For those interested in the nature - or even the possibility - of objectivity, facts and truth, here are extracts from the Wikipedia article repeatedly recommended by TimeSeeker entitled 'All models are wrong'. (It's at:
https://en.wikipedia.org/wiki/All_models_are_wrong). I'm reproducing this material to clarify the nature of our argument about objectivity.
"All models are wrong" is a common aphorism in statistics. It is generally attributed to the statistician George Box.
Quotations of George Box
The first record of Box saying "all models are wrong" is in a 1976 paper published in the Journal of the American Statistical Association.[1] The paragraph containing the aphorism is below.
Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity.
Box repeated the aphorism in a paper that was published in the proceedings of a 1978 statistics workshop.[2] The paper contains a section entitled "All models are wrong but some are useful". The section is copied below.
Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an "ideal" gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.
For such a model there is no need to ask the question "Is the model true?". If "truth" is to be the "whole truth" the answer must be "No". The only question of interest is "Is the model illuminating and useful?".
Comments and discussions
There have been varied comments and discussions about the aphorism. For instance, the statistician Sir David Cox has commented as follows.[6]
... it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model.
Burnham & Anderson, in their much-cited book on model selection,[7] state the following (§1.2.5).
A model is a simplification or approximation of reality and hence will not reflect all of reality. ... Box noted that “all models are wrong, but some are useful.” While a model can never be “truth,” a model might be ranked from very useful, to useful, to somewhat useful to, finally, essentially useless.
The statistician J. Michael Steele has argued somewhat against the aphorism as follows.[8]
If I say that a map is wrong, it means that a building is misnamed, or the direction of a one-way street is mislabeled. I never expected my map to recreate all of physical reality, and I only feel ripped off if my map does not correctly answer the questions that it claims to answer. My maps of Philadelphia are useful. Moreover, except for a few that are out-of-date, they are not wrong.
The statistician Andrew Gelman countered that, saying in particular the following.[9]
I take his general point, which is that a street map could be exactly correct, to the resolution of the map.
... The saying, “all models are wrong,” is helpful because it is not completely obvious....
This is a simple point, and I can see how Steele can be irritated by people making a big point about it. But, the trouble is, many people don’t realize that all models are wrong.
The statistician David Hand made the following statement in 2014.[10]
In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality—a point well made by George Box in his oft-cited remark that “all models are wrong, but some are useful”.
In 2011, a workshop on model selection was held in The Netherlands. The name of the workshop was "All models are wrong...".[11]
Additionally, the aphorism has been recommended to be a core part of the Applied Statistician's Creed.[12]
Historical antecedents
Although the aphorism seems to have originated with George Box, the underlying idea goes back decades, perhaps centuries. For example, in 1960, Georg Rasch said the following.[13]
… no models are [true]—not even the Newtonian laws. When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential…. Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must of course be investigated. This also means that a model is never accepted finally, only on trial.
Similarly, in 1947, John von Neumann said that "truth … is much too complicated to allow anything but approximations".[14]
I think there are questions to ask of those who claim that all models are wrong.
1 Could a model of reality be 'right' - correct, accurate, complete, or true? Is that a possibility? If not, then why say 'all models are wrong'?
2 What would a 'right' model of reality be like? How much 'inessential' detail would it have to contain? What does 'the whole truth' - or even just 'truth' - look like? And if that question is silly, why is 'approximation to the truth' a meaningful idea?
