Abstract
Most scientific models are not physical objects. But what sort of objects are they? What is truth in a model, and how do we learn about models? In this first part of this chapter I develop an answer to these questions based on the so-called pretense theory of literary fiction. In the second part I draw on the analogy between maps and models to develop an account of scientific representation and discuss in detail the Newtonian model of the planetary system to illustrate how the account works.
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Notes
- 1.
Some scientific models are material objects (for instance the wood models of a car that we put into a wind tunnel), but most models are not of this kind. I here focus on models that are, in Hacking’s (1983, 216) words, “something you hold in your head rather than your hands”.
- 2.
- 3.
- 4.
This is not meant to be a definition of fiction. A failure of reference, although typical for fiction, is neither necessary nor sufficient for a text to qualify as fiction. I come back to this point later on.
- 5.
Sometimes structures are defined so that they also include operations. Although convenient in some contexts, this is unnecessary because ultimately operations reduce to relations (Boolos and Jeffrey 1989, 98–99).
- 6.
See Russell (1919, 60) for clear account of this feature of structures.
- 7.
A relation is transitive iff it is true that whenever the relation holds between objects a and b, and between b and c, then it also holds between a and c. Examples for transitive relations are more expensive than and taller than; and example for a non-transitive relation is liking (since it may well be that a likes b, and b likes c, but a does not like c at all).
- 8.
For a discussion of this example see Smith (2007, 24–29).
- 9.
Strictly speaking this is not a structural formulation of the model, but a structural version could easily be constructed from the equation defining the Fibonacci numbers. However, since such a construction requires some setting up and nothing in my conclusion depends on having such a formulation, I will not dwell on this point here.
- 10.
Other suggestions include partial isomorphism, homomorphism, and embedding—nothing in what follows depends on which one of these one chooses.
- 11.
This definition is adapted from Cartwright (1999, 39).
- 12.
This is what Downes has in mind when he says that there is no empirical system corresponding to the equation of the ideal pendulum (1992, 145), and what Thomson-Jones (2007) emphasizes when he points out that science is full of “descriptions of missing systems”; in a different way the same point is also made by Cartwright (1983, Chapter 7) who emphasizes that we have to come up with a “prepared description” of the system in order to make it amenable to mathematical treatment.
- 13.
One could try to avoid the commitment to hypothetical systems by renouncing a literal understanding of the relevant descriptions and arguing that it does not follow from the fact that descriptions are poor or highly idealized that they are not descriptions of the target at all; it just means that they are idealized descriptions. This move is of no avail. Being an idealized description is not a primitive concept and it calls for analysis. On the most plausible analysis, D is an approximate description of object O iff what D literally describes is in some relevant sense an idealization of O. But what D literally describes is a hypothetical system, and so we find ourselves back where we started.
- 14.
The German structuralists explicitly acknowledge the need for a concrete description of the target-system (Balzer et al. 1987, 37–38). Moreover, they consider these “informal descriptions” to be “internal” to the theory. Unfortunately they do not say more about this issue. Nevertheless, it is important to emphasize that there is no conflict between structuralism thus construed and the view developed in this chapter; in fact they can be seen as complementary.
- 15.
- 16.
There is an exegetic question here. Although structuralists certainly suggest that representation is data matching, they never explicitly say so. I here explore the stronger version of the view on which representation indeed consists in data matching since the weaker version, on which data matching is distinct from representation, does not provide a viable criticism of the above argument from abstractness.
- 17.
McAllister (1997) presents an antirealist critique of Bogen and Woodward. But his concern is orthogonal to mine: even if one construes phenomena in an antirealist way they turn out to be more than just data.
- 18.
The model I am talking about here is not the so-called standard model of elementary particles as a whole. Rather, what I have in mind is one specific model about the interaction of certain particles of the kind one would find in a theoretical paper on this experiment.
- 19.
To underwrite this claim consider the following example. Parallel to the research at CERN, the NAL in Chicago also performed an experiment to detect weak neutral currents. The data obtained in this experiment were quite different, however. They consisted of records of patterns of discharge in electronic particle detectors. Though the experiments at CERN and at NAL were totally different and the data gathered had nothing in common, they were meant to provide evidence for the same theoretical model. But the model does not contain any of these contextual factors. It posits certain particles and their interaction with other particles, not how detectors work or what readings they show. The model is not idiosyncratic to a special experimental context in the way the data are, and therefore it is not surprising that the model does not contain a substructure that could plausibly be claimed to be isomorphic to the data. The model represents an entity—weak neutral currents—and not data used in its discovery.
- 20.
This section and the next are based on my (2010).
- 21.
