nLab
ex falso quodlibet

Ex falso quodlibet is Latin for “from falsehood, anything”. It is also called the principle of explosion. In logic it refers to the principle that when a contradiction can be derived in a system, then any proposition follows. In type theory it is the elimination rule of the empty type.

Ex falso quodlibet holds in many logics, such as classical logic and intuitionistic logic, but it fails to hold in paraconsistent logic, which was devised to allow controlled inconsistency.

Variants of the principle’s name include ex falso sequitur quodlibet, “from falsehood, anything follows”, and ex contradictione (sequitur) quodlibet, “from contradiction, anything (follows)”).

Last revised on September 7, 2018 at 01:59:50. See the history of this page for a list of all contributions to it.