What Is a Model?

by Gene Callahan

I’ve been pondering this point a bit lately, and this seems like a good place to share my musings and get some feedback. The main questions I’ve been pondering are things like, ‘How is a model “accurate”?’ ‘What makes something a model of one thing and not another?’ ‘How do we know how to “use” the model in some activity?’

Let’s consider a blueprint for a house. It consists of some blue lines on white paper. You give it to me, ignorant of building practice, and tell me ‘Build this right here’, and indicate a piece of ground. I see there is a scale conversion on the blueprint, say, 1 inch = 3 feet. I figure out the requisite enlargement of the figure — then I go and paint a white rectangle on the ground of that size, and proceed to paint blue lines on it.

Obviously, I have gotten the model ‘all wrong’. And yet, notice that what I created looks much more like the model then the ‘correct’ house would. What makes this blueprint a ‘good’ model for building a house, and a little, scaled-down model of the house a bad model?

My preliminary thoughts here are that Wittgenstein was on the right track in his discussion of ‘following a rule’. Ultimately, no rule or model can explain itself. Sure, you could supply some set of rules as to how to ‘follow’ the model — but how does the recipient know she is following the rules correctly? On the Underground in London, there are signs at the top of the escalator saying ‘Pets must be carried’. Why do people not turn around and fetch a dog or budgie if they find themselves without a pet?

Wittgenstein says it’s because rules and models are embedded in a way of life, and it is only from within this way of life that they ‘make sense’. A bunch of letters, numbers, and signs on paper, on the surface, look like they ought to have nothing to do with pouring an acidic solution into a basic one — the symbols certainly don’t react together and precipitate a salt, for instance! And yet to one initiated into the world of chemistry, those symbols are a perfectly good model of the reaction that occurs.

But is there more we can say? Why does chemistry use that model rather than some other one? Was the choice motivated, or arbitrary? If we think the models of chemistry are fine, but those of neoclassical economics are flawed, what can we say about the difference? Just how does this idea of a ‘way of life’ help us to understand a model?

Any ideas?

14 thoughts on “What Is a Model?

  1. Modelling is the science of determining what you can afford to ignore.

    The physical sciences have always understood this. The social sciences never have.

  2. Doesn’t this all boil down to personal opinion?: What is good to me is not good to others.
    I’ll consult PhilPapers for the meantime.

  3. One view is that the purpose of science is to boil down knowledge to the most concentrated form possible. This means a handful of axoms/assumptions from which meaningful results can be logically deduced. This requires a language in which the assumptions can be expressed, and a reality in which the can either be valid or invalid.

    Language and logic don’t necessarily relate in an obvious way to reality, but they are the way humans convey information about it.

    I like KipEsquire’s aphorism : “Modelling is the science of determining what you can afford to ignore.”

  4. Very interesting! I am sure all of these considerations have relevance in the interpretation of laws. Many jurisprudes (yes, that is the word!) have attacked this problem from different angles. And yet one point is obvious: laws mean what they do in a social context. If the context changes the law will also. This is part of what Glen Whitman and I were thinking about in our work on slippery slopes.

  5. “Doesn’t this all boil down to personal opinion?: What is good to me is not good to others.”

    Whatever the answer to this puzzle is, I’m absolutely sure this is not it. Astronomers did not switch from the Ptolemaic to the Copernican model of the solar system out of ‘personal opinion’. In fact, given the social embededness of models, that’s just what would render a model worthless: that it was solely my personal favourite.

  6. Wittgenstein is talking about how any public symbol can have a shared significance in the community.

    There are a couple of things that Wittgenstein adds to the “going on together” insight.

    One thing he adds is shared natures — we share a common nature, which leads us “naturally” to go on together in the same way in most instances. We “get it” the same way because we are built the same way. Mises and Hayek both make this same point.

    The point is extended into economics — we “go on together” in the same way in ordering our preferences and making our plans, and in learning in the context of changing relative prices and changing local conditions.

    Economists working under Marvel Comics picture of “science” say we can’t “know” what is going on in “another persons head” – and this is outside “science” because we can’t text it and “confirm” it, etc.

    But this is an abuse of “science” and the word “know” — an abuse suggested to us by Descartes and Plato and Hume, etc.

    Wittgenstein and Hayek and Mises are right — we go on together and the whole basis of public language and a universe of social cooperation is grounded on this door turning fact.

  7. Kuhn has a lot of good stuff on how “models” in the textbook hook up with the world through training in the lab and training with competent scientists.

    Much recommended, and very “Wittgensteinian”.

    You might contact Larry Wright at UC Riverside for so thoughts on this.

    He is the best “Wittgensteinian” philosopher of science in world.

    Or, you might say, he’s the best philosopher of science who is also a Wittgensteinian.

  8. Gene — the answer to your question is a very, very, very long conversation.

    Again, I’d recommend Kuhn as very helpful when thinking about all this.

  9. Right, Kuhn in “Structure”. He’s also got some essays touching on this topic in his “Essential Tension”.

    Read Kuhn again and remind yourself that Kuhn is a reader of Wittgenstein.

  10. The usefulness of models is always restricted by the purpose for which they are used and how robust their validation. Unfortunately, like most climate models, many economic models may be poorly validated and, worse, placed in service beyond their capabilities.

  11. I believe that models should be built in two steps;

    1. Functional Model

    This results from an enumeration of all the relevant factors of, and an outline of the general structure of the system being modeled. This is the overview stage, from which we build a block diagram or ‘boilerplate’, to use an older term.

    2. Behavioural Model

    Defines how and why the function model operates, thus becoming predictive in the process.

    Perhaps there should also be an explanatory model, to handle the why, separate to and following the behavioural model that (only) defines the how. For example;

    1. Functional Model – Copernicus
    2. Behavioural Model – Kepler
    3. Explanatory Model – Newton

    Then how about a fourth stage;

    4. Revised Explanatory Model – Einstein

  12. Andrew, I can’t see your three examples fitting your ideal types at all. Copernicus’s model certainly was predictive. Kepler added no more ‘why’ then Copernicus had, and he certainly didn’t explain the ‘how’ of Copernicus’s model — in fact, he threw out Copernicus’s model and replaced it with a new one. And Newton’s theory of gravitation, as he himself well recognized, did not explain what was going on at all, but simply showed the mathematical laws that gravity — whatever in the world it was and however it functioned — happened to obey.

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