Abstract
In recent decades, philosophers of science have devoted considerable efforts to understand what models represent. One popular position is that models represent fictional situations. Another position states that, though models often involve fictional elements, they represent real objects or scenarios. Though these two positions may seem to be incompatible, I believe it is possible to reconcile them. Using a threefold distinction between different signs proposed by Peirce, I develop an argument based on a proposal recently made by Kralemann and Lattman (in Synthese 190:3397–3420, 2013) that shows that the two aforementioned positions can be reconciled by distinguishing different ways in which a model representation can be used. In particular, on the basis of Peirce’s distinction between icons, indices and symbols, I argue that models can sometimes function as icons, sometimes as indexes and sometimes as symbols, depending on the context in which they are considered and the use that they are developed for because they all have iconic, indexical and symbolic features. In addition, I show that conceiving models as signs enables us to develop an account of scientific representation that meets the main desiderata that Shech (in Synthese 192:3463–3485, 2015) presents.
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Notes
It is important to emphasize here that the debates are parallel, but not identical. The RF versus RR debate is about what models represent (fictional situations vs. real objects) whereas the IR versus DR debate is about how models represent (indirect or two-stage representation vs. direct or one-stage representation).
In a prior version of this article, a reviewer asked whether there is a one-to-one correspondence between RF and IR on one side, and RR and DR on the other, and if this is so, whether this entails that they are two different sides of the same coin, so to speak. Though these questions are important, I set them aside here for the sake of space, though I intend to address them in future work.
Toon (2010, pp. 84–85) articulates what is at stake here as follows: “What exactly are ‘imagined physical systems’ of ‘hypothetical entities’? Like a number of other authors, Frigg compares model systems to fictional entities, like unicorns or Count Dracula. Of course, the nature of fictional entities, and the particular question of whether such entities exist at all, is itself the subject of considerable controversy.”
In a recent paper, Frigg and Nguyen (2016, p. 228) attempt to address this question by introducing the notion of I-instantiation. The basic idea behind this notion is that a model M (say, a physical ball-and-stick model of a water molecule) I-instantiates a property P (say, the property of having the sticks form a \(104.45{^{\circ }}\) angle) iff its target T (say, a water molecule) instantiates a property P’ (say, having a bent three-dimensional structure where the covalent bonds between the hydrogen atoms and the oxygen atom are arranged in a \(104.45{^{\circ }}\) angle) and P’ is mapped onto P under a certain interpretation I. For Frigg and Nguyen, ‘this allows a model to I-instantiate properties that it does not instantiate’.
I owe this example to Catherine Legg.
By this, I do not mean that denotation is sufficient for representation in the case of signs. Rather, my point here is the same that Shech (2015, p. 3468, fn12) makes: ‘the concept of representation presupposes that something is being represented, and it is in this minimal sense that representations are intentional objects.’ Thus, in my view, the concept of sign presupposes that there is something the sign stands for.
Even though some authors treat abstraction as a certain type of idealization (e.g., McMullin 1985), I follow here Jones (2005, p. 175) in distinguishing idealization from abstraction in the following manner: ‘we should take idealization to require the assertion of a falsehood, and take abstraction to involve the omission of a truth.’
To put this idea in other words, if we conceive representing as a polyadic relation, we must, as Giere (2004, p. 743) puts it, ensure that ‘one place, of course, goes to the agents, the scientists who do the representing’.
In a prior version of this paper, a reviewer pointed out that French (2003, p. 1474) seems to defend the idea that models may represent by themselves without any agents to the extent that he claims that “whereas intentions are typically drawn upon in art in order to distinguish ‘artistic’ objects from other kinds, this is not the case in science.” Now, I think that French’s view can be reconciled with Giere’s position in virtue of the following. When he discusses the parallels between artistic and scientific representation, French cites approvingly an insight of Budd (1993, p. 162) according to which ‘representation consists in the perceived isomorphism of structure.’ To illustrate this, French goes over an example discussed by Budd (i.e., the case of the anamorphic skull in Holbein’s The Ambassadors) and he remarks that, though the picture is not isomorphic to a skull when one stands in front of the painting, it is isomorphic when one looks at the painting from the perspective of a spectator in an oblique position. On the basis of this insight, one could argue that what French holds is that, though it may seem that some models represent in isolation since there no actual agents who do the representing, in fact they always represent in relation to the perspective of some possible agent.
