In the context of mathematical logic
and more specifically, Boolean algebra
, consistency is an important notion.
A collection of statements is said to be consistent
if the statements can all be true simultaneously
A simple way of determining if a (hopefully small) collection of statements is consistent or not is to use a truth table
The concept of consistency is important in refutation strategy
, a method of determining the validity
of an argument. In this method, the conclusion
to the proposed argument is negated, then all the statements are checked for consistency. If the argument and the negated conclusion are mutually inconsistent
, then the original conclusion must be valid.