A taboo, for a particular flavor of mathematics or formal system, is a simple statement that is known to be not provable therein, and that can therefore be used to establish the unprovability of other statements without the need to descend into metamathematical considerations (such as syntactic analysis or construction of countermodels) or, in some cases, even to decide on a particular formal system to be working in.

For example, the law of excluded middle (LEM) is a taboo for constructive mathematics. Therefore, if some statement $P$ implies LEM, then one can be sure that $P$ is also not provable in constructive mathematics.