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.

# Consistency

## See also

Axiomatic Set Theory, Axiomatic System, Complete Axiomatic Theory, Consistency Strength, Gödel's First Incompleteness Theorem, Gödel's Second Incompleteness Theorem## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Consistency." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Consistency.html