Contradiction

A contradiction is when there are two or more statements that cannot all be true at the same time. A contradiction in logic can also be used to denote a self-contradictory statement, in which case it sometimes denoted by the symbol ${\displaystyle \bot }$ or ${\displaystyle 0}$.^[1][2]

A story that shows what a contradiction is comes from China. In this story, there is a merchant who sells both spears and shields. He says that his spears are so sharp that they could break through any shield. At the same time, he says that his shields are so strong that they could block any spear. This is a contradiction, because these two statements cannot both be true. Either spear will break the shield or the shield will block the spear, but not both. For this reason, the word for contradiction in Chinese is máodùn (矛盾), which literally means "spear and shield".^[3]

In Aristotle's logic, it is said that two contradictory propositions cannot both be true.^[4] For example, the propositions "A is B" and "A is not B" are mutually exclusive, meaning that only one, and not both, can be true. For example, the statements "the Pope is Catholic" and "the Pope is not Catholic" cannot both be true. Only one of the statements, and not the other, is true.

• Law of noncontradiction
• Paradox
• Reductio ad absurdum