Note: This is an essay I wrote when I was in college and still a baby philosopher. I wrote this essay back in 2013 for my Philosophy of Science course.
We know that scientists have been using models since the times of Galileo, Bacon and Copernicus. A model is a simplified version, or representation for something you are trying to study or trying to predict. For example, a model of the earth is a simplified representation of the earth. We use that model of the earth in order to understand, analyze, or make predictions. The model of the earth, the globe, is a physical representation of the earth, but are physical models the only types of models we have?
The answer is obviously no; we have plenty of models and they all function in different ways. Trying to define a model is a tricky thing since the word model can mean different things to different people. A model could be meant to refer to a person who is wearing clothes at a runway. The one thing this model has in common with scientific models is that it is a representation of how other people will look with in those clothes, and it makes predictions about what the next fashion trends will be. Representation and prediction are what all models have in common. So, if the word “model” can mean different things to different people, what might the word model signify to scientists? Even within the community of scientists there is no one concrete definition of what a model is, for some scientists a model might mean a physical object, like the globe we just mentioned. According to an entry at plato.standford.edu “physical models are referred to as material models. The class of material models compromises anything that is a physical entity and that serves as a scientific representation of something else.” This could be a globe, or a model of an airplane, or a car, or even a physical model of a house. There is not much problem understanding this type of model but what about fictional object models?
Some models are not physical, for instance the Bohr model of the atom is in the scientist’s mind rather than in a laboratory. This is a bit more difficult to understand; it is a model that even scientists and philosophers argue about even trying to define it. “The issue of how to understand fictions in science has been the subject matter of a recent debate in the philosophy of modeling.* Barberousse and Ludwig (2009), Contessa (2010), Frigg (2010a, 2010b), Godfrey-Smith (2006, 2009) We have talked about physical models, fictional models but perhaps if we asked a mathematician what a model meant for him he might respond that for him a model is an equation. Equations are also referred to as models in mathematics and economics. One example of this type of the equation model is ‘’the Black-Scholes model.’’ The Black-Scholes model was a model used for “an option-formula for pricing, a mathematical model of a financial market containing certain derivative investment instruments.” (Duffie, 1998) Models of equations could also refer to algebraic equations.
What about descriptive models? Descriptions are “a time-honored position in which scientists display in scientific papers and textbooks when they present a model where there more or less stylized descriptions of the relevant target systems.” (Achinstein 1968). Models of descriptions have also been a topic of debate between scientists, the debate has focused on how to differentiate a model from a description and how does a model become a description. Other models that are also just downsized or enlarged copies of their target systems and these are called scale models. An example of this would be a model of a train, or a globe. The scale model can be considered as a “naturalistic replica or a truthful mirror image of the target; for this reason scale models are sometimes also referred to as ‘true models.” (Achinstein 1968) We have talked about some types of models but another question arises. How is it possible to learn from models? We know that models are things created in order to understand the world around us better, but how is that so? How do models function and how do we learn from them?
Models are tools that help us better understand the world around us. A lot of studies and scientific investigation is done on models rather than in physical reality itself. “By studying a model we can discover features of and certain facts about the system the model stands for; in brief, a model allows for surrogative reasoning.” (Swoyer 1991) An example of this is the way we study the nature of the hydrogen atom, or for instance in sociology how dynamics of populations are studied, they are both examples of things that are studied by models instead of by their physical existence. Models have been acknowledged, used, and accepted not only by physicists but by sociologists, mathematicians, economists, etc. Some even argue that models “give rise to a new style of reasoning, called ‘model-based reasoning.’” (Magnani 2002)
A general framework has also been provided to answer this question. Hughes (1997) created this general framework, which claimed that learning through models took place in three stages. Those stages are “denotation, demonstration, and interpretation.” The denotation aspect of learning is established by a representation of a relationship between the model and the target. After this is done the features of the model are investigated in order to demonstrate certain claims about its internal mechanism. The demonstration aspect is finally when we learn about and from the model. Hughes refers to this step as “interpretation.”
Once we have gained knowledge about the model how do we then gain knowledge about the world? “Models can instruct us about the nature of reality only if we assume that (at least some of) the model’s aspects have counterparts in the world. But if learning is tied to representation and if there are different kinds of representation (analogies, idealizations, etc.), then there are also different kinds of learning.” (Frigg, Roman and Hartmann, Stephan) To answer this question we must first know what type of model is being used to understand the target system. It is not the same to use a physical model than a fictional mode. They both involve different techniques and they different results. Numerous cases have been done in order to understand how certain specific models work, and there is still no general knowledge of how this goal is achieved.
We also need to understand how models are distinct from theories. “Theories do not provide us with algorithms for the construction a model; they are not ‘vending machines’ into which one can insert a problem and a models pops out 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.” (Cartwright 1999, Ch. 8) Models function independently from theories, and models have often times been seen as “complements of theories.” What this means is that a theory may be incompletely specified in the sense that it has certain restraints and concrete/specific situation and these may be provided by a model.
“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.” Other times models “step in when theories are too complex to handle.” (Frigg, Roman and Hartmann, Stephan)
When theories become too complicated to handle a model may be used to facilitate its solution. “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).” Here we see an example of theories and models working together in order to achieve a result. Models can also work as preliminary theories. This term was coined by Leplin (1980) who pointed out “how useful models were in the development of early quantum theory and is now used as an umbrella notion covering cases in which models are some sort of a preliminary exercises to theory.” The purpose of these models is to test new theoretical tools that are later used to build upon representation models.
Another problem that arises is one of a philosophical nature. It is true that scientific models are used to understand the natural world and discover “laws of nature” but philosophers have faced the challenge of explaining what laws of nature are. One possible response is “to argue that laws of nature govern entities and processes in a model rather than in the world. Fundamental laws, on this approach, do not state facts about the world but hold true of entities and processes in the model.” Different variants of this view have been advocated by Cartwright (1983, 1999), Giere (1999), and van Fraassen (1989). I have tried to give a description of different types of models, and the problems that arise from these, I have tried distinguishing them and mark their differences and similarities but the task that I have found the hardest is trying to define what a model is.
Frigg, Roman and Hartmann, Stephan, “Models in Science”, The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/fall2012/entries/models-science/.
Barbrousse, Anouk and Pascal Ludwig (2009), “Fictions and Models”, In Mauricio Suárez (ed.): Fictions in Science, Philosophical Essays on Modelling and Idealisation, London: Routledge, 56–75.
Contessa, Gabrielle (2007) “Scientific Representation, Interpretation and Surrogative Reasoning”, Philosophy of Science 74(1): 48–68.
Frigg, Roman (2006), “Scientific Representation and the Semantic View of Theories”, Theoria 55: 37–53.
Godfrey-Smith, P. (2006), “The Strategy of Model-based Science”, Biology and Philosophy, 21: 725–740.
Achinstein, Peter (1968), Concepts of Science. A Philosophical Analysis. Baltimore: Johns Hopkins Press.
Black, Merton and Scholes: Their Central Contributions to Economics. Darrell Duffie The Scandinavian Journal of Economics, Vol. 100, No. 2 (Jun., 1998), pp. 411-423
Magnani, Lorenzo, and Nancy Nersessian (eds.) (2002), Model-Based Reasoning: Science, Technology, Values. Dordrecht: Kluwer.
Swoyer, Chris (1991), “Structural Representation and Surrogative Reasoning”, Synthese 87: 449–508.