Atkin (2013) characterizes the notion of index in Peirce’s theory of signs as follows: ‘If (...) our interpretation [of a sign standing for an object] comes in virtue of some brute, existential fact, causal connections say, then the sign is an index.’ Now, given that a sign functions as an index if we come to interpret it as standing for an object through some brute, existential fact, causal relations usually provide the basis for something to function as an index for Peirce (as in the case of a weathercock, which indicates the direction of the wind), but entities may also function as indexes in virtue of other brute, existential facts (e.g., topological or mereological relations). For instance, the road sign with a stylized airplane may function as an index of the direction of the airport in virtue of a topological relation between both objects and an emerged periscope may function as an index of a submerged submarine in virtue of a mereological relation between both objects.
Iranzo (2013, p. 67) makes this point using this specific example. In fact, Iranzo also remarks that the view that scientific representation is based on structural similarity comes in different varieties. For instance, some proposals such as those of Van Fraassen (1980) and of Da Costa and French (2003) emphasize the use of structural isomorphism for scientific representation while other proposals such as that of Giere (2010) involve a more complex view that includes structural similarity but also appeals crucially to the intentions of the agents using the model.
Darwin([1859] 2009, p. 129) describes his model in the following fashion: ‘The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. The green and budding twigs may represent existing species; and those produced during each former year may represent the long succession of extinct species.’ This view of scientific models, according to which they represent their targets via some analogical or metaphorical relations, is defended in the works of Black (1962) and Hesse (1963).
For Leonelli (2008, p. 522), material abstraction is a process that ‘involves selecting a set of material features of Arabidopsis wild types as potentially interesting for research purposes, devising ways in which these properties can be incorporated into a unique specimen, making sure that specimens with those characteristics can actually be grown, and constructing a toolkit of guidelines, materials and instruments allowing researchers worldwide to grow specimens in the same way’.
In a prior version of this article, a referee pointed out that two of the functions that a sign may exhibit (i.e., index and symbol) seem to be conflated in my discussion of Leonelli’s example. Part of the problem is that Leonelli herself does not separate clearly these two functions in her discussion of how material abstraction is used to create models of Arabidopsis. I have tried to clarify things by stressing that a certain specimen of Arabidopsis may represent some wild specimens (qua index) in virtue of some causal links between the organisms and that some of the features of this specimen may represent features in other plants (qua symbols) in virtue of a certain conventions established by scientists.
Callender and Cohen (2006, p. 74) illustrate this feature using the following example: ‘Can your left hand represent the Platonic form of beauty? Of course, so long as you stipulate that the former represents the latter. Then, when your dinner partner asks what you are thinking about, you can direct attention to your left hand with the reasonable intention that your doing so will activate in your audience the belief that you are thinking about the Platonic form of beauty’.
For Liu (2015, p. 47), the insufficiency of mere conventional or symbolic relations to do all the main work in instances of scientific representation is illustrated using this example: ‘I have never been to Africa, yet I can acquire a good sense of what an African savannah looks like through vehicles of model representation. That is not possible if I can have access only to symbolic vehicles, even if I know and consent to all the symbols that relate to African savannahs (...)’.
Different authors use different terminology. For instance, Suárez (2003, p. 225) refers to a representational vehicle as the source of a representation in order to distinguish it from what he calls the target of the representation (which is the object represented). I will use here, following Callender and Cohen as well as Liu, the term ‘representational vehicle’ since the term ‘source’ does not quite convey the idea that scientific models are used as tools to represent certain objects.
In particular, Liu (2015, p. 48) argues that, while some may be reluctant to separate epistemic vehicles from symbolic ones since some objects often seem to play both roles, the distinction is justified since they play both roles in different contexts as the following example shows: ‘The double helix model of DNA as a model showing the relevant structure of the molecules is rarely used as a convenient symbol in the context of scientific research and pedagogy. When it is used as a symbol, it is used as a symbol of a great scientific achievement; and then, and usually only then, is a fully realized replica of the model (...) necessary to be placed somewhere to do the job of a scientific representation’.
The fact that this model was devised and constructed by its builders to represent a portion of the real world is underscored by Weisberg (2013, pp. 1–3), who writes: ‘The Corps recognized the benefits that the Reber plan might bring to the area, but it was certain that damning the bay would have serious, unintended consequences. It recognized that a battle of words would not be advisable in advising regional authorities; it needed hard data. But how such data be collected without actually building the dams and risking harm to the bay? Its solution was to build a massive hydraulic scale model of the San Francisco bay’.
The primary indexical role of the San Francisco bay model is further highlighted by the fact that the model had to be calibrated so that it could to be used effectively to represent the tidal flows. For further discussion of this, see Sect. 4 below.
