law of excluded middle
E838588
The law of excluded middle is a classical logical principle stating that every proposition is either true or false, with no third option, and is central to debates between classical and intuitionistic logic.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
classical logic principle
ⓘ
law of logic ⓘ logical principle ⓘ |
| denies | the existence of a third truth value between truth and falsity ⓘ |
| formulatedAs | P ∨ ¬P ⓘ |
| hasAlternativeName |
LEM
NERFINISHED
ⓘ
no third is given ⓘ principle of excluded middle ⓘ tertium non datur ⓘ |
| hasConsequence |
every statement is either true or its negation is true
ⓘ
there are no truth-value gaps in classical logic ⓘ |
| hasDomain |
first-order logic
ⓘ
propositional logic ⓘ |
| hasHistoricalRootIn | Aristotelian logic NERFINISHED ⓘ |
| implies | principle of bivalence in classical settings ⓘ |
| isAcceptedIn |
Boolean logic
ⓘ
classical logic ⓘ standard first-order logic ⓘ standard propositional logic ⓘ |
| isCentralTo | classical logic ⓘ |
| isCentralToDebateBetween | classical logic and intuitionistic logic ⓘ |
| isContestedIn |
constructivism
ⓘ
intuitionism ⓘ philosophy of mathematics ⓘ |
| isDistinctFrom | law of non-contradiction NERFINISHED ⓘ |
| isEquivalentToInClassicalLogic |
¬P → (P → Q)
ⓘ
¬¬P → P ⓘ |
| isFormalizedIn |
Hilbert-style proof systems
ⓘ
sequent calculi for classical logic ⓘ |
| isNotGenerallyValidIn |
fuzzy logic
ⓘ
many-valued logics ⓘ paraconsistent logics ⓘ topos-theoretic internal logics ⓘ |
| isOmittedFrom | axiomatizations of intuitionistic logic ⓘ |
| isRejectedIn |
constructive mathematics
ⓘ
intuitionistic logic NERFINISHED ⓘ |
| isRelatedTo |
double negation elimination
ⓘ
non-contradiction ⓘ principle of bivalence ⓘ |
| isUsedIn |
classical analysis
ⓘ
classical proofs by contradiction ⓘ classical set theory ⓘ non-constructive existence proofs ⓘ |
| states |
every proposition is either true or false
ⓘ
for any proposition P, either P is true or its negation ¬P is true ⓘ |
| wasCriticizedBy | L. E. J. Brouwer NERFINISHED ⓘ |
| wasDefendedBy | David Hilbert NERFINISHED ⓘ |
| wasDiscussedBy | Aristotle NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.