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The nature of paradox
  
  Imagine a postcard on which one side is written the statement "What is stated on the other side is true" and on the other side is the statement "This statement is false". When combined, both statements create a circular argument- if false, then true, and/or if true, then false.  
  The word "paradox" is most often used to describe such examples and statements such as "before the universe existed, UCA both did and didn't exist". The word itself is derived from the Greek words para (para) meaning 'alongside of, by, past, beyond' and doxa (opinion) . Originally paradox simply meant "a statement contrary to received opinion or belief; sometimes with favorable, sometimes with unfavorable connotation. However, around 1569, the word was given the meaning "a statement that is seemingly self contradictory or absurd, thought possibly well funded or essentially true."  
  In science, paradoxes are considered the most loathsome of arguments as the heart of science is the quest for provable knowledge- a or b, true or false.  
  Paradoxes of self-reference have the same form. They both assert and deny themselves. They have the logical form of a contradiction. A AND not-A, and they vex mathematicians and Western philosophers.  
  Paradoxes of self reference have the same form:  
  A implies not-A, and not A implies A.  
  So A and not-A are logically equivalent: A = not-A.  
  The Yin Yang equation. So they have the same truth values: t(A) = t(not-A).  
  Here we face a bivalent contradiction of either 0 = 1 or 1 = 0.  
2.15.1 The use of the proof theory reducio ad absurdum  
  As mentioned earlier, paradoxes are hated with a passion within western schools of knowledge, all of which are built upon the logic framework of argument. Therefore, for a new theory to be accepted within the current structure of any accepted western science, it must by definition be devoid of any paradoxes.  
  The most popular method of defining paradoxes out of existence is the proof strategy reductio ad absurdum, whereby an assumption is made and then shown to lead to contradictions or "absurdities". Once this is achieved, the principle assumption made can be denied as defective.  
  However, the theory of reductio ad absurdum only works if the combatants choose to meet on the field of logic, but one system of thinking. On the multivalent field of argument, reductio ad absurdum does not work.  
  For bivalent logicians, this presents no problem as multivalent by definition is argued as "unreasonable" and "irrational" (see the previous section for an explanation of this argument). As a result, few scholars accept to do battle on the field of multi valence.  
2.15.2 The great 20th century plan to eliminate paradoxes  
  Apart from the success of the reductio ad absurdum method of eliminating opposing ideas to your own, the early part of the 20th Century saw one of the most ambitious projects ever undertaken- the goal to eliminate all paradoxes from formal mathematics- creating the perfect book of truth.  
  One of the main players in this quest was Bertrand Russell who in the 1920's set out to methodically write out all the axioms of mathematics to continue the work of the Boolean algebra language of expressing "logical arguments.  
  The word not only seemed hopeful, but a certainty. For the world of science at this point arrogantly believed that mathematics had developed to such a point that all that was required to do was simply create a clear system and add up all the axioms.  
  However, after progressing relatively quickly, Russell's project came to an abrupt brick wall- the concept of the set of all sets.  
  Simply, the problem rested on the argument "if the definition of a set of things is that it does not belong to itself, but a higher set of things- what does the set of all sets belong?" If the answer is itself, then the set of all sets is not a set as well as a set- a self referencing paradox. If the answer is no sets, then it is not a set and no sets can exist by logic.  
2.15.3 Godel and the destruction of the grand plan
  There are many propositions in mathematics to which no exceptions have been found and yet, no proofs have been obtained to demonstrate whether they are true or not. As an instance, all perfect numbers known today are even numbers, we have no reason to believe that odd perfect numbers exist, but no proof has been found to demonstrate their nonexistence.  
  Before 1931 it was believed that the axioms of arithmetic were consistent and adequate to prove or disprove any mathematical conjecture. However, in 1931, Kurt Godel, Czech- American mathematician and logician, published his famous incompleteness, or undecidability theorem stating that any consistent formal system adequate to describe arithmetic must contain statements which can neither be proven nor disproved within this system ( in other words paradoxes). At the same time, Alfred Tarski, Polish-American mathematician and logician, studied the notion of truth in formal systems.  
  Godels argument is simple. Let us say we wish to show a proof that 1 + 1 = 2. Our common sense tells us the answer and proof is self evident. However, in a formal process we must start with defining the variables. Therefore we begin:  
  Let 1 = the unit of 1  
  This appears fine doesn't it? What then supports the argument 1 = 1? For if there is no defined truth that supports the argument 1 = 1, then this definition is merely an assumption, not a truth.  
  Taken to extreme, we would require an infinite array of definitions 1 = 1, 1 = 1 ... 8 to support 1 = 1 as fact. Since no definition can be proven as being true and all formulas rely on their definitions then no formula in any scientific definition can be considered 100% true ( in spite of often vigorous arguments to the contrary.)  
  While Godel and Tarski discovered that every mathematical formula can be deconstructed to a state of incompleteness, one and only one statement stood out as being both complete and 100% true. The problem was that the same statement also appeared 100% false. 1 = 0. The purest mathematical language to describe the paradox.  
2.15.4 The implication of Godel's discovery  
  That paradoxes exist in mathematics at their heart might not appear all that earth shattering, until you consider the implication that all mathematical axioms must begin from a paradox.  
  Not surprisingly, few people outside mathematics circles have heard of Godel's incompleteness theorem and the implication that ALL mathematical theories at best are based on assumptions as no theory can be 100% proven. For the most part, mathematicians and scientists continue to advance their respect fields, largely ignoring the theorem.  
  By Godel's discovery and the work of Bertrand Russell, all systems of classification of absolute systems- must by definition begin with the primary paradox. We call this primary paradox- UCA- Unique Collective Awareness. In other words, Godel and Tarski proved in 1931 that UCA exists at the heart of mathematics.  
     
 
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