Berry paradox
E73102
The Berry paradox is a self-referential logical paradox arising from phrases like “the smallest positive integer not definable in under eleven words,” which appears to define exactly such a number while claiming it cannot be defined.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Berry paradox canonical | 3 |
| Berry’s paradox | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T568426 — 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: Berry paradox Context triple: [liar paradox, relatedTo, Berry paradox]
-
A.
Barber paradox
The Barber paradox is a self-referential logical puzzle about a barber who shaves all and only those who do not shave themselves, illustrating a contradiction similar to Russell’s paradox.
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B.
Russell’s paradox
Russell’s paradox is a foundational logical contradiction in naive set theory that reveals problems with sets that contain themselves, leading to major developments in modern logic and the axiomatization of set theory.
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C.
Burali-Forti paradox
The Burali-Forti paradox is a foundational logical contradiction in set theory that arises from considering the set of all ordinal numbers, showing that such a totality cannot consistently exist as a set.
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D.
Epimenides paradox
The Epimenides paradox is a classic self-referential logical puzzle arising from a Cretan philosopher’s claim that all Cretans are liars, illustrating the problem of statements that refer to their own truth or falsehood.
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E.
Cantor’s paradox
Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
- 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: Berry paradox Target entity description: The Berry paradox is a self-referential logical paradox arising from phrases like “the smallest positive integer not definable in under eleven words,” which appears to define exactly such a number while claiming it cannot be defined.
-
A.
Barber paradox
The Barber paradox is a self-referential logical puzzle about a barber who shaves all and only those who do not shave themselves, illustrating a contradiction similar to Russell’s paradox.
-
B.
Russell’s paradox
Russell’s paradox is a foundational logical contradiction in naive set theory that reveals problems with sets that contain themselves, leading to major developments in modern logic and the axiomatization of set theory.
-
C.
Burali-Forti paradox
The Burali-Forti paradox is a foundational logical contradiction in set theory that arises from considering the set of all ordinal numbers, showing that such a totality cannot consistently exist as a set.
-
D.
Epimenides paradox
The Epimenides paradox is a classic self-referential logical puzzle arising from a Cretan philosopher’s claim that all Cretans are liars, illustrating the problem of statements that refer to their own truth or falsehood.
-
E.
Cantor’s paradox
Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
logical paradox
ⓘ
philosophical paradox ⓘ self-referential paradox ⓘ semantic paradox ⓘ |
| category |
paradoxes of definability
ⓘ
paradoxes of self-reference ⓘ |
| concerns |
finite descriptions of numbers
ⓘ
positive integers ⓘ |
| describedBy | the phrase "the smallest positive integer not definable in under eleven words" ⓘ |
| field |
foundations of mathematics
ⓘ
logic ⓘ mathematical logic ⓘ philosophy of mathematics ⓘ |
| hasAlternativeName |
Berry paradox
ⓘ
surface form:
Berry’s paradox
|
| hasKeyFeature |
arises from quantifying over all definitions expressible in a language
ⓘ
can be avoided by formalizing the notion of definition ⓘ depends on informal notions of definition and word length ⓘ illustrates limitations of naive talk about definability ⓘ motivates precise meta-mathematical frameworks ⓘ shows tension between arithmetic and natural language descriptions ⓘ uses a phrase that appears to define a number while asserting it is not definable ⓘ |
| historicalNote |
based on an observation attributed to G. G. Berry
ⓘ
discussed by Bertrand Russell ⓘ |
| illustrates |
the need to distinguish object language from meta-language
ⓘ
the non-absolute nature of definability ⓘ |
| influenced |
development of algorithmic information theory
ⓘ
studies of definability in arithmetic ⓘ |
| involvesConcept |
arithmetization of language
ⓘ
definability ⓘ description length ⓘ liar-type construction ⓘ meta-language ⓘ natural language ⓘ self-reference ⓘ |
| namedAfter | G. G. Berry ⓘ |
| relatedTo |
Kolmogorov complexity
ⓘ
surface form:
Chaitin’s incompleteness theorem
Grelling–Nelson paradox ⓘ Gödel's incompleteness theorems ⓘ
surface form:
Gödel’s incompleteness theorems
Kolmogorov complexity ⓘ Richard paradox ⓘ Russell’s paradox ⓘ definability in arithmetic ⓘ liar paradox ⓘ semantic paradoxes ⓘ set-theoretic definability ⓘ |
| resolutionApproach |
formalization of the notion of definition
ⓘ
use of precise syntactic measures instead of informal word counts ⓘ |
| usedInArgument |
arguments about the limits of formal systems
ⓘ
arguments for the necessity of a hierarchy of languages ⓘ |
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: Berry paradox Description of subject: The Berry paradox is a self-referential logical paradox arising from phrases like “the smallest positive integer not definable in under eleven words,” which appears to define exactly such a number while claiming it cannot be defined.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Berry’s paradox