Structural realism and the nature of structure

by Scientia Salon

Our new pick for a “notable” paper is Jonas R. Becker Arenhart and Otavio Bueno’s “Structural realism and the nature of structure,” published in the European Journal for Philosophy of Science, 5:111-139, 2015. (Full text here, free.)

Here is the abstract:

Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scien- tific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure is undermines the realist component of the view. Given the difficulties, either realism should be dropped or additional metaphysical components not fully endorsed by science should be incorporated.

The paper is a very thorough, well argued critique of the now very fashionable “ontic structural realism,” as proposed, for instance, by James Ladyman and Don Ross in their Every Thing Must Go. The context for this discussion is the long standing debate in philosophy of science between realists and anti-realists, about both scientific theories and the entities (e.g., electrons) that they posit.

Here are some choice bits from the paper:

The ontic structural realist advances a metaphysical thesis to the effect that structures and relations are the fundamental components of the world; objects are secondary— they should either be eliminated or at best re-conceptualized in structural terms.

Our aim in this paper is to show that it is unclear that a proper characterization of structure suitable for ontic structural realism can be offered. We argue that there are far too many distinct ways of characterizing structure and relations, and as a result, the combination of realism and a metaphysics of structures becomes, at best, prob- lematic and, at worst, incoherent.

On the one hand, ontic structural realists argue that theories are better characterized in accordance with the semantic approach, rather than in terms of the syntactic view of theories and related approaches to structure based on Ramsey sentences.

On the other hand, the semantic approach is typically formulated in terms of set-theoretic structures. But this commitment to set theory, we argue, introduces objects as key components in the characterization of structures, and is responsible for the tension.

This strategy is called the “Poincare` manoeuvre” by Steven French (2012, p. 23). According to it, objects are used merely as heuristic devices or stepping stones to obtain the structure. After the structure is characterized, the objects are left behind: either they are taken as metaphysically irrelevant entities or are only conceived as being derived from the relations, depending on the kind of OSR that is assumed.

This maneuver, however, faces significant difficulties. First, in set theory, struc- tures are obtained as elements of the set-theoretic hierarchy. As noted, on the set-theoretic account of structure, objects are used to construct relations and struc- tures, not vice versa.

The indispensability argument aims to establish commitment to objects that are indispensable to our best theories of the world (for discussion and references, see Colyvan 2001). It was originally designed by W. V. Quine (see, e.g., 1960) to force those who are realist about scientific theories to become realist about the mathematics that is indispensably used in such theories.

We understand the “indispensability thesis” as the claim that scientific theories cannot be formulated without reference to mathematical objects, relations and functions. We understand the “inseparability thesis” as the claim that it is not possible to separate the nominalistic content and the mathematical content of a scientific theory. The indispensability thesis may entail the inseparabil- ity thesis, but not the other way around.

The deflationary nominalist grants that mathematics is indeed indispensable to science, but resists the conclusion that this provides any reason to be committed to the existence of mathematical objects and structures. This is achieved by distinguishing quantifier commitment (the mere quantification over the objects of a given domain, independently of their existence) and ontological commitment (the quantification that commits one ontologically to the existence of something).

The problem with the introduction of ontologically neutral quantifiers in the con- text of structural realism is that, given these quantifiers, it is unclear how structural realists will manage to specify what their realism amounts to. Unless they provide an independent mechanism of access to, and specification of, the structures they are realist about, the use of ontologically neutral quantifiers will ultimately remove all ontological content from structural realism.

Mathematical structures only represent the nominalistic (physical) content, which is the content structural realists are ultimately committed to; they need not be committed to the mathematical content. In other words, the set theory that structural realists invoke only play a representational role; it does not provide any guide to the commitments structural realists have.

In response to the point that OSR does not entail mathematical platonism, the sit- uation is more complex than it may initially appear. On the surface, it may seem that the two views are independent from one another. After all, OSR is a form of realism about the (fundamental) structure of reality. As such, it seems to make no claim about the existence of mathematical structures—which is the scope of a structuralist version of platonism (that is, a form of realism about mathematical structures). But, in fact, if the mathematical content of a theory cannot be separated from its physical (nominalistic) content (Azzouni 2011), it is unclear how the struc- tural realist can restrict ontological commitment only to the physical content without having first already nominalized mathematics.

A structure is characterized (in a loose sense) by both objects and relations, but for the structural realist only relations are primary ontologically. This is a good indication that relations are the fundamental components of the world, and indeed ontic structural realists emphasize this point (see, in particular, French 2010). But this means that in order to understand the nature of structures, we need to understand the nature of relations and of the connections they bear to objects. Metaphysically speaking, relations are far from being uncontroversial. They are at least as controversial as properties. To speak of relations as primary components of reality, one cannot speak of them as being somehow abstracted from objects— since, in this case, they would be ontologically dependent on objects. Rather, in order to have ontological primacy, relations need to constitute such objects.

Given that structure gives rise to objects (which are read off from the relations), how can one make sense of the disparate objects that emerge in distinct theories that share part of an underlying structure? Since some part of the structure is the same in the old and in the new theories, at least one of two options should obtain: (i) some features of the resulting objects should be the same in distinct theories, that is, there is also a form of objectual continuity through theory change, or (ii) since some structural preservation should be maintained throughout, this induces some continuity at the level of objects too, since these objects are characterized in terms of the relevant structures. However, both options entail a form of objectual continuity through theory change, something the structural realist has banned, given the pessimist meta-induction.

By positing some essential structure that gets accumulated, structural realists end up admitting that in the long run (even if it is supposed to be a very long run), as scientific theories get closer to the truth, the objects will get progressively closer to being fixed by the accumulated relations, and so realism about objects will be justified too.

If the structural realist does not allow for some fixed, essential structure to be preserved through scientific revolutions—allowing for modifications even in the parts considered essential—then there is no reason to suppose that in the long run, after many instances of theory change, any structure will be ultimately preserved.

Given the considerations above, ontic structural realists are unable to specify the nature of the structure they are supposed to be realist about. There is underdetermination both at the mathematical and the metaphysical levels.

If OSR is the best combination of realism and structuralism in philosophy of science that is also able to make sense of quantum physics, perhaps the realist component needs to be dropped. The very idea that there is a true, fundamental, underlying structure of the world—in whose existence we must believe—is difficult to make sense of, as the above arguments have indicated.

One needs to acknowledge that the truth or plausibility of the proposed metaphysics will not be settled on purely scientific grounds. By giving up on a strict naturalistic methodology in the metaphysics of science, one can introduce discussions about theoretical virtues in metaphysics, and then invoke those virtues to claim that OSR fares better than the alternatives, at least on prag- matic grounds. However, if a naturalistic metaphysics must go, then we must abandon the idea that OSR is a metaphysics tailored to fit our physics, and without this most cherished motivation, OSR is leveled with other metaphysical packages, disputing priority on a priori grounds.