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Oxford University Press eBooks

Scenes from the Lost History of Structuralism

Steven French

Published Jan 30, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.1093/acprof:oso/9780199684847.003.0004

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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.
Standard quantum mechanics poses serious challenges to some principles deeply entrenched in traditional metaphysics. In particular, the theory defies the ontological category of individual object through three of its features: contextuality, non-separability, and indistinguishability. The difficulties have prompted the development of non-traditional ontological frameworks intended to account for the quantum domain. Some approaches advocate replacing the classical conception of a realm of objects endowed with properties by an ontology that either dispenses with the category of object altogether or treats it as a derivative notion. The Modal-Hamiltonian Interpretation (MHI) of quantum mechanics and Ontic Structural Realism (OSR) exemplify this position. MHI proposes an ontology in which quantum systems are non-objectual bundles of properties linked by definite physical relations. The OSR defends the ontological primacy of structures, within which objects are construed as nodes of relations. The aim of this article is to compare these two ontological approaches, highlighting both their points of convergence and their divergences, particularly in light of the ontological challenges posed by quantum mechanics. With this aim, the article is structured as follows. Section 2 outlines the ontology of MHI, introducing the distinction between type-properties and case-properties, characterizing quantum systems as non-objectual bundles, and analyzing the role of symmetry groups in providing physical content to the theory and governing actualization. Section 3 turns to OSR, examining its motivations, its distinction between physical and mathematical structures, and the modal character of structures. Section 4 offers a systematic comparison of the two approaches, considering their respective motivations and scope, their shared commitment to an object-free ontology, the role played by symmetry groups within each framework, and their contrasting interpretations of modality. Finally, Section 5 presents some concluding remarks.
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.
In this paper, I shall discuss the heuristic role of symmetry in the mathematical formulation of quantum mechanics. I shall first set out the scene in terms of Bas van Fraassen's elegant presentation of how symmetry principles can be used as problem-solving devices (see van Fraassen [1989] and [1991]). I will then examine in what ways Hermann Weyl and John von Neumann have used symmetry principles in their work as a crucial problem-solving tool. Finally, I shall explore one consequence of this situation to recent debates about structural realism (SR) and empiricism in physics (Worrall [1989], Ladyman [1998], and French [1999]).