Minimal Structuralism Is Not Constructive Empiricism

Van Fraassen's constructive empiricism might look superficially similar to the position I have been calling minimal structuralism; however, as I attempt to show in this section, the positions are radically different under the surface. The superficial similarity, and ultimate difference, concerns the distinct understandings of the notion of observable. Firstly, and in its essentials only, what is constructive empiricism? After answering this it will be clear that my differs does indeed differ.

Constructive empiricism is founded on the claim that belief should be restricted to that which is accessible to direct observation—this is the source of the problems with constructive empiricism and the ultimate difference between our positions. Belief is not equivalent to acceptance; one can perfectly well accept a theory without believing it (the theory might have some heuristic value, for example). Science does not aim for truth—this forms the basis of van Fraassen's rejection of realism—rather, its aim is to provide us with empirically adequate theories. It should preserve the 'phenomena 'or the 'appearances'; these are understood to be the objects and structures of experience, experience that is not gained through 'non-sensory' technical instruments (e.g. telescopes; spectroscopes, etc.). Van Fraassen presents us with an example that is supposed to make these points clearer: the moons of Jupiter in fact cannot be seen with the naked eye from Earth; we use telescopes to view them. But they are nonetheless observable since "they can seen without a telescope if you are close enough" ([1980], p. 16). 'Observable' thus means actually or possibly observable with the naked senses; things not satisfying this criterion are consigned to the realm of the 'unobservable'.

& Ladyman's ontic brand of structuralism would also offer a straightforward response to this problem: simple eschew the subjects of the correlations and deal with the correlations themselves. However, the elimination of objects that goes with this view—standardly signaled by a shift to a reduced space description—will be underdetermined by the physics. 302 Of course, Eddington's structuralism is far more wide-ranging this simple 'package view' suggests (see the article by French (ibid.) for a detailed analysis of some of the other aspects). I don't wish to be aligned with all aspects of Eddington's structuralism; only with the idea that the package view is best equipped to deal with the problems I have drawn attention to. This view can be seen, for example, in his take on the relationship between a group-structure and its elements: "the significance of a part cannot be dissociated from the system of analysis to which it belongs. As a structural concept the part is a symbol having no properties except as a constituent of the group-structure of a set of parts" ([Eddington, 1958], p. 145). In other words, structure and elements are inextricably intertwined; the correlates in a correlation exist in something like the same way a hole and its outer surface exist: they are inextricably bound together.

Though science may shift the line between 'observable' and 'unobservable', the distinction will always hold, and will always thus constrain what can be said about the link between epistemology and ontology. While van Fraassen allows that there can be perfectly meaningful theoretical statements about matters 'beyond' the line of observability, and that can be true or false, our attitude or stance towards these statements should be one of agnosticism. This viewpoint is able to avoid the problematic underdetermination that one faces when trying to interpret physical theories. An interpretation of a theory, you will recall, provides an ontology for that theory; it tells us how the world could be the way the theory says it is. Van Fraassen couches this idea in the semantic approach to theories, according to which a physical theory is a collection of models, the elements of which are taken to represent a possible way for the actual world to be—a mere possible representation only becomes actual if the model and physical reality are isomorphic. The problem is that there are in general many such ways, many such models, with no way, internal to the physical theory itself, of deciding between them. What we have at best, instead, is empirical adequacy; the models have sub-models that represent the observables, the actual appearances, and these are isomorphic and, therefore, good candidates for belief. Empirical adequacy for van Fraassen is just this isomorphism between empirical sub-models and phenomena. What is not captured in this isomorphism is not a candidate for rational belief. Hence, Van Fraassen's agnostic stance: one model might well be the One True Model, isomorphic to the physical world, but we can never know for there are multiple empirically adequate interpretations (models). Thus van Fraassen gives us the following example:

If someone likes to talk in terms of spheres, I can reconstrue his every assertion an assertion about points. And vice versa! This is not to deny that it is possible for a person to believe that points are the only real concrete individuals—what we cannot do is to say that geometry forces this view on us. ([van Fraassen, 1991], p. 451)

I agree with this, and agree that much the same holds in the context of physics. However, there are elements in both geometry and physics that we can be sure about, that we can be realist about without the shame of underdetermination; we can be realist about the invariant structure, and that just is the geometry. Points and spheres simply provide us with different ways of talking about the same structure. This is the point at which my position becomes distinct from constructive empiricism; the invariant structure—that which is invariant under symmetries, for example—is not necessarily observable in van Fraassen's sense, and I don't believe that there is a straightforward distinction to be made between observable and unobservable in van Fraassen's sense.

Empirical adequacy is a primary constraint on an interpretation, and I agree that a nice way of cashing the notion out is through the sub-models and isomorphisms of the semantic approach, but the aim of science goes beyond that, and can give us more than that. The minimal structuralism I outlined above goes beyond merely empirical structure. For example, let's consider the gauge invariance of general relativity. Suppose we have a simple universe with a triangle of three objects; the structure that is preserved by applying a diffeomorphism (the gauge symmetry) to the spacetime they occupy is the relative distances of the objects and the topological (and 'finer') properties of the spacetime manifold. The relative distances will count as observable according to van Fraassen, but the topological and other properties will certainly not count as such. There is no measurement— certainly not unaided!—we could perform to determine the total 4-volume of a compact universe, and yet this is an observable in my sense. We can be realist about this quantity, and it is its gauge invariance that allows us to do so with impunity; to put the point another way, we may say that the 4-volume is an observable but is not a beable, it is not something we measure. Yet this is included in my account. We don't need to devise an experiment that will provide us with some new empirical data, a reading on a computer monitor for example; even if we could, according to van Fraassen the 4-volume itself would not be observable, only the reading on the screen would be. We have a clear-cut case of disagreement, and it is a fundamental one. It goes further. Van Fraassen thinks that science is an exercise in model-building, rather than a truth-finding mission; scientists construct models that fit the observable facts, and certain models, with different ways of representing the unobservable realm, might be more useful than others. That just grinds against what I take science to be about, namely that it does aim to furnish us with TRUE stories about the world and its workings. The idea that the line between what can and cannot qualify as true belief (observable vs unobservable) is based on human physiology (cf. van Fraassen [1980], p. 17) and what I say is that the observables have nothing to do with us. I think that I have dispelled some of the problems besetting realism, that in part guided van Fraassen's rejection of it, well enough: the empirical equivalence and underdetermination that result from symmetries can be squared with realism, but not to the extent that the ontologi-cal structural realists believe, and certainly not to the extent that standard entity realists believe. The position that results can be viewed usefully as providing the safest base from which to construct ontologies in the context of modern physics; I claimed that this is best understood as a structuralist position.

