“Models and the Locus of their Truth,” U. Maki (2011)

“I hope the reader who is willing to spend some time and attention on my work will not take exception to the imaginary assumptions I make at the beginning because they do not correspond to conditions in reality, and that he will not reject these assumptions as arbitrary or pointless. They are a necessary part of my argument, allowing me to establish the operation of a certain factor, a factor whose operation we see but dimly in reality, where it is in incessant conflict with others of its kind.”

Von Thunen, arguably the inventor of the economic model (though Malthus has some claim here), wrote the above in his 1826 work on agricultural land use patterns. And this is a model that has stood the test of time: interesting work on, for instance, the “polycentric city” has only appeared in the past decade! Since we economists spend most of our time writing models, it’s worth asking to what extent a model can be “true” or can contain “truth”. I should point out that modern philosophers are not Platonists: true does not necessarily mean a fact proven conclusively. Truth in basically any brand of contemporary philosophy has a subjective component. The arch-pragmatist William James once said that truth is “what it is better for us to believe.” Nonetheless, there is some agreement on what domains the concept of truth can apply to. This is clearly an unsatisfying summary, but here I have only space to introduce a caveat rather than a school of thought.

Maki wishes to counter two conceptions of truth in models. The first is that models are inherently untrue because they both simplify the real world and only describe a subset of the real world. The second, as in Giere’s 1988 Explaining Science, is that models are non-linguistic abstract models which cannot be truth-valued, and that linguistic statements within the model are tautological. The first conception suggests that “better” modeling, meaning models closer to the truth, are necessarily broader and more complex. The second does not allow for aspects of models to contain any truth at all.

Maki notes that models are representations of the real world, meant to be studied in and of themselves. To understand models, then, one must understand how that studying takes place. An economist uses a model to represent a real system, for some purpose, directed to some audience, prompting through description of, and commentary on, the model a resemblance between the model and the real system to arise in the mind of the audience. I like this definition because it includes the audience as a critical part of modeling, and because it notes that commentary on a model, and not simply the model, provide the most important links to analysis of the real world.

But what of truth? As Giere pointed out, the model qua model is an abstract and not a linguistic object, and hence cannot be truth-valued. But aspects of the model, and their link to the real world, can be truth-valued. In von Thunen’s book, the uses of agricultural land are described using a flat, featureless plain radiating around a city. In his model, distance from the city determines land use in concentric rings; for instance, lumber harvesting and tomato growing is done close to the city because of the high cost of transporting lumber and the fact that tomatoes spoil quickly. Wheat can be harvested further from the city. The assumptions (a featureless plain) are obviously false, as it the conclusion, that land use is divided into concentric rings around a city. But the mechanism, that distance from cities affects land use when rational landowners can choose which crop to grow in a free market for farmland, is a truth-claim. It is the role of commentary on models to separate which parts of the model are truth-claims from those that are truth-valueless; models in isolation tell us little.

Note that this conception of truth is models is not the same as in Friedman (1953), which has a much heavier emphasis on prediction. In any case, I like Maki’s idea that untrue models can contain a locus of truth – call this a “tool for intuition” – even if the assumptions and implications more generally are deliberately stylized. Perhaps we may find two parties in the wrong: both the critics of economists’ stylized models and the economists who evade responsibility for truth claims by arguing that the models do not have any truth-value.

http://www.helsinki.fi/tint/publications/ModelsSyntheseDa.pdf (Final working paper – final version published in issue 180 of Synthese, a top journal in analytic philosophy that regularly publishes work of interest to game theorists and decision theorists)