Monday, January 2, 2017

All models are wrong, but some are useful

Have you heard this statement,
All models are wrong, but some are useful?

You can check the Wikipedia for more details: https://en.wikipedia.org/wiki/All_models_are_wrong


Peculiarly, as stated, this must be false, for reasons reminiscent of the Russell's paradox, Turing's Haling Problem, Kleene's Fixed Point Theorem and Gödel's incompleteness theorems. The very idea that there is reality and there are approximations or "models" of reality is itself a model. So if it were true, then it itself would have to also be wrong, albeit useful.

Technically, we could save the situation by calling models about models "class 2 models" and building a whole infinite hierarchy, and then merely saying that "all class 1 models are wrong", without mentioning models about models. But where exactly is the hole in the original statement? Is reality that mysterious that we can't describe it other than by calling it Zen or Dao, or is it just a limitation of our language, or perhaps of our thinking?

If reality can only be approximated, is there reality after all? Or is it just a convenient abstraction?