constituents of the world are ontologically derivative of them. This paper develops a novel ontology for non-relativistic quantum mechanics which gives precise metaphysical content to this vision.

The feasibility of establishing a proper notion of a distinguishable object in the context of the de Broglie–Bohm approach to quantum mechanics seems, at first sight, uncontroversial by virtue of the fact that this theory can supposedly be interpreted in terms of a system of objective particles distinguished by individuating properties. However, after conducting a critical revision and evaluation of this trivial interpretation, and having assessed different alternatives that have been proposed in recent literature, I argue that within this theory (...) an appropriate notion of a distinguishable object can only be articulated by means of the following theoretical and metaphysical strategies: firstly, by appealing to a pre-existing, symmetrized Bohmian framework that is empirically indistinguishable but physically distinguishable from the standard Bohmian formulation; and secondly, by suggesting a different interpretation of this symmetrized formulation based upon a relational notion of the distinguishable object that can only be appropriately conceived from a structuralist point of view. (shrink)

One of the reasons provided for the shift away from an ontology for physical reality of material objects & properties towards one of physical structures & relations (Ontological Structural Realism: OntSR) is that the quantum-mechanical description of composite physical systems of similar elementary particles entails they are indiscernible. As material objects, they 'whither away', and when they wither away, structures emerge in their stead. We inquire into the question whether recent results establishing the weak discernibility of elementary particles pose a (...) threat for this quantum-mechanical reason for OntSR, because precisely their newly discovered discernibility prevents them from 'whithering away'. We argue there is a straightforward manner to consider the recent results as a reason in favour of OntSR rather than against it. (shrink)

Structural realism as developed by John Worrall and others can claim philosophical roots as far back as the late 19th century, though the discussion at that time does not unambiguously favor the contemporary form, or even its realism. After a critical examination of some aspects of the historical background some severe critical challenges to both Worrall's and Ladyman's versions are highlighted, and an alternative empiricist structuralism proposed. Support for this empiricist version is provided in part by the different way in (...) which we can do justice to Worrall's original demands and in part by the viewpoint it provides (in contrast to e.g. Michael Friedman's) on the stability maintained through scientific theory change. Planck against the heretics 1.1 Poincaré on the meaning of Maxwell's equations 1.2 Two responses: reification and structuralism On the road to structuralism 2.1 The microscope 2.2 Mathematization of the world picture 2.3 The 18th–20th century The new structural realism 3.1 From scientific realism to structuralism 3.2 The Ladyman variant: objectivity and invariance 3.3 How is structural realism supported? An empiricist structuralism 4.1 Royal succession in science 4.2 Defence of the empiricist version 4.3 Structure: an empiricist view. (shrink)

Fundamental physics contains an important link between properties of elementary particles and continuous symmetries of particle systems. For example, properties such as mass and spin are said to be 'associated' with specific continuous symmetries. -/- These 'associations' have played a key role in the discovery of various new particle kinds, but more importantly: they are thought to provide a deep insight into the nature of physical reality. The link between properties and symmetries has been said to call for a radical (...) revision of perceived metaphysical orthodoxy. However, if we are to use claims about an 'association' between properties and symmetries in the articulation of metaphysical views, we first need to develop a sufficiently precise understanding of the content of these claims. The goal of this paper is to do just that. (shrink)

Ontic structural realism is a thesis of fundamentality metaphysics: the thesis that structure, not objects, has fundamental status. Claimed as the metaphysic most befitting of modern physics, OSR first emerged as an entreaty to eliminate objects from the metaphysics of fundamental physics. Such elimination was urged by Steven French and James Ladyman on the grounds that only it could resolve the ‘underdetermination of metaphysics by physics’ that they claimed reduced any putative objectual commitment to a merely ‘ersatz’ form of realism. (...) Few, however, have joined French and Ladyman either in acknowledging that such underdetermination exists or in attributing to it such drastic consequences. However, an alternative view that physics does sanction objects, albeit merely as ontologically secondary entities, represents a different and seemingly less extreme route to the same conclusion regarding the fundamentality of structure. But since what it means to be ‘ontologically prior’ is itself a vexed philosophical question, a stance must be taken as to how we are to understand priority before its prospects may be evaluated. In an earlier paper, I outlined how Fine’s notion of ontological dependence might be utilized to defend the priority-based approach to structuralism. Since then, however, I have become convinced that that ontological dependence is not a relation of priority after all. As a result, the arguments outlined in that paper stand in need of reassessment. In this work, I consider the prospects for priority-based structuralism when expressed in the idiom of determination. My conclusion will be that it has yet to be vindicated by our best physical theories, owing to the failure of symmetry structures to determine the world’s inventory of fundamental kinds. Nevertheless, the same symmetry considerations point towards there being renewed prospects for eliminativism—an eliminativism, moreover, of more naturalistic appeal than that hitherto associated with OSR. 1Introduction 2Structuralist Strategies 3Defining Ontological Priority: Dependence or Determination? 4Structuralism in the Idiom of Determination 4.1Determining plurality 4.2Determining kind properties 5A Reinvigorated Eliminativism. (shrink)

