In the strictest sense, “adding” sheep is a category error. Sheep are physical objects, you can put two sheep in a pen or imagine putting two sheep in a pen, but you aren’t “adding” them, that’s for numbers. Arithmetic is merely a map that can be fruitfully used to model (among many other things) certain aspects of sheep collection, separating sheep into groups, etc, under certain circumstances. When mathematical maps work especially well, they risk being confused with the territory, which is what I think is going on here. The “female sheep + male sheep” example should be thought of as an aspect of “putting sheep in pens for long periods of time” which addition does not model, not as an exception to “1+1=2”.
In the strictest sense, adding anything except abstract numbers is a category error.
My point has less to do with the map not correlating to the territory, as that the map is not necessarily as intuitive, as a map, as we might expect; arithmetic may be a lot more tightly correlated to a distinctly human way of perceiving the world than naive expectation would lead to be the case.
In the strictest sense, “adding” sheep is a category error. Sheep are physical objects, you can put two sheep in a pen or imagine putting two sheep in a pen, but you aren’t “adding” them, that’s for numbers. Arithmetic is merely a map that can be fruitfully used to model (among many other things) certain aspects of sheep collection, separating sheep into groups, etc, under certain circumstances. When mathematical maps work especially well, they risk being confused with the territory, which is what I think is going on here. The “female sheep + male sheep” example should be thought of as an aspect of “putting sheep in pens for long periods of time” which addition does not model, not as an exception to “1+1=2”.
In the strictest sense, adding anything except abstract numbers is a category error.
My point has less to do with the map not correlating to the territory, as that the map is not necessarily as intuitive, as a map, as we might expect; arithmetic may be a lot more tightly correlated to a distinctly human way of perceiving the world than naive expectation would lead to be the case.