The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

See also

Axiomatic Set Theory, Axiomatic System, Complete Axiomatic Theory, Consistency Strength, Gödel's First Incompleteness Theorem, Gödel's Second Incompleteness Theorem

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Cite this as:

Weisstein, Eric W. "Consistency." From MathWorld--A Wolfram Web Resource.

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