We present a precise form of structural realism, called group structural realism, which identifies ‘structure’ in quantum theory with symmetry groups. However, working out the details of this view actually illuminates a major problem for structural realism; namely, a structure can itself have structure. This article argues that, once a precise characterization of structure is given, the ‘metaphysical hierarchy’ on which group structural realism rests is overly extravagant and ultimately unmotivated. 1 Introduction 2 What is (Group) Structural Realism? 2.1 The basic picture 2.2 Wigner’s legacy 2.3 Accounting for theory change 3 The ‘Higher Structures’ Problem 3.1 The structure of a structure 3.2 Higher structures and theory change 3.3 Any way out for the groupies? 3.3.1 Chopping down the tower 3.3.2 Playing favorites 3.3.3 Adopting the whole shebang 4 Conclusion Appendix
We present a precise form of structural realism, called group structural realism, which identifies ‘structure’ in quantum theory with symmetry groups. However, working out the details of this view actually illuminates a major problem for structural realism; namely, a structure can itself have structure. This article argues that, once a precise characterization of structure is given, the ‘metaphysical hierarchy’ on which group structural realism rests is overly extravagant and ultimately unmotivated. 1 Introduction 2 What is (Group) Structural Realism? 2.1 The basic picture 2.2 Wigner’s legacy 2.3 Accounting for theory change 3 The ‘Higher Structures’ Problem 3.1 The structure of a structure 3.2 Higher structures and theory change 3.3 Any way out for the groupies? 3.3.1 Chopping down the tower 3.3.2 Playing favorites 3.3.3 Adopting the whole shebang 4 Conclusion Appendix
Both advocates and critics of structural realism have conducted their debate under the shadows of Poincaré and Russell. However, if antecedents of a structural realism informed by quantum mechanics are to be looked for, then the historical focus should be shifted forward a few years, to the commentaries and reflective ontological work of Cassirer and Eddington. Here forms of structural realism can be found that are informed by the powerful mathematical framework of group theory that had been developed and applied to the new quantum mechanics by Weyl and Wigner. As Cassirer and Eddington both realized, one of the crucial features of modern physics is the increased significance of the role of symmetry and it is to this that group theory gives mathematical expression. OSR is informed by the role of symmetry and invariance in just the manner that Cassirer and Eddington advocated and the rest of the book is taken up in trying to articulate an appropriate metaphysics for such an informed perspective.
According to scientific realism, science gives us an approximately true description of what the world is like. But what does it mean? In this chapter, we focus on the ontological and metaphysical aspects of this discussion. That is, we are concerned with the following questions: what there is, according to our best scientific theories? And how are these things that theories say exist? We start from the assumption that a genuine scientific realism must deal with these issues. Taking non-relativistic quantum mechanics as a case study, we discuss some of the challenges currently faced by a genuinely realistic stance. We argue, first, that in the ontological aspect, realists are in the same boat as science, that is, without sufficient epistemic justification to adopt the belief in the entities postulated by a single quantum theory, given that experience (currently) is not able to decide between rival theories; in the metaphysical aspect, realists also encounter problems with theory choice, given the possibility of associating more than one metaphysical theory with the description of the entities postulated by each quantum theory. The same goes for structuralist alternatives, since, even if we accept that scientific theories are committed to the existence of structures, but not objects, we still do not know what structures are, metaphysically. Finally, we move forward in the discussion with the meta-Popperian method, which serves to reduce the metaphysical alternatives associated with the ontological postulates of scientific theories. We may not know what the correct alternative is, but we have been able to progressively check which metaphysical alternatives are incompatible with each scientific theory.
Abstract Quantum entanglement poses a challenge to the traditional metaphysical view that an extrinsic property of an object is determined by its intrinsic properties. So structural realists might be tempted to cite quantum entanglement as evidence for structural realism. I argue, however, that quantum entanglement undermines structural realism. If we classify two entangled electrons as a single system, we can say that their spin properties are intrinsic properties of the system, and that we can have knowledge about these intrinsic properties. Specifically, we can know that the parts of the system are entangled and spatially separated from each other. In addition, the concept of supervenience neither illuminates quantum entanglement nor helps structural realism.
Abstract I point out an underdetermination of physics, in particular of Quantum Mechanics: that of the relation between the operators and their physical meaning. The set of operators for which we attribute physical meaning is, from relational, structural, and dynamical points of view, indistinguishable from any set of operators obtained from the former by a unitary transformation that commutes with the Hamiltonian. The same is true for the structures inhabiting the world, in particular there are structures isomorphic to the structure of an observer, but they would attribute the meaning of position and other physical meanings to different operators. In particular, space itself is underdetermined from the structure of the theory. Different structures that are isomorphic to an observer would call “position” different observables, and consequently would call “space” different structures. I show that they are highly non-unique. A solution would be that all possible assignments of physical meaning to the operators allowed by the symmetries of the formalism are equally valid. But this leads to a problem: there would be no correlation between the content of the mind of an observer about the external world, and the actual properties of the external world. This has unexpected consequences: it refutes structural realism, and it shows that, in addition to the structure, the substance underlying the structures matters for consciousness to exist.
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.
The scientific realist wants to read the metaphysical picture of reality through our best fundamental physical theories. The traditional way of doing so is in terms of objects, properties, and laws of nature. For instance, there are families of fundamental particles individuated by their properties of mass and charge, which determine how they move. One could call this view an object-oriented metaphysics grounded on properties. In this paper, I wish to present an alternative view that one can dub a thin object-oriented metaphysics grounded on structure: there are fundamental entities with no fundamental properties other than the one(s) needed to specify their nature. I argue that my view has several advantages over the received one. In particular, I compare my proposal to the traditional view in the quantum domain and I argue that my view provides a better fit for both approaches to quantum metaphysics, namely the primitive ontology program and wave-function realism.