The Contradictory Nature of Equality as a Foundational Axiom in Arithmetic

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Eodnhoj7
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The Contradictory Nature of Equality as a Foundational Axiom in Arithmetic

Post by Eodnhoj7 » Fri Jan 25, 2019 8:03 pm

The Contradictory Nature of Equality as a Foundational Axiom in Arithmetic


Properties of Equality

First, we define three basic properties as follows:

a = a
If a = b then b = a
If a = b and b = c, then a = c.


1. a = a requires, a=b and b=a; hence (a,b)=(a,b)

2. a=b and b=c, then a=c; hence b=(a,c) where subject to point 2 ((a,b)=(a,b))=c

3. with (a,b)=c necessitating c=c with c=d and d=c; hence (c,d)=(c,d)

4. repeat of point 2 through axioms of point 3.

5. Thus the property of equality is subject to the fallacy of circularity and infinite regress while being subject as an unjustified axiom in itself in accords to the Munchauseen Trillema.

6. This continual recursion necessitates equality as fundamentally "=" as fundamentally a state of indefiniteness where it is a foundation of contradiction.

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