For want of space I cannot discuss competing approaches. In a nutshell, their problems seem to be the following. The paraphrase account (Russell 1905) does not offer a workable theory of truth in fiction (Crittenden 1991, Chapter 1). The neo-Meinongean view (Parsons 1980) runs into difficulties with incompleteness (Howell 1979, Section 1) and as a consequence does not offer a satisfactory answer to (Q5). Finally, Lewis’ (1978) account is too permissive about what counts as true in a fictional context (Currie 1990, Section 2.3, Lamarque and Olsen 1994, Chapter 4).
- 22.
Strictly speaking, Walton (1990) restricts the use of “pretense” to verbal (or more generally behavioral) participation, which does not include the activity of someone reading on his own. However, it has become customary to use “pretense” as synonymous with “make-believe” and I stick to this wider use in what follows.
- 23.
I here discuss pretense theory as it is presented by Walton (1990); Currie (1990) and Evans (1982, Chapter 10) develop different versions. Parenthetical references in the text of this and the following section are to Walton’s book.
- 24.
The distinction between primary and inferred truths is not always easy to draw, in particular when dealing with complex literary fiction. Walton also guards against simply associating primary truth with what is explicitly stated in the text and inferred ones with what follows from them; see Walton (1990, Chapter 4) for a discussion. For the purpose of the present discussion these subtleties are inconsequential.
- 25.
- 26.
There is controversy over this issue even within pretense theory. It is beyond the scope of this chapter to discuss the different proposals and compare them to one another. In what follows I develop an account of truth in fiction that is based on elements from different theories and that is tailored towards the needs of a theory of model-systems.
- 27.
- 28.
Notice that while transfictional statements are recognizable by the presence of terms that are foreign to the work under discussion, intrafictional and metafictional statements are recognizable as such only as a function of the context in which they appear. There are also statements that are difficult to classify. As these typically involve emotional reactions on the part of the reader to the novel (halfway through the book a reader exclaims “I fear the worst for Zapp”), they need not occupy us here.
- 29.
I here follow Currie (1990, Chapter 2) and assume that sentences like “Zapp drives a convertible” express propositions, something that Walton denies (1990, 391). This assumption greatly simplifies the statement of truth conditions for fictional statements, but nothing in the present paper hangs on it. Essentially the same results can be reached only using sentences and pretense (1990, 400–405).
- 30.
Fictional worlds thus defined are rather different from possible worlds as used in modal logic, the most significant difference being that the former are incomplete while the latter are not. See Currie (1990, 53–70) for a discussion of possible worlds and fiction.
- 31.
An interesting consequence of this identity condition is that not all models with the same prop are identical, because they can operate with different rules of indirect generation. This is the case, for instance, when the “same model” is treated first classically and then quantum mechanically; on the current view, the classical and the quantum model are not identical.
- 32.
In some places Walton ties the truth of such statements to authorized games (e.g., 1990, 397–398). This restriction seems unnecessary as the analysis works just as well for unauthorized games.
- 33.
- 34.
A more intuitive choice of terminology would be to refer the term “representation” for what I here call t-representation, and refer to p-representation as “presentation”. However, since this would stand in conflict with the use of “representation” in pretense theory I stick to the somewhat less elegant terminology of p- and t-representation.
- 35.
Model-systems without targets (and hence without t-representation) not only play a role when explaining failures; they are also important as means to explore certain technical tools, in which case they are often referred to as “probing models”, “developmental models”, “study models”, “toy models”, or “heuristic models”. The purpose of such model-systems is not to represent anything in nature; instead they are used to test and study theoretical tools that are later used to build representational models. In field theory, for instance, the so-called φ4-model has been studied extensively, but not because it represents anything in the world (it was well known right from the beginning that it does not), but because its simplicity allows physicists to study complicated techniques such as renormalization in a simple setting and get acquainted with mechanisms—in this case symmetry breaking—which are important in other contexts (Hartmann 1995). It is an advantage of the proposed view of modeling that it can account for this practice.
- 36.
- 37.
As an example consider Galileo’s law of equal heights (Sorensen 1992, 8–9). Take a u-shaped cavity, put a ball on the edge of one side, and let the ball roll down into the cavity. Galileo then argued that it would have to reach the same height at the other side—this is the law of equal heights. Of course Galileo realized that the ball’s track was not perfectly smooth and that the ball faced air resistance, which is why the ball in an actual experiment does not reach equal height on the other side. So Galileo considered an idealized situation in which there are neither friction nor air resistance and argued that the law was valid in that scenario. This thought experiment fits the above account of model-systems: Galileo considered a fictional scenario specified by a simple description, yet the conclusion he wanted to reach was not part of that description and was reached by using certain general principles that he took to be valid in situations like the one considered. Moreover, had Galileo used a mathematical machinery to derive his conclusion instead of informal arguments, physicists would refer to the product of his endeavor as a model. One would write down a curve specifying the shape of the cavity (for instance a parabola), specify its mechanical properties (frictionlessness), use mechanical laws to calculate the trajectory of the ball, and then find that it ends up at equal height on the other side. This is the sort of thing we find in mechanics textbooks, and which are referred to as mechanical models of a situation.
