Models, Modeling, and Perspectives

            What models are and what modeling is, are not easy questions to tackle down due, partly, to the fact that models are at the first glance overlapping with the concept of scientific theory. Are those really related in the sense that models and theories are on the same par? Or are models autonomous agents and we should be dismissive towards a theoretical-centered view? In this entry-article, I pursue rather the idea that models, whatever they are in regard with their fundamental ontology, are at the same time points of view or scientific perspectives about a physical phenomenon and, on the other hand, modeling is the locus of scientific activity which consists in the representational practice of depicting the physical phenomenon in the terms of a given perspective (Giere 2004, p.60). I call this latter approach “perspectival modeling”, borrowing the concept from Michela Massimi’s work, in order to restate Giere’s argument for models as perspectives (Massimi 2017, p.3).  Modeling and models are intertwined in the sense that modeling is the scientific activity that relies on models (as vehicles of scientific representation).

            In the first place, I consider various accounts of what models could be: either fictional, artifactual, abstract, or, rather, mathematical structures, or logic-linguistic propositions. Whatever models could be (here it comes the long disjunction of alternatives!), and whatever view one buys into, she should accept that models are also points of view about physical systems (target-systems). I argue henceforth that the perspectivist approach is consistent with (almost) any view about what models are. My guiding analogy would be, following Giere, the idea of a map that depicts the physical world (Giere 2004, pp.70-75). If models are perspectives, those are maps about the physical world. Within this view, we can conclude that models deliver perspectival, partial, and idealized scientific knowledge about phenomena (Massimi 2018, pp.166-167).

            What models could be (a shortlist of much-debated approaches and examples):

  •              Models as interpretations of theories (the Syntactic View): According to this approach, models are alternative interpretations to the abstract calculus of a theory. In turn, a theory is “an abstract calculus” and “a set of rules” that relate the calculus to “empirical content” (Nagel 1979, p.90). Models are, in other words, models for theories, or “are just the theories themselves” (French 2020, p.6). A classic example would be the billiard ball model of a gas, where the formal calculus (Newton’s laws of mechanics) is expressed not in terms of gas atoms, but in terms of a set of observable objects that enhance the scientific understanding (motion, momentum, mass) (French 2020, p.5). Models become mere psychological tools.
  •             Models as mathematical structures (the Semantic View): Within this approach, models are extra-linguistic objects (contra the Syntactic View) since models can get multiple linguistic formulations.– models have, in this regard, a “linguistic independence” from the overarching theory (French 2020). Instead, under this construal, theories stand for “families of structures, its models” (van Fraassen 1980, p.64) – such that models are in fact mathematical structures. Take the previous example. The billiard ball model as a structure provides a representation of the gas atoms – the representation is an isomorphism (sharing the same structure) between the model and the physical system that is represented (the gas atoms).
  •              Models as fictions: Models are on the same ontological par with fictions, meaning that there are no ontic differences between the billiard ball model, Hans Castorp, and The Magic Mountain (French 2020, pp.152-154). For instance, propositions regarding models are not literally true, but true only relative to the domain delineated by the model. Engaging with models in scientific practice, scientists are pretending ‘as if’ the models are real existing entities – being involved in a game of pretension. The entire game is “delineated by a kind of convention or principle of agreement” among scientists (French 2020, p.21).
  •              Models as real abstract entities: Models are real entities, living in a Third World (basically, a realm of theories, models, artworks, paintings, literary fictions or music pieces) that is further distinguished from the First World (the physical world – the realm of physical entities) and the Second World (the mental world – made of mental states) (French 2020, pp.116-118). In this view, the process of building models is one of the discovery of a certain kind of entities that are out there in the world.
  •              Models as metaphors: Another option is to define models as metaphors. In this view, metaphors are expressions involving interactions between a primary system and a secondary system (Hesse 1966, pp.158-159). If we take models as metaphors,  the gas atoms (as the primary system) are conceived like billiard balls (as the secondary system). In this case, what hold between the former and the latter are multiple analogies of a certain kind. We assume from the onset that the primary and the secondary systems share some features (what is called positive analogy – for instance, kinetic properties), others properties are not shared (negative analogye.g. atoms are not made out of plastic), and there are also features about which I do not know (yet) if are shared (neutral analogy) (Hesse 1960, pp.8-9). Accordingly, a model could embody positive, negative, and neutral analogies with respect to the target-system.

             Whatever alternative from (a) to (e) we pick out to define what a model is, models are going to provide scientific knowledge about the target-system similarly with how a map represents a specific delineated field. The latter thesis is an epistemic view about how scientific knowledge is generated within scientific practices – while our lists of approaches are, mainly, competing ontologies of models. Whether we decide that models are fictions, or abstract entities, or metaphors, models still work out as perspectives about the target-system. How? Let’s consider the following picture:

Washington, D.C subway map (link: https://washington.org/navigating-dc-metro)

             It depicts a partial subway map of Washington. The main information (knowledge) carried by the map is the topological ordering of stations (Giere 2004, p.74). What one resident of Washington can do with the subway map is “to know when one is at the stop before one’s desired destination” (Giere 2004, p.74). Regarding the target-system, the subway map is modeling Washington’s subway system from the point of view of how stations are ordered one after another. As a representation, Washington’s subway map is a one-to-one correspondence between the real order between stations and the mapped order between those. Also, many details or features are left out: we see no actual streets, the distance expressed in kilometers between stations is also lacking, no people in stations, or no subway schedule. Consequently, we can conclude that “every map reflects a perspective on the region mapped, a perspective built by the mapmakers” (Giere 2004, p.75). In our case, the Washington subway map reflects the perspective or the point of view of the relevant topological order. In the previous example, we can point out the central features of a map. Maps are partial since only some features of the place in question are subsequently represented (Giere 2004, pp.71-72). Maps are of limited accuracy because the relative distances on the map do not stand exactly for the relative distances on the ground (Giere 2004, p.72). Maps are idealized renderings of a physical system – as we have already seen, a lot of details from the ground are missing. (Giere 2004, p.72). Maps and mapmaking depend on conventions for interpretation, what and how maps represent is culturally dependent  (Giere 2004, pp.74-75).

