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One, two, …
I was having a back-and-forth with a colleague on modeling types (see this post for a modeling hierarchy) and falsifiability. It’s crucial we distinguish essential and empirical models, but first a word why falsifiability is not especially interesting. Regular readers know that I have no great love for falsifiability.
If a probability model says a thing has any positive probability, no matter how small, and the thing happens, the model has not been falsified. How could it have been? The model said the thing could happen: it did: the model was right. Saying the model has been “practically falsified” is like saying “She’s practically a virgin.”
For large, complex models, say of the climate or behavior, even if a model says a thing has zero probability for a thing which happens, all are reluctant to toss out the actually falsified model and instead say, “Close enough.”
There’s lots more to say, which I’ll skip. The crucial element is that we must never confuse probability and decision. They are not the same. This is why all hypothesis testing methods, p-values or Bayes factors, are wrong-headed. They all conflate probability and decision. See Uncertainty for a book-length discussion (I have not said all there is to the topic in three paragraphs).
Quick: how many legs do dogs have?
Even a Loyola graduate fresh from her safe space knows the answer is four. Dogs have four legs. Why? Who knows? They just do. It is in the nature of dogs to have four legs. The essence of a dog, partly, is to have four legs. Not three, not five: four.
Here is our essential model, which says, “Dogs have four legs”. Everybody understands what you mean by this. Nobody is confused. Everybody knows you mean to address the essence of dogginess. Essence or nature is easy! It is the universal quality of dogs to have four legs.
Notice that our model is incomplete. It doesn’t tell us all about dogs; it only mentions one essential feature. There is more to dogs than four legs, which everybody also knows. Our model also doesn’t tell us why. Why do dogs have four legs? Maybe you know, maybe you don’t. It doesn’t matter. Our model is silent on this important question. Our model is still correct and even obvious, though. It doesn’t have to say why to be useful, just like you don’t have to understand how a diesel engine works to drive a truck and know you are driving.
Now the big twist! “Dogs have four legs” can be taken in a strictly empirical sense, as a model that predicts every dog you see will have four legs. That a good model? No: my number-two son has a three-legged dog, for instance. The empirical model “Dogs have four legs” has failed; it has been falsified. It is not true.
The falsification of the empirical model does not—of course it does not!—falsify the essential model. Everybody knows that something has caused this particular three-legged dog to fail in its essence. You don’t have to know what this cause is to know that it must exist (or must have existed). There could be any number of causes. Indeed, I know I was told, but I forgot, why Ramona (the pooch) lost its leg. Or if it ever had it. Whichever, I know that it should have the fourth leg to be a “complete” dog.
I know, and you know, that something is wrong with the mutt, where “wrong” is used in the essential and not empirical sense. Nothing can ever be “wrong” in the empirical sense. Things are the way they are, and aren’t the way they aren’t, a tautology and a truth. But things can be askew essentially. Take a side away from a triangle and you’re left, empirically, with two lines, and there’s nothing wrong with two lines, unless you mean it to be a triangle, and then something essentially has gone wrong. The word “wrong” is not “judgmental”, but a plain statement of fact.
You can see the difficulty, since the model “Dogs have four legs” can be take essentially or empirically, mistakes can be made. The wings of equivocation beat the air. All models aspire to be essential, but most are empirical. The problem is too many empirical models are claimed to be essential.
“Objection!” some bright student will say, “It is possible, and people have been known, to make mistakes in identifying the essence of a thing, therefore all that is left to us is empiricism.” False, student, for many more have made empirical mistakes. Are we to deny the weatherman his profession because he occasionally calls a sunny day rainy? And are we thus to abandon all empirical measurement?
No, that our ultimate goal is always essence (or nature), and that we sometimes fail is no dissuasion.
More on this most important subject in Uncertainty: The Soul of Modeling, Probability & Statistics.