Studies in History and Philosophy of Modern Physics 43 (2012) 95–104 Contents lists available at SciVerse ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb Empirical factors and structure transference: Returning to the London account Ota´vio Bueno a,n, Steven French b, James Ladyman c a Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA b Department of Philosophy, University of Leeds, Leeds, LS2 9JT, UK c Department of Philosophy, University of Bristol, Bristol, BS8 1TB, UK article info abstract Article history: We offer a framework to represent the roles of empirical and theoretical factors in theory construction, Received 16 September 2010 and examine a case study to illustrate how the framework can be used to illuminate central features of Received in revised form scientific reasoning. The case study provides an extension of French and Ladyman’s (1997) analysis of 13 January 2012 Fritz and Heinz London’s model of superconductivity to accommodate the role of the analogy between Accepted 8 February 2012 superconductivity and diamagnetic phenomena in the development of the model between 1935 and 1937. We focus on this case since it allows us to separate the roles of empirical and theoretical factors, Keywords: and so provides an example of the utility of the approach that we have adopted. We conclude the paper Theory construction by drawing on the particular framework here developed to address a range of concerns. Models & 2012 Elsevier Ltd. All rights reserved. Semantic approach Partial structures Superconductivity London and London model When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics 1. Introduction partial structures version of the semantic approach. Second, we explore a particular case study using this framework. The episode It is a commonplace to say that theory construction involves in question admits of a separation of the respective roles of the both empirical and theoretical constraints. How these constraints empirical and theoretical factors, and thus provides an example of interact, however, is a much more contested matter. Empirical the utility of the approach that we have adopted. considerations often limit the scope of possibilities for theoretical The case study extends French and Ladyman’s analysis of Fritz elaboration, while the latter typically suggest avenues for further and Heinz London’s model of superconductivity to cover the role research, particularly since they are usually associated with of the crucial diamagnetic analogy in the development of the heuristic principles. In many cases, it is very difficult to map out model between 1935 and 1937 (French and Ladyman, 1997). This the contributions of each of these types of consideration. We are feature of the episode has not, to our knowledge, been studied interested in particular in the way such experimental results can previously and here we see an interesting shift from a ‘macro- help drive the move to a new model of the phenomena. As we scopic’ model, dealing with current densities and magnetic fields shall see, the move may be more complex than is generally strengths, to a microscopic interpretation, based on the motion of appreciated and, indeed, we shall suggest that it can be concep- electrons, that, although not able to offer a full theoretical tually divided into two distinct stages, which we will call, explanation of superconductivity (for reasons that shall become respectively, the characterization and explanatory stages. clear), greatly reduced the range of options available. What is Our goal in this paper is thus twofold: First, we present a particularly interesting are the roles of, first, a crucially important formal account of these stages within the framework of the experiment (associated with what came to be known as the Meissner effect), and, second, a fundamental analogy with the theory of diamagnetism. The construction of the London and n London model was crucially dependent on this experimental Corresponding author. E-mail addresses: [email protected] (O. Bueno), result, which was effectively ‘built into’ the model. However, this [email protected] (S. French), [email protected] (J. Ladyman). move does not render the model ad hoc, since the intention was 1355-2198/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.shpsb.2012.02.003 96 O. Bueno et al. / Studies in History and Philosophy of Modern Physics 43 (2012) 95–104 not to explain the relevant phenomenon behind this result, but to shall be considering here—that take us from the phenomena to characterize it in a way that allows the resources of the theory of the theoretical level (Bueno, 1997): electomagnetism to be brought to bear. The manner of character- Sk ¼ /Dk,Rk1,Rk2,Rk3,...,RknS ization was determined, in part, by the analogy with diamag- SkÀ1 ¼ /DkÀ1,RðkÀ1Þ1,RðkÀ1Þ2,RðkÀ1Þ3,...,RðkÀ1ÞnS netism, that was increasingly drawn upon to construct the ... underlying ‘microscopic’ model which was presented as a partial S ¼ /D ,R ,R ,R ,...,R S explanation. 3 3 31 32 33 3n / S Thus, what we have here, as we shall see, is not simply a case S2 ¼ D2,R21,R22,R23,...,R2n / S of filling in the value of a quantity which in the construction of S1 ¼ D1,R11,R12,R13,...,R1n the theory had been left open. Instead, the experimental result 1 2 3 where each Rij is a partial relation of the form /Rij, Rij, RijS—with ruled out the older model and motivated the construction of a 1 2 Rij representing the n-tuples that (we know) belong to Rij, Rij, the new one. As will become clear, in the context of our case study, 3 ones that (we know) do not belong to Rij, and Rij, those for which the two stages of characterization and explanation correspond to it is not defined whether they belong or not—such that, for every the schema adopted by one of the principal protagonists, Fritz 3 3 i,1rirk, card(Rij)4card(R(iþ1)j)(Bueno 1997, p. 601). The London, in his own reflective view of theory construction. It is partial relations are extended as one goes up the hierarchy, in perhaps unusual to find theory construction separated so expli- the sense that at each level, partial relations which were not citly into stages in this manner, but it very nicely sheds light on defined at a lower level come to be defined, with their elements the role of empirical factors in theory construction. belonging to either R1 or R2. However, we shall also examine the fundamental role of the Now, empirical results can be accommodated within this theoretical analogy with diamagnetism and the way in which hierarchy in various ways and as we indicated above, we wish further structure was imported into the superconducting domain to focus on the way such results can help drive the move to a new in order to frame the developing microscopic model. Such a model of the phenomena. Such a move can be represented within transfer of structure can also be nicely accommodated within our formalism as follows: the partial structures account of theories (see, for example, ¼ / S - 0 ¼ / 0 S da Costa and French, 2003) which represents the relationships A D,Rk k A K A D,Rk k A K between such theories in terms of partial isomorphisms and where, as we shall see, some of the theoretical relations used to homomorphisms. help obtain A may be retained by A0. In constructing the new model, various heuristic principles may be drawn upon but, again, we shall be particularly interested in the transfer of structure, that is, where structure in one domain is drawn upon to help 2. The characterization-explanation framework determine the relevant structure in another. In transferring such structure, analogies may often play a heuristic role, as will The formal details underpinning our framework have been become clear below. Here one may represent the situation with given elsewhere (see, e.g., da Costa and French, 2003), but we two different models—differing in their respective domains, shall summarize them before considering how this framework D and D0—and which can be related via partial isomorphisms can accommodate the above two-stage process: A partial struc- (or other morphisms): ture is a set-theoretic construct A¼/D, RiSiAI, where D is a non- / S 0 / 0 0 S empty set and each Ri is a partial relation. A partial relation Ri over A ¼ D,Rk k A K and A ¼ D ,Rk k A K D is a relation which is not necessarily defined for all n-tuples of In this case, the ontology of the models is different, and what elements of D (see da Costa and French, 1990, p. 255). Each partial matters is the way in which the relations from one model are / S relation R can be viewed as an ordered triple R1, R2, R3 , where mapped into the other. n R1, R2, and R3 are mutually disjoint sets, with R1[R2[R3¼D , and These two factors—the empirical and the transfer of such that: R1 is the set of n-tuples that (we take to) belong to R; R2 structure—may then work together to contribute to what we call is the set of n-tuples that (we take) do not belong to R, and R3 is the characterization stage, where a determinate characterization of the set of n-tuples for which it is not defined whether they belong the relevant phenomenon is constructed. What is involved in such or not to R. a characterization is the stabilization of a given phenomena such / S 0 / 0 If we have two partial structures, A¼ D, Rk kAK and A ¼ D , that it is amenable to further theoretical development.