What we understand of contradiction is primarily a deficiency in structure of an axiom. We observe something and this observation is not proportional in one degree or another.

Take for example the simple math problem 2 + 2 = 5

By all accounts this qualifies as a contradiction. The problem occurs with what forms the contradiction itself. "2", "+", "2", "=" and "5" are all axioms in themselves and true on their own account. The structuring of these axioms results in a disproportionality that inherently leads to a deficiency in "structure".

In this respect all contradictions fundamentally are a deficiency in structure and not a thing in themselves. This deficiency in structure can be purely:

1) subjective (as a person claims it is contradictory because it is not proportional to the axioms they observe)

2) objective (2 + 2 will always equal 4 therefore it cannot equal 5)

As all contradiction is strictly deficiency in axiomatic structure, the nature of contradiction is neutralized through structural propagation.

The continual propagation of structure, which may appear random, does not imply contradiction. Structures which may appear contradictory, such as 2 + 2 = 5, may not always contradict if they continually reflect through an observer as a unifying median. To further this example:

2 + 2 = 5

→

2 + 2 ≠ 5

→

2z + 2z = 5 ↔ z = 1.25

→

2x + 2y = 5 ↔ {x = |1...0| y = |1.5…2.5|} ∨ { x = |1.5…2.5| y = |1...0|} with x≜y

→

ad infinitum; therefore:

2 + 2 = 5 ↔ (2 + 2 = 5) = -□

In this respect all axioms maintain a degree of contradiction where they lack symmetry or balance. However observing the contradiction as a contradiction is a simultaneously solution.

In this respect all axioms maintain a duality of truth and falsity as contradiction exists where definition is deficient.

## The Failure of the Contradiction?

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