Grelling–Nelson paradox

E357180

logical paradox self-referential paradox semantic paradox

The Grelling–Nelson paradox is a self-referential logical paradox arising from classifying adjectives as "autological" or "heterological," leading to a contradiction when considering whether "heterological" describes itself.

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All labels observed (2)

Label	Occurrences
Grelling–Nelson paradox canonical	2
Grelling paradox	1

Statements (47)

Predicate	Object
instanceOf	logical paradox ⓘ self-referential paradox ⓘ semantic paradox ⓘ
alsoKnownAs	Grelling–Nelson paradox ⓘ surface form: Grelling paradox
assumes	every adjective is either autological or heterological ⓘ no adjective is both autological and heterological ⓘ
basedOn	natural language semantics ⓘ set-theoretic comprehension ⓘ
category	paradoxes of self-reference ⓘ philosophical logic ⓘ
concerns	adjectives that describe themselves ⓘ adjectives that do not describe themselves ⓘ
describes	classification of adjectives ⓘ
exposes	limits of naive classification in natural language ⓘ self-referential inconsistency ⓘ
field	logic ⓘ philosophy of language ⓘ set theory ⓘ
formalization	set of all heterological adjectives ⓘ
hasComponent	definition of autological adjective ⓘ definition of heterological adjective ⓘ
illustrates	problems with naive set formation ⓘ self-referential paradoxes in ordinary language ⓘ
influenced	development of formal semantics ⓘ later work on semantic paradoxes ⓘ
involvesQuestion	whether the adjective "heterological" is autological ⓘ whether the adjective "heterological" is heterological ⓘ
language	German ⓘ
leadsTo	logical contradiction ⓘ
motivated	hierarchies of languages ⓘ restrictions on semantic predicates ⓘ type-theoretic solutions ⓘ
namedAfter	Kurt Grelling ⓘ Leonard Nelson ⓘ
problemType	vagueness and self-application in predicates ⓘ
relatedConcept	Tarski's undefinability theorem ⓘ surface form: Tarski undefinability theorem semantic hierarchy ⓘ truth predicate ⓘ
relatedTo	Berry paradox ⓘ Russell’s paradox ⓘ surface form: Russell paradox liar paradox ⓘ semantic paradox ⓘ
timePeriod	early 20th century ⓘ
usesConcept	autological adjective ⓘ heterological adjective ⓘ liar paradox ⓘ self-reference ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Epimenides paradox → relatedTo → Grelling–Nelson paradox ⓘ

Berry paradox → relatedTo → Grelling–Nelson paradox ⓘ

Grelling–Nelson paradox → alsoKnownAs → Grelling–Nelson paradox ⓘ

this entity surface form: Grelling paradox