Before inquiring into the aim and achievements of science, it is worth being clear on the nature of one of its main products, scientific theories. The second chapter of Modal Empiricism reviews how the way philosophers have conceived of theories has evolved in time.
From Statements to Models
It was once commonplace to think of scientific theories as linguistic entities, akin to general statements or description of the world. In the tradition of logical empiricism, it was typically thought that a theory could be ideally reconstructed as a set of axioms expressed in a theoretical vocabulary complemented with correspondence rules establishing links between theoretical terms and an observation vocabulary. In this view, the role of scientific models is merely psychological, but they become superfluous once one is in possession of an axiomatised theory.
As is well known, this view has been challenged for various reasons during the second half of the twentieth century. The semantic distinction between theoretical and observation vocabulary on which it rests was criticised, as well as the status of correspondence rules, that encompass heterogeneous aspects (linguistic meaning, experimental practices, etc.). This “statement view” became seen as overly abstract and disconnected from scientific practice. It became increasingly recognised, in particular, that scientific models actually play a central role in science.
It is more common, nowadays, to think of scientific theories as families of models rather than as linguistic entities. According to this so-called “semantic view”, the statements or equations found in scientific textbooks do not really constitute the theory: they merely describe a family of models. Of course, a family of models cannot be said to be true or false, so the theory must also be qualified by “various hypotheses linking those models with systems of the real world” (Giere 1988, p, 85). This link between models and real systems can be analysed in terms of similarity, or, in a structuralist spirit, in terms of mathematical relations between theoretical and real structures (Bueno and French 2011). Concerning confrontation with experience in particular, the idea that is generally put forth is that some relevant parts of theoretical models are directly compared to data models (Van Fraassen 1980), so that models rather than statements play the central role.
Arguably, language still plays a mediation role in this picture, because we need a language in order to organise models and to specify how they are related to the world. The difference between the semantic view and the statement view should not be overstated. Yet, the focus on models and structures instead of axioms or general statements induces a different philosophical approach towards science which has arguably proved fruitful. According to its defenders, this approach offers a finer analysis of inter-theory relations and of the relation between theory and experience. It allows, for example, these analyses to operate at the local level of particular models rather than at the level of whole theories. This could be compared to the way translating or interpreting languages generally operates at the level of particular sentences rather than at the level of whole languages.
The focus on models has also proved fuitful in a way that was not necessarily intended by early defenders of the semantic view. It has allowed for the introduction of pragmatic considerations in philosophical accounts of the functioning of science.
From Semantics to Pragmatics
Various authors sharing with the semantic view its emphasis on models in science started to defend more pragmatist-oriented views towards the end of the twentieth century (perhaps starting from Cartwright (1983)). The main characteristic of these approaches is an emphasis on scientific practice and on contextual aspects, rather than on formal relations between theories and the world.
A first aspect addressed by pragmatists concerns the relation between theories and models. One of the main observations is that models enjoy a certain autonomy from scientific theories (Morgan and Morrison 1999). Model construction is an art rather than a systematic procedure. Models can incorporate domain-specific assumptions, ad-hoc postulates (Cartwright, Shomar and Suárez 1995), phenomenological laws or values for constants derived from experience. Scientists often use approximations or simplifications that distort theoretical laws, such as perturbation techniques in quantum mechanics, or the assumption that the sun is fixed in a referential frame in a Newtonian model of the solar system. They can even combine incompatible theories, for example when modeling a quantum system in a classical environment.
Despite these aspects, one could suspect that an integration of models into overarching theories remains important in science (for example, it seems important to find theoretical accounts of ad-hoc hypotheses (Potters 2019)), but the model–theory relation is not as staightforward as one could think.
Pragmatist philosophers have also put forth the idea that users play a role in establishing the model–world relationship. They often put emphasis on the sensitivity to purposes of modeling practices (Bailer-Jones 2003, Giere 2010). It can be argued, for instance, that the way scientists idealise targets of representation depends on the variables they are interested in and on the levels of precision that they are expecting from their models. This means that the model–world relation will be relative to a given perspective on phenomena.
A final pragmatist theme has to do with the practical aspects of experimentation. Idealisations in science are sometimes accompanied by suitable experimental interventions, the aim of which is to physically neutralise uninteresting factors, for example, when creating vacuum in experiments of free fall. Establishing a representation relation between a model and a concrete object often involves controlling the object and its environment and performing various manipulations. All these aspects do not rest on explicit formal theory–world relations. They rest on informal, tacit practical knowledge, a learnt ability to identify phenomena of interest or to use a telescope or a microscope for example. Furthermore, the particular context is often involved: for example, knowledge of specific sources of noise in a laboratory or instrument calibration.
