samedi 27 mars 2021

Chap. 3: Contextual Use and Communal Norms

View of Ueno-Nakasendo railway from Ueno station2

The second chapter of Modal Empiricism ended with the idea that there is a tension between the contextual aspects of experimentation and the unifying power of scientific theories. Both are important for an empiricist who wishes to pay attention to experience while maintaining that science is directed towards a unified aim. The third chapter of my book presents an account of epistemic representation that resolves this tension, and constitutes the framework for the analyses of the rest of the book.

Note that although I will mostly use scientific example, this account could apply to any kind of epistemic representation, for example, city maps.

First Stage: Contextual Use

The two-stage account of representation presented in this third chapter rests on a distinction between the contextual use of models in experimentation and their general status in the community of scientists. According to this account, contextual use entirely rests on the mental states of users: a concrete vehicle of representation (such as a map or equations written on paper) represents an object simply if the user assumes or pretends that she can learn about this object from the model.

This stage depends on the purposes of the user, which can be captured by the notion of a context. A context specifies a particular target of representation, an object or a set of object, and a set of properties of interest, for example, a pendulum and the position of the pendulum along an axis assuming some finite degrees of precision. These properties can be expressed using a theoretical vocabulary, but I assume that they are in principle accessible by empirical means in context (the way theoretical vocabulary is linked to experience will be addressed later). Given these properties of interest, a set of configurations or histories (possible trajectories for the pendulum ) are a priori conceivable for this object, and during an experiment, exactly one of these configurations is realised. The user will typically want to know in advance which configurations or histories are possible or not. The context expresses what the user wants to know, without presupposing the result. In the book, I propose a semi-formalisation of this notion of context (as well as the ones introduced below) in terms of sets of conceivable histories for a system.

In order to make inferences about the target system, the user manipulates a concrete vehicle. Some component parts of this vehicle have a symbolic function: they stand for particular properties or possible manipulations on the system specified by the context. Not all symbols of the model are necessarily interpreted, because the user is only interested in coarse-grained, empirically accessible properties, and therefore, the context can be more limited than what the model affords. We could say that the model is projected onto the context. In any case, the structure of the model constrains which conceivable configurations of the target should be considered possible or not, for example, which trajectories of a pendulum are possible. This is how the vehicle affords inferences, and the vehicle represents the target system in so far as the user assumes, or pretends for the sake of an experimental test, that the conclusions of these inferences are true.

In sum, the context specifies a set of conceivable states or histories for a target system, and a model, interpreted in terms of this target system, limits this set to a sub-set of states or histories “permitted” by the model. We shall say that the model is accurate, or empirically successful, if the actual state or history realised by the system during an experiment is among the ones permitted by the model. This notion of accuracy will play an important role for defining modal empiricism.

This presentation is rather schematic. In science, models would typically assign probabilities to possible states or histories rather than just permit or exclude them, and so a model can be more or less accurate. However, this will be enough for our purpose.

Note that nothing is presupposed, at this stage, concerning the reasons why the user thinks that the vehicle is reliable.

First steam train leaving Yokohama1

Second Stage: Communal Status

Imagine a confused person using a map of Mexico City in order to navigate New York City. Since this person is interpreting the symbols of the map in order to make inferences about the street configurations of New York City, and assumes that it is reliable, the account presented so far would imply that the map of Mexico City represents New York City, which seems wrong. But why do we call it a map of Mexico City in the first place?

I argue in the book that the reason is that the appropriate use of this object, the one that is licensed by our community, is as a tool to navigate Mexico City. There are actually two senses of representation: the map is used to represent New York City by its user, but its general status, from the point of view of the community, is that of a representation of Mexico City, and this communal status has to do with norms of appropriate use.

I argue in this third chapter of my book that this second sense of representation applies to abstract scientific models, for example when presented in classrooms:
they convey norms of appropriate use. The Lotka-Volterra model tells us how concrete prey–predator systems ought to be represented (or at least, it gives us one appropriate way of representing them), and the model of the hydrogen atom tells how hydrogen atoms ought to be represented in experimental contexts. Theoretical scientists are in the business of developing norms of representation. These norms are not arbitrary of course: they serve an aim, which, presumably, has to do with the accuracy of their applications, and perhaps with other criteria that are important to scientists. Part of the debate on scientific realism is precisely about this aim and these criteria.

I have explained that interpreting a model in context involves taking its symbols to stand for properties of interest specified by the context. Norms of appropriate use can be understood as telling us which interpretations are licensed and which are not, depending on the context. They can be formalised as a function from contexts to sets of legitimate interpretations, which we can call (by analogy with the analysis of indexicals in philosophy of language) a character. An abstract model is a symbolic structure endowed with a character, for example, the mathematical structure of the simple pendulum, and a norm that tells us that the x symbol should stand for the position of the salient pendulum relative to its rest position in every context. If there is no pendulum in a context, then no interpretation is licensed, which means that this context is outside of the domain of application of the model. So, the character of a model also delimits its domain of application.

Let us say that an interpretation of a model in context is relevant if it is allowed by the character of a scientific model. This notion of relevance will be important for defining modal empiricism.

