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@LouisIngenthron If you are refering to the one and not hte rock then you are talking about the first case not the second. In the first case there are no rocks, just "1" which you have defined and circularly used.

In the second case im talking about the idea withouth the numbers, which english isnt equipped to do. But i am talking about the fact that rocks are a comparable quantity irrespective of any numbers described to accomplish that. That is, that the qty is preseved from the individual components in the larger collection. That is, the actual real world scenario that math is being represented before the math or numbers were concepts that were defined.

In other words, imagine a person with no linguistic or math understanding adding quantities of rocks using purely abstract understanding (no internal dialog). There is no 1 in that situation, there is an idea of a one in a very abstract sense that is rooted not by the concept of 1 but by the concept of where the boundaries of a rock is where beyond that boundary is a "different rock".

To put it yet another way, without the numbers you are left needing to define where a thing begins and end. One you throw the numbers back in you realize it didnt really change that. Youjust have two things you need to define, its all still circular and by definition.

As a counter argument we actually have math where 1+1 is either undefined or equals something other than 2, it just depends on the system of math and definition your using. In math we define these as what is called "rings", not all rings even allow for addition operations. In other words addition is a nonsensical operation under some systems of math, so how can 1+1=2 be universally true if it is only true under specific mathematical systems and false or undefined under others?