How Models Are Used To Represent Physical Reality
(Draft for presentation only.  Not to be quoted without permission of the author.)
Ronald N. Giere
Department of Philosophy
Center for Philosophy of Science
University of Minnesota

1. Introduction.  The title of this symposium “The Pragmatics of Scientific Representation,” suggests that there might be something like a syntax and a semantics of scientific representation, to which the pragmatics is an additional layer.  I think that this suggestion, taken over from modern logic, has things upside down, at least when it comes to understanding how scientists represent the world.  Some recent thinking about the nature of natural languages suggests that language is primarily a cultural achievement.  It is, if you will, a cultural artifact.  Learning a language is learning to be a member of a culture with its history and mores.  In so far as it makes sense to talk about levels here, this all takes place at the level of pragmatics.  I wish to carry over this idea to the more specialized context of scientific cultures.  The scientific practices of representing the world are fundamentally pragmatic.  Anything corresponding to semantics or syntax would be an abstraction from the pragmatics.  It is always an open question the extent to which any particular abstraction is useful.  My view is that, however useful these abstractions have been in the study of logic and the foundations of mathematics, they interfere with a fruitful understanding of science.
2.  Representing.  Rather than focusing on representation as a two-place relationship between a symbol and a thing, I think we should begin with the activity of representing which, if thought of as a relationship at all, should have at least four places with roughly the following form:
			S uses M to represent W for purpose P.
Here S can be an individual scientist, a scientific group, or a larger scientific community.  M is a model or type of model.  W is a piece of the real world, a (kind of) thing or event.  So, more informally, the relationship to be investigated has the form: Scientists use models of a particular type to represent something in the world for a specific purpose.
Here I should note, as has been urged by a number of students of the scientific enterprise, that scientists use models for all sorts of purposes other than representing the world.  In focusing on representation, I do not mean to deny this or to belittle it.  I do think, however, that representing the world is a very important function of models and is often presupposed in discussions of other roles for models.  So a focus on representing is more than well justified.

3.  Models.  What are models that they may be used to represent things in the world?  Or, what is it about models that makes it possible to use them in this way?  The things that are called models form a quite heterogeneous class including physical models, scale models, analogue models, and mathematical models, just to name a few.  I think we should try to understand models in a way that encompasses this heterogeneity as much as is possible.
 The first step is to think of models as being things, but not including linguistic things such as words, sentences, propositions, or equations.  So Watson’s original tin and cardboard model of DNA counts as a genuine scientific model in my sense.  It was clearly a physical model; one can debate the extent to which it was also a scale model.  Rutherford’s solar system model of atoms is another famous example of a physical model.  Many would also call it an analog model, thinking of atoms as being analogous to the solar system.  Then there is the Bohr model of the atom and the de Sitter model of space-time.  There are also equilibrium models in economics and drift models in evolutionary biology.  These latter may or not be thought of as analogue models, but they pretty clearly are not physical.  What are they?
I like to think of them as abstract entities and adopt as simple as possible a view of what abstract entities are.  I take abstract entities to be human constructions, the ability to create such constructions being made possible by symbolic artifacts such as language and mathematics.  But abstract models are definitely not to be identified with linguistic entities such as words or equations.  Any particular abstract model can be characterized in many different ways.  Nor should abstract models be thought of as merely formal.  They are created already interpreted.
To take a homey example, we all know how to plan a trip to a supermarket, including making a shopping list.  Such a planned trip is an abstract entity.  I would even call the plan a model of a trip, a model that might never apply to anything if, for example, the shopping trip is simply called off.  Most abstract scientific models are much more complex, of course, but they should not be regarded as any more mysterious than a planned shopping trip.
4.  Principles.  In some sciences, models are constructed according to explicitly formulated principles.  Physics is especially rich in such principles:  Newton’s principles of mechanics; Maxwell’s principles of electromagnetic radiation; the principles of thermodynamics; the principles of relativity; and the principles of quantum mechanics.  But evolutionary biology also has its principle of natural selection and economics boasts various equilibrium principles.
What I am here calling principles have typically been interpreted by scientists and empiricist philosophers as empirical laws, that is, generalizations that are both universal and true.  My view, which I share with Nancy Cartwright and some others, is that, if understood as universal generalizations, the resulting statements are either vacuously true or else false, and known to be so.  The suggested alternative is to regard the principles as methodological rules for the construction of models.  Thus, Newton’s principles instruct one to look for all the forces acting on a body and set this total force equal to its mass times its acceleration.  The resulting equation then becomes part of the characterization of a model (more or less general or specific).  As such, the resulting equation may indeed be regarded as true, but it is true only of the model in the way that definitions are true.  The empirical question is how well the model fits its intended object (or objects).