A scientific model can incorporate knowledge or postulates about a particular type of target, and the fact that this model is licensed as relevant by the scientific community conveys this knowledge. For example, a model of the solar system must have eight planets for its use to be considered appropriate in the community, which conveys the factual knowledge that there are eight planets in the solar system, or a model of virus progression in an organism incorporates as a component the model of a particular protein, which conveys the knowledge that the virus binds to this protein. Another aspect conveyed by norms of relevance concerns when the use of idealisations is appropriate. For example, if a metro map distorts distances between stations, interpretations mapping distances on the map to distances in reality should not be licensed.

This account of representation is deflationary in spirit, which might be unsatisfactory for realist philosophers. They might think that models are interpreted in a more pictorial or metaphysical way than by simply mapping symbols to accessible properties, or giving norms to this effect. However, anti-realists are also able to represent the world, so it would be a mistake to bake realist assumptions into our account of representation (nevertheless, later in the book, I sketch a realist account of representation for the sake of the discussion). Perhaps models are often interpreted in a pictorial way (we imagine a molecule in space), but I would say that this is a mere psychological aspect that is not essential to scientific practice.

One source of frustration could be that we generally take scientific models to be explanatory, and it does not appear clearly how they could be in this account of representation. However, as I explain in the book, in this view, models constrain the configurations that should be considered possible for particular systems, which is compatible with counterfactual accounts of explanations (Woodward 2003). Abstract models unify various potential contexts of application, by prescribing to use the same structure or “pattern of inference” in all these contexts, which is compatible with unification accounts of explanations (Kitcher 1989). Contexts correspond to a given perspective on an object, which is compatible with pragmatic accounts of explanations (Van Fraassen 1980 ch. 5). So, there is no obstacle to consider that models are explanatory and provide a kind of understanding.

View of Ueno-Nakasendo railway from Ueno station1

The Norms of Representation in Science

In sum, representation in context amounts to interpret a vehicle in terms of properties of interest so as to infer which configurations of these propreties are possible or not, and representation in general corresponds to norms of appropriate representations in context. This account applies to scientific models, but also to other kinds of representations such as maps.

There are specificities in science, however, not in what representation consists in at any of these two levels, but in the way models are licensed or not by the scientific community. One prominent aspect of scientific models is that they are generally embedded in a unifying framework: the theory.

If models convey norms, theories convey meta-norms that constrain model construction. They tell us, among other things, what form explanations should take within a discipline, for example, that they should involve forces in Newtonian mechanics, or environmental selection in biology, and how simple models can be combined into more complex ones. These meta-norms are expressed by the fundamental laws and by the mathematical formalism of the theory. They allow the theory be prescriptive about its own extension to yet unexplored domains of experience. However, they are sufficiently flexible for models to incorporate domain-specific assumptions, and local infringements of these norms do not matter if they make no empirical difference.

A theory is characterised by these meta-norms and by the set of models respecting these meta-norms that are licensed by the community for specific kinds of applications. This set of models can evolve when new phenomena are modelled, or when old models are revised, in which case the theory evolves, but the meta-norms remain fixed (this is analogous to Lakatos (1978)’s distinction between the core of a research program and its protective belt).

Another specificity of science is that models and laws are expressed in a theoretical vocabulary, and the way theoretical terms are operationalised can be quite complex. Nevertheless, it seems reasonable to assume that experimental practice also follows norms of appropriate use: that positions must be measured in such or such a way for instance. Although theories can inform experimental practices, experimental and theoretical norms are generally distinct, because experimental techniques often evolve independently of theories and survive theory change. Furthermore, scientists are interested in theoretical properties, not in needles or computer screens, and measuring instruments are (precisely) instrumental: they give access to these properties, but in general, it does not matter how a theoretical model is operationalised, in so far as this operationalisation is reliable. So, at least in particular experimental contexts, we should distinguish between the theoretical and the experimental layers of scientific representation and associated norms.

Experimentation is often mediated by by models of experiments (Suppes 1962), which are themselves epistemic representations. This implies several layers of representation: a theoretical model is interpreted in terms of a context (a set of theoretical properties of interest), which itself constitutes a model of the experiment interpreted in terms of needles, apparatus and associated manipulations and observations. Shall we go even further, and assume other layers of representation, until we reach purely mental representations? Perhaps, but this is a topic for another day.

Shimbashi Station Hiroshige III

Epistemic Values and the Debate on Scientific Realism

If we accept this account of representation, the debate on scientific realism can bear on the criteria by which representational norms are selected in science, that is, by which models and theories come to be accepted by the community as good normative constraints on appropriate representations of the world.

Presumably, an important criteria of acceptance is the accuracy of uses licensed by these norms. A city map is considered appropriate because it is reliable, and a scientific model because it is empirically successful in all contexts. According to an empiricist, this is the main criteria of acceptance for scientific models, while a realist would typically think that this criteria is merely an instrumental means of achieving a more important aim: truth. In any case, empirical success remains central in science.

I have proposed a precise understanding of model accuracy in context in this chapter. However, a theory is constituted by more than one model, and a model can be used in more than one context, so further analysis is required in order to understand what empirical success amounts to for a theory. This analysis is provided in chapter 4 of the book, which will be presented in the next article. This is where the notion of empirical adequacy that characterises modal empiricism is introduced.

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