Abstract
My goal is to develop a structuralist approach to the objects of physics that is realist – but there are obstacles in the way. This paper is about three of them. The first is familiar, having received a great deal of attention in the recent literature, and concerns the suggestion by structural realists French and Ladyman that we should give up talk of objects. This leaves me in the uncomfortable position of being pro-structuralist and pro-realist, but siding with some opponents of structural realism (at least in its ontic form, about which more below) when it comes to objects, so I had better have something to say. In fact I do (see Section 3.4), and I think this obstacle can be moved out of the way. The other two obstacles I have yet to overcome, and the purpose of this paper is to explain what they are, how they arise, and why they are a problem for the structural realist specifically. The resources open to the scientific realist in facing these obstacles are not available to the structural realist, and the reason is the same in both cases.
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- 1.
The term “model” in science is, of course, replete with connotations of representation, and the temptation might perhaps be for users of the semantic view of theories, with its Tarskian models, to slide between models as truth-makers and models as representations without offering a justification. This is not acceptable, but I will not pursue this issue here.
- 2.
Of course, this is somewhat vague until we say what is meant by “relevant structure”, and that will depend on the case at hand. What can be said in general is that for any given physical theory we will have some handle on what the relevant elements and relations appearing in our models are; the requirement that we can map all these elements at one level of the hierarchy onto the elements at another level, preserving the relations between them, is not trivial.
- 3.
Based on Table 1 on p. 259 of Suppes (1962).
- 4.
One line of response might be to assert that mediating models occur only when the related theory is not mature. I side with those who don’t think that this is right, but making my case would require detailed discussions of appropriate case studies. While such discussions lie outside the scope of this paper, I recognize this is an as-yet undischarged responsibility.
- 5.
Our theoretical models satisfy our equations, and in this sense might be thought analogous to Tarskian truth-makers. However, we should not take this analogy too seriously, and indeed it has recently been argued that the models of the semantic view are in any case not best understood along Tarskian lines. See Thomson-Jones (2006) and Morrison (forthcoming). The account we arrive at may no longer be most aptly termed a “semantic” view of theories, but that is a discussion for another day.
- 6.
See Brading and Landry (2006).
- 7.
This has led to a lot of noise about whether there can be relations without relata.
- 8.
- 9.
French and Ladyman (2003) go to strenuous lengths to resist the idea that we can continue talking of objects, simply reconceiving them as nothing more than the relations in which they stand, but I still take it that this is because the objects of physics fail to satisfy conditions which they assume are associated with object-hood. I don’t find a conclusive argument here.
- 10.
This need not be a sharp criterion for when an object is present.
- 11.
In other words, I am leaving open the possibility that we can apply predicates to the theoretical kinds of objects without it following that the resulting statements can be re-expressed using a universal quantifier over particular theoretical objects that are the members of the kind. Relatedly, I am not yet convinced that the physical objects instantiating the kind must have theoretical counterparts that are logical objects, or that this is necessary in order for us to be able to represent and talk about the world. But I don’t have arguments spelling out these latter points.
- 12.
Moreover, there may be structure important for certain purposes that is shared by certain mediating models and a subset of the theoretical models. What shared structure counts as relevant is dependent on the purpose for which we are using the theory and the models. I will not discuss this further here.
- 13.
As noted above, French and his collaborators seek to replace isomorphism with a weaker type of morphism (arguing for this in their “partial structures” approach), but reject the generalizing move to “shared structure”, where the type of morphism is left unspecified at the general philosophical level and specified only in relation to specific examples. Nevertheless, they too will have to take into account the structural incompatibilities between collections of models within a single hierarchy. I think that the problem I am discussing here affects all structural realism projects once the isomorphism requirement is relaxed (as it needs to be).
- 14.
This approach affords a special status to the models associated with the high level theory, and to the high level theory itself. It might be argued that this is a benefit of the approach. See, for example, Morrison (forthcoming), who argues that with the rise of the semantic view of theories and its emphasis on models we risk losing sight of the special role played by theory.
- 15.
It is compatible with this claim that the high level theory be identified with a collection of models, as some advocates of the semantic view of theories maintain.
- 16.
As noted above (see Section 3.3), representation is carried out in two steps: first the link between the models of the high level theory and the data models; second the link between the data models and the world. I will not discuss the second step here.
- 17.
Or, if you prefer, for any sub-system of the world there is a model of the theory that accurately represents the structure of that sub-system.
- 18.
Note that this applies equally to the version of structural realism favored by French and his collaborators.
- 19.
