A hugely influential aphorism from the statistician George E. P. Box is, "all models are wrong, but some are useful." For example, it is often useful to model a random variable as normally distributed even though huge quantities of data will almost always give you the statistical power to reject normality. In my field of finance, asset pricing theorists argue that asset pricing models should be judged on whether their theories help you understand the data, not whether a model is or isn't statistically rejected. I could go on and on with theorists invoking Box.

Which line of thought in the philosophy of science does Box's statement (or perhaps Box's broader writings) most align with?

Is the quote consistent with idealization? Instrumentalism?

(Philosophy is not my field, but is a key philosophical distinction whether models are regarded as false because they simplify or whether scientific realism is rejected altogether?)

  • Jamesian pragmatism:"only test of probable truth is what works best in the way of leading us, what fits every part of life best and combines with the collectivity of experience's demands, nothing being omitted... True is the name for whatever idea starts the verification process, useful is the name for its completed function in experience". Typically abbreviated as "truth is what works". Peirce, pragmatism's founder, considered James's theory of truth "disastrous".
    – Conifold
    May 14 '18 at 22:39
  • Is not Box's statement rather obvious? No model is the real thing.
    – user20253
    May 15 '18 at 11:15

The literature on model-based science is extremely relevant to Box's aphorism. I would specifically recommend Wimsatt's "False Models as a Means to Truer Theories", Weisberg's "Forty Years of 'The Strategy'", Parker's "Scientific Models and Adequacy-for-Purpose", and Potochnik's "The Diverse Aims of Science".

None of these papers are about statistical models, but I still think they're relevant to the way Box's aphorism plays out in the way scientists and others use statistics. (I'm currently writing a paper arguing that this is because many philosophers of science know relatively little about statistics, and see it as just "curve fitting.")

Potochnik argues that idealization plays an important role in the ways models support understanding. One implication of both Box's aphorism and the model-based science literature is that realism/instrumentalism fades away as a problem. Good models don't need to be True, in the strong sense that realists want. But they also can't be black-box prediction machines, like instrumentalists want. (That's a key difference between inferential statistics and machine learning.) In statistics, a good model needs to represent the data generating process "accurately," but there are different aspects to accurate representation (see especially Weisberg), and the standards of accuracy depend on what we're trying to do with the model (Parker). We also care much less about finding the one true model, and instead working through a series of models that get at different aspects of the target system (Wimsatt).

  • Thanks again for the thoughtful answer and useful references! Nov 20 '18 at 18:05

Fallibilism (the wikipedia and its IEP source) seems to be the general case and for philosophy of science Popper's falsificationism offers a good perspective.

"All models are wrong, but some are useful" can be rephrased as "No model is true but some are hard to falsify". Popperianism has many critics but this has to be expected as it is more concrete than fallibilism. Charles Peirce is credited for outlining this idea and of course he is another pragmatist (confirming Cornifold's "Jamesian pragmatism" perhaps).

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