nLab ex falso quodlibet




The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms

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 logical system, then any proposition follows.

In type theory it is the elimination rule of the empty type (see there).

Ex falso quodlibet holds in many systems of logic, 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 January 26, 2023 at 08:46:43. See the history of this page for a list of all contributions to it.