Demonstrating the utility of the notion of shared structure requires the elaboration of detailed case studies, and that will not be carried out here. My concern in this paper is rather with highlighting one of the (problematic) consequences of moving to this more general notion, one that arises as a matter of principle even before the elaboration of case studies.
- 20.
This is prior to, and independent of, any attempt to give a specific account of representation.
- 21.
In Section 3.5.1, above, we noted that one might insist that in the characterization of realism the term “theory” applies to the entire hierarchy, rather than to the high level theory alone, thereby avoiding the need to account for the “transparency of the hierarchy”. We are now in a position to see why this will not help the structural realist. What could it mean to be realist about incompatible structures?
- 22.
For now we ignore the enormous amount of work that gets us even to this point, since it is possible to construe this work as discovery of pre-existing quantities.
- 23.
Separating pattern from noise is not the problem of induction: so construed, it would assume that there is a correct separation (depending perhaps on the completed history of the universe) that – if we hit upon it – would remove the incompatibility between data models. I take McAllister’s point to be that the element of human choice is ineliminable in principle, not just in practice.
- 24.
Notice that this problem of different data models being compatible with the same phenomena poses a problem not just for the structural realist but also for the structural empiricist. Paralleling our characterizations of scientific realism and structural realism, we might attempt to characterize structural empiricism as follows:
Structural empiricism
(1)Science aims to give us, in its theories, an accurate representation of the structure of the phenomena.
(2)We have good reason to believe that science is successful with respect to this aim.
I reject both the above realist and empiricist versions of structuralism for two reasons. First, I think that we have good reason to suppose that there is no such thing as the structure of the world or the structure of the phenomena. (I offer support for this claim with my argument for objects of physics as objects FSPP (“for some practical purposes”), but I will not rehearse this argument here.) Second, I think that set up like this both the realist and the empiricist project are doomed to failure because of the problem of representation – the problem of what justifies us in believing that our theories represent the world or the phenomena. In the realist case, we will have only the “no miracles” intuition to justify our claim that our theories represent the structure of the world, and in the empiricist case it seems that in order to achieve representation van Fraassen (for example) ends up collapsing the distinction between data models and the phenomena, which it seems to me collapses empirical adequacy of a theory with respect to the phenomena into organizational adequacy of the theory with respect to the data models.
- 25.
- 26.
Note that in practice, for the theories that we have and are developing, the specification of necessary and sufficient conditions may not be complete, there may be consistency problems, and so forth.
- 27.
I follow E. Landry in my use of this terminology.
- 28.
This is not to say that structural realism is an untenable position, when incorporating modal realism, but only that the arguments for structural realism do not get us to such a position: additional arguments relating explicitly to the modal claim need to be supplied.
- 29.
Chakravartty (2004) has argued for a structuralism grounded in causal properties, in which he emphasizes the distinction between the nature of entities and the structural relations obtaining between those entities. On the view advocated here, the nature of entities (as members of kinds) is characterized in structural terms. Marrying the two approaches, the conclusion would be that it is not merely that our knowledge of the causal properties of entities is structural (knowledge of relations), as Chakravartty argues, but further that the ontological ground of these causal properties is itself structural. Working out the details of how this would go is a task for another day.
- 30.
How the loophole might work for (2) has been indicated above. In the case of (1), a first step would be to claim that the shared structure of the collection of models characterizing the high level theory gives sufficient conditions for an object to instantiate a kind, but that the necessary conditions need more careful handling in the face of the proliferation of models.
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Acknowledgements
Versions of material in this paper were presented at the Boston Colloquium for Philosophy of Science meeting on “Structural approaches in philosophy of physics” (February 2005), the University of Santa Clara conference on “The Metaphysics of Physics: Philosophical Implications of Contemporary Physical Theories” (May 2006), and at the Banff Workshop on Structuralism (August 2007). I am grateful to the participants at these meetings for their comments. I am also grateful to Elena Castellani, Elaine Landry, Margaret Morrison, Antigone Nounou, and Zanja Yudell for their comments on various aspects of this work. This paper makes extensive use of the “methodological structuralism” developed with Elaine Landry (see Brading and Landry 2006). My thanks also go to the editors of this volume. This paper was completed during research leave (2007–2008) supported by the National Science Foundation (NSF SES–0724383 Brading 201201), project title ‘Structuralist Approaches to Physics’.
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Brading, K. (2010). Structuralist Approaches to Physics: Objects, Models and Modality. In: Bokulich, A., Bokulich, P. (eds) Scientific Structuralism. Boston Studies in the Philosophy and History of Science, vol 281. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9597-8_3
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