We each identify ourselves as “me” and those we are addressing as “you”. The two are mutually exclusive. Each is one, not the other. The relationship between the two is symmetrical. In communications between the two, the members of the relationship switch effortlessly between the inversions of meanings of “me, not you” and “you, not me”. The dual logic that draws a distinction between “me, not you” and “you, not me” does not privilege one side of the relationship over the other.
The logic that draws a distinction between what is and what is not a countable object in conventional mathematics does privilege one side of the relationship over another. The logic is inherently incapable of accommodating each side being identified by self-reference (as with “me”) such that each side is also not the other (as with “you”). For example, if the relationship is between 1 and 1, 1 can identify by self reference (1 turns 1 into 1), and 1 can represent not 1, but 1 cannot also identify by self-reference (1 turns 1 into 1). The logic that enables 1 to identify by self-reference (1 turns 1 into 1) is the mirror image of the logic that enables 1 to self-identify. Two mirror opposite ways of drawing distinctions between 1 and 1 are needed. These are provided by the truth tables for the mirror opposite logic gates XOR and XNOR. In one logic, “me” is 1 and “you” is 1, while in the mirror opposite logic “me” is 1 and “you” is 1. Put them together and in the resultant dual logic, each “me” and each “you” in our relationship can be treated symmetrically.