In this paper I focus on the impact on structuralism of the quantum treatment of objects in terms of symmetry groups and, in particular, on the question as to how we might eliminate, or better, reconceptualise such objects in structural terms. With regard to the former, both Cassirer and Eddington not only explicitly and famously tied their structuralism to the development of group theory but also drew on the quantum treatment in order to further their structuralist aims and here I (...) sketch the relevant history with an eye on what lessons might be drawn. With regard to the latter, Ladyman has explicitly cited Castellani's work on the group-theoretical constitution of quantum objects and I indicate both how such an approach needs to be understood if it is to mesh with Ladyman's 'ontic' form of structural realism and how it might accommodate permutation symmetry through a consideration of Huggett's recent account. (shrink)

The view that it is symmetries, not particles, that are fundamental to nature is frequently expressed by physicists. But comparatively little has been written either on what this claim means or whether it should be regarded as true. After placing the claim into a general fundamentality framework, I consider whether the priority of symmetries over particles can be defended. The conclusions drawn are largely negative.

Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and methodology for interpreting (...) such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity. (shrink)

Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a carefully coded expression of our experience then its effectiveness is quite reasonable. Its effectiveness is built into its design. We consider group theory, the logic of symmetry. We examine the premise that symmetry is identity; that group theory encodes our experience of identification. To decide whether group theory describes the world in such an elemental way we catalogue (...) the detailed correspondence between elements of the physical world and elements of the formalism. Providing an unequivocal match between concept and mathematical statement completes the case. It makes effectiveness appear reasonable. The case that symmetry is identity is a strong one but it is not complete. The further validation required suggests that unexpected entities might be describable by the irreducible representations of group theory. (shrink)

In this paper we we will argue against the orthodox definition of quantum entanglement which has been implicitly grounded on several widespread presuppositions which have no relation whatsoever to the formalism of QM. We will show how these presuppositions have been introduced through a naive interpretation of the quantum mathematical structure which assumes dogmatically that the theory talks about "small particles" represented by pure states which suddenly "collapse" when a measurement takes place. In the second part of this paper we (...) will present a non-collapse approach to QM which makes no use whatsoever of particle metaphysics, escaping the need to make reference to space-time separability or the restriction to certain predictions of definite valued binary properties. Our paper ends up concluding the essential need to redefine the notion of quantum entanglement, at least in the cases of: i) non-collapse interpretations of QM; or, ii) any other interpretation which abandons the idea that QM makes reference to "small particles". (shrink)

In this paper we attempt to discuss what has Kochen-Specker theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties within the orthodox formalism of quantum mechanics. Through an analysis of the meaning of physical invariance and quantum contextuality we will derive a Corollary to KS theorem that proves that a vector in Hilbert space cannot be interpreted coherently as an object possessing physical properties. As a consequence, (...) the notion of quantum object can be only defined in terms of nomological properties. We conclude the paper by analyzing the consequences of this Corollary to KS theorem for the ongoing debate about quantum individuality. (shrink)

In this paper we derive a theorem which proves that the physical interpretation implied by the first postulate of quantum mechanics is inconsistent with the orthodox formalism. In order to expose this inconsistency we will analyze how the concept of ‘physical system’ is built within classical theories through the notion of invariance and explain in what sense a vector in Hilbert space is not capable of fulfilling these same mathematical conditions. Through an analysis of the mathematical formalism we derive a (...) No Dynamical Invariance theorem which proves that, contrary to what is claimed in the first postulate, a vector in Hilbert space cannot be interpreted coherently as the state of a physical system. We conclude the paper by analyzing the consequences of the NDI theorem with respect to several ongoing debates in QM. (shrink)