An apple is not definitively defined; the atoms making up the apples are what make up the "apple" sets. In your example the sets don't match.
This is a result, it don't say anything about the "action". And there is a possibility that 1+1 = 0, when the gate glitches.
I voted no to the question if you want you model to represent reality. The reason is that you could never know what all the variables are within the system. And if you did you couldn’t keep them from changing. The best that you will do is creating a statistical model.
Models are tools to...