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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| law of excluded middle canonical | 2 |
| law of non-contradiction | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10055567 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: law of excluded middle Context triple: [Hilbert–Brouwer controversy, about, law of excluded middle]
-
A.
De Morgan's laws
De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.
-
B.
Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
-
C.
Logik
Logik is a foundational work on formal logic by German philosopher and mathematician Gottlob Frege, contributing significantly to the development of modern logic and the philosophy of language.
-
D.
square of opposition
The square of opposition is a classical logical diagram that illustrates the relationships of contradiction, contrariety, subcontrariety, and subalternation among four types of categorical propositions.
-
E.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: law of excluded middle Target entity description: 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.
-
A.
De Morgan's laws
De Morgan's laws are fundamental rules in Boolean algebra and set theory that relate conjunctions and disjunctions through negation, forming a cornerstone of classical logic.
-
B.
Herbrand disjunction
Herbrand disjunction is a logical formula formed as a finite disjunction of ground instances of a first-order formula, central to Herbrand’s theorem in proof theory and automated reasoning.
-
C.
Logik
Logik is a foundational work on formal logic by German philosopher and mathematician Gottlob Frege, contributing significantly to the development of modern logic and the philosophy of language.
-
D.
square of opposition
The square of opposition is a classical logical diagram that illustrates the relationships of contradiction, contrariety, subcontrariety, and subalternation among four types of categorical propositions.
-
E.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
- F. None of above. chosen
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
ⓘ
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 ⓘ |
| 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
ⓘ
linked to:
law of excluded middle
|
| 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 ⓘ
linked to:
intuitionism
|
| 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
ⓘ
linked to:
Luitzen Egbertus Jan Brouwer
|
| wasDefendedBy | David Hilbert ⓘ |
| wasDiscussedBy | Aristotle ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: law of excluded middle Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: law of excluded middle