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?