The intermediate map resolves the map-territory problems with arithmetic, but doesn’t really address the problem here, which is more than that the map of arithmetic doesn’t correspond perfectly with the territory, but that there are -other valid maps- of that same territory which can evaluate the same real-world operation (adding a sheep to a field) on the basis of a different abstract operation.
“What are you counting” is the operative question here; arithmetic only makes sense if you count additive properties.
The intermediate map resolves the map-territory problems with arithmetic, but doesn’t really address the problem here, which is more than that the map of arithmetic doesn’t correspond perfectly with the territory, but that there are -other valid maps- of that same territory which can evaluate the same real-world operation (adding a sheep to a field) on the basis of a different abstract operation.
“What are you counting” is the operative question here; arithmetic only makes sense if you count additive properties.