Double negative elimination
In logic and the propositional calculus, double negative elimination is a rule that states that double negatives can be removed from a proposition without changing its meaning:
- It's not the case that it's not raining.
- It's raining.
¬ ¬ A ∴ AAlso:
¬ ¬ ¬ A ∴ ¬ AThe rule of double negative introduction states the converse, that double negatives can be added without changing the meaning of a proposition.
This rule is true in classical logic, but in intuitionistic logic, the statement, It's not the case that it's not raining. is weaker than It's raining.. As a slightly clearer example, It's not unreasonable is slightly less direct than It's reasonable.