T-O Medieval Map (link: https://www.historyhit.com/medieval-maps-of-the-world/)

             To make this latter point clear, Giere considers a Medieval map of the world. The outer circle refers to the world’s oceans, while the top part stands for Asia. The bottom left stands for Europe and the bottom right represents Africa. Without information (the relevant conventions) in place, we do not know “what a map is a map of” (Giere 2004, p.75)

             Knowing better now what a map is and how it works, we can further extend the map case to models and modeling. Take the previous example of the billiard ball model. A perspectivist reading of it could say that the kinetic properties of small particles of matter are regarded from the point of view of the billiard ball. Within this perspective, atoms are depicted as bouncy balls that collide, exhibit momentum, are subject to change due to motion, are subject to the law of conservation of mass. The model is partial, it depicts certain features (the motion of the balls – the law of conservation) and no others (the material out of which the balls are made); the model is idealized, some features are neglected (certain friction forces due to air resistance); of limited accuracy (the relative size of the balls do not stand for the size of the atoms); and, finally, culturally dependent on certain conventions. In this regard, the billiard ball model is dependent upon Dalton’s atomic theory, which fits in the broader Newtonian classical mechanical view on how physical objects interact. Knowing all these particular details of the billiard ball model, we can certainly know what the model is a model of – what target-system is truly modeling. In other words, the billiard ball model reflects a perspective on the physical system that is mapped.

Dalton’s “Billiard Ball” Model (link: https://www.timetoast.com/timelines/models-of-the-atom-fdf2db44-a8ad-4258-9617-ab7f40aeae3a)

             If models are like maps, then it follows that models are perspectives. How is in turn defined as perspectival modeling? The billiard ball model is a proper vehicle of representation for the gas atoms – it fixes up what features of the model correspond to which features of the targeted system. Models are designed such that elements of the model can be identified with features of the real world (Giere 2004, p.63). How modeling takes place? One way to obtain representations is to build one-to-correspondences that hold in certain respects (motion, the law of conservation in our toy example) but no others (size and the make-up material). By now, it is plausible to stress that representations are done not ex nihilo, or from almost any perspective, but the relevant models are representational tools within a specific perspective, namely the billiard ball model of gas atoms. If we are to abandon the billiard ball model and take into consideration the plum-cake model or Bohr’s model of the atom, we are gone to obtain different representations that are generated within other distinct perspectives. This train of thought shows nothing more than that scientific modeling is perspectival in the sense that it takes place from the point of view of a given scientific model.

             Perspectival modeling provides understanding and insight of the target-system into question: how gas atoms behave as they do and why this behavior is subject to certain regularities (Bailer-Jones 2009, p.13). Moreover, modeling has an informational stage since there is a transfer of information from the physical system to the model – we are going to transfer the empirical information that we got directly to the billiard ball model. The next step is interpretation, where we take “the results of the derivation stage back to the target system” and interpret them in the light of our predictions about the gas atoms (French 2020, p.71).

             Our detour to models as perspectives shows it does not presuppose beforehand what models are in regard to their fundamental ontology. Instead, the perspectivist reading puts models at work in scientific practices – explaining how scientists reason with models to generate knowledge. It is not a matter of ontology (not a fundamental ontological issue at least), but mostly a matter of knowledge acquisition or of epistemology (of science). We can live up with perspectivism regardless to which fundamental ontology of models we accept.

             Seminar proposal: I would like to ask the students that are enrolled in the “Contemporary Trends in Philosophy of Science” course to read in advance the fourth chapter (“Scientific Theorizing”, pp.59-96) of Scientific Perspectivism as a starting point for our seminar discussion on models and modeling (15th December).

             Works cited:

 Bas C.Van Fraassen (1980), The Scientific Image, Oxford: Oxford Claredon Press.

 Daniela Bailer-Jones (2009), Models in Philosophy of Science, Pittsburgh: University of Pittsburgh Press.

 Ernest Nagel (1979), The Structure of Science, Indianapolis Cambridge: Hackett Company.

 Mary Hesse (1966), Models and Analogies in Science, Indiana: Notre Dame Press

 Michela Massimi (2017), “Perspectival Modeling”, pp.1-23, draft

 Michela Massimi (2018), “Perspectivism” from The Routledge Handbook of Scientific realism (ed J.Saatsi), pp.164-175, Oxford: Routledge

 Pierre Duhem (1991), The Aim and Structure of Physical Theory, trans. from French by Philip F. Wiener Princeton: Princeton University Press.

 Ronald Giere (2004), Scientific Perspectivism, Chicago: The University of Chicago Press.

 Steven French (2020), There Are No Such Things As Theories, Oxford: Oxford University.

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