[lalaithion]

> the number of roots even for the same quadratic equation may depend on "private" thoughts such as whether complex roots are of interest

You are confusing ambiguity in a problem statement due to human language being imprecise with two well-specified identical experimental results having different results due to the intentions of the human carrying them out.

Is arithmetic a religion because there's "one true way" of adding integers?

[d0mine]

It is not about human language being imprecise. I can formulate the questions using the math language precisely with the exact same result (different number of roots are possible for different formulations of the problem for the same "physical" (coefficients of the quadratic equation) setup).

The Map is not the Territory.

Different maps can be useful. No true map.

[kevindamm]

I can think of at least two ways to add integers.. the categorical way that applies a mapping from the set into itself, and the set-theoretic way that deals with unwrapping and rewrapping successor relations. The latter is sometimes resorted to in heavily-relational contexts like Datalog.

[lalaithion]

Yes, this is addressed in the original article... there are multiple "lawful" ways of adding integers which all give the same results, and likewise in probability all "lawful" ways of analyzing data should give the same results. If you have two different ways of adding numbers which give different results, one is not lawful.