nLab
ex falso quodlibet
Context
Foundations
foundations

The basis of it all
mathematical logic

deduction system , natural deduction , sequent calculus , lambda-calculus , judgment

type theory , simple type theory , dependent type theory

collection , object , type , term , set , element

equality , judgmental equality , typal equality

universe , size issues

higher-order logic

Set theory
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)”).

References
Last revised on January 26, 2023 at 08:46:43.
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