5.  Laws.  Among the statements called “laws of nature” are many that do indeed function more like lower level generalizations than grand principles.  These abound in physics, Hook’s law, Snell’s law, and Galileo’s law of the pendulum being traditional examples.  The prevalence of such laws goes down as one moves up Comte’s hierarchy through chemistry, biology, and psychology to the social sciences.  Even in physics, however, the simple statements of such laws cannot be both universal and true.  There are always known restrictions and exceptions.  The question is what to make of this situation.
One solution is not to take these law statements at face value, but to regard them either as being tacitly supplemented with imbedded ceteris paribus clauses or as being accompanied by separate qualifications.  The problem with this sort of solution, from my point of view, is either that it requires being definite about something that is decidedly indefinite, and so the resulting package ends up being incomplete.  Alternatively, in trying to be indefinite, this approach ends up making laws vacuous, claiming, in effect, that such and such unless not such and such.
A better solution, I think, is to keep the simple law statements, but understand them as characterizing an abstract model and thus being true of the model.  The required qualifications, then, concern only the range of application of the model.  One need only indicate, tacitly or explicitly, where it applies or not, and to what degree of exactness.  It can safely be left open where else it may or may not apply.  To say the model applies where it applies is a harmless tautology.  The empirically interesting question is where does it apply or not.
Note that in this latter approach claims of universality are abandoned.  I think such claims are not needed.  They are an ideological hold over from early ages whose function is now mostly rhetorical.  This does not mean one cannot have good reasons for thinking that a particular type of model will apply in a previously unknown context, but one can never be sure without actually trying.  
6.  Similarity.  I think nothing I have ever published has been as much criticized as the claim that models represent real things by virtue of being similar to those things in relevant respects and degrees.  It has been complained both that I have not provided a general analysis of similarity and also that this can’t be done.  It has also been argued that, without an objective measure of similarity, scientific claims could not be sufficiently objective.  We would fall into a relativistic constructivism.  By being more explicit about the pragmatic character of representing in science, one can show why such claims are misguided.
I agree that one cannot define an objective similarity relationship between an abstract model and any physical objects.  In fact, I don’t think anything is objectively similar to anything else except in the vacuous sense that every thing is similar to anything else in at least a countable infinity of ways.  But the activity of representing the world as characterized above does not require an objective notion of similarity.  The way scientists use a model to represent some real system is by picking out some specific features of the model which are then claimed to be similar to features of the real system to some, perhaps fairly loosely indicated, degree of fit.  It is the existence of the specified similarities that makes possible the use of the model to represent the real system.
To take an obvious example, it was the similarities in physical structure that made possible Watson’s use of his tin and cardboard model to represent the structure of DNA.  He clearly was not saying that DNA is similar to his model with respect to being composed of tin and cardboard.  Part of being able using a model to represent some aspect of the world is being able to pick out the relevantly similar features.
Another part of using a model to represent something is having some reasonable idea of how good a fit might be expected.  The angles in Watson’s model used to represent bonding angles in DNA were not exactly the bonding angles later determined for samples of DNA.  But no one doubted they were close enough to conclude that DNA has a double helical structure.  Moreover, the angles in the model were somewhat adjustable, and so could be made better to fit the angles in DNA as more precisely determined by later experiments.