In virtue of this, one of the advantages of adopting the Peircean framework that I present and defend here is that we don’t need to make a distinction (as Frigg does) between different kinds of representation. On my view, there is just one relation of representation that admits different grounds (iconic, indexical or symbolic) and that may hold between different items.
The term ‘epistemic’ that Barberousse and Ludwig use is potentially misleading since models may be used produce knowledge even if they do not tell us what the world is like. In virtue of this, I prefer the terminology (as well as the associated distinction) that Shech (2015, p. 3464) puts forth in the following passage: ‘Scientists routinely use representational structures such as models to make inferences about the world (epistemological aspect) and to tell us what it is like (ontological aspect).’ Though both aspects are usually deployed in tandem while building and employing scientific models (since one usually draws inferences from what there is in the world, as a reviewer pointed out in a previous version of this article), I believe that it is important to distinguish them because they correspond to different functions: an inferential one and a descriptive one. The importance of separating these functions can be further supported by considering the fact that statisticians traditionally distinguish inferential statistics from descriptive statistics.
I am very grateful here to a reviewer who suggested presenting my position in these terms.
One of the best examples of this trait of scientific models is provided by Prandtl’s hydrodynamical model of a liquid with a very thin boundary layer, which is amply discussed by Morrison (1999, pp. 53–60).
I will explain below what all these terms, which are termini tecnici, mean and how the conditions they impose are met by the account I presented here.
The following passage from Kralemann and Lattman (2013, pp. 3402–3403) shows that, if one adopts the view they propose, scientific models turn out to be intentional objects with both reference and specific semantic contents: ‘models are signs which represent something else, i.e., their objects; nonetheless they do not act as signs by themselves, but only when they are made to do so by an interpretative act of a subject that pursues a specific objective and who explicitly or implicitly chooses a theoretic or linguistic context including a frequently semantically coded prior knowledge, which in the concrete act of modeling connects the model with a specific semantic content, i.e., its interpretation’.
Peirce (1976: NEM, IV, 353) ‘(...) in all reasoning there must be something amounting to a diagram before the mind’s eye and the act of inference consists in observing the relation between the parts of that diagram that have not entered yet into the design of its construction’.
This last point by Shech is important since it echoes a rather plausible claim made by Łukasiewicz and mentioned in Gyedimin (1986, p. 198), which is that the search for the universal laws of nature (which is presumably one of the tasks of science) could be compared to the deciphering of a coded message when the code is unknown.
It is important to make a clarification here: in a sense, all models misrepresent their targets since they are all built using both abstraction and idealization, which involve willful and explicit distortions or omissions. However, this does not prevent us from judging some models as more ontologically faithful than others since, as Shech (2015, p. 3480) observes, ‘faithfulness and accuracy are matters of degree’.
A reviewer has pointed out that, though the Peircean framework that I articulated here is interesting, I have not done enough to show that Peirce’s conception of signs is strong enough to carry the epistemic roles that scientific models must fulfill in the practice of science—roles which include, not only representation, but also learning and testing hypotheses (e.g., Downes 2011). Undertaking this project is beyond this paper. However, I think that the framework has the resources to develop an account of other epistemic roles that models have—in particular, of how scientists develop and choose models to learn. In the case of learning, the gist of the argument would be the following: granting that models are signs, we can in principle explain how they are used by scientists to learn by reflecting on how toddlers make doodles and combine them in different ways to learn and recall information, since doodling appears to promote learning according to psychological research. For more details on the connection between doodling and learning, see Andrade (2010).
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Acknowledgements
A previous version of this paper was presented at the 2016 meeting of the Canadian Society for the History and Philosophy of Science held at the University of Calgary. I am very grateful for generous comments and feedback provided on that occasion by the audience, especially by Carlos Mariscal, Adrian Currie and Elay Shech. I am also thankful to some Peircean scholars who generously provided a sounding board for the ideas in this paper in its earliest stages: Paniel Reyes Cárdenas, Douglas Niño, Shannon Dea and, especially, Catherine Legg. Three anonymous reviewers for Synthese also offered at various stages extremely valuable suggestions that contributed greatly to better the manuscript. Last, but not least, I want to thank my colleague Brian Hutchinson for reading carefully the manuscript and suggesting many stylistic and substantial changes that helped to improve it.
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Gallegos, S.A. Models as signs: extending Kralemann and Lattman’s proposal on modeling models within Peirce’s theory of signs. Synthese 196, 5115–5136 (2019). https://doi.org/10.1007/s11229-018-1700-4
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DOI: https://doi.org/10.1007/s11229-018-1700-4