- 38.
Roughly, the Reality Principle says that if p 1 … p n are direct fictional truths, then proposition q is an indirect fictional truth iff: were it the case that p 1 … p n, then it would be the case that q. The Mutual Belief Principle says that that if p 1 … p n are direct fictional truths, then proposition q is a indirect fictional truth iff: it is mutually believed in the artist’s society that were it the case that p 1 … p n, it would be the case that q. See Walton (1990, Chapter 4) for a discussion of these principles.
- 39.
- 40.
Elgin’s account is based on the notion of exemplification. This account is on the right track, and a worked out version of the account I propose below will draw on many of its insights. However, at least in its basic form, this account does not cover cases in which the representational vehicle and the target do not share the relevant properties. The account suggested below is more permissive in that respect.
- 41.
Throughout this chapter I use a realistic idiom in the sense that I assume that what is represented, the target system, exists. This is for the ease of formulation and my position could be restated from the point of view of metaphysical antirealism. What I want to remain non-committal about is scientific realism, roughly the position that theories are more or less truthful mirror images of reality. At a general level representing something does not amount to giving a mirror image, or to make a copy of that item. A representation can be alike to its target, but it does not have to be. There is nothing in the notion of a representation that ties it to imitation or copying. A general account of representation has to make room for non-realistic representations in this sense.
- 42.
Maps are of course real and not fictional objects. It will become clear as we proceed that representation works in the same way for fictional and real objects. Hence that maps, unlike model-systems, are material objects is no impediment to using them in the current context.
- 43.
The first condition is Goodman’s (1976, Chapter 1) who has argued that denotation lies at the heart of representation.
- 44.
Common alternatives to the current proposal are isomorphism and similarity accounts of representation; see Frigg (2006) and Suárez (2003) for discussions. Other alternatives have been proposed by Contessa (2007), Hughes (1997), Suárez (2004, 2006) and Toon (2010). For want of space I cannot discuss these here.
- 45.
Nautical maps, for instance, use the Mercator projection system and do not preserve distances; they preserve angles and one obtains wrong results when translating the distance between two points on a map into the distance between two locations. And this mistake has been made over and over again. As Sismondo and Chrisman (2001, 42–43) point out, about half of a sample of 137 international maritime boundaries are not where they were meant to be. When diplomats met to draw the boundaries between territories they had these charts on the table. They intended to draw the border half way between two territories and so they drew the line on the map mid-point between the territories. This is mistake: even relatively close to the equator the line thus drawn can be over 7 km away from the actual line of equidistance.
- 46.
In passing I would like to point out that this account of representation satisfies the conditions of adequacy that I presented in my (2006). The ontological puzzle is addressed by the account of model-systems presented in section “The Anatomy of Scientific Modeling”. The enigma of representation is met by (R1) and (R2). The problem of style now becomes the question of how denotation works and what keys are used.
- 47.
Although this is reminiscent of Giere’s claim that models are connected to their target systems with a “theoretical hypothesis” (1988, 80), the point is a different one. In Giere’s account we call a claim to the effect that the model is similar to the target in specific way a theoretical hypothesis; the current view, by contrast, emphasizes the hypothetical—fallible, tentative, and conjectural—character of keys attributed to a model.
- 48.
For a more extensive discussion of Callender and Cohen’s argument see Toon (2010).
- 49.
I have smuggled in a premise here: that it makes sense to quantify differences in the friction of surfaces and the behavior of spinning tops in terms of numbers. This is not implausible and could be made precise, for instance, by using friction coefficients and a geometrical measure for the closeness of trajectories. The following two questions are more pressing. First, how can we know whether or not a certain model-system is an ideal limit of the target at hand? Second, what is the relation between ɛ and δ? In real applications on would like to know how close to the limit one would have to come to get a result that is precise to a particular degree. Typical mathematical existence results are of no help here. These are open questions that need to be addressed.
- 50.
This corresponds to Rohrlich’s distinction between factual and counterfactual limits (1989, 1165).
- 51.
See, for instance, Feynman, Leighton, and Sands (1963, Sections 9.7 and 13.4) and Young and Freedman (2000, Chapter 12 ).
- 52.
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Acknowledgements
I would like to thank José Díez, Matthew C. Hunter, and Julian Reiss for helpful discussions and comments on earlier drafts. Large parts of this chapter have been written when I was a visiting fellow at the Sydney Center for the Foundations of Science. I would like to thank the Center for its hospitality and a travel grant that made the visit possible.
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Frigg, R. (2010). Fiction and Scientific Representation. In: Frigg, R., Hunter, M. (eds) Beyond Mimesis and Convention. Boston Studies in the Philosophy of Science, vol 262. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3851-7_6
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