# Group Structural Realism (Part 1)

Note: This post later turned into a paper, which turned into a forthcoming article in BJPS. You can read the full preprint here: PhilSci Archive.

Part 1 | Part 2 | Part 3 | Part 4
Introduction

Group theory plays a special role in the foundations of quantum theory. Today, I want to discuss a philosophical view that uses this role as its jumping-off point. I call the view, Group Structural Realism..

Structural Realism (A Brief Intro). The positive claim of structural realism differs greatly from author to author. However, there is one core consequence that follows from nearly every account of structural realism (as a metaphysical view):

The Structural Realist Hierarchy. The existing entities described by a scientific theory are organized into a hierarchy, in which ‘structure’ occupies the top, most fundamental position.

What it means to be ‘metaphysically fundamental’ is cashed out in various ways. For example, Ladyman and Ross characterize it using the notion of supervenience on properties:

Ontic Structural Realism (OSR) is the view that the world has an objective modal structure that is ontologically fundamental, in the sense of not supervening on the intrinsic properties of a set of individuals. According to OSR, even the identity and individuality of objects depends on the relational structure of the world. (Ladyman and Ross 2007, 130.)

An analogy: the droplets of paint on a canvas are perhaps more metaphysically fundamental than the images in the painting. Similarly: the atoms in a molecule are more fundamental than the molecule, which is more fundamental than the substance. Structural realists argue that at the very top, at the most most fundamental layer of this hierarchy, there is structure. Although there may be further concern about what kind of shadowy existence this structure might have, it is the metaphysical hierarchy that underwrites the view.

For this discussion, let’s bracket the shadowy stuff, and focus on the hierarchy.

Broadly speaking, structural realism gets proposed with one of two main goals. First: structural realism aims to provide a general, programmatic account of science and scientific discovery. Worrall’s structural realist account of theory change is the canonical example. Second: structural realism aims to solve specific problems in the interpretation of a theory. For example, it has been proposed as a solution to the problem of identical particles (Ladyman and Ross 2007, §3.1) and to the problem of interpreting spacetime points (Dorato 2000).

Standing between structural realism and what it endeavors to achieve is the meaning of the word structure. Bas van Fraassen has described one broad agreement among critics: “As almost every commentator has somewhat sadly remarked, this key word has its own problems” (van Fraasen 2006, 303). Ladyman and French themselves note that “Because of the width of its embrace and its complex history, defining what is meant by structure and characterising the tendency in general, is problematic” (French and Ladyman forthcoming, §1). Ladyman and Ross similarly accept the criticism that structural realism may not be well ‘worked out.’ However, they retort that “it is far from clear that OSR’s rivals are ‘worked out’ in any sense that OSR isn’t (Ladyman and Ross 2007, 155).

Clearly, we ought to work something out. As a start, I will try to show that, using the resources of group theory and quantum mechanics, a precise characterization of ‘structure’ can be worked out in as much detail as you like. The specific view that I propose we work out is the following:

Group Structural Realism (GSR). The existing entities described by quantum theory are organized into a hierarchy, in which a particular symmetry group occupies the top, most fundamental position.

GSR has a good deal of precedent among structural realists. For example, Aharon Kantorovich argues for a conception of particle physics in which “internal symmetry is the deepest layer in the ontological hierarchy,” and in particular, that “flavor SU(3) symmetry was ontologically prior to hadrons… whereas SU(5) is ontologically prior only to baryons” (Kantorovich 2003, 673). Holger Lyre has suggested an account of objects that “takes the group structure as primarily given, group representations are then construed from this structure and have a mere derivative status” (Lyre 2004, 663). Similarly, Ladyman and Ross argue that, “elementary particles are hypostatizations of sets of quantities that are invariant under the symmetry groups of particle physics” (Ladyman and Ross 2007, 147).

In the next post, we will discuss some of the physical results that make GSR plausible. By identifying which structures are of interest in one particular context, GSR may stand a worthy chance of finding some connection to the physical quantities that we actually observe and measure in the lab. This step is absolutely essential. Bothersome though it may be, any acceptable account of reality must show some connection to the observable world.

Next post: Group Structural Realism (Part 2).

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## 3 thoughts on “Group Structural Realism (Part 1)”

1. Bryan

Hi Jim,

Thanks for the link to your very nice post. I agree there is urgent need for as much precision as possible in this debate. However, I’m skeptical about the logico-semantic approach.

Ontic structural realism was originally proposed as a position about scientific realism. We want to know what the unobservable ‘reality behind the physics’ is like. OSR councils that this reality is characterized by ‘structure.’

What is ‘structure’? You suggest we follow Quine and identify structure with existentially quantified sentences. This is an approach that was originally suggested by Ramsey. However, there are several major logical problems it (see section 3.2 of the website you mention).

One example is that if all the purely observational consequences of a consistent theory are true, then by Craig’s theorem, the entire (existentially quantified) Ramsey sentence is true — and so the Quine-approach reduces to radical empiricism! This isn’t appropriate for structural realism, for then the ‘unobservable’ scientific entities would be completely unnecessary.

The main problem I have with the approach this: it presumes we can express physical theories in first-order (or perhaps second-order) logical language. This strikes me as highly implausible — Reichenbach (arguably) axiomatized special relativity, but we haven’t made it much farther than that.

Still, the Quine-approach you describe does have one important virtue: it’s a shot at describing ‘structure’ in precise terms. My own suggestion is that the best terms to explicate structure are in scientific terms. As I’ve tried to show, structure can be fruitfully identified as an algebraic group.

Unfortunately, I’m still not sure about the prospects of structural realism as a coherent metaphysical view!

2. Jim Bowery

The main problem I have with the approach this: it presumes we can express physical theories in first-order (or perhaps second-order) logical language.

You may have a point there since it appears that to quantum mechanics requires rather radical departure from ordinary logic. Specifically, if one posits absence of observation of a state as a case count of 0 (false) and presence of observation of a state as case count >0 (truth), quantum states may require negative case counts.