[danrisso3]

I pretty much agree with this position, although I find the "fill ... together" and "bring ... together" metaphors silly.

For example, if you have two jars containing 50 plutionium coins each, putting all of them in the same jar will have some unforeseen consequences. However, this does not change the fact that there are 100 coins altogether.

[jules]

It fails because you apply the model to a situation where it isn't applicable. This isn't very different than applying Newtonian physics with objects moving near the speed of light.

By the way, numbers aren't defined as jars of coins. Numbers are a device to make predictions, and you can apply that device to make predictions about jars of coins.

I think you find it silly because you know too much about numbers and have forgotten the early years when you learned about numbers. When you teach a little kid numbers you don't start with Peano's axioms, you start with jars of coins and then you build an abstract model and you convince the kid that the abstract model makes accurate predictions with a series of (thought) experiments.