Principle of Non-Contradiction
- If we can conclude both $\phi$ and $\neg \phi$, we may infer a contradiction.
- $p, \neg p \vdash \bot$
This means: if we have managed to deduce that a statement is both true and false, then the sequence of deductions show that the pool of assumptions upon which the sequent rests contains assumptions which are mutually contradictory.
The Principle of Non-Contradiction is otherwise known as:
- Principium contradictionis, Latin for principle of contradiction
- Rule of not-elimination
- Law of contradiction
- Law of non-contradiction