Model-world relationship

One of the many debates concerning the practice of modelling regards the relationship between the model and the real-world phenomena that it is taken to represent. This leads us to the interesting but hard question: in virtue of what is a model a representation of the real-world phenomena? In this section we explore the suggestions made in the literature of philosophy of science.

Description

Abstract, mathematical models can be described by a set of sentences, the ‘model description’. In the eyes of some philosophers, for instance Suppes’ (1960), scientific models are the same as logician’s models, and can therefore be said to satisfy their model description. Ronald Giere criticises this view as being too narrow and not accounting for all scientific models. He gives a more general picture of the relation between the model description, the model and the world, represented in Figure 4.1. (Giere 1988, 1999) According to Giere, the model description, which can take the form of statements, equations or diagrams,defines the model. Weisberg, a decade later, criticises in turn Giere’s account as too strict, because oftentimes model descriptions are not so specific that they can single out a unique model. He therefore suggests that the relation between model description and model is one ofspecification, a weaker relationship than satisfac- tion or definition that still accounts for ‘picking out’ the model. (Weisberg 2007a, 12)

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For a more elaborate discussion of this we refer to Roman Frigg’s work. (Frigg 2010)

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Example taken from Suarez 1999.

Figure 4.1. (Giere 1999, 55, figure 9)

Giere’s picture of the relations between model description, model and the real-world system provides a good starting point for our discussion of the relationship between the latter two. Models somehow fit or represent some real-world phenomenon, but what precisely is the relationship between the two? In virtue of what does the model represent the phenomenon?

Similarity

Giere’s answer to the previous questions issimilarity. Other candidates have been isomorphism (Van Fraassen 1980) or partial isomorphism (Da Costa and French 2003), but these have been criticised as not being general enough to account for all scientific models.9 Moreover, in practice it turns out that even in mathematised sciences often (partial) isomorphism is too strong a re- quirement. (Lloyd 1994)

Far the most promising and most discussed relationship then, is some form of similarity. However, assessing the relationship in terms of similarity has led to much criticism in the philosophy of science. Goodman (1970) calls it too vague; after all to a certain extent everything can be said to be similar to everything. A response by Giere is that the model is similar to the target system in relevant respects in a high enough degree. (Giere 1988, 81) Teller adds to this that both the aspects in which the model and the phenomenon agree, and those in which they differ, play a role in the assessment of the similarity. However, this is still relatively vague: we do not have a general account of what counts as relevant similarity. Teller remarks that it is senseless to look for such a general account, because what counts as relevant similarity will always depend on the details at hand. The aim, the by the researcher intended applications and the context will determine what counts as relevant.10 (Teller 2001, 401-2) Use of the models is a key issue. This pragmatic-contextual dimension of similarity is best explained via the often discussed map analogy.

Map analogy

An ordinary city map has a lot in common with a model, and can therefore be used as an in- structive analogy along whose lines the debate about models may progress. Like models, a map

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Another critique, voiced by Mauricio Suarez, is that isomorphism is only structural identity. Structural identity, a limiting case of structural resemblance, will never be sufficient nor necessary for representation. Peter Achinstein gives a similar argument. See for details of these arguments either Suarez 1999, 77-9, or Achinstein 1964, 28,38,41. Furthermore, there are problems regarding to what the model has to be isomorphic to. A real-world phenomenon as it is, is not always ready to be compared. Oftentimes the phenomenon has to be prepared, data has to be extracted and the raw data has to be made fit for comparison. By means of ‘data reduction’ and ‘curve fitting’ one can create so-called ‘data models’ (Suppes 1960) that are fit for comparison; other related notions are ‘prepared descriptions’ by Cartwright, ‘appearances’ or ‘surface models’ by Van Fraassen, and ‘parametrised target systems’ by Weisberg. Once such a data model has been created, it can be compared to the (predictions of) the constructed model. A more thorough discussion of this issue is outside of the scope of this thesis.

is a partial representations of something in the real world. An object that represents another object. Maps demonstrate only limited accuracy and represent in virtue of only one or more specific aspects of similarity, in this case spatial similarity between the map and the region it maps. We want to know how the streets are located relative to each other, but we usually do not need to know their elevation, or superfluous details like colours of buildings. Maps, like models, are socially constructed in accordance with criteria, interests and conventions among their con- structors and users. They are context-sensitive, depend on the specific use they are intended for and the era in which they are produced. The similarities between the map and mapped region are relevant to the user: for their interests spatial relations are most important.

We can compare this example with the map of, for instance, a metro system of a big city. For users of a metro map, exact locations of metro stops and distances between them are not of utmost importance. For the intended use of these kind of maps, travelers get by with just bold approximations of the locations. What matters most now, is that the connections between metro stops are represented correctly: the user wants to know the order of the stations, and where to change lanes. Yet another example is the diagram of some electrical circuit. Here spatial rela- tions do not matter at all for getting the right information out of the diagram; representing the connections between parts of the circuit is the sole purpose.11 What these examples show is that the intended use, and therefore the user –the interpreting subject– is of vital importance. Van Fraassen stresses the importance of the interpreting subject in the model world relationship even more. He argues that representation is always representation-as (in respect to some repre- sentational system) and is a function of the context of use. The dyadic model-world relationship discussed sofar has therefore to be seen as a triadic relationship between model, world and user.

Properties

Having discussed the nature of the representational relationship between model and the real-world phenomenon, we may now ask how a possibly abstract object may be similar to some real-world phenomenon. This is a question that has been raised by critics of the similarity approach. Com- monly this question turns into the question of a comparison of properties, wherein one wonders if it is possible for abstract objects to have properties. Hughes, for instance, argues that it cannot be the case that an abstract object resembles a concrete object, as they cannot possess similar properties simply because of their different nature. (Hughes 1997, 329-30)

Other philosophers have suggested ways out of this. Following Giere, we may say that properties are ascribed to the abstract systems. (Giere 1988, 78) Another interesting approach is that of Roman Frigg, who compares models to literary fictions, and talks about properties that we are entitled to imagine. (Frigg 2010) To capture all possible versions of connecting properties to an abstract concept, we may say that the properties areassociated with the model. (Godfrey-Smith 2009, 6)