Some of these practical aspects can be seen as a means for scientists to eliminate contextual variations in order to reach cross-contextual stability. Bogen and Woodward (1988) propose to distinguish between brute experimental data and stable phenomena on this basis. They note that experimental data are cleaned up and synthesised using statistical techniques before they are compared to theoretical models. According to them, the role of a model is not to account for messy data, but for the phenomena that cause these data. Phenomena are typically accessible by means of various kinds of instruments: they have a certain cross-contextual stability.
Nevertheless, our empirical access to stable phenomena is not entirely captured by formal theories. For example, it is not necessary to model measuring instruments to use them reliably. As observed by Hacking (1983), telescopes had been used for centuries before scientists had a complete theory of their functioning. One could entertain the idea that mature theories and models result from a mutual adjustment between theoretical and practical considerations. Finally, as I argue in this second chapter, the fact that controls are involved in experimentation, so that a model induces certain manipulations, could let us think that intentional aspects, or what the model purports to achieve, must be taken into account to understand what constitutes the representation relation.
From Users to Communities
A focus on the role of users and their purposes seems to threaten a certain unity of science: if science were nothing but a patchwork of activities directed towards contextual purposes, it could not be characterised by one unified aim. Pluralist philosophers are willing to embrace this conclusion (Cartwright 1999), but this would be unsatisfying to many philosophers: after all, great theoretical achievements can often be seen as resolving tensions between various domains of knowledge: for example, relativity theory resolving the tension between Newtonian mechanics and electromagnetism. In the last section of this second chapter of Modal Empiricism, I explain that the pluralist conclusion can be avoided by providing a clear articulation between the contextual and the communal components of scientific representation.
Let us first say a bit more about user-centred accounts of scientific representation. Some of these accounts are deflationary in spirit: they mainly focus on the function played by representations for their users. According to Suárez (2004) for example, a model represents a target system if it has “representational force” (it points to the system) and allows this user to draw inference regarding this system. According to Contessa (2007), this is achieved if the user assumes a certain mapping between parts of the model and objects and properties of the target, and it does not matter which mapping is selected by the user. Even more minimally, according to Callender and Cohen (2006), it is enough that the user stipulates that the model represents the target system. Representation entirely rests on the mental states of users.
This is also a characteristic feature of fictionalist accounts, which have been proposed recently. When scientists and teachers present a scientific model, for example the simple pendulum, they often talk as if they were describing a concrete system (a pendulum composed of a point mass attached to an unstrechtable string) even though no such system exists. According to fictionalist accounts, models are instructions for imagination, and these fictions can then be compared with reality (Frigg 2010 Toon 2010 Levy 2015).
Callender and Cohen’s approach has been criticised because it does not distinguish between epistemic and symbolic representation: a symbol merely picks a referent, but an epistemic representation allows its user to learn about its object (Liu 2015). It has also been observed that scientific models have a history of construction, acceptance and use by the scientific community, and that more than mere stipulation is involved (Boesch 2017). Similar kinds of criticisms can be addressed to Contessa’s account. Fictionalist accounts have also been criticised for not explaining how models produce knowledge about their targets. They do not discern between what in the model is held true or false by modellers (Poznic 2016), and they lead to a problem of coordination between the imagination of various scientists (Knuuttila).
In all these cases, the problem seems to be that what a model represents does not depend only on the attitudes and purposes of users, but that there are external constraints, or communal norms of representation at play in science. This is related to the idea just mentioned that science would have a unified aim, associated with the capacity of theories to unify various representations.
A Tension Between Contextuality and Unity
As we can see, there is a tension between the willingness to take into account the contextual aspects of experimentation and the unifying power of scientific theories. I have argued in Ruyant (2021) that we can resolve this tension by distinguishing two senses of representation: on the one hand, a concrete model represents a concrete object if it is used as such by a user, and on the other hand, an abstract model represents a type of object if it is considered appropriate, within our epistemic community, to use one of its concrete instances to represent an object of this type. This is a distinction that follows that, proposed by Grice in philosophy of language, between speaker-meaning (what a speaker means by uttering a particular sentence, which depends on the context) and expression-meaning (the “timeless” meaning of sentences). According to Grice, the latter plays a normative role with regards to the former.
I think that this two-stage theory of representation can at the same time acknowledge the importance of users and their purposes in science, and preserve a notion of unity of science, which would rest on the norms of appropriate representation of the scientific community. This is, in sum, a middle ground between purely formal accounts of theory–world relations that do not take into account contextual and user-centred aspects, and purely user-centred accounts that do not take into account the unifying power of scientific theories. This account is the framework that I use for developing modal empiricism, which can be understood as a position about the norms of representation of science and their aim. Developing this two-stage account of representation is the purpose of the third chapter of the book that I will present in the next article.
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