This article will continue the series on the use of models in science. It is of crucial importance for the psychological researcher to understand different ways in which models might be used in the representation of psychological phenomena.
Some argue that “models” are more or less just descriptions of the target system. But things can be described in different ways. Does this mean that each new description is a new model? This seems strange and hard to accept. Furthermore, a description can be translated into other languages, but it seems counterintuitive to say that there is therefore a different model for each language. Others argue that models be understood in terms of equations, i.e., “mathematical models.” Examples of this include the Mundell-Fleming model of the open economy or the Black-Scholes model of the stock market. However, the same situation can be described with different co-ordinates, which results in different equations. Nevertheless, like the descriptive understanding of the model, one would not thereby say that a different model resulted.
Perhaps the ontology of models exhibits a high degree of overlap such that they contain elements of different kinds of objects. Thus, they might have narratival or structural elements, as well as having elements in common with descriptions.In any case, models can be fruitfully used to learn about the world. The use of models in learning about the world may be called “surrogative” reasoning or model-based reasoning. Thus: “For instance, we study the nature of the hydrogen atom, the dynamics of populations, or the behavior of polymers by studying their respective models. This cognitive function of models has been widely acknowledged in the literature, and some even suggest that models give rise to a new style of reasoning, so-called ‘model based reasoning.'”
One writer articulates a model-based account of learning in the following way:
1) Denotation – a representation-relation is established between the target and the model.
2) Demonstration – We learn about the model, or “investigate the features of the model in order to demonstrate certain theoretical claims about its internal constitution or mechanism.”
3) Interpretation – Findings are converted into claims about the target system.
Knowledge about a model will allow this knowledge to be “translated” into knowledge of the target system. It should go without saying that representations are important in this respect. One must be able to trust that some of the components of the model have counterparts in the real world.
What sorts of relations obtain between models and theories? The two are sometimes used to refer to the same thing. Should there be a distinction between the two at all?
“In common parlance, the terms ‘model’ and ‘theory’ are sometimes used to express someone’s attitude towards a particular piece of science. The phrase ‘it’s just a model’ indicates that the hypothesis at stake is asserted only tentatively or is even known to be false, while something is awarded the label ‘theory’ if it has acquired some degree of general acceptance. However, this way of drawing a line between models and theories is of no use to a systematic understanding of models.”
The syntactic view of theories was an important part of the logical positivist understanding of science. Theories are understood as sentences axiomatized in first order logic:
“Within this approach, the term model is used in a wider and in a narrower sense. In the wider sense, a model is just a system of semantic rules that interpret the abstract calculus and the study of a model amounts to scrutinizing the semantics of a scientific language. In the narrower sense, a model is an alternative interpretation of a certain calculus (Braithwaite 1953, Campbell 1920, Nagel 1961, Spector 1965). If, for instance, we take the mathematics used in the kinetic theory of gases and reinterpret the terms of this calculus in a way that makes them refer to billiard balls, the billiard balls are a model of the kinetic theory of gases. Proponents of the syntactic view believe such models to be irrelevant to science. Models, they hold, are superfluous additions that are at best of pedagogical, aesthetical or psychological value (Carnap 1938, Hempel 1965; see also Bailer-Jones 1999).”
Opposed to this view is the semantic theory of models, according to which there ought to be no formal calculus whatsoever, and instead, theories ought to be seen as a group of models.
Some take the model has having two aspects:
1) Construction – models are not derived from either data or theory. Theories do not tell us how to construct a model. It is instead a kind of art.
“Model building is an art and not a mechanical procedure. The London model of superconductivity affords us with a good example of this relationship. The model’s principal equation has no theoretical justification (in the sense that it could be derived from electromagnetic or any other fundamental theory) and is motivated solely on the basis of phenomenological considerations (Cartwright et al. 1995). Or, to put it another way, the model has been constructed ‘bottom up’ and not ‘top down’ and therefore enjoys a great deal of independence from theory.”
2) Functioning – “The second aspect of the independence of models is that they perform functions which they could not perform if they were a part of, or strongly dependent on, theories.”
Models help complement theories insofar as theories may be silent about concrete details of a situation. It may be difficult to imagine what a theory would look like in practice without models to function as examples or instantiations of the theories.
“A special case of this situation is when a qualitative theory is known and the model introduces quantitative measures (Apostel 1961). Redhead’s example for a theory that is underdetermined in this way is axiomatic quantum field theory, which only imposes certain general constraints on quantum fields but does not provide an account of particular fields.”
Sometimes models are used when theories are too complicated to handle:
“Quantum chromodynamics, for instance, cannot easily be used to study the hadron structure of a nucleus, although it is the fundamental theory for this problem. To get around this difficulty physicists construct tractable phenomenological models (e.g. the MIT bag model) that effectively describes the relevant degrees of freedom of the system under consideration (Hartmann 1999). The advantage of these models is that they yield results where theories remain silent. Their drawback is that it is often not clear how to understand the relationship between the theory and the model as the two are, strictly speaking, contradictory.”
Models can sometimes function as preliminary theories. They can be used as “developmental” models, as they were in the development of early quantum theory. This is related to the idea of a probing model, also known as a toy model or a study model. These models do not serve a representational function.
“The purpose of these models is to test new theoretical tools that are used later on to build representational models. In field theory, for instance, the so-called φ4-model has been studied extensively not because it represents anything real (it is well-known that it doesn’t) but because it serves several heuristic functions. The simplicity of the φ4-model allows physicist to ‘get a feeling’ for what quantum field theories are like and to extract some general features that this simple model shares with more complicated ones. One can try complicated techniques such as renormalization in a simple setting and it is possible to get acquainted with mechanisms—in this case symmetry breaking—that can be used later on (Hartmann 1995). This is true not only for physics. As Wimsatt (1987) points out, false models in genetics can perform many useful functions, among them the following: the false model can help to answer questions about more realistic models, provide an arena for answering questions about properties of more complex models, ‘factor out’ phenomena that would not otherwise be seen, serve as a limiting case of a more general model (or two false models may define the extreme of a continuum of cases in which the real case is supposed to lie), or it can lead to the identification of relevant variables and the estimation of their values.”
Frigg, Roman and Hartmann, Stephan, “Models in Science”, The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), Edward N. Zalta (ed.), URL = <plato.stanford.edu/archives/fall2012/entries/models-science/>.