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In the realm of statistics and machine learning, a lot of discussion has arisen recently around the difference between explaining and predicting: That the two are not the same, and that the difference between the two should be taken into account when choosing what type of model to use, or which model is best amongst a set of competing models, and which metrics should be used to evaluate a model. See this paper by Galit Shmueli for an in-depth discussion. This isn't just a question of transparent statistical models vs. black box machine learning models, the distinction applies even within different types of statistical models. Shmueli for example argues that more complex models are better for prediction, while simpler models are better for explanation.

That in itself surprises me: shouldn't it be the other way around? A simple model is useful for making split decision predictions, while a complex model gives a more nuanced representation of reality, but becomes too unstable and noisy in the process, no?

But that's not what really bugs me. What I can't wrap my head around is how can a theory or model explain the world, without having predictive value? Isn't the fundamental definition of a good explanation, that it is reproducible, i.e. that it predicts future events?

My understanding is that almost all philosophers of science agreed on this: The only way to evaluate a theoretical explanation of empirical facts was by its predictive ability. From the original scientific method of the enlightenment, to the logical positivists, to Popper, all the way to Quine, all seemed to settle on the fact that a scientific explanation of a phenomenon was only as good as the predictions it made. Even Feyerabend, with his epistemological anarchy, argued that science is only as good as it is useful (In some ways Feyerabend was the first black-box machine learning algorithm advocate - any algorithm goes, as long as it give good results on the out of sample test set).

What they disagreed about was mainly the status of science with regards to other intellectual pursuits, and the nature of the epistemological tools that are permissible in science (i.e how to distinguish science from mythology, or from ethics, what is the status of non-observable entities, what constitutes evidence in a scientific context, etc...).

But again they all seemed to agree that a scientific theory must have predictive value. I.e it must conform to the laymen's definition of the experimental method: An explanation of a phenomenon is correct if it successfully predicts the outcome of future experiments. If a theory only explains the past, without (at least partially) predicting the future, then it is either bad science, or unscientific all together.

So with this in mind, here are my questions:

  • Is my understanding correct that almost all philosophers of science agreed on the idea that a scientific theory (i.e. an explanation of a phenomenon) must have predictive value?

  • If my above statement is not correct, then what it is the scientific status of a theory that explains but doesn't predict? Wouldn't such a theory fail most demarcation criteria (verification, falsification, Khun's and Lakatos' notions of theories that are progressing, etc....)?

  • Are Shmueli and other statisticians who argue for the explain vs. predict distinction simply wrong (because they are statisticians, not philosophers or physical scientists)?

P.S: Shmueli mentions in section 1.5 of her paper that this distinction has been discussed in philosophy of science. She cites several authors, but I haven't heard of any of the references besides Hempel and Oppenheim, 1948, and that paper is pretty much in alignment with what I said about the equivalence of explanation and predictive power. I know that ideally I should read the other sources she cited, but I feel that need to wrap my head around the questions I asked here first, especially my second bullet point

  • You probably read SEP's Scientific Explanation, but it is clear from it that "explanatory goodness" is an epistemic goal distinct from predictive value, and even concludes that "writers on explanation have not always paid adequate attention" to the relation between the two. The "prediction at the core" motive can be traced in the "classical" DN/IS theory of Hempel et al., but, far from almost all philosophers of science agreeing, most developments since can be seen as clearly breaking with it. Even in DN/IS prediction is not enough. – Conifold Jun 14 at 7:56
  • @Conifold "but, far from almost all philosophers of science agreeing, most developments since can be seen as clearly breaking with it." Ok - faire enough. Am I at least correct in assuming that the big names from my Phil. Sci 101 course (L.P, Popper, Quine, Khun, Lakatos,..) up until the 1960s all agreed to some extent with "prediction at the core"? Or did the deviation from DN/IS start even before that? – Alexander S King Jun 14 at 8:09
  • @Conifold also, care to weigh in on this? I was going to have those issues addressed in this post as well, but then the post would have been too long (it already got a close vote as it is) - plus the companion post is somewhat more technical. – Alexander S King Jun 14 at 8:15
  • That's fair, at least for the analytic mainstream. But even if we accept predictive value as a sin qua non of a scientific theory, it is not the only one, explanatory virtues still come into play after the minimal empirical adequacy test is met. Moreover, if predictive and explanatory values are independent/competing goals, context dependent tradeoffs come into play, even if the former is primary: simple and roughly right might be preferable to precise but obscure. So it is not like explain/predict split needs to account for the extreme of theories that explain, but don't predict at all. – Conifold Jun 14 at 8:23
  • Think of it like this: Why are Newtonian mechanics still taught at school? It is a simpler explanation. Though technically wrong, it gives students a frame of reference for further studies and deeper understanding. It follows that explanatory theories are useful not for being 'correct', i.e. good predictors, but rather for enabling conceptualization of the subject matter. Predictive theories are of course useful in getting us to the moon. – christo183 Jun 14 at 8:56

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