Steven French

Thirty years after the conference that gave rise to The Structure of Scientific Theories, there is renewed interest in the nature of theories and models. However, certain crucial issues from thirty years ago are reprised in current discussions; specifically: whether the diversity of models in the science can be captured by some unitary account; and whether the temporal dimension of scientific practice can be represented by such an account. After reviewing recent developments we suggest that these issues can be accommodated within the partial structures formulation of the semantic or model-theoretic approach

Stein once urged us not to confuse the means of representation with that which is being represented. Yet that is precisely what philosophers of science appear to have done at the meta-level when it comes to representing the practice of science. Proponents of the so-called ‘syntactic’ view identify theories as logically closed sets of sentences or propositions and models as idealised interpretations, or ‘theoruncula, as Braithwaite called them. Adherents of the ‘semantic’ approach, on the other hand, are typically characterised as taking them to be families of models that are set-theoretic, according to Suppes and others, or abstract, as Giere has argued. da Costa and French (Science and Partial Truth. OUP, Oxford, 2003) suggested that we should refrain from ontological speculation as to the nature of scientific theories and models and focus on their appropriate representation for various purposes within the philosophy of science. Such an approach allows both linguistic and non-linguistic resources to play their appropriate role (see also French and Saatsi, Philosophy of Science, Proceedings of the 2004 PSA Meeting, 78:548–559, 2006) and can be supported by recent case studies illustrating the heterogeneity of scientific practice. My aim in this paper is to further develop this ‘quietist’ view, and to indicate how it offers a fruitful way forward for the philosophy of science.

Within the philosophy of science there has been a great deal of rather vague talk about the 'heuristic fruitfulness' (or what Peirce called the 'esperable uberty') of theories. It is my aim in the present paper to add some precision to these discussions by linking this 'fruitfulness' to the satisfaction of certain heuristic criteria. In this manner the demarcation between 'discovery' and 'pursuit' becomes blurred. As a case study, I present the competition between the paraparticle and colour models of quarks in the late 1960s. I argue that the eventual appraisal of the latter as the more fruitful of the two was based on the incorporation of a particular symmetry principle, regarded as a heuristic guideline, rather than on non-epistemic factors concerning 'cognitive resources' and the like.

Although Eddington's philosophy of physics has been subjected to critical re-evaluation in recent years, neither the exact nature of his structuralist views nor his response to criticism by the likes of Braithwaite have been made clear. In this paper I trace, in particular, the incorporation into Eddington's structuralism of the non-classical indistinguishability of quantum objects. His metaphysical view of such objects as the product of group-theoretical analysis is crucial for understanding his response to Braithwaite's criticisms of the whole structuralist endeavor. These criticisms closely resemble more recent attacks on structural realism in the philosophy of science. I conclude with a brief comparison between these more modern forms of structuralism and Eddington's.

Dispositionalist accounts of scientific laws are currently at the forefront of discussions in the metaphysics of science. However, Mumford has presented such accounts with the following dilemma: if laws are to have a governing role, then they cannot be grounded in the relevant dispositions; if on the other hand, they are so grounded, then they cannot perform such a role. Mumford’s solution is drastic: to do away with laws as metaphysically substantive entities altogether. Dispositionalist accounts are also deficient in that they either make no mention of the significant role of symmetries in science, or attempt to inappropriately eliminate this role. Here we shall attempt to motivate a structuralist view of laws by showing how it evades Mumford’s dilemma and accommodates the role of symmetry principles. In addition we shall consider how this view deals with a number of issues that dispositionalism finds problematic and indicate how the supposed necessity of laws and the explanation of relevant counterfactuals look from this structuralist perspective.

In this essay I shall focus on the adoption of the Semantic Approach by structural realists, including myself, who have done so on the grounds that it wears its structuralist sympathies on its sleeve. Despite this, the SA has been identified as standing in tension with the ontological commitments of the so-called ’ontic’ form of this view and so I shall explore that tension before discussing the usefulness of the SA in framing scientific representation and concluding with a discussion of the implications of the ontological status of theories and models themselves.

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described.

I first outline the standard dispositionalist account and indicate how this account has been extended from the everyday to the realm of modern physics – from vases to quarks, in effect. Here I note a fundamental obstacle: the role of symmetries as constraints on the fundamental laws in physics. One of the great virtues of the standard dispositionalist account is that it supposedly yields laws from dispositions but it remains unclear, at best, how it can accommodate such symmetry principles. I then outline some ways the dispositonalist might try to do that but in effect I close off each option by indicating how the problem merely gets pushed back a step or two. Ultimately, the dispositionalist will have to ascribe her dispositions to objects that are metaphysically very ‘thin’, in the sense that they are mere placeholders within the physical structure, and also give up the standard Stimulus + Manifestation account. Of course, that will be music to the ears of certain other critics within and outwith the powers camp and I conclude by considering some recent proposals and evaluating whether they might be ‘fit for purpose’ within the context of modern physics.

Within the philosophy of science, the realism debate has been revitalised by the development of forms of structural realism. These urge a shift in focus from the object oriented ontologies that come and go through the history of science to the structures that remain through theory change. Such views have typically been elaborated in the context of theories of physics and are motivated by, first of all, the presence within such theories of mathematical equations that allow straightforward representation of the relevant structures; and secondly, the implications of such theories for the individuality and identity of putative objects. My aim in this talk is to explore the possibility of extending such views to biological theories. An obvious concern is that within the context of the latter it is typically insisted that we cannot find the kinds of highly mathematised structures that structural realism can point to in physics. I shall indicate how the model-theoretic approach to theories might help allay such concerns. Furthermore, issues of identity and individuality also arise within biology. Thus Dupre has recently noted that there exists a ‘General Problem of Biological Individuality’ which relates to the issue of how one divides ‘massively integrated and interconnected’ systems into discrete components. In response Dupre advocates a form of ‘Promiscuous Realism’ that holds, for example, that there is no unique way of dividing the phylogenetic tree into kinds. Instead I shall urge serious consideration of those aspects of the work of Dupre and others that lean towards a structuralist interpretation. By doing so I hope to suggest possible ways in which a structuralist stance might be extended to biology

The semantic, or model-theoretic, approach to theories has recently come under criticism on two fronts: (i) it is claimed that it cannot account for the wide diversity of models employed in scientific practice—a claim which has led some to propose a “deflationary” account of models; (ii) it is further contended that the sense of “model” used by the approach differs from that given in model theory. Our aim in the present work is to articulate a possible response to these claims, drawing on recent developments within the semantic approach itself. Thus, the first is answered by utilizing the notion of a “partial structure”, first introduced in this context by da Costa and French in 1990. The second claim is undermined by consideration of van Fraassen's understanding of “model” which corresponds well with that evinced by modem mathematicians. This latter discussion, in particular, has an impact on the continuing debate regarding the relative merits of the semantic and syntactic views and the developments presented here can be taken to provide further support to the former.