Against models (essay)

In modern civilization, there are two perspectives on what the task and nature of science is. One perspective, which I will call the "identification perspective," is that the task of science is to identify facts of reality. Another perspective, which I will call the "model perspective," is that the task of science is to create a mathematical model, which models reality. My thesis is that the latter perspective, though it can have some limited successes, is fundamentally mistaken.

Main points:

• The concept model came from things like model trains or whatever. What makes an object a model is that it behaves in a way that corresponds to how the real thing behaves. But concepts don't just act. We have to apply them.
• You wouldn't say "I'm modeling that as a dog." So when you say "I'm modeling that as a circle," you're treating the concept of "circle" as fundamentally different from the concept of "dog." That's what mathematical Platonists believe you should do, but it's not what I think. To say that we have two types of concepts would concede their whole point. If we did have two types of concepts, all the problems with Platonism would now be problems for me.

My view is like Reality > Concepts > Symbols. Symbols are meant to make their perceiver think of concepts, and concepts can be used to identify things in reality.

The formalist view is like: Reality > Symbols > Concepts. It says concepts refer to symbols, and symbols (along with their symbolic rules) behave in a way that is isomorphic to how reality behaves.

Identification perspective

This perspective is how people think about everyday things, like books and hair and wallets and the sun. Those are entities out there in the world, and we can identify facts about them: this book was published in 1957, that hair is being cut, etc.

This perspective is also how some people think about classical mechanics, though I believe it is uncommon.

All the mathematical concepts in classical mechanics refer to some concrete thing.

For example, when we talk about the position, we literally mean there's some entity in the world,

In this perspective, classical mechanics is not about modeling a ball as a point in a symplectic manifold, it is about saying: "This ball is at this location, and it has this orientation, and it will behave in such-and-such a way."

Model perspective

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Criticism of the model perspective

The model perspective is Kantian

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