Argument:

You cannot avoid paradox at the general level when paradox is the foundation for all phenomenon. All measurement begins with a localization of some facet of "being". This in itself is an act of seperation resulting in a base dualistic state:

1) "Identity Axiom 1" as "△•△"

where "•" equivocates to any symbolic notation of relation and "△" equivocates to any variable, observes a base dualism where the act of observing a relation results in a basic dichotomy of the variable "△ and △" thus leaving the symbolic notation of "•" effectively undefined. This is isomorphically reflected in Point 2 an as such is determined by it and observed as a divergence of and convergence to Point 3.

2) "Identity Axiom 2" as "•△•"

The symbol notatation of relation, observed as "•" is in itself a variable and as a variable and can only be defined by a dichotomy. This "symbolic" variable of relation in turn is defined by the variables through which it relates; hence results in a base dualism. This is isomorphically reflected in Point 1 and as such is determined by it and observed as a divergence of and convergence to Point 3.

3) "Identity Axiom 3" as "◬"

The nature of the symbol of relation as variable and the variable existing through relation necessitates a dualism of form and function as observed by the dualistic nature of Points 1 and 2. This is a contradiction as there is no equilibrium to maintain a balance. This Dualistic nature of form/function in symbolism requires a form of inherent synthesis from which the dualism of Points 1 and 2 converge and diverge as Point 3 with Point 3 proven through Points 1 and 2.

## The Axiom of Identity

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