To sum up this section, and indeed this book, let me state my position more plainly.303 The underdetermination that van Fraassen is motivated by also motivated the ontological structural realists, though in very different ways! Van Fraassen argues that the underdetermination, the multiplicity of interpretations or models, should push us into retracting our belief when the interpretation goes beyond the observable (i.e. beyond the empirical sub-model). Thus, the under-determination motivates van Fraassen's anti-realism; he focuses on the empirical

303 Recently, Esfeld [2004] has argued for a position superficially similar to the one I have outlined. His idea is to take from the ontic structural realists the claim that there are no intrinsic properties of things that yield structure, but to retain the things as an independent ontological category, grounding their qualitative character in the relations they bear to one another. He calls this a "moderate metaphysics of relations" in contrast to the ontic structuralists "radical metaphysics of relations". His position is based on the premise that relations do require relata—in this sense he is very close to Dorato's spacetime structural realism. I dispute this, and think that relations can be self-standing, or prior to relata. The reason I choose not to dispense with relata (objects) tout court is simply that the dispensation is not something that can be decided by the physics because of the equivalences holding between the pictures with and without them. I simply wish to clear the ground for the proper interpretation of physics (at least those with gauge-symmetries); physics must be supplemented by some suitable metaphysics to support the kinds of views associated with there being and not being objects. In any case, if Esfeld's position is to work, and be coherent, I think he has to adopt the kind of package deal view I prefer. Without this the relata are, in themselves, mere bare particulars and that is a metaphysics that physics can do without.

content of a theory, the bits that can be observed unaided—though this might include plates from particle collision experiments, it is the plates and not the particles that are observed. On the other hand, the same difficulty pushes the ontological structural realists into shifting their beliefs onto the structure that is common between the underdetermined interpretations, the multiply realized structure (most naturally described, as I said, by the equivalence class, within a reduced space approach). The different underdetermined interpretations, models, or solutions are simply different ways of getting to the physically real core of the world, different ways of representing the same structural facts.

Structural realists will want to say something about what happened during the particle collision experiment, rather than what happens when one observes the end result, the plate itself. The theory will furnish this, even though there will, or may be many apparently competing interpretations: for the structural realist there is really no competition, the true ontology is that which connects the many interpretations. The story they give will be different from that of a standard realist who will most likely wish to tell something in terms of the theoretical entities postulated by the theory, the individual particles, fields, or whatever; the structural realist story will allow for particles, but only as derivative from the 'wider' structure. This I disagree with, and I side, to a certain extent, with van Fraassen. In this chapter I have tried to show how the ontological structural realist position is subject to an underdetermination of its own; one cannot read off the physics whether there is structure that 'lives on top' of objects or is primitive, brute. The reason underlining this new underdetermination is that even with objects one can escape the traditional kinds of underdetermination that pushed van Fraassen and the structural realists; one simply looks at the observables and notes that they are insensitive to matters concerning permutations of the objects. But the structure of the observables is what I say we should focus on, this should be the object of the structural realist's devotion; it is that which is invariant under swaps of gauge related states, of certain permutations (those which do not result in a structural change) of the individual elements of the theory. But just because it is invariant under a change of the individual elements of a domain does not mean that the objects should be dispensed with; because this tyre is as good as that qualitatively identical tyre and so can be swapped, does not mean that my car can run without tyres! The view I prefer, and which sits best with general relativity and quantum gravity, was a view whereby the observables are (gauge invariant) correlations between (gauge variant) quantities (i.e. correlata) that cannot be viewed as independent from the whole correlation: the correlata are measurable in virtue of the fact that the correlation is predictable and measurable. Thus, interpretively speaking, the structure comes before the individuals since the individuals are not measurable. These observables, the correlations, are insensitive to matters concerning the individualistic ontology of spacetime points. It is in this sense that they are structural, and—given the further claim that the observables give a true account of the world—the ontology based upon them is structural realist. It is minimal because it does not say that all there is this structure.304 This is the most minimal realist core that can be read

304 I should perhaps quickly distinguish this from an epistemic version of structural realism. Recall that that position says that there is more to the world than structure, but that all we can know is the structural aspects of this "more". I say that off the physics without falling prey to either anti-realism or metaphysical (interpretative) underdetermination.

whether there is more than the structure cannot be answered, it is underdetermined by the physics: one can be realist about the structure without holding that there is nothing but the structure. Thus, when da Costa & French say that "all that there is, is structure" ([2003], p. 189), they are staking out a radical metaphysical territory, they are not reading that thesis from off the formal representation of physical theories. In this sense one can shoot the ontic structural realists with their own gun; their gripe with standard entity realism is precisely that it is metaphysics not physics (cf. French & Ladyman [2003], p. 45). But regardless of this, we can still know that structural aspects are physically real, and knowable, despite the fact that we might not be able to observe them.

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