7.  Purposes.  Thus far I have assumed that models are being used for the general purpose of simply learning what something is like.  Watson used his model simply to represent the physical structure of DNA.  His goal at that time was to discover this structure.  Of course he also had other, longer-term goals, such as understanding the mechanisms of inheritance.  But these goals required that one first have a good model of the physical structure.  That is the goal he reached in 1953.
	Models are also used for more specific purposes.  Here is an example that has been used by both Margaret Morrison and Paul Teller.  If one is investigating diffusion or Brownian motion, one models water as a collection of molecules.  However, if one’s concern is the behavior of water flowing through pipes, the best fitting models are those that treat water as a continuous fluid.  Thus, the type of model one uses to represent water depends on the kind of problem one faces.  Note that there is no conflict in saying that scientists use continuous fluid models to represent water for the study of fluid flow and also use molecular models to represent water for the study of Brownian motion.  
Of course, one wants to ask, “But what is water really?”  And the answer had better be, “Molecules.”  But the overall superiority of molecular models is easy to justify because there is a clear asymmetry in favor of a molecular perspective.  That is, from within a molecular framework, one can, in principle, explain how a macroscopic fluid made up of microscopic molecules could be fitted very well within a framework based on principles regarding continuous fluids.  We just don’t know how to construct molecular models of macroscopic fluids, and maybe we never will.  On the other hand, there is no way to construct models using continuous fluid principles to model Brownian motion.  So we can say that the world is such that there is, in principle, a molecular model for all of the many manifestations of water.  This is a close as we can come to saying what water “really” is.  In practice, there are many manifestations of water that are most usefully modeled within other frameworks.  

8.  Natural Intentionality.  I would like for all the above to fit comfortably in a naturalistic framework.  It might be objected that this is not possible if the fundamental notion of representing includes reference to human purposes.  Things like purposes, norms, or intentionality, it is often thought, fall outside any naturalistic framework.  I disagree.  There is nothing so natural as human purposes.
From a naturalistic point of view, one of the most important facts about humans is that they evolved by natural selection.  Moreover, human societies evolved by means less well understood, but surely no less natural.  So, if humans now have goals, values, norms, etc., how could having these things not be natural?  In claiming these things are not natural one must be employing a rather more restrictive notion of what can be natural.  Here there are several possibilities.
One way of restricting the realm of the natural is to insist that what counts as natural can be studied scientifically.  Add the assumption that science aims at the discovery of natural laws and it seems that human purposes are beyond the purview of natural science since there seems little possibility of stating laws about human purposes that might be universally true.  If, on the contrary, one thinks science aims at the creation of models that may fit more or fewer things more or less well, the objection evaporates.  The models of folk psychology, even the models individuals have of other individuals, are not fundamentally different from scientific models.  They are just less well developed and more restricted in scope than required for the development of a scientific field (though one might claim that much of philosophy is de facto devoted to the study of folk models of all sorts).
Another argument against purposes being natural derives from a reductionist impulse, though I find it difficult to formulate a convincing version of such an argument.  But try this.  We agree that humans are totally made up of molecules (atoms, elementary particles; pick your favorite level).  Molecules don’t have purposes, so purposes are not part of a scientific study of molecules.  So, ultimately, a science of humans would not include purposes either.  But of course humans have lots of properties not possessed by individual molecules.  Humans are born, they breathe, they bathe.  So why can’t they have purposes?  Lots and lots of different kinds of molecules organized in exquisite ways can do lots of things individual molecules can’t.

9.  Conclusion.  Most recent philosophical thought about the scientific representation of the world has focused on dyadic relationships between language-like entities and the world, particularly semantic relationships, but also evidentiary relationships.  I have said nothing about evidentiary relationships here, but in other works I have argued that these should be thought of in terms of human decisions to accept or reject hypotheses in light of their various interests.  Here I have argued that scientific representation should be though of in the same general way, that is, in terms of the use of models by scientists to represent aspects of the world for various purposes.  My hope is that by not abstracting away from the activity of doing science one may achieve a better understanding of the nature of modern science.