What an object is and what it is not are mutually exclusive. Each is itself, not it’s opposite. The physical identifier black is black, not white and white is white, not black. The meaning same is same, not distinct and distinct is distinct, not same. Altogether there are four components, for example black, not white; white, not black; same, not distinct; and distinct, not same.
For the purposes of counting, each “what an object is” is separated from each other “what an object is” by a “what an object is not”, and each “what an object is not” is separated from each other “what an object is not” by a “what an object is”. The two opposites are mutually exclusive, like black and white squares on a chess board. Instead of counting being conducted in objects identified singly as a, b and c, counting is conducted in what each of a, b and c is and what it is not.
Whenever an object is counted, what it is and what it is not are both erased (/ /) from consideration and the two sides of a new object recording the